Abstract

The recent advances in far-field super-resolution (SR) microscopy rely on, and therefore are limited by the ability to control the fluorescence of label molecules. We suggest a new, label-free, far-field SR microscopy based on temperature dependence of Raman scattering. Here, we present simulation and experimental characterization of the method. In an ultrafast pump-probe scheme, a spatial temperature profile is optically excited throughout the diffraction-limited spot; the Raman spectrum is probed with an overlapping laser. Thermally induced shifts, recorded in a specific spectral region of interest (ROI), enable spatial discrimination between areas of different temperature. Our simulations show spatial resolution that surpasses the diffraction limit by more than a factor of 2. Our method is compatible with material characterization in ambient, vacuum and liquid, thin and thick samples alike.

© 2015 Optical Society of America

1. Introduction

The desire to understand the structure, dynamics and function of nanoscale materials has inspired many different optical imaging techniques. In particular, optical microscopy has succeeded in surpassing the Abbé resolution limit (~λ/2) by far-field super-resolution (SR) techniques. The first pioneering work in the field, based on stimulated emission depletion (STED) [1,2], was soon followed by photo-activated localization microscopy (PALM) [3], stochastic optical reconstruction microscopy (STORM) [4,5] saturable absorption [6] (SAX), structured illumination [7], SR optical fluctuation imaging (SOFI) [8], and quantum emitter microscopy [9]. A number of algorithmic methods, have also been introduced [10–12]. All these fluorescence-based techniques are important when functional groups can be reliably and selectively labeled. For that reason they were established as major research tools in life sciences.

However, in many cases it is necessary or preferable to work without additional chromophores. This will be important for in-vivo studies of tissue, organs or animals, as it circumvents photo-bleaching or photo-induced toxicity of dyes. Moreover, label free SR microscopy is of particular relevance in materials research where it can be used for characterizing new nanomaterial surfaces, nano-electronics and electro-optical systems. Very recently, a first demonstration of label-free transmission microscopy was based on the ground state depletion of the charge carriers in graphene-like structures [13]. Nonlinear photo-thermal microscopy was shown in a fluid medium [14]. Photo-acoustics microscopy has been recently developed to demonstrate label free super resolution [15,16]. Another relevant approach is third harmonic generation (THG) microscopy [17,18], yet it lacks chemical specific contrast.

Raman microscopy, which discriminates between distinct molecules by their unique Raman spectra, provides a label free counterpart to fluorescence based microscopy. In particular, tip enhancement methods [19] combining scanning probe microscopy, such as scanning tunneling microscopy [20] or atomic force microscopy [21] and Raman spectroscopy provide rich information with nanometric resolution on the studied system, however practical use of such tip enhanced method is limited to the surface of the examined system.

The far field sensitivity of Raman microscopy has been vastly improved by the development of coherent non-linear Raman microscopies. Microscopy based on Coherent Anti Stokes Raman Scattering [22] (CARS), is developed to the extent of diffraction limited video rate imaging. However, CARS microscopy suffers from non-resonant background, and the nonlinear signal dependence on the concentration of the target molecule.

Stimulated Raman Scattering (SRS) is free of these problems. Recently, SRS microscopy was successfully demonstrated [23–26]. SRS sensitivity provides rather sensitive label free microscopic tool (~104 Raman-active molecules) for biological systems. Even though SRS sensitivity is adequate for the detection of nano-scale objects, no methodology for SR SRS microscopy has been suggested so far.

Several suggestions [27–35] and two experimental [36,37] realizations, for sub-diffraction CARS microscopy were reported recently. Some of the suggestions involve a control beam with intense center for generation of large Rabi frequency shift [27,28]. Others use a donut shape beam to diminish signals at the rim of the diffraction limited spot either by controlling the ground state and vibrational state coupling [29–31] or by phonon depletion [34]. Gong et al suggested a scheme for, Stimulated Raman scattering based also on saturation at the rim of the focus, using a donut beam [35]. Other SR approaches for CARS involves structure illumination [33] and focal volume engineering [32]. A first realization of sub diffraction CARS microscopy [36], utilizes a Torlado-style pupil phase, which narrows down the point spresd function (PSF) by a factor of two. A second realization of SR CARS uses photonic nanojets injection [37] to reach ~200nm using 1.0 NA lens and 796nm wavelength in CARS configuration.

2. Principles of the method

In a recent publication, we have demonstrated a far field label-free SR methodology which relies on the nonlinear response of the reflectance to photo-modulation by a pump laser [38]. It depended on the fact that the focused ultrafast pump laser imprints spatial distribution of temperature and charge carrier populations on the sample that induce nonlinearity in the photo-modulated reflection. Detection of these nonlinearities, by recording the high harmonics of the photo-modulated reflectivity, provides label-free SR, with spatial resolution down to 100nm. Here we extend the idea by utilizing photo-modulated Raman scattering. The added value of using Raman scattering lies in its intrinsic capability of material recognition.

Our method relies on the generation of temperature spatial distribution within the photo-excited diffraction limited spot by an ultra-short laser pulse (pump). After a short delay, adjusted to allow for the thermal mode distribution within the excited region, the Raman scattering is probed by another co-focused laser. Raman scattering is sensitive to temperature. The integral intensity of the Raman peaks as well as the peak frequency (energy) and shape change with the local temperature, and reflect the changes of relative population in the ground and excited phonon states. We show that by scanning the sample while monitoring specific spectral regions of interest (ROI) in the Raman peak that change strongly with temperature, super resolution can be achieved.

We present simulations which show significant improvement (2-3x) in resolution over the diffraction limit. We also demonstrate experimentally the validity of the concept by monitoring the changes in the total intensity of the Raman peaks and show mild resolution enhancement (2).

The temperature dependence of Raman spectra is well-known [39–41]. It is possible to extract the sample temperature using Raman spectroscopy by measuring the ratio of the Stokes (S) to anti-Stokes (AS) intensities, by the recording the frequency shift of the Raman of S or AS lines, or by recording line width of the S and/or AS Raman peaks.

A carefully chosen pump-probe time delay window is essential in our SR method. A pump-probe delay of a few ps is required to allow the electronically excited material to transfer it energy to phonons [42]. The delay should be limited, though, to ~10ps to prevent the blurring of the initial spatial temperature distribution by heat diffusion (Fig. 1(b)). We demonstrate here that it is possible to achieve SR by monitoring the non-equilibrium thermal excitation in a few ps timescale delay.

 figure: Fig. 1

Fig. 1 Key elements of the proposed method. a- The spectral changes in Raman Stokes peak in 300K silicon (Blue) due to heating to 700K(Red). Note the changes in integrated intensity, line shape broadening and frequency shift. The Hot and Cold ROI mark spectral regions which change extensively upon heating. Top left insert – Heating simulation of silicon by a 400nm, 1ps laser pulse, with a Gaussian intensity profile. 3D simulation of temperature distribution is depicted at t = 1ps after the short pulse. b- Temperature profiles at different delays after excitation. Each line represents a temporal snapshot of the spatial temperature distribution. Heat diffusion blurs the initial heating pattern.

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Simulations show that the heated material stays at elevated temperatures only about 5x10−4 of the measurement time (~20ps out in a 12ns measurement cycle). Consequently, the probability of thermally induced structure and chemical changes is vastly diminished.

The key element in the method is recording the change of the Raman signal at a given spectral region of interest (ROI) upon scanning (Fig. 1(a)). A hot spectral ROI is defined at low energies (left side) of the spectra whereas the cold ROI is defined at the high energy part of the Raman spectra (right side). Since the intensity change at these ROIs is highly nonlinear with temperature (Fig. 2(b)), the spectral detection enables spatial separation of different temperature zones inside the diffraction limited spot.

 figure: Fig. 2

Fig. 2 Response of a silicon Raman emitter to temperature a-. Calibration measurements. Experimental temperature dependence of silicon Raman spectra using a temperature stabilized heating plate. b- The integrated Raman signal for a point emitter as a function of temperature. Black –integrated Stokes signal. Red- integrated Stokes signal in the ROI (defined in 2a). Note the nonlinear response. Top left insert – Focused beams and Si point targets on sapphire substrate.

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3. Simulations

Due to the vast interest and knowledge in its characterization, silicon has been chosen as the material on which the simulations as well the experimental proof of concept are performed. The Raman peak of silicon at ~523cm−1 at room temperature and is modeled by a Lorentzian

1π*12Γ(T)(ωvibωs(T))2+(12Γ(T))2 
where ωvib is the vibration frequency, ωs(T) is the temperature dependent peak of the Raman shift and Γ(T) is the temperature dependent full width at half maximum (FWHM) of the Lorentzian Raman peak, Γw(T), convoluted with the excitation laser. The constants for silicon were found to be [43,44]:

With the constants A = 1.295 and B = 0.105 in wavenumbers for silicon. The excitation laser spectrum was modeled as a sech function with FWHM of 3cm−1. The temperature dependence of the Raman peak shift arises from the anharmonicity of the interatomic potentials in the lattice and is given by:

Γw(T)= A(1+2e(ω02KBT)1 )+B(1+3e(ω03KBT)1+3(e(ω03KBT)1)2)
ωs(T)=ω0+C(1+2e(ω02KBT)1 )+D(1+3e(ω03KBT)1+3(e(ω03KBT)1)2)
With the constants ω0=528, C = −2.96 and D = −0.174 in wavenumbers for silicon. This model fits well our calibration experiments of the temperature dependent Raman spectra (Fig. 2(a)), and was used in the simulation.

While the temperature dependence of AS / S ratio is well defined [39], we are not aware of a theory which describes the change of an integrated Raman peak intensities in a solid with temperature. Consequently, we have used the relative total intensities of our experimental calibration data of silicon Raman spectra in our simulations.

In our approach, the Raman active sample is scanned by two co-focused Gaussian shaped beams and Raman scattering of the probe beam is measured. The pump beam induces a Gaussian distribution of temperature and as a result, each point inside the diffraction limited spot contributes to the observed Raman spectrum according to its local temperature. The change in the frequency dependent intensity of the Raman signal, Δ IRaman(ω), due to the pump heating represents our experimental measurement and is given by:

ΔIRaman(ω)=r=0Iprobe(r){σRaman(ω, T(r))σRaman(ω, 300K)}dr
Where σRaman(ω,T(r)) is the frequency dependent cross section per unit area of the Raman peak at temperature T, and Raman frequency  induced by the pump laser, and it is practically governed by the spatial intensity distribution of the pump laser. Iprobe(r) represents the intensity profile of the co-focused probe beam and 300K is the reference “cold” room temperature. Changes in the Raman signal at a given spectral ROI are obtained by integrating ΔIRaman(ω) over the corresponding frequency range.

The geometry of the examined targets dictates the complexity of the simulation. When scanning a point Raman emitter, no spatial averaging is required. However in line or surface scan, the averaging of temperature distribution in the sample becomes important for the analysis and our modelling includes the required averaging over the range of temperatures and the geometry.

In order to optimize the spatial resolution enhancement it is important to monitor the ROIs with a spectrally narrow probe laser. We have performed our simulation with a 3 cm−1 laser and with both pump and probe at about 400nm wavelength. The laser’s bandwidth corresponds to a 5ps transform limited probe pulse, short enough to avoid significant loss of resolution due to spatial spread of the temperature profile induced by the pump laser.

Figure 2(a) depicts the calibration measurements of the Raman spectra of silicon in the temperature range of 300-900K. The experiment was performed using a heating plate and a continuous wave 532nm excitation. Upon heating, the Raman peak shifts to lower vibrational energies, broaden and decrease its total intensity. The spectral “hot” ROI for detection in the simulation is marked. In our simulations we modeled these spectral changes while scanning different sample geometries (point, line and surface) and formed images according to the intensity inside the spectral ROI. We assumed that the probe laser is monitoring a surface that has reached full thermalization as imprinted by the focused pump laser, without any significant blurring by heat diffusion. These conditions are practically achieved in a pump probe delay of about 5ps, as experimentally demonstrated and discussed in section 5.

The intensity changes with temperature of the Raman peaks in selected spectral ROIs are depicted in Fig. 2(b). While the integrated intensity of the whole Raman peak changes almost linearly with temperature (black curve), the intensity of the Raman peak in a specific spectral ROI (Gray rectangle in Fig. 2(a)) is equivalent to introducing a fourth order non-linear response to temperature (red curve). This dependence is the key for achieving SR.

In Fig. 3 we present the results of the scan-simulation over a point silicon Raman emitter, with pump and probe lasers of ~400nm wavelength, focused through a diffraction limited 0.95NA objective. The spectral changes are monitored at the ROI of 485-495cm−1 as depicted in Fig. 2(a). The spatial resolution, as depicted in Fig. 3, is ~100nm compared to the 210nm of the pump and probe laser PSFs, showing resolution enhancement of ~X2 over the diffraction limit. The two fold resolution improvement (√4) is consistent with the fourth order dependence of the signal in the ROI on temperature.

 figure: Fig. 3

Fig. 3 Simulation of the PSF of the Raman ROI super resolution method. A Raman point source was scanned using a Gaussian heating beam and a Raman gaussian probe beam with 210nm FWHM each. Red – Pump and probe intensity profile. Blue – Super resolution based on the heated Stokes peak integrated in the defined spectral ROI. Black –The difference due to heating in the ROI. In this curve the heated Raman signal in the ROI is subtracted form the unheated peak (achieving better resolution). Resolution of ~100nm can be achieved, x2 enhancement over the diffraction limit. Identical simulation results were obtained for the corresponding anti-Stokes peak.

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In our simulation the ROI spectral range was optimized for resolution enhancement of a given maximal temperature. Resolution can be further improved by increasing the maximum transient temperature using a higher fluence pumping. According to simulations, by pump heating just below damage threshold excitation, at 1500K, and using transform limited probe pulse with 3cm−1 spectral width, x4 enhancement in resolution can be achieved.

Realization of this method results with very poor signal to noise ratio (SNR) and is not practical with our experimental setup. This low SNR consequences from combination of the low cross section of spontaneous Raman scattering, the need to detect narrow bandwidth in a well-defined ROI (less than 10% of the total Raman scattering signal) and the small Raman active volume. The relevant Raman signal amounts to 1-2 photon per sec. In parallel, the background due to residual spontaneous emission and blackbody radiation induced by the pump laser amounts to hundreds of photons per sec, resulting in high shot noise. The fluences of both the pump and probe lasers could not be substantially increased, due to potential damage by the pump and heating by the probe beams.

However, the method of Stimulated Raman Scattering (SRS) which is blessed with orders of magnitude higher sensitivity could be adopted as the probe to our methodology. By tuning The SRS frequency difference (between the SRS pump and Stokes lasers) to the optimal hot ROI, with a few picosecond delay after the heating pump laser, super resolution maps can be acquired efficiently. Since SRS is tuned to a hot ROI, it monitors solely the heated portions of the sample and is blind to room temperature material. Background emission and blackbody radiation will not be detected by SRS. Typical SRS resolution of 3 cm−1 (corresponding to transform limited 5ps pulses) should provide the resolution improvement as calculated in our simulations. Moreover, since SRS is a nonlinear, two beam process, additional improvement in resolution can be expected. We foresee that by using a pump laser at 400nm (to heat the sample to 800K), followed by co-focused, simultaneous SRS pump and Stokes lasers at ~500nm, resolution of 90nm FWHM can be achieved for silicon structures.

In what follows, we describe characterization measurement of the pump-probe Raman system along with an experimental realization of resolution enhancement in Raman microscopy, based on recording the total intensity changes of Raman spectra, induced by the pump heating. The results show mild resolution enhancement relative to the probe laser resolution. This preliminary demonstration indicates the potential of using photo-modulated Raman scattering for achieving SR.

4. Experimental setup for Raman SR

The experimental setup is illustrated in Fig. 4. A Ti-Sapphire oscillator (Tsunami, Spectra physics) was set to 2ps pulse length at 785nm, with 10 nJ pulses at 80MHz. The laser beam passes through an optical isolator and is focused by a 100mm achromatic lens into a BBO crystal (L = 5mm) to produce second harmonic 392nm pulses. The 785nm and 392nm beams are expanded, collimated and split by a dichroic mirror (DM). Each beam is spatially filtered and further expanded. The time delay between pulses is adjusted by using a variable delay line in the path of the 785nm beam, using a retro-reflector riding on a translation stage with 1µm resolution. The two spatially overlapped beams are focused by a 0.95NA objective (Nikon CF Plan APO EPI 150X) on the sample surface.

 figure: Fig. 4

Fig. 4 Diagram of the optical setup. In a pump probe configuration a 785nm probe pulse and 392nm pump are temporally synchronized and spatially overlapped into a scanning microscope and focused on the sample by a high NA air objective. Detection modalities include both Raman scattering spectral detection and Thermoreflectance (in which RM is removed and the chopper is activated). RM- removable mirror .DM- dichroic mirror. BS – beam splitter. PD –photo diode. LLF- laser line filter.

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For narrowing the spectral width of the probe pulse a laser line filter (LLF) (LaserOptik IF798nm/6°) was used, with angle of incident of 20°. The effective excitation laser spectrum FWHM was 12cm−1, slightly wider than transform limited pulse. The pump and probe beams are merged using a DM and enter the Raman microscope. Scattered light is removed by a notch filter (Chroma ZET785nf) and the Raman spectra are detected by a spectrograph (Shamrock 303i) with a 1800 line/mm or a 600lines/mm grating coupled to a CCD camera (Andor IDUS). Sample is scanned by an x-y stage with 10nm resolution (Thorlabs DRV517 and BPC303). In another SR mode the same system is tuned to measure linear and nonlinear thermoreflectance (TR) [38]. Due to its high signal levels we used the TR capabilities of the system for optimizing the pump and probe spatial alignment and temporal synchronization on the sample.

5. Results –characteristics of photo-modulated Raman scattering

The experiments were performed on 150nm thick silicon stripes patterned on sapphire fabricated as described in Ref 38. The pump fluence was set to ~50mJ/cm2 (10mW) and the estimated peak temperature of silicon at these conditions is ~700K. The probe fluence was set to ~12mJ/cm2 (5mW). First, we evaluate the time evolution of the Raman spectrum as a function of pump-probe delay. Figure 5(a) depicts the dynamics of photo-excited charge carriers and optical phonons in the Silicon on Sapphire (SOS) sample. The pump and probe lasers are parked over a fixed point of a 100nm layer of silicon on sapphire. It shows that optical phonon are excited within 5-7 ps after photo-excitation, while the charge carriers, detected by the TR signal, are excited in a sub ps time scale and start to decay soon after the pump pulse. Accordingly, a time delay of 5ps was chosen to monitor the Raman spectrum after photo-heating by the pump laser. The need for a delay for monitoring thermal shifts in the Raman scattering precludes the possibility of using a single ultrafast pulse in such experiments.

 figure: Fig. 5

Fig. 5 Experiment characterization: a - time resolved Raman intensity and TR as a function of pump probe delay at a fixed point on the silicon. Integrated intensity of the Stokes Raman peak (Red) and the Transient TR (blue) as a function of the pump-probe delay. Thermalization time for electron phonon scattering is marked in black. b –Raman spectra of silicon, cold (blue) and hot (red) taken at delays of timing of −5ps and 5ps respectively, relative to the pump laser, and difference spectrum (black).

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The Raman signal, induced by the spatially wider probe laser beam, originates from the heated as well as cold portions of the sample. In order to extract only the effect of heating, we monitored the difference Raman spectra between the heated and non-heated sample. A delay of −5ps was chosen to represent the cold spectra. The −5ps delay occurs 12.5ns after the previous pump pulse, a time delay in which the sample reaches room temperature. This methodology was chosen to exclude various background effects on the spectra resulting from the pump pulse only, such as fluorescence background, blackbody radiation and laser power fluctuations. Figure 5(b) depicts Hot and Cold Raman spectra, with a pump probe delay of 5ps and −5ps respectively, with the pump and probe co-focused over the same surface. Note the decrease in the Stokes line intensity upon heating. This decrease is consistent with our calibration measurements (Fig. 2(a)), which show that the integrated Stokes intensity is reduced as the temperature increases.

The spectral shifts in the Raman spectrum are indiscernible in this measurement due to several experimental difficulties. In particular; the low spontaneous Raman scattering of nanostructures, the high emission background and high contributions of Room temperature Raman scattering monitored by the larger beam of the 785nm probe. We succeeded in enhancing resolution of the photo-modulated Raman microscopy by scanning the changes in the integrated Stokes Raman signal.

Figure 6 depicts line scans orthogonal to a 125nm wide silicon stripe. The difference Stokes signal is taken at 0.1 Hz, a low frequency modulation that enhances the SNR of measurement.

 figure: Fig. 6

Fig. 6 Resolution enhancement in photo-modulated Raman microscopy. a- Experimental Raman scan of a single SOS strip. Blue – cold Raman scan (pump probe delay of −5 ps). Red – hot Raman scan (pump probe delay of + 5 ps). Black- The difference signal, IΔRaman b –Simulation: Scan of a line Raman emitter: The difference signal, IΔRaman, (black), Cold Stokes (blue) and the Hot Stokes (red) scan profiles. c- Black – Difference Raman signal of single SOS stripe (Cold –Hot). Blue – rescaled cold Raman scan. The curve is rescaled to the height of the black (photo-modulated) curve to highlight the differences is widths (resolution). Top left insert- SEM image of the scanned SOS sample.

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The difference scan spectrum, depicted in Fig. 6(b), shows enhanced resolution, improving from FWHM of 650 ± 50 nm in the Raman Stokes scanning to 440 ± 50 nm FWHM in the difference Stokes scanning.

Figure 6(b) depicts the results of our simulations on the integrated Stokes signal. They include the “hot-cold” difference of S integrated intensity, for a point Raman emitter in our experiments. This is a special case in which the spectral ROI for detection spans all the frequencies of the Raman peaks (460 – 550 cm−1). Note in Fig. 2(b), that in this case the dependence on temperature is practically linear, resulting in a smaller enhancement in resolution compared to the ROIs discussed before. The simulations also examined several other schemes for resolution enhancement, such as AS difference spectra, and the ratio of AS/S, multiplied by the cold Stokes intensity. With minor differences, all of these monitoring modes result in PSF of ~330nm FWHM, for Gaussian pump and probe beams with 350nm and 700nm FWHM respectively. The convolution of the simulated PSF with a 125nm stripe of silicon results in 340nm. It fits mildly our experiment (440 ± 50nm), yet supports the validity of our approach.

The resolution improvement achieved by the intensity based detection is limited to 2 of the narrowest beam between the pump and probe, as discussed in the supporting information of [38]. For a linear dependence of the change in the Stokes signal with temperature the effective width of the photo-modulated Raman, WPM_Raman, should scale with the widths of the pump, Wpump, and the probe, Wprobe, as:

WPM_Raman=Wpump2Wprobe2/(Wpump2+ Wprobe2)

6. Summary

In summary, we have presented a novel concept for SR imaging by utilizing the temperature dependence of Raman scattering. Such Raman based methods are free of fluorescence labeling, while enabling chemical recognition. We discussed the experimental requirements for the realization of this method and the potential of utilizing the method in non-linear Raman based methods. The realization of this method with SRS as probe could enable Video rate SR imaging with high SNR. The key advantage of SRS microscopy over Spontaneous Raman and CARS microscopy is that it provides background-free chemical imaging with improved image contrast and it monitors solely the heated portions of the sample. In contrast to Spontaneous Raman microscopy the photo-modulated SRS signal will be a third order nonlinear process and therefore encompasses higher resolution and sectioning. By using a 1.4NA oil-immersion objective and shorter wavelengths for probe and pump, the absolute spatial resolution could further enhanced. Material recognition is an inherent part of this SR imaging method and can be further exploited to differentiate nanoscale hetero-structures. Considerable temperature dependent Raman scattering has been reported on materials such as Ge, Sn [45], SiC [46], GaN [47], GaAs [48], and diamond [49]. We expect that high spectral resolution SRS would enable SR imaging of those and many other materials.

Finally we wish to emphasize that the Raman approach can be extended by probing any physical properties that depend on temperature, such as luminescence, reflection and absorption edge.

Acknowledgment

This work was support by the Israel Science foundation (grant 1716/13). We thank Artium Khatchatouriants for his assistance with the Raman calibration measurements. We thank Alex Pevzner for sample fabrication. We thank Yehiam Prior for useful discussions. The samples were prepared in the Tel Aviv University center for nanoscience and nanotechnology.

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26. Y. Ozeki, F. Dake, S. Kajiyama, K. Fukui, and K. Itoh, “Analysis and experimental assessment of the sensitivity of stimulated Raman scattering microscopy,” Opt. Express 17(5), 3651–3658 (2009). [CrossRef]   [PubMed]  

27. W. P. Beeker, C. J. Lee, K.-J. Boller, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 1–4 (2010). [CrossRef]  

28. W. P. Beeker, C. J. Lee, K. J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011). [CrossRef]  

29. W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009). [CrossRef]   [PubMed]  

30. C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Ground-state depletion for subdiffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012). [CrossRef]  

31. C. Cleff, P. Groß, C. Fallnich, H. Offerhaus, J. Herek, K. Kruse, W. Beeker, C. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013). [CrossRef]  

32. V. Raghunathan and E. O. Potma, “Multiplicative and subtractive focal volume engineering in coherent Raman microscopy,” J. Opt. Soc. Am. A 27(11), 2365–2374 (2010). [PubMed]  

33. K. M. Hajek, B. Littleton, D. Turk, T. J. McIntyre, and H. Rubinsztein-Dunlop, “A method for achieving super-resolved widefield CARS microscopy,” Opt. Express 18(18), 19263–19272 (2010). [CrossRef]   [PubMed]  

34. W. Liu and H. Niu, “Diffraction barrier breakthrough in coherent anti-Stokes Raman scattering microscopy by additional probe-beam-induced phonon depletion,” Phys. Rev. A 83(2), 023830 (2011). [CrossRef]  

35. L. Gong and H. Wang, “Breaking the diffraction limit by saturation in stimulated-Raman-scattering microscopy: A theoretical study,” Phys. Rev. A 90(1), 013818 (2014). [CrossRef]  

36. H. Kim, G. W. Bryant, and S. J. Stranick, “Superresolution four-wave mixing microscopy,” Opt. Express 20(6), 6042–6051 (2012). [PubMed]  

37. P. K. Upputuri, Z. Wu, L. Gong, C. K. Ong, and H. Wang, “Super-resolution coherent anti-Stokes Raman scattering microscopy with photonic nanojets,” Opt. Express 22(11), 12890–12899 (2014). [CrossRef]   [PubMed]  

38. O. Tzang, A. Pevzner, R. E. Marvel, R. F. Haglund, and O. Cheshnovsky, “Super-resolution in label-free photomodulated reflectivity,” Nano Lett. 15(2), 1362–1367 (2015). [CrossRef]   [PubMed]  

39. Z. Ioffe, T. Shamai, A. Ophir, G. Noy, I. Yutsis, K. Kfir, O. Cheshnovsky, and Y. Selzer, “Detection of heating in current-carrying molecular junctions by Raman scattering,” Nat. Nanotechnol. 3(12), 727–732 (2008). [CrossRef]   [PubMed]  

40. M. R. Abel, T. L. Wright, W. P. King, and S. Graham, “Thermal metrology of silicon microstructures using Raman spectroscopy,” IEEE Trans. Compon. Packag. Tech. 30(2), 200–208 (2007). [CrossRef]  

41. A. Milner, K. Zhang, V. Garmider, and Y. Prior, “Heating of an atomic force microscope tip by femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 99(1), 1–8 (2010). [CrossRef]  

42. S. K. Sundaram and E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater. 1(4), 217–224 (2002). [CrossRef]   [PubMed]  

43. M. Balkanski, R. F. Wallis, and E. Haro, “Anharmonic effects in light scattering due to optical phonons in silicon,” Phys. Rev. B 28(4), 1928–1934 (1983). [CrossRef]  

44. J. B. Cui, K. Amtmann, J. Ristein, and L. Ley, “Noncontact temperature measurements of diamond by Raman scattering spectroscopy,” J. Appl. Phys. 83(12), 7929 (1998). [CrossRef]  

45. J. Menendez and M. Cardona, “Temperature dependence of the first-order Raman scattering by phonons in Si, Ge, and a-Sn: Anharmonic effects,” Phys. Rev. B 29(4), 2051–2059 (1984). [CrossRef]  

46. H. Y. Sun, S.-C. Lien, Z. R. Qiu, H. C. Wang, T. Mei, C. W. Liu, and Z. C. Feng, “Temperature dependence of Raman scattering in bulk 4H-SiC with different carrier concentration,” Opt. Express 21(22), 26475 (2013). [CrossRef]  

47. M. S. Liu, L. Bursill, S. Prawer, K. W. Nugent, Y. Z. Tong, and G. Y. Zhang, “Temperature dependence of Raman scattering in single crystal GaN films,” Appl. Phys. Lett. 74(21), 3125 (1999). [CrossRef]  

48. J. R. Shealy and G. W. Wicks, “Investigation by Raman scattering of the properties of III-V compound semiconductors at high temperature,” Appl. Phys. Lett. 50(17), 1173 (1987). [CrossRef]  

49. J. B. Cui, K. Amtmann, J. Ristein, and L. Ley, “Noncontact temperature measurements of diamond by Raman scattering spectroscopy,” J. Appl. Phys. 83(12), 7929 (1998). [CrossRef]  

References

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  22. J. Cheng and X. S. Xie, “Coherent anti-Stocks Raman scattering microscopy: instrumentation, theory, and applications,” J. Phys. Chem. B 108(3), 827–840 (2004).
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    [Crossref] [PubMed]
  27. W. P. Beeker, C. J. Lee, K.-J. Boller, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 1–4 (2010).
    [Crossref]
  28. W. P. Beeker, C. J. Lee, K. J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
    [Crossref]
  29. W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
    [Crossref] [PubMed]
  30. C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Ground-state depletion for subdiffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
    [Crossref]
  31. C. Cleff, P. Groß, C. Fallnich, H. Offerhaus, J. Herek, K. Kruse, W. Beeker, C. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
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    [Crossref]
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    [PubMed]
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    [Crossref] [PubMed]
  38. O. Tzang, A. Pevzner, R. E. Marvel, R. F. Haglund, and O. Cheshnovsky, “Super-resolution in label-free photomodulated reflectivity,” Nano Lett. 15(2), 1362–1367 (2015).
    [Crossref] [PubMed]
  39. Z. Ioffe, T. Shamai, A. Ophir, G. Noy, I. Yutsis, K. Kfir, O. Cheshnovsky, and Y. Selzer, “Detection of heating in current-carrying molecular junctions by Raman scattering,” Nat. Nanotechnol. 3(12), 727–732 (2008).
    [Crossref] [PubMed]
  40. M. R. Abel, T. L. Wright, W. P. King, and S. Graham, “Thermal metrology of silicon microstructures using Raman spectroscopy,” IEEE Trans. Compon. Packag. Tech. 30(2), 200–208 (2007).
    [Crossref]
  41. A. Milner, K. Zhang, V. Garmider, and Y. Prior, “Heating of an atomic force microscope tip by femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 99(1), 1–8 (2010).
    [Crossref]
  42. S. K. Sundaram and E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater. 1(4), 217–224 (2002).
    [Crossref] [PubMed]
  43. M. Balkanski, R. F. Wallis, and E. Haro, “Anharmonic effects in light scattering due to optical phonons in silicon,” Phys. Rev. B 28(4), 1928–1934 (1983).
    [Crossref]
  44. J. B. Cui, K. Amtmann, J. Ristein, and L. Ley, “Noncontact temperature measurements of diamond by Raman scattering spectroscopy,” J. Appl. Phys. 83(12), 7929 (1998).
    [Crossref]
  45. J. Menendez and M. Cardona, “Temperature dependence of the first-order Raman scattering by phonons in Si, Ge, and a-Sn: Anharmonic effects,” Phys. Rev. B 29(4), 2051–2059 (1984).
    [Crossref]
  46. H. Y. Sun, S.-C. Lien, Z. R. Qiu, H. C. Wang, T. Mei, C. W. Liu, and Z. C. Feng, “Temperature dependence of Raman scattering in bulk 4H-SiC with different carrier concentration,” Opt. Express 21(22), 26475 (2013).
    [Crossref]
  47. M. S. Liu, L. Bursill, S. Prawer, K. W. Nugent, Y. Z. Tong, and G. Y. Zhang, “Temperature dependence of Raman scattering in single crystal GaN films,” Appl. Phys. Lett. 74(21), 3125 (1999).
    [Crossref]
  48. J. R. Shealy and G. W. Wicks, “Investigation by Raman scattering of the properties of III-V compound semiconductors at high temperature,” Appl. Phys. Lett. 50(17), 1173 (1987).
    [Crossref]
  49. J. B. Cui, K. Amtmann, J. Ristein, and L. Ley, “Noncontact temperature measurements of diamond by Raman scattering spectroscopy,” J. Appl. Phys. 83(12), 7929 (1998).
    [Crossref]

2015 (1)

O. Tzang, A. Pevzner, R. E. Marvel, R. F. Haglund, and O. Cheshnovsky, “Super-resolution in label-free photomodulated reflectivity,” Nano Lett. 15(2), 1362–1367 (2015).
[Crossref] [PubMed]

2014 (6)

P. K. Upputuri, Z. Wu, L. Gong, C. K. Ong, and H. Wang, “Super-resolution coherent anti-Stokes Raman scattering microscopy with photonic nanojets,” Opt. Express 22(11), 12890–12899 (2014).
[Crossref] [PubMed]

A. Barsic, G. Grover, and R. Piestun, “Three-dimensional super-resolution and localization of dense clusters of single molecules,” Sci Rep 4, 5388 (2014).
[Crossref] [PubMed]

D. A. Nedosekin, E. I. Galanzha, E. Dervishi, A. S. Biris, and V. P. Zharov, “Super-resolution nonlinear photothermal microscopy,” Small 10(1), 135–142 (2014).
[Crossref] [PubMed]

A. Danielli, K. Maslov, A. Garcia-Uribe, A. M. Winkler, C. Li, L. Wang, Y. Chen, G. W. Dorn, and L. V. Wang, “Label-free photoacoustic nanoscopy,” J. Biomed. Opt. 19(8), 086006 (2014).
[Crossref] [PubMed]

J. Yao, L. Wang, C. Li, C. Zhang, and L. V. Wang, “Photoimprint photoacoustic microscopy for three-dimensional label-free subdiffraction imaging,” Phys. Rev. Lett. 112(1), 014302 (2014).
[Crossref] [PubMed]

L. Gong and H. Wang, “Breaking the diffraction limit by saturation in stimulated-Raman-scattering microscopy: A theoretical study,” Phys. Rev. A 90(1), 013818 (2014).
[Crossref]

2013 (4)

C. Cleff, P. Groß, C. Fallnich, H. Offerhaus, J. Herek, K. Kruse, W. Beeker, C. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field imaging of non-fluorescent species with subdiffraction resolution,” Nat. Photonics 7(6), 449–453 (2013).
[Crossref] [PubMed]

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
[Crossref] [PubMed]

H. Y. Sun, S.-C. Lien, Z. R. Qiu, H. C. Wang, T. Mei, C. W. Liu, and Z. C. Feng, “Temperature dependence of Raman scattering in bulk 4H-SiC with different carrier concentration,” Opt. Express 21(22), 26475 (2013).
[Crossref]

2012 (3)

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

H. Kim, G. W. Bryant, and S. J. Stranick, “Superresolution four-wave mixing microscopy,” Opt. Express 20(6), 6042–6051 (2012).
[PubMed]

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Ground-state depletion for subdiffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

2011 (4)

W. Liu and H. Niu, “Diffraction barrier breakthrough in coherent anti-Stokes Raman scattering microscopy by additional probe-beam-induced phonon depletion,” Phys. Rev. A 83(2), 023830 (2011).
[Crossref]

W. P. Beeker, C. J. Lee, K. J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

Y. Shechtman, Y. C. Eldar, A. Szameit, and M. Segev, “Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing,” Opt. Express 19(16), 14807–14822 (2011).
[Crossref] [PubMed]

R. Henriques, C. Griffiths, E. Hesper Rego, and M. M. Mhlanga, “PALM and STORM: unlocking live-cell super-resolution,” Biopolymers 95(5), 322–331 (2011).
[Crossref] [PubMed]

2010 (4)

V. Raghunathan and E. O. Potma, “Multiplicative and subtractive focal volume engineering in coherent Raman microscopy,” J. Opt. Soc. Am. A 27(11), 2365–2374 (2010).
[PubMed]

K. M. Hajek, B. Littleton, D. Turk, T. J. McIntyre, and H. Rubinsztein-Dunlop, “A method for achieving super-resolved widefield CARS microscopy,” Opt. Express 18(18), 19263–19272 (2010).
[Crossref] [PubMed]

W. P. Beeker, C. J. Lee, K.-J. Boller, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 1–4 (2010).
[Crossref]

A. Milner, K. Zhang, V. Garmider, and Y. Prior, “Heating of an atomic force microscope tip by femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 99(1), 1–8 (2010).
[Crossref]

2009 (5)

2008 (2)

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(80), 1857–1861 (2008).

Z. Ioffe, T. Shamai, A. Ophir, G. Noy, I. Yutsis, K. Kfir, O. Cheshnovsky, and Y. Selzer, “Detection of heating in current-carrying molecular junctions by Raman scattering,” Nat. Nanotechnol. 3(12), 727–732 (2008).
[Crossref] [PubMed]

2007 (3)

M. R. Abel, T. L. Wright, W. P. King, and S. Graham, “Thermal metrology of silicon microstructures using Raman spectroscopy,” IEEE Trans. Compon. Packag. Tech. 30(2), 200–208 (2007).
[Crossref]

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, “Femtosecond stimulated Raman microscopy,” Appl. Phys. B 87(3), 389–393 (2007).
[Crossref]

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99(22), 228105 (2007).
[Crossref] [PubMed]

2006 (3)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

L. Novotny and S. J. Stranick, “Near-field optical microscopy and spectroscopy with pointed probes,” Annu. Rev. Phys. Chem. 57(1), 303–331 (2006).
[Crossref] [PubMed]

2004 (2)

B. Pettinger, B. Ren, G. Picardi, R. Schuster, and G. Ertl, “Nanoscale probing of adsorbed species by tip-enhanced Raman spectroscopy,” Phys. Rev. Lett. 92(9), 096101 (2004).
[Crossref] [PubMed]

J. Cheng and X. S. Xie, “Coherent anti-Stocks Raman scattering microscopy: instrumentation, theory, and applications,” J. Phys. Chem. B 108(3), 827–840 (2004).
[Crossref]

2003 (1)

A. Hartschuh, E. J. Sánchez, X. S. Xie, and L. Novotny, “High-resolution near-field Raman microscopy of single-walled carbon nanotubes,” Phys. Rev. Lett. 90(9), 095503 (2003).
[Crossref] [PubMed]

2002 (1)

S. K. Sundaram and E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater. 1(4), 217–224 (2002).
[Crossref] [PubMed]

2001 (1)

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(6), 066613 (2001).
[Crossref] [PubMed]

2000 (2)

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97(15), 8206–8210 (2000).
[Crossref] [PubMed]

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(Pt 2), 82–87 (2000).
[Crossref] [PubMed]

1999 (1)

M. S. Liu, L. Bursill, S. Prawer, K. W. Nugent, Y. Z. Tong, and G. Y. Zhang, “Temperature dependence of Raman scattering in single crystal GaN films,” Appl. Phys. Lett. 74(21), 3125 (1999).
[Crossref]

1998 (2)

J. B. Cui, K. Amtmann, J. Ristein, and L. Ley, “Noncontact temperature measurements of diamond by Raman scattering spectroscopy,” J. Appl. Phys. 83(12), 7929 (1998).
[Crossref]

J. B. Cui, K. Amtmann, J. Ristein, and L. Ley, “Noncontact temperature measurements of diamond by Raman scattering spectroscopy,” J. Appl. Phys. 83(12), 7929 (1998).
[Crossref]

1997 (1)

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922–924 (1997).
[Crossref]

1987 (1)

J. R. Shealy and G. W. Wicks, “Investigation by Raman scattering of the properties of III-V compound semiconductors at high temperature,” Appl. Phys. Lett. 50(17), 1173 (1987).
[Crossref]

1984 (1)

J. Menendez and M. Cardona, “Temperature dependence of the first-order Raman scattering by phonons in Si, Ge, and a-Sn: Anharmonic effects,” Phys. Rev. B 29(4), 2051–2059 (1984).
[Crossref]

1983 (1)

M. Balkanski, R. F. Wallis, and E. Haro, “Anharmonic effects in light scattering due to optical phonons in silicon,” Phys. Rev. B 28(4), 1928–1934 (1983).
[Crossref]

Abel, M. R.

M. R. Abel, T. L. Wright, W. P. King, and S. Graham, “Thermal metrology of silicon microstructures using Raman spectroscopy,” IEEE Trans. Compon. Packag. Tech. 30(2), 200–208 (2007).
[Crossref]

Amtmann, K.

J. B. Cui, K. Amtmann, J. Ristein, and L. Ley, “Noncontact temperature measurements of diamond by Raman scattering spectroscopy,” J. Appl. Phys. 83(12), 7929 (1998).
[Crossref]

J. B. Cui, K. Amtmann, J. Ristein, and L. Ley, “Noncontact temperature measurements of diamond by Raman scattering spectroscopy,” J. Appl. Phys. 83(12), 7929 (1998).
[Crossref]

Balkanski, M.

M. Balkanski, R. F. Wallis, and E. Haro, “Anharmonic effects in light scattering due to optical phonons in silicon,” Phys. Rev. B 28(4), 1928–1934 (1983).
[Crossref]

Barad, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922–924 (1997).
[Crossref]

Barsic, A.

A. Barsic, G. Grover, and R. Piestun, “Three-dimensional super-resolution and localization of dense clusters of single molecules,” Sci Rep 4, 5388 (2014).
[Crossref] [PubMed]

Bartels, R. A.

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
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Beeker, W.

C. Cleff, P. Groß, C. Fallnich, H. Offerhaus, J. Herek, K. Kruse, W. Beeker, C. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

Beeker, W. P.

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Ground-state depletion for subdiffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

W. P. Beeker, C. J. Lee, K. J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

W. P. Beeker, C. J. Lee, K.-J. Boller, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 1–4 (2010).
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W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
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Berner, S.

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, “Femtosecond stimulated Raman microscopy,” Appl. Phys. B 87(3), 389–393 (2007).
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Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
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Biris, A. S.

D. A. Nedosekin, E. I. Galanzha, E. Dervishi, A. S. Biris, and V. P. Zharov, “Super-resolution nonlinear photothermal microscopy,” Small 10(1), 135–142 (2014).
[Crossref] [PubMed]

Boller, K. J.

W. P. Beeker, C. J. Lee, K. J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
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Boller, K.-J.

C. Cleff, P. Groß, C. Fallnich, H. Offerhaus, J. Herek, K. Kruse, W. Beeker, C. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Ground-state depletion for subdiffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

W. P. Beeker, C. J. Lee, K.-J. Boller, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 1–4 (2010).
[Crossref]

W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
[Crossref] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Bryant, G. W.

Bullkich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Bursill, L.

M. S. Liu, L. Bursill, S. Prawer, K. W. Nugent, Y. Z. Tong, and G. Y. Zhang, “Temperature dependence of Raman scattering in single crystal GaN films,” Appl. Phys. Lett. 74(21), 3125 (1999).
[Crossref]

Cardona, M.

J. Menendez and M. Cardona, “Temperature dependence of the first-order Raman scattering by phonons in Si, Ge, and a-Sn: Anharmonic effects,” Phys. Rev. B 29(4), 2051–2059 (1984).
[Crossref]

Chen, Y.

A. Danielli, K. Maslov, A. Garcia-Uribe, A. M. Winkler, C. Li, L. Wang, Y. Chen, G. W. Dorn, and L. V. Wang, “Label-free photoacoustic nanoscopy,” J. Biomed. Opt. 19(8), 086006 (2014).
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Cheng, J.

J. Cheng and X. S. Xie, “Coherent anti-Stocks Raman scattering microscopy: instrumentation, theory, and applications,” J. Phys. Chem. B 108(3), 827–840 (2004).
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Cheng, J. X.

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field imaging of non-fluorescent species with subdiffraction resolution,” Nat. Photonics 7(6), 449–453 (2013).
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Cheshnovsky, O.

O. Tzang, A. Pevzner, R. E. Marvel, R. F. Haglund, and O. Cheshnovsky, “Super-resolution in label-free photomodulated reflectivity,” Nano Lett. 15(2), 1362–1367 (2015).
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Z. Ioffe, T. Shamai, A. Ophir, G. Noy, I. Yutsis, K. Kfir, O. Cheshnovsky, and Y. Selzer, “Detection of heating in current-carrying molecular junctions by Raman scattering,” Nat. Nanotechnol. 3(12), 727–732 (2008).
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Cleff, C.

C. Cleff, P. Groß, C. Fallnich, H. Offerhaus, J. Herek, K. Kruse, W. Beeker, C. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Ground-state depletion for subdiffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

W. P. Beeker, C. J. Lee, K. J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
[Crossref] [PubMed]

Cohen, O.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Cohen-Hyams, T.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
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Colyer, R.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Cui, J. B.

J. B. Cui, K. Amtmann, J. Ristein, and L. Ley, “Noncontact temperature measurements of diamond by Raman scattering spectroscopy,” J. Appl. Phys. 83(12), 7929 (1998).
[Crossref]

J. B. Cui, K. Amtmann, J. Ristein, and L. Ley, “Noncontact temperature measurements of diamond by Raman scattering spectroscopy,” J. Appl. Phys. 83(12), 7929 (1998).
[Crossref]

Dake, F.

Dana, H.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Danielli, A.

A. Danielli, K. Maslov, A. Garcia-Uribe, A. M. Winkler, C. Li, L. Wang, Y. Chen, G. W. Dorn, and L. V. Wang, “Label-free photoacoustic nanoscopy,” J. Biomed. Opt. 19(8), 086006 (2014).
[Crossref] [PubMed]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Dertinger, T.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Dervishi, E.

D. A. Nedosekin, E. I. Galanzha, E. Dervishi, A. S. Biris, and V. P. Zharov, “Super-resolution nonlinear photothermal microscopy,” Small 10(1), 135–142 (2014).
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Deutsch, Z.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
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Dorn, G. W.

A. Danielli, K. Maslov, A. Garcia-Uribe, A. M. Winkler, C. Li, L. Wang, Y. Chen, G. W. Dorn, and L. V. Wang, “Label-free photoacoustic nanoscopy,” J. Biomed. Opt. 19(8), 086006 (2014).
[Crossref] [PubMed]

Dyba, M.

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97(15), 8206–8210 (2000).
[Crossref] [PubMed]

Egner, A.

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97(15), 8206–8210 (2000).
[Crossref] [PubMed]

Eisenberg, H.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922–924 (1997).
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Eldar, Y. C.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
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Y. Shechtman, Y. C. Eldar, A. Szameit, and M. Segev, “Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing,” Opt. Express 19(16), 14807–14822 (2011).
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Enderlein, J.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Engel, E.

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(6), 066613 (2001).
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Ertl, G.

B. Pettinger, B. Ren, G. Picardi, R. Schuster, and G. Ertl, “Nanoscale probing of adsorbed species by tip-enhanced Raman spectroscopy,” Phys. Rev. Lett. 92(9), 096101 (2004).
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Fallnich, C.

C. Cleff, P. Groß, C. Fallnich, H. Offerhaus, J. Herek, K. Kruse, W. Beeker, C. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Ground-state depletion for subdiffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

W. P. Beeker, C. J. Lee, K. J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
[Crossref] [PubMed]

Feng, Z. C.

Freudiger, C. W.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(80), 1857–1861 (2008).

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K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99(22), 228105 (2007).
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Fukui, K.

Galanzha, E. I.

D. A. Nedosekin, E. I. Galanzha, E. Dervishi, A. S. Biris, and V. P. Zharov, “Super-resolution nonlinear photothermal microscopy,” Small 10(1), 135–142 (2014).
[Crossref] [PubMed]

Garcia-Uribe, A.

A. Danielli, K. Maslov, A. Garcia-Uribe, A. M. Winkler, C. Li, L. Wang, Y. Chen, G. W. Dorn, and L. V. Wang, “Label-free photoacoustic nanoscopy,” J. Biomed. Opt. 19(8), 086006 (2014).
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Garmider, V.

A. Milner, K. Zhang, V. Garmider, and Y. Prior, “Heating of an atomic force microscope tip by femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 99(1), 1–8 (2010).
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Gazit, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Gilch, P.

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, “Femtosecond stimulated Raman microscopy,” Appl. Phys. B 87(3), 389–393 (2007).
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Gong, L.

L. Gong and H. Wang, “Breaking the diffraction limit by saturation in stimulated-Raman-scattering microscopy: A theoretical study,” Phys. Rev. A 90(1), 013818 (2014).
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P. K. Upputuri, Z. Wu, L. Gong, C. K. Ong, and H. Wang, “Super-resolution coherent anti-Stokes Raman scattering microscopy with photonic nanojets,” Opt. Express 22(11), 12890–12899 (2014).
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Graham, S.

M. R. Abel, T. L. Wright, W. P. King, and S. Graham, “Thermal metrology of silicon microstructures using Raman spectroscopy,” IEEE Trans. Compon. Packag. Tech. 30(2), 200–208 (2007).
[Crossref]

Griffiths, C.

R. Henriques, C. Griffiths, E. Hesper Rego, and M. M. Mhlanga, “PALM and STORM: unlocking live-cell super-resolution,” Biopolymers 95(5), 322–331 (2011).
[Crossref] [PubMed]

Groß, P.

C. Cleff, P. Groß, C. Fallnich, H. Offerhaus, J. Herek, K. Kruse, W. Beeker, C. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Ground-state depletion for subdiffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

W. P. Beeker, C. J. Lee, K. J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

Gross, P.

Grover, G.

A. Barsic, G. Grover, and R. Piestun, “Three-dimensional super-resolution and localization of dense clusters of single molecules,” Sci Rep 4, 5388 (2014).
[Crossref] [PubMed]

Gustafsson, M. G.

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(Pt 2), 82–87 (2000).
[Crossref] [PubMed]

Haglund, R. F.

O. Tzang, A. Pevzner, R. E. Marvel, R. F. Haglund, and O. Cheshnovsky, “Super-resolution in label-free photomodulated reflectivity,” Nano Lett. 15(2), 1362–1367 (2015).
[Crossref] [PubMed]

Hajek, K. M.

Haro, E.

M. Balkanski, R. F. Wallis, and E. Haro, “Anharmonic effects in light scattering due to optical phonons in silicon,” Phys. Rev. B 28(4), 1928–1934 (1983).
[Crossref]

Hartschuh, A.

A. Hartschuh, E. J. Sánchez, X. S. Xie, and L. Novotny, “High-resolution near-field Raman microscopy of single-walled carbon nanotubes,” Phys. Rev. Lett. 90(9), 095503 (2003).
[Crossref] [PubMed]

He, C.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(80), 1857–1861 (2008).

Hell, S. W.

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(6), 066613 (2001).
[Crossref] [PubMed]

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97(15), 8206–8210 (2000).
[Crossref] [PubMed]

Henriques, R.

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A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Sidorenko, P.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Silberberg, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922–924 (1997).
[Crossref]

Slipchenko, M. N.

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field imaging of non-fluorescent species with subdiffraction resolution,” Nat. Photonics 7(6), 449–453 (2013).
[Crossref] [PubMed]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Steiner, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
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Stranick, S. J.

H. Kim, G. W. Bryant, and S. J. Stranick, “Superresolution four-wave mixing microscopy,” Opt. Express 20(6), 6042–6051 (2012).
[PubMed]

L. Novotny and S. J. Stranick, “Near-field optical microscopy and spectroscopy with pointed probes,” Annu. Rev. Phys. Chem. 57(1), 303–331 (2006).
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Sun, H. Y.

Sundaram, S. K.

S. K. Sundaram and E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater. 1(4), 217–224 (2002).
[Crossref] [PubMed]

Szameit, A.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Y. Shechtman, Y. C. Eldar, A. Szameit, and M. Segev, “Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing,” Opt. Express 19(16), 14807–14822 (2011).
[Crossref] [PubMed]

Tenne, R.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
[Crossref] [PubMed]

Tong, Y. Z.

M. S. Liu, L. Bursill, S. Prawer, K. W. Nugent, Y. Z. Tong, and G. Y. Zhang, “Temperature dependence of Raman scattering in single crystal GaN films,” Appl. Phys. Lett. 74(21), 3125 (1999).
[Crossref]

Tsai, J. C.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(80), 1857–1861 (2008).

Turk, D.

Tzang, O.

O. Tzang, A. Pevzner, R. E. Marvel, R. F. Haglund, and O. Cheshnovsky, “Super-resolution in label-free photomodulated reflectivity,” Nano Lett. 15(2), 1362–1367 (2015).
[Crossref] [PubMed]

Upputuri, P. K.

Volkmer, A.

P. Nandakumar, A. Kovalev, and A. Volkmer, “a Kovalev, and a Volkmer, “Vibrational imaging based on stimulated Raman scattering microscopy,” New J. Phys. 11(3), 033026 (2009).
[Crossref]

Wallis, R. F.

M. Balkanski, R. F. Wallis, and E. Haro, “Anharmonic effects in light scattering due to optical phonons in silicon,” Phys. Rev. B 28(4), 1928–1934 (1983).
[Crossref]

Wang, H.

P. K. Upputuri, Z. Wu, L. Gong, C. K. Ong, and H. Wang, “Super-resolution coherent anti-Stokes Raman scattering microscopy with photonic nanojets,” Opt. Express 22(11), 12890–12899 (2014).
[Crossref] [PubMed]

L. Gong and H. Wang, “Breaking the diffraction limit by saturation in stimulated-Raman-scattering microscopy: A theoretical study,” Phys. Rev. A 90(1), 013818 (2014).
[Crossref]

Wang, H. C.

Wang, L.

J. Yao, L. Wang, C. Li, C. Zhang, and L. V. Wang, “Photoimprint photoacoustic microscopy for three-dimensional label-free subdiffraction imaging,” Phys. Rev. Lett. 112(1), 014302 (2014).
[Crossref] [PubMed]

A. Danielli, K. Maslov, A. Garcia-Uribe, A. M. Winkler, C. Li, L. Wang, Y. Chen, G. W. Dorn, and L. V. Wang, “Label-free photoacoustic nanoscopy,” J. Biomed. Opt. 19(8), 086006 (2014).
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Wang, L. V.

A. Danielli, K. Maslov, A. Garcia-Uribe, A. M. Winkler, C. Li, L. Wang, Y. Chen, G. W. Dorn, and L. V. Wang, “Label-free photoacoustic nanoscopy,” J. Biomed. Opt. 19(8), 086006 (2014).
[Crossref] [PubMed]

J. Yao, L. Wang, C. Li, C. Zhang, and L. V. Wang, “Photoimprint photoacoustic microscopy for three-dimensional label-free subdiffraction imaging,” Phys. Rev. Lett. 112(1), 014302 (2014).
[Crossref] [PubMed]

Wang, P.

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field imaging of non-fluorescent species with subdiffraction resolution,” Nat. Photonics 7(6), 449–453 (2013).
[Crossref] [PubMed]

Weiss, S.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Wicks, G. W.

J. R. Shealy and G. W. Wicks, “Investigation by Raman scattering of the properties of III-V compound semiconductors at high temperature,” Appl. Phys. Lett. 50(17), 1173 (1987).
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Winkler, A. M.

A. Danielli, K. Maslov, A. Garcia-Uribe, A. M. Winkler, C. Li, L. Wang, Y. Chen, G. W. Dorn, and L. V. Wang, “Label-free photoacoustic nanoscopy,” J. Biomed. Opt. 19(8), 086006 (2014).
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M. R. Abel, T. L. Wright, W. P. King, and S. Graham, “Thermal metrology of silicon microstructures using Raman spectroscopy,” IEEE Trans. Compon. Packag. Tech. 30(2), 200–208 (2007).
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Wu, Z.

Xie, X. S.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(80), 1857–1861 (2008).

J. Cheng and X. S. Xie, “Coherent anti-Stocks Raman scattering microscopy: instrumentation, theory, and applications,” J. Phys. Chem. B 108(3), 827–840 (2004).
[Crossref]

A. Hartschuh, E. J. Sánchez, X. S. Xie, and L. Novotny, “High-resolution near-field Raman microscopy of single-walled carbon nanotubes,” Phys. Rev. Lett. 90(9), 095503 (2003).
[Crossref] [PubMed]

Xu, X.

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field imaging of non-fluorescent species with subdiffraction resolution,” Nat. Photonics 7(6), 449–453 (2013).
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K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99(22), 228105 (2007).
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Yang, C.

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field imaging of non-fluorescent species with subdiffraction resolution,” Nat. Photonics 7(6), 449–453 (2013).
[Crossref] [PubMed]

Yao, J.

J. Yao, L. Wang, C. Li, C. Zhang, and L. V. Wang, “Photoimprint photoacoustic microscopy for three-dimensional label-free subdiffraction imaging,” Phys. Rev. Lett. 112(1), 014302 (2014).
[Crossref] [PubMed]

Yavneh, I.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Yutsis, I.

Z. Ioffe, T. Shamai, A. Ophir, G. Noy, I. Yutsis, K. Kfir, O. Cheshnovsky, and Y. Selzer, “Detection of heating in current-carrying molecular junctions by Raman scattering,” Nat. Nanotechnol. 3(12), 727–732 (2008).
[Crossref] [PubMed]

Zhang, C.

J. Yao, L. Wang, C. Li, C. Zhang, and L. V. Wang, “Photoimprint photoacoustic microscopy for three-dimensional label-free subdiffraction imaging,” Phys. Rev. Lett. 112(1), 014302 (2014).
[Crossref] [PubMed]

Zhang, G. Y.

M. S. Liu, L. Bursill, S. Prawer, K. W. Nugent, Y. Z. Tong, and G. Y. Zhang, “Temperature dependence of Raman scattering in single crystal GaN films,” Appl. Phys. Lett. 74(21), 3125 (1999).
[Crossref]

Zhang, K.

A. Milner, K. Zhang, V. Garmider, and Y. Prior, “Heating of an atomic force microscope tip by femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 99(1), 1–8 (2010).
[Crossref]

Zharov, V. P.

D. A. Nedosekin, E. I. Galanzha, E. Dervishi, A. S. Biris, and V. P. Zharov, “Super-resolution nonlinear photothermal microscopy,” Small 10(1), 135–142 (2014).
[Crossref] [PubMed]

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
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Zibulevsky, M.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
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E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, “Femtosecond stimulated Raman microscopy,” Appl. Phys. B 87(3), 389–393 (2007).
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Annu. Rev. Phys. Chem. (1)

L. Novotny and S. J. Stranick, “Near-field optical microscopy and spectroscopy with pointed probes,” Annu. Rev. Phys. Chem. 57(1), 303–331 (2006).
[Crossref] [PubMed]

Appl. Phys. B (1)

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, “Femtosecond stimulated Raman microscopy,” Appl. Phys. B 87(3), 389–393 (2007).
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Appl. Phys. Lett. (3)

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922–924 (1997).
[Crossref]

M. S. Liu, L. Bursill, S. Prawer, K. W. Nugent, Y. Z. Tong, and G. Y. Zhang, “Temperature dependence of Raman scattering in single crystal GaN films,” Appl. Phys. Lett. 74(21), 3125 (1999).
[Crossref]

J. R. Shealy and G. W. Wicks, “Investigation by Raman scattering of the properties of III-V compound semiconductors at high temperature,” Appl. Phys. Lett. 50(17), 1173 (1987).
[Crossref]

Appl. Phys., A Mater. Sci. Process. (1)

A. Milner, K. Zhang, V. Garmider, and Y. Prior, “Heating of an atomic force microscope tip by femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 99(1), 1–8 (2010).
[Crossref]

Biopolymers (1)

R. Henriques, C. Griffiths, E. Hesper Rego, and M. M. Mhlanga, “PALM and STORM: unlocking live-cell super-resolution,” Biopolymers 95(5), 322–331 (2011).
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IEEE Trans. Compon. Packag. Tech. (1)

M. R. Abel, T. L. Wright, W. P. King, and S. Graham, “Thermal metrology of silicon microstructures using Raman spectroscopy,” IEEE Trans. Compon. Packag. Tech. 30(2), 200–208 (2007).
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J. B. Cui, K. Amtmann, J. Ristein, and L. Ley, “Noncontact temperature measurements of diamond by Raman scattering spectroscopy,” J. Appl. Phys. 83(12), 7929 (1998).
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J. Biomed. Opt. (1)

A. Danielli, K. Maslov, A. Garcia-Uribe, A. M. Winkler, C. Li, L. Wang, Y. Chen, G. W. Dorn, and L. V. Wang, “Label-free photoacoustic nanoscopy,” J. Biomed. Opt. 19(8), 086006 (2014).
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J. Microsc. (1)

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(Pt 2), 82–87 (2000).
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J. Phys. Chem. B (1)

J. Cheng and X. S. Xie, “Coherent anti-Stocks Raman scattering microscopy: instrumentation, theory, and applications,” J. Phys. Chem. B 108(3), 827–840 (2004).
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J. Raman Spectrosc. (1)

W. P. Beeker, C. J. Lee, K. J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
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Nano Lett. (2)

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
[Crossref] [PubMed]

O. Tzang, A. Pevzner, R. E. Marvel, R. F. Haglund, and O. Cheshnovsky, “Super-resolution in label-free photomodulated reflectivity,” Nano Lett. 15(2), 1362–1367 (2015).
[Crossref] [PubMed]

Nat. Mater. (2)

S. K. Sundaram and E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater. 1(4), 217–224 (2002).
[Crossref] [PubMed]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Nat. Methods (1)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

Z. Ioffe, T. Shamai, A. Ophir, G. Noy, I. Yutsis, K. Kfir, O. Cheshnovsky, and Y. Selzer, “Detection of heating in current-carrying molecular junctions by Raman scattering,” Nat. Nanotechnol. 3(12), 727–732 (2008).
[Crossref] [PubMed]

Nat. Photonics (1)

P. Wang, M. N. Slipchenko, J. Mitchell, C. Yang, E. O. Potma, X. Xu, and J. X. Cheng, “Far-field imaging of non-fluorescent species with subdiffraction resolution,” Nat. Photonics 7(6), 449–453 (2013).
[Crossref] [PubMed]

New J. Phys. (1)

P. Nandakumar, A. Kovalev, and A. Volkmer, “a Kovalev, and a Volkmer, “Vibrational imaging based on stimulated Raman scattering microscopy,” New J. Phys. 11(3), 033026 (2009).
[Crossref]

Opt. Express (7)

Opt. Lett. (1)

Phys. Rev. A (5)

W. Liu and H. Niu, “Diffraction barrier breakthrough in coherent anti-Stokes Raman scattering microscopy by additional probe-beam-induced phonon depletion,” Phys. Rev. A 83(2), 023830 (2011).
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L. Gong and H. Wang, “Breaking the diffraction limit by saturation in stimulated-Raman-scattering microscopy: A theoretical study,” Phys. Rev. A 90(1), 013818 (2014).
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C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Ground-state depletion for subdiffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
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C. Cleff, P. Groß, C. Fallnich, H. Offerhaus, J. Herek, K. Kruse, W. Beeker, C. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
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W. P. Beeker, C. J. Lee, K.-J. Boller, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 1–4 (2010).
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Phys. Rev. B (2)

M. Balkanski, R. F. Wallis, and E. Haro, “Anharmonic effects in light scattering due to optical phonons in silicon,” Phys. Rev. B 28(4), 1928–1934 (1983).
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Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(6), 066613 (2001).
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Phys. Rev. Lett. (4)

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99(22), 228105 (2007).
[Crossref] [PubMed]

J. Yao, L. Wang, C. Li, C. Zhang, and L. V. Wang, “Photoimprint photoacoustic microscopy for three-dimensional label-free subdiffraction imaging,” Phys. Rev. Lett. 112(1), 014302 (2014).
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B. Pettinger, B. Ren, G. Picardi, R. Schuster, and G. Ertl, “Nanoscale probing of adsorbed species by tip-enhanced Raman spectroscopy,” Phys. Rev. Lett. 92(9), 096101 (2004).
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A. Hartschuh, E. J. Sánchez, X. S. Xie, and L. Novotny, “High-resolution near-field Raman microscopy of single-walled carbon nanotubes,” Phys. Rev. Lett. 90(9), 095503 (2003).
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Proc. Natl. Acad. Sci. U.S.A. (2)

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97(15), 8206–8210 (2000).
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T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
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Sci Rep (1)

A. Barsic, G. Grover, and R. Piestun, “Three-dimensional super-resolution and localization of dense clusters of single molecules,” Sci Rep 4, 5388 (2014).
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Science (2)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(80), 1857–1861 (2008).

Small (1)

D. A. Nedosekin, E. I. Galanzha, E. Dervishi, A. S. Biris, and V. P. Zharov, “Super-resolution nonlinear photothermal microscopy,” Small 10(1), 135–142 (2014).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 Key elements of the proposed method. a- The spectral changes in Raman Stokes peak in 300K silicon (Blue) due to heating to 700K(Red). Note the changes in integrated intensity, line shape broadening and frequency shift. The Hot and Cold ROI mark spectral regions which change extensively upon heating. Top left insert – Heating simulation of silicon by a 400nm, 1ps laser pulse, with a Gaussian intensity profile. 3D simulation of temperature distribution is depicted at t = 1ps after the short pulse. b- Temperature profiles at different delays after excitation. Each line represents a temporal snapshot of the spatial temperature distribution. Heat diffusion blurs the initial heating pattern.
Fig. 2
Fig. 2 Response of a silicon Raman emitter to temperature a-. Calibration measurements. Experimental temperature dependence of silicon Raman spectra using a temperature stabilized heating plate. b- The integrated Raman signal for a point emitter as a function of temperature. Black –integrated Stokes signal. Red- integrated Stokes signal in the ROI (defined in 2a). Note the nonlinear response. Top left insert – Focused beams and Si point targets on sapphire substrate.
Fig. 3
Fig. 3 Simulation of the PSF of the Raman ROI super resolution method. A Raman point source was scanned using a Gaussian heating beam and a Raman gaussian probe beam with 210nm FWHM each. Red – Pump and probe intensity profile. Blue – Super resolution based on the heated Stokes peak integrated in the defined spectral ROI. Black –The difference due to heating in the ROI. In this curve the heated Raman signal in the ROI is subtracted form the unheated peak (achieving better resolution). Resolution of ~100nm can be achieved, x2 enhancement over the diffraction limit. Identical simulation results were obtained for the corresponding anti-Stokes peak.
Fig. 4
Fig. 4 Diagram of the optical setup. In a pump probe configuration a 785nm probe pulse and 392nm pump are temporally synchronized and spatially overlapped into a scanning microscope and focused on the sample by a high NA air objective. Detection modalities include both Raman scattering spectral detection and Thermoreflectance (in which RM is removed and the chopper is activated). RM- removable mirror .DM- dichroic mirror. BS – beam splitter. PD –photo diode. LLF- laser line filter.
Fig. 5
Fig. 5 Experiment characterization: a - time resolved Raman intensity and TR as a function of pump probe delay at a fixed point on the silicon. Integrated intensity of the Stokes Raman peak (Red) and the Transient TR (blue) as a function of the pump-probe delay. Thermalization time for electron phonon scattering is marked in black. b –Raman spectra of silicon, cold (blue) and hot (red) taken at delays of timing of −5ps and 5ps respectively, relative to the pump laser, and difference spectrum (black).
Fig. 6
Fig. 6 Resolution enhancement in photo-modulated Raman microscopy. a- Experimental Raman scan of a single SOS strip. Blue – cold Raman scan (pump probe delay of −5 ps). Red – hot Raman scan (pump probe delay of + 5 ps). Black- The difference signal, I ΔRaman b –Simulation: Scan of a line Raman emitter: The difference signal, I ΔRaman , (black), Cold Stokes (blue) and the Hot Stokes (red) scan profiles. c- Black – Difference Raman signal of single SOS stripe (Cold –Hot). Blue – rescaled cold Raman scan. The curve is rescaled to the height of the black (photo-modulated) curve to highlight the differences is widths (resolution). Top left insert- SEM image of the scanned SOS sample.

Equations (5)

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1 π * 1 2 Γ(T) ( ω vib ω s (T)) 2 + ( 1 2 Γ(T)) 2  
Γ w (T)= A( 1+ 2 e ( ω 0 2 K B T ) 1   )+B( 1+ 3 e ( ω 0 3 K B T ) 1 + 3 ( e ( ω 0 3 K B T ) 1 ) 2 )
ω s ( T )= ω 0 +C( 1+ 2 e ( ω 0 2 K B T ) 1   )+D( 1+ 3 e ( ω 0 3 K B T ) 1 + 3 ( e ( ω 0 3 K B T ) 1 ) 2 )
Δ I Raman (ω)= r=0 I p r obe ( r ){ σ Raman ( ω, T( r ) ) σ Raman ( ω, 300K )}d r
W PM_Raman = W pump 2 W probe 2 /( W pump 2 +  W probe 2 )

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