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Enhancing the sensitivity of nano-FTIR spectroscopy

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Abstract

Synchrotron radiation-based nano-FTIR spectroscopy utilizes the highly brilliant and ultra-broadband infrared (IR) radiation provided by electron storage rings for the infrared spectroscopic characterization of samples at the nanoscale. In order to exploit the full potential of this approach we investigated the influence of the properties of the radiation source, such as the electron bunch shape and spectral bandwidth of the emitted radiation, on near-field infrared spectra of silicon-carbide (SiC). The adapted configuration of the storage ring optics enables a modification of the transverse electron bunch profile allowing an increase of the measured near-field signal amplitude. Additionally, the decay of the signal amplitude due to the decreasing storage ring current is also eliminated. Further options for improving the sensitivity of nano-FTIR spectroscopy, which can also be applied to other broadband radiation sources, are the adaption of the spectral bandwidth to the wavelength range of interest or the use of polarization optics. The sensitivity enhancement emerging from these options is verified by comparing near-field spectra collected from crystalline SiC samples. The improvement in sensitivity by combining these approaches is demonstrated by acquiring nano-FTIR spectra from thin organic films, which show weak resonances in the IR-regime.

© 2017 Optical Society of America

1. Introduction

Optical spectroscopic techniques, such as Fourier transform infrared (FTIR) spectroscopy, are nowadays widely used in different fields of physics, materials science, chemistry, biology, and medicine owing to their sensitivity to molecular vibrations, phonons, and charge carrier concentrations [1, 2]. The achievable spatial resolution of conventional optical techniques is, however, limited by diffraction. This prevents to achieve a lateral resolution significantly below half of the wavelength of the incident radiation, thus limiting the achievable resolution for the mid-infrared (IR) range to a few µm. This limitation can be overcome by applying near-field based techniques, such as scattering-type scanning near-field optical microcopy (s-SNOM) [3–5].

s-SNOM is based on the principle of an atomic force microscope (AFM) and utilizes a sharp metal-coated or solid metal tip brought into close proximity to the sample surface. By simultaneously illuminating the near-field probe with a focused photon beam the tip acts as an antenna which strongly confines the incident electric field around the tip apex, thus providing a nanoscale light source for high-resolution imaging. Subsequent raster scanning of the sample provides beside topographic data also information on the optical properties of the surface with a significantly improved lateral resolution as compared to conventional far-field IR techniques. Additionally, for performing nano-FTIR spectroscopy in the mid-IR range the radiation source has to fulfill certain requirements. Laser-based sources, such as continuous wave or pulsed femtosecond lasers can provide already access to a relatively broad spectral range and cover an increasing number of possible applications [6]. However, for spectroscopy over the full mid-IR spectral range radiation sources with an ultra broad emission spectrum are required, covering the wavenumber range from about 400 cm−1 to 4000 cm−1 (corresponding to wavelengths from 2.5 µm to 25 µm). During the last years several groups reported on different approaches to circumvent this limitation. Various laser-based sources, such as tunable gas lasers [7, 8], pulsed femtosecond lasers [6, 9, 10], and continuum sources [11, 12] have the advantage of high irradiance. However, the accessible spectral range of most sources is yet not covering the full fingerprint region in the mid-IR range or they show relatively high intensity fluctuations. Therefore, also other approaches that are based on thermal sources, such as heating of a tungsten or ceramic filament [13, 14], were recently evaluated for broadband nano-FTIR spectroscopy despite the incoherent nature of the emitted radiation and the associated low spectral irradiance. An alternative approach to obtain near-field IR spectroscopic information is thermal emission by heating the sample surface either by the tip itself [15,16] or the sample holder [17]. A further promising approach uses free electron laser sources, which are capable to provide coherent radiation over a relatively broad spectral range [18].

Another light source which provides spectrally ultra broad radiation with the advantages of having additionally a high brilliance and up to three orders of magnitude higher intensity compared to thermal sources is synchrotron radiation (SR). The first successful demonstration of a SR-based near-field measurement was performed in 2004 in the THz regime [19]. During the last years SR-based near-field spectroscopy has been also evaluated for nano-FTIR spectroscopy [20,21] followed by the first successful measurement on simple test structures [22]. Since the first experiments this approach has attracted further interest and was applied in various configurations for the nanoscale spectroscopic characterization of semiconductor materials [23,25,26], crystals [23], organic samples [23], and boron nitride monolayers [27]. Recently, SR-based infrared spectroscopy was also successfully demonstrated by exploiting photothermal effects [28].

In the present work we report on the adaption of storage rings optics at the electron storage ring Metrology Light Source (MLS) [29] for near-field spectroscopic measurements in the mid-IR range. For this purpose, the transverse size of the electron bunch profile was reduced for increasing the photon density within the incident beam and to improve the spatial coherence properties of the SR. Furthermore, a method is described how the decay of the near-field signal amplitude due to the temporal decrease of the current in the storage ring can be compensated thus enabling nano-FTIR measurements with almost unchanged signal amplitude. By adjusting the spectral bandwidth of the incident ultra broadband radiation to the spectral region of interest and by applying polarization optics the sensitivity of nano-FTIR spectroscopic investigation can be significantly increased. This is demonstrated by the acquisition of near-field FTIR spectra from samples with relatively weak resonances, such as films of polymethyl-methacrylate (PMMA) and polydimethylsiloxane (PDMS), as well as dexamethasone (C22H29FO5) [31] nanocrystals. The improvement of the adapted spectral bandwidth is also confirmed by a theoretical description which is presented, as well.

2. Experimental setup

The experiments described in the following were performed on a scattering-type scanning near-field optical microscope (s-SNOM) (Neaspec GmbH, Germany) consisting of an AFM operated in tapping mode and an asymmetric Michelson interferometer. The tapping amplitude during the experiments was set between 60 nm and 80 nm. The Au coated Si cantilevers (Nanosensors™ PPP-NCSTAu) had a resonance frequency in the range between 76 kHz and 263 kHz and a typical tip diameter below 50 nm.

The experimental setup is shown in Fig. 1. The measurements were performed at the Metrology Light Source (MLS) [29], an energy ramped electron storage ring that can be operated with electron energies between 50 MeV and 629 MeV. The results shown in this paper were obtained with the ring operated at 629 MeV. The ring current can be adjusted in a range of over 11 orders of magnitude starting from a single electron (1 pA) up to 200 mA. It has a circumference of 48 m and is designed as an asymmetric double-bend achromate with twofold symmetry. The MLS has been operated in different modes summarized in Fig. 2. In the so-called standard user mode the MLS is operated with 80 electron bunches providing a pulse repetition rate of 500 MHz with a bunch length of about 20 ps at 629 MeV.

 figure: Fig. 1

Fig. 1 Schematic diagram of the experimental IR s-SNOM/nano-FTIR setup at the MLS, from [25]. The broadband IR synchrotron radiation is coupled out from a bending magnet and is directed by a set of mirrors (not shown in the image) to the nano-FTIR setup. The ZnSe beamsplitter separates the radiation into a reference beam and a second beam which is focused by a parabolic mirror on tip and sample. The reference mirror can be moved over a distance of up to 1500 µm. The signal is detected by a liquid nitrogen cooled MCT detector.

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 figure: Fig. 2

Fig. 2 Summary of the different storage ring modes.

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The IR radiation is coupled out from the electron storage ring by a planar water cooled mirror and is guided to the experimental setup by several planar and cylindrical mirrors. A set of diamond windows at the end of the beamline separates the ultra-high vacuum from the ambient conditions under which the s-SNOM system is operated. The IR beam at the end of the beamline is rectangular-shaped with the dimensions of approximately 25 mm (horizontal) and 10 mm (vertical) in the visible range of the emitted radiation. The measured power at this position at a ring current of 100 mA is about 2 mW integrated over a wavenumber range from 500 cm−1 to 10000 cm−1.

A periscope arrangement of mirrors is used to convert the horizontal polarization of the SR into vertical polarization since this is more advantageous for near-field experiments on the described s-SNOM setup. For the latter case the electric field vector has a significantly larger component parallel to the tip-axis enabling a stronger electric field enhancement in the close vicinity of the tip apex. The light backscattered from the tip and sample is collected by a parabolic mirror and is analyzed by the Michelson interferometer. The planar mirror in the reference arm is mounted on a motorized stage which can be moved over a distance of up to 1500 µm corresponding to a spectral resolution limit of about 3 cm−1. The second arm of the interferometer contains the near-field probe and the sample. The interferogram as a function of the optical beam path difference is recorded by a liquid nitrogen cooled Mercury-Cadmium-Telluride (MCT) detector (model number: J15D12M204-S050U-60, Teledyne Judson Technologies, United States). The MCT detector is sensitive over a wavelength range from about 2 µm to 13.5 µm corresponding to a wavenumber range from 740 cm−1 to 5000 cm−1, respectively. The active area (square shaped) of the detector is 50 µm × 50 µm.

The IR beam is focused on the sample surface under an angle of about 65 degrees and has in standard user operation a typical diameter of about 80 µm on the sample surface. Therefore, an illumination of the tip shaft and sample cannot be avoided, leading to strong background contribution in the detected signal. The separation of the intense far-field signal from the relatively weak near-field contribution is achieved by lock-in demodulation of the interference signal at higher harmonics of the cantilevers oscillation frequency. This ensures that at higher harmonics (n > 1) the background contribution is significantly reduced [25,30].

The influence of the modified storage ring optics as well as from the reduced spectral range by optical filters on the recorded near-field IR spectra is investigated on a bulk 6H-SiC sample. For demonstrating that the adapted storage ring optics and the reduced spectral bandwidth improve the sensitivity of SR-based near-field IR spectroscopy sufficiently for characterizing thin organic layers with much weaker resonances than 6H-SiC nano-FTIR spectra are recorded from PMMA, PDMS, and dexamethasone. The three samples were deposited on Si and Au substrates. The PMMA and PDMS layers were prepared by spin-coating and had a film thickness of about 40 nm and 60 nm, respectively. A thin layer of dexamethasone was deposited on Au substrate by spin-coating. After drying, dexamethasone forms small rod-like nanocrystals with a typical diameter below 100 nm and a length of several µm.

3. Results and discussion

The advantage of the synchrotron radiation provided by storage rings is not only the high brilliance and extremely broad radiation spectrum from hard X-rays to THz, but also the flexibility to adapt the emission properties to the experimental requirements. This is achieved by controlling of the number of stored electrons, their energy and the shape of the electron bunches, in turn determining, e.g., size and divergence of the resulting photon source. In order to exploit these properties of the synchrotron radiation source we investigated the influence of different electron storage ring optics on the near-field spectra recorded from a bulk 6H-SiC sample. The measurements described in the following were performed under identical conditions, where only the storage ring optics was changed.

The MLS facility allows different operation modes, such as various transverse electron bunch profiles. The shape of the electron bunches has an influence on the emitted optical beam size as well as the intensity distribution. The vertical bunch size is controlled by an excitation and the horizontal size by the storage ring optics. Some of these configurations of electron storage ring optics may be more advantageous for near-field experiments than others, as is systematically investigated in this work.

In the standard user operation mode the typical pulse length is about 20 ps. The vertical bunch size is kept at a constant value of about 260 µm, at the beamline source point in the storage ring. The horizontal bunch size has a typical value of 380 µm. The size is fixed during the decay of the storage ring current, which has a typical lifetime of about 6 h. The intensity distribution of the focused IR beam at the end of the beamline can be qualitatively visualized by a focal plane array (FPA) consisting of 128 by 128 pixels, attached to a Hyperion 3000 plus Vertex 80v Bruker FTIR spectrometer system. It is expected that the intensity distribution of the focus at the FPA corresponds qualitatively to the distribution at the plane of the AFM tip. For the standard operation mode the obtained intensity distribution is illustrated in Fig. 3(a) showing a spot with the dimensions of about 220 µm for the long and about 40 µm for the short axis.

 figure: Fig. 3

Fig. 3 Comparison of beam size for different storage ring optics of the MLS facility. The scale bar corresponds to a length of 100 µm. By reducing the size of the electron bunches the focal spot of the emitted SR can also be significantly reduced. This is illustrated for three different storage ring optics: (a) standard user optics (electron bunch size: 380 µm (horizontal) and 260 µm (vertical)), (b) low-alpha optics (electron bunch size: 400 µm (horizontal) and 850 µm (vertical)), and (c) low-emittance optics (electron bunch size: 190 µm (horizontal) and 180 µm (vertical)). The images recorded with a focal plane array are normalized to the ring current.

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In another operation mode, denoted as low-alpha the MLS storage ring optics are especially optimized for shorter electron bunches and by that for the generation of coherent synchrotron radiation in the far-IR and THz regimes [32]. In this case the pulse duration is reduced to about 2 ps, with a corresponding reduction in its longitudinal size. Simultaneously, the transversal size of the bunches is increased by about 100% to 400 µm for the horizontal and 850 µm for the vertical axis. The resulting intensity distribution recorded with the focal plane array is shown in Fig. 3(b) showing a considerably larger SR beam spot with the dimensions of about 200 µm × 150 µm.

In a further configuration, the so called low-emittance optics [Fig. 3(c)], the transverse dimensions of the electron bunches at the reference point is reduced to 190 µm × 180 µm while the longitudinal bunch length is slightly increased compared to the standard operation mode to about 30 ps. The corresponding intensity distribution recorded with the focal plane array shows a reduced spot size compared to the standard operation configuration. Since the recorded intensity data for all three storage ring optics are normalized to the ring current the obtained intensity values can be directly compared to each other.

For the low-alpha optics an area that is three-fold larger than for the standard user optics is illuminated on the focal plane array. The maximum intensity for this storage ring optics is, however, 50% lower than for the standard optics setting. In contrast, the low-emittance optics with the smaller electron bunches illuminates a slightly smaller area on the focal plane array but the maximum intensity value is twice as high as observed for the standard operation mode. Additionally, the position of the highest intensity is slightly shifted off the center of the focal spot compared to the two other configurations. Note, that especially in Fig. 3(c) a second high intensity tail is visible. These features are duplicates of the focal spot as a result of multiple reflections when coupling external radiation from the beamline off-axis into the FTIR spectrometer system.

To analyze these experimental results in the context of nano-FTIR spectroscopy ray tracing calculations [33] were performed for these three storage ring optics. The calculated intensity distributions of the focus at the plane of the AFM tip are illustrated in Fig. 4(a)–(c). The scale bar corresponds to a length of 100 µm. As also observed experimentally the largest SR spot and the lowest intensity are obtained from low-alpha optics [Fig. 4(b)]. The area with the highest intensity is clearly visible in the calculated intensity distribution for the low-emittance operation optics [Fig. 4(c)]. Furthermore, the distribution becomes slightly asymmetric which can be attributed to the emission characteristics of the electrons at the bending magnet, where the emitted IR radiation is coupled out from the storage ring into the beamline. This asymmetric intensity distribution becomes even more pronounced in the ray tracing calculations for the low-emittance optics and confirms the experimentally observed shift of the highest intensity from the center to the edge of the long axis. The higher peak intensity in the intensity distribution recorded by the focal plane array is also reproduced by ray tracing calculations and confirms that a reduced electron bunch size results in a higher peak intensity in a small area within the focal spot. Since in near-field experiments the beam is focused on a tip with a typical diameter below 100 nm the detected near-field signal originates from a relatively small area. If the near-field probe apex is placed in the area with the highest intensity, the detected signal amplitude should be higher compared to the signal amplitude obtained from standard operation mode.

 figure: Fig. 4

Fig. 4 Intensity distribution of the IR radiation focused onto the sample obtained from ray tracing calculations [33] for the three different storage ring optics illustrated in Fig. 3. The scale bar corresponds to a length of 100 µm. The electron bunch size for standard user optics is illustrated in (a). The lowest intensity values as well as the largest SR spot are obtained from low-alpha optics (b). For further decreasing electron bunch size the focused IR beam becomes increasingly asymmetric and the peak intensity increases as compared to standard user optics (c).

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For verification the same type of near-field probe (Au-coated Si-tip) and identical experimental parameters (tapping amplitude and integration time) were used to measure the near-field signal amplitude from bulk 6H-SiC. For this purpose, the tip was brought into close proximity of the sample surface and placed at the position of the highest intensity within the focused SR spot. In Fig. 5 the near-field IR spectra acquired from the SiC sample surface for the three different storage ring optics are compared to each other. In all recorded nano-FTIR spectra the characteristic longitudinal optical SiC phonon mode appears around 926 cm−1. For a better comparison the SiC spectra are normalized to a ring current of 90 mA. The observed pronounced phonon resonance at this position also confirms near-field signal detection. The lowest signal intensity is obtained from the near-field spectrum recorded in the low-alpha optics configuration. Compared to the standard user configuration the signal intensity is about 50% lower. In contrast, for the low-emittance configuration the near-field signal intensity in the nano-FTIR spectrum is increased by about 200% compared to the standard storage ring optics. If for the low-emittance optics the near-field probe is placed in an area where the radiation intensity has a maximum the sensitivity of SR-based nano-FTIR spectroscopy can be increased significantly.

 figure: Fig. 5

Fig. 5 Influence of the storage ring optics and beam size on intensity of 6H-SiC nano-FTIR spectrum. The variation of the beam size compared to the standard user optics results in an enhanced signal intensity of about 200% for low-emittance optics and a signal decay of 50% for low-alpha optics. For a better comparison the spectra are normalized to a ring current of 90 mA.

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A disadvantage of this reduced transverse dimension of the electron bunches is a shorter lifetime of the storage ring current of about 2 h which requires more frequent injections and continuous normalization to the ring current. This effect is illustrated in Fig. 6(a) showing nano-FTIR spectra recorded from 6H-SiC for different ring currents. The peak intensity of the phonon polariton of SiC at around 926 cm−1 decreases with decaying ring current, thus requiring a normalization to the actual ring current during the acquisition time. Since the change of the ring current cannot be neglected during the acquisition of a single spectrum the normalization procedure becomes more complex. In order to eliminate this effect from the recorded nano-FTIR spectra the vertical size of the electron bunches was simultaneously reduced with decaying ring current by adjusting the excitation accordingly. This enabled to keep the incident photon density within the beam center almost independent from the ring current. For verification near-field spectra were recorded at the same position from SiC for different ring currents showing a fluctuation of less than 6% [Fig. 6(b)] during the decay of the ring current from 177 mA to about 117 mA, indicating that this correction provides reliable results. Note, however, that deviations still occur, which may partially be attributed to a non-linear detector response, discussed below.

 figure: Fig. 6

Fig. 6 Comparison of 6H-SiC near-field spectra recorded by the (a) standard and (b) the optimized low-emittance storage ring optics of MLS. Due to the relatively short life time in the low-emittance mode the signal amplitude in subsequently recorded near-field spectra decreases due to the decay of the storage ring current. This variation of the signal amplitude can be minimized by allowing a change of the electron bunch size with decreasing ring current thus providing an almost constant photon flux. The change in the peak intensity as function of ring current is shown in the inset of (b).

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The asymmetric interferometer configuration employed in this work typically results in a small modulation depth on top of a large background signal. In such configurations a detector with a high responsivity at high irradiance is desirable. In Fig. 7(a) the signal amplitude of the MCT detector is presented as a function of the ring current. By gradually reducing the number of electrons in the storage ring at fixed bunch size the ring current can be reduced without altering the optical beam path (unlike, e.g. by neutral density filters). The obtained curve demonstrates that throughout the available ring current range the detector is operated in the non-linear regime which is a common characteristic of MCT detectors [34]. In particular within the current range used for nano-FTIR measurements from 80 mA to 175 mA the detector responsivity is progressively reduced.

 figure: Fig. 7

Fig. 7 Dependence of MCT signal amplitude from storage ring current (a) and recorded nano-FTIR spectra from SiC recorded with and without a polarizer (b). For the measurements the number of electrons in the storage ring was gradually reduced so that the optical beam path remained unchanged. The amplitude shows a strong non-linear behavior for ring currents under which the MCT detector was typically operated (between 80 mA and 170 mA). A nearly linear increase in signal amplitude is observed only for ring current values below 10 mA. The incident SR contains to a certain portion also waves with a vertical polarization (perpendicular to tip axis). However, these waves do not contribute significantly to the electric field enhancement at the illuminated tip apex, but rather drive the detector more into the non-linear regime. By using a polarizer these waves can be removed from the incident SR beam resulting in a signal enhancement of about 100% in the recorded SiC near-field spectra (b) compared to the measurement without polarizer.

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Therefore, two strategies have been investigated to reduce the detector load while keeping the information containing signal. The emitted SR also contains a certain portion of electromagnetic waves with a non-horizontal electric field vector [35,36]. The contribution of these waves to the electric field enhancement at the tip apex, which is crucial for the strong sensitivity increase, can be neglected, since the electric field is oriented perpendicular to the tip axis. However, these waves increase the irradiance on the active area of the detector thus driving it more into saturation and result in a reduced responsivity of the MCT detector. In order to remove these waves from the incident SR a polarizer (InfraSpecs Far-IR grid array polarizer) with an average transmittance of about 80% in the mid-IR range was placed into the beam path. In Fig. 7(b) the near-field spectra of the SiC sample recorded without (green curve) and with a polarizer (red curve) are shown. The orientation of the polarizer was optimized to the highest near-field signal intensity, i.e. with the reference arm of the interferometer blocked. The signal amplitude of the IR-spectrum recorded with the polarizer is enhanced by up to 100% compared to the spectrum recorded without the polarizer. One also has to consider that this signal enhancement occurred despite the reduced transmittance of the polarizer. Therefore, an even higher signal enhancement can be expected for a polarizer with higher transmittance values. Another possibility to increase the signal amplitude, if the detector is operated in the non-linear regime, may be achieved when the relevant spectral range of the investigated sample is known a priori. In this case one could apply spectral filtering to block the non-relevant part of the IR-spectrum, which is demonstrated in the following.

For this purpose different edge filters for the mid-IR range were inserted in front of the ZnSe beam splitter of the asymmetric Michelson interferometer into the optical beam path. This allowed us to reduce the signal intensity in the high-frequency part of the IR spectrum. The recorded interferograms from 6H-SiC sample are presented in Fig. 8(a) showing two interferograms obtained from filters with a cut-off edge at about 3330 cm−1 (blue curve) and 1818 cm−1 (red curve), respectively. The interference pattern recorded with a filter with a cut-off edge at about 1818 cm−1 is much more pronounced compared to the pattern measured with a cut-off edge at 3330 cm−1. The corresponding near-field IR spectra obtained from Fourier transformation are shown in Fig. 8(b) together with other nano-FTIR spectra recorded with filters with different cutoff edges values. The strong phonon resonance of the 6H-SiC sample appears in all near-field IR spectra at about 926 cm−1. However, with decreasing spectral bandwidth Δν the signal amplitude in the corresponding near-field spectra increases significantly. The highest signal amplitude is measured for the narrowest spectral bandwidth providing a signal enhancement compared to the spectrum recorded with the 3330 cm−1 cut-off edge of up to 2000%.

 figure: Fig. 8

Fig. 8 Influence of reduced spectral bandwidth on interferograms (a) and near-field IR spectra (b) recorded from bulk 6H-SiC (5th harmonic). The reduction of the spectral bandwidth of ultrabroadband synchrotron radiation by spectral filters to the wavelength range of interest has significant influence on the signal amplitude in the interferograms (a) and corresponding near-field spectra (b). The limitation of the spectral range by using edge filters in front of the asymmetric Michelson-Interferometer can significantly increase the intensity in the near-field spectra. The values in (b) indicate the upper limit of the wavenumber position above which the light intensity is reduced to almost zero, corresponding to the line color of the respective IR-spectrum and interferogram. A stepwise reduction of the spectral range by using different optical filters provides a signal enhancement of up to 2000% for the edge filter at 1818 cm−1.

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The detector responsivity may in principle also be enhanced by inserting a neutral density filter in front of the reference arm mirror, leaving the information containing signal from the tip unchanged. However, this will reduce the signal enhancement effect of the asymmetric interferometer, and is therefore not as efficient as spectral filtering, as shown in the following. With the optical signal s(t) being characterized by its Fourier transform S(ω)=12πs(t)eiωtdt the signal arriving at the detector after passing through the interferometer can be written as

S(ω)=[n0+eiωΔl/cnSNOM(ω,t)]S0(ω),
with n0 < 1 describing the attenuation due to the neutral density filter, Δl is the path difference and c the speed of light. The signal scattered by the tip and re-collected by a parabolic mirror is given as the time varying fraction nSNOM ≪ 1 of the signal S0(ω) incident at the interferometer. The temporal variation, which is slow compared to IR frequencies, comes from the height modulation of the tip in the 100 kHz range and the corresponding modulation of the scattering cross section. The power measured by the detector is given by
P(Δl,t)|S(ω)|2dω=(n02+2Re[eiωΔl/cnSNOM(ω,t)]+|nSNOM(ω,t)|2)|S0(ω)|2dω=n02|S0(ω)|2dω+2Re[n0eiωΔl/cnSNOM(ω,t)|S0(ω)|2dω]+|nSNOM(ω,t)|2|S0(ω)|2dω.
The last term of the above expression will typically be negligible so that the detector load is dominated by the first two terms. The second integral describes the modulation of the measured power as the reference arm length, Δl, is varied. The corresponding modulation depth and the power at center burst position, Δl = 0, will be reduced by the attenuation of the neutral density filter n0. On the other hand, reducing the spectral bandwidth Δν of the incoming radiation S0(ω) will not affect this integral since the ratio nSNOM will be small for ω outside the resonance of the sample. Hence, reducing Δν will be more efficient in enhancing the signal-to-noise ratio than broad band attenuation.

We note that, unlike for the above case in symmetric FTIR spectroscopy, bandpass filters are applied to reduce the photonic noise [37]. If the required time resolution lies well below the MHz limit needed above, detectors showing linearity over a large intensity range have been demonstrated [38] for which spectral filtering is not expected to result in signal enhancement.

Compared to laser-based radiation sources that were recently used for investigating organic materials [6], radiation provided by thermal and SR sources has a much broader bandwidth [39]. However, the power of such broadband sources is typically relatively low allowing almost only the excitation of strong phonon or plasmon resonances. The improvements described above should also be applicable for various nano-FTIR spectroscopy setups using other broadband radiations sources. The applied approaches for enhancing the sensitivity of SR based nano-FTIR spectroscopy should be sufficient for enabling the acquisition of near-field spectroscopic information from organic substances with much weaker resonances despite the relative low incident power of about 2 mW for the mid-IR range. For this purpose we demonstrate in the following the acquisition of near-field IR spectra from thin layer samples, such as PMMA, PDMS, and dexamethasone. The integrated power over the full fingerprint region in front of the ZnSe beamsplitter and behind spectral edge filter at 1810 cm−1 and polarization filter during the described measurements was at about 750 µW. This is considerably below the values which are reached by laser-based sources. These provide a typical spectral irradiance of the order of mW/cm2/cm−1 [24].

In the following the use of the above developments is shown for fingerprint near-field IR spectroscopy of PMMA deposited on a Au substrate and PDMS on Si. Due to the flat spectral response of Au and Si in the mid-IR regime the spectra obtained from the exposed substrate material are used as reference spectra. The resulting near-field IR absorption spectra of PMMA and PDMS are displayed in Fig. 9(a) and (b), respectively. The recorded near-field IR spectrum of the PMMA layer with a thickness of 40 nm shows the typical molecular absorption bands such as C-O-C deformation (969 cm−1, 994 cm−1), CH2-bending (1151 cm−1), C-O-C bending (1207 cm−1), C-C-O stretching (1270 cm−1), CH2 and CH3 deformation (1451 cm−1 and 1489 cm−1), and the strong C=O stretching band of the acrylat carboxyl group at about 1739 cm−1. The near-field absorption bands are shifted to higher wavenumbers compared to far-field FTIR measurements, as also reported in other investigations [40]. For the 60 nm thin PDMS layer on a Si substrate also the characteristic absorption bands appear in the near-field IR spectrum displayed in Fig. 9(b). The band around 800 cm−1 can be assigned to the CH3 rocking vibration, the broad band between 900 cm−1 and 1100 cm−1 with several peaks is attributed to the Si-O-Si asymmetric stretching modes, and the relatively sharp band around 1259 cm−1 is due to the absorption of CH3 vibrations. The acquisition time for the two near-field spectra presented in the Fig. 9(a) and (b) is 240 s at a spectral resolution of 6 cm−1. The recorded spectra with SR-based nano-FTIR spectroscopy demonstrate that spectroscopic information can be obtained from a broad wavenumber range. The adaption of the storage ring optics as well as the reduction of the spectral bandwidth to the frequency range of interest enables the acquisition of spectra even at an incident radiation power of a few hundred µW.

 figure: Fig. 9

Fig. 9 Near-field spectra from poly(methyl methacrylate) (PMMA) (a) and polymethlysilox-ane (PDMS) (b) recorded using the optimized low-emittance optics of the MLS storage ring and a spectral bandwidth reduced to the wavenumber range from about 1820 cm−1 to 750 cm−1. The 40 nm PMMA layer was deposited on a Au substrate. The PDMS layer had a thickness of about 60 nm and was deposited on a Si substrate.

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For demonstrating that SR-based near-field spectroscopy also enables nano-imaging of organic samples with a complex spectrum, such as dexamethasone nanorods the reference arm of the Michelson interferometer is moved to the position (white light position) where the sample and reference arm have approximately the same optical beam path length. At this position all frequencies are in phase thus yielding a strong detector signal. Dexamethasone ((11β,16α)-9-fluoro-11,17,21-trihydroxy-16-methylpregna-1,4-diene-3,20-dione, C22 H29 FO5) is an antiinflammatory drug which can be used for the treatment of inflammatory skin diseases. It has been investigated before by X-ray spectromicroscopy [31, 41]. When drying dexamethasone dissolved in ethanol on a Au-surface the substance forms nanorods, as shown in the topography image in Fig. 10(a). The corresponding optical image (3rd harmonic) recorded in the white light configuration is presented in Fig. 10(b). The rods in the scanned area on the Au surface have a typical diameter of about 100 nm and a length of several µm. The Figs. 10(c) and (d) show the broadband Fourier-transform near-field amplitude and phase spectra, respectively, normalized to the Au reference spectrum. The near-field IR spectrum of a dexamethasone nanorod is relatively complex, showing several distinct resonances at about 893 cm−1, 1668 cm−1, and 1700 cm−1. In Fig. 10(e) and (f) we demonstrate nanoscale IR-spectroscopic mapping of the local amplitude and phase, respectively. While scanning across the dexamethasone edge (red bar in Fig. 10(b)) an IR spectrum is recorded at each position. The distance between two adjacent measurement points was 50 nm. All acquired near-field IR spectra were normalized to the Au reference spectrum. In the map showing the amplitude image the signal decays strongly when scanning from the Au surface onto the dexamethasone nanorod. This effect can be explained by the decreasing near-field interaction between tip and Au substrate when scanning across the edge of dexamethasone structure compared to the bare Au surface. The topography related change of the signal at the Au/dexamethasone edge disappeared in the corresponding phase image [Fig. 10(f)] completely. The strong resonance observed in the near-field IR spectrum [Fig. 10(d)] at around 893 cm−1 appears instantly at the edge in agreement with the previously determined high spatial resolution of < 50 nm of this technique [25].

 figure: Fig. 10

Fig. 10 SR-based imaging and nano-FTIR spectroscopy on dexamethasone. Topography (a) and corresponding 3rd harm. near-field image (b) from a 5 µm × 5 µm large sample area. The optically dark wire-like structures are formed by dexamethasone crystals whereas the optically light regions indicate the exposed Au surface. Diagrams in (c) and (d) show the magnitude and phase of the near-field spectrum, respectively. The spectra corresponding to the red bar in (a) are shown as magnitude in (e) and phase in (f).

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4. Conclusions

In the present work we demonstrated the adaption of electron storage ring optics in combination with an improvement of the temporal coherence properties of ultra-broadband SR. The smaller transverse electron bunch profile and the reduction of the bandwidth to the spectral region of interest significantly enhances the sensitivity for nano-FTIR spectroscopy. The disturbing influence of a decaying current of the storage ring on the signal amplitude and the required normalization can be eliminated by the controlled reduction of the transverse bunch size with decreasing ring current. This allows us to keep the photon flux within the SR beam almost unchanged for the duration of the measurements. The described adaptations increase the sensitivity of SR-based nano-FTIR spectroscopy significantly, thus allowing the acquisition of near-field IR spectra of organic substances with relatively weak resonances within a reasonable time. This is successfully demonstrated by recording near-field infrared spectra from thin organic layers and by performing nanoscale spectroscopic mapping.

Funding

University of Latvia (AAP2016/B031 (VK)); EMRP and EMPIR programmes; German Research Foundation (SFB 1112, project B02).

Acknowledgments

The authors thank Godehard Wüstefeld from the Helmholtz-Zentrum Berlin for discussion and his support at the MLS. Discussions with S. Kröger, R. Ferber, and M. Tamanis are gratefully acknowledged.

References and links

1. Helmut Günzler and Hans-Ulrich Gremlich, IR Spectroscopy: An Introduction (Wiley-VCH, 2012).

2. Yujun Zhong, Shyamala Devi Malagari, Travis Hamilton, and Daniel Wassermann, “Review of mid-infrared plasmonic materials,” J. Nanophotonics 9, 093791 (2015). [CrossRef]  

3. B. Knoll and F. Keilmann, “Infrared conductivity mapping for nanoelectronics,” Appl. Phys. Lett. 77, 3980–3982 (2000). [CrossRef]  

4. F. Keilmann and R. Hillenbrand, “Near-field nanoscopy by elastic light scattering from a tip,” in Nano-Optics and Near-Field Optical Microscopy, A. Zayats and D. Richard, eds. (Artech House, 2009).

5. A. Hartschuh, “Tip-enhanced near-field optical microscopy,” Angew. Chem. Int. Ed 47, 8178–8191 (2008). [CrossRef]  

6. F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12, 3973–3978 (2012). [CrossRef]   [PubMed]  

7. A. J. Huber, J. Wittborn, and R. Hillenbrand, “Infrared spectroscopic near-field mapping of single nanotransistors,” Nanotechnol. 21, 235702 (2010). [CrossRef]  

8. S. Berweger, Duc M. Nguyen, E. A. Muller, H. A. Bechtel, T. T. Perkins, and M. B. Raschke, “Nano-chemical infrared imaging of membrane proteins in lipid bilayers,” J. Am. Chem. Soc. 135, 18292–18295 (2013). [CrossRef]   [PubMed]  

9. S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83, 045404 (2011). [CrossRef]  

10. X. G. Xu, M. Rang, I. M. Craig, and M. B. Raschke, “Pushing the sample-size limit of infrared vibrational nanoscopy: From monolayer toward single molecule sensitivity,” J. Phys. Chem. Lett. 3, 1836–1841 (2012). [CrossRef]   [PubMed]  

11. R. Huber, A. Brodschelm, F. Tauser, and A. Leitenstorfer, “Generation and field-resolved detection of femtosecond electromagnetic pulses tunable up to 41 THz,” Appl. Phys. Lett. 76, 3191–3193 (2000). [CrossRef]  

12. C. Calabrese, A. M. Stingel, L. Shen, and P. B. Petersen, “Ultrafast continuum mid-infrared spectroscopy: probing the entire vibrational spectrum in a single laser shot with femtosecond time resolution,” Opt. Lett. 37, 2265–2267 (2012). [CrossRef]   [PubMed]  

13. M. Ishikawa, M. Katsura, S. Nakashima, K. Aizawa, T. Inoue, H. Okamura, and Y. Ikemoto, “Modulated near-field spectral extraction of broadband mid-infrared signals with a ceramic light source,” Opt. Express 19, 12469–12479 (2011). [CrossRef]   [PubMed]  

14. F. Huth, M. Schnell, J. Wittborn, N. Ocelic, and R. Hillenbrand, “Infrared-spectroscopic nanoimaging with a thermal source,” Nat. Mater. 10, 352–356 (2011). [CrossRef]   [PubMed]  

15. A. C. Jones and M. B. Raschke, “Thermal Infrared Near-Field Spectroscopy,” Nano Lett. 12, 1475–1481 (2012). [CrossRef]   [PubMed]  

16. B. T. O’Callahan, W. E. Lewis, A. C. Jones, and M. B. Raschke, “Spectral frustration and spatial coherence in thermal near-field spectroscopy,” Phys. Rev. B 89, 245446 (2014). [CrossRef]  

17. Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006). [CrossRef]   [PubMed]  

18. F. Kuschewski, H.-G. von Ribbeck, J. Döring, S. Winnerl, L. M. Eng, and S. C. Kehr, “Narrow-band near-field nanoscopy in the spectral range from 1.3 to 8.5 THz,” Appl. Phys. Lett. 108, 113102 (2016). [CrossRef]  

19. U. Schade, K. Holldack, P. Kuske, G. Wüstefeld, and H.-W. Hübers, “THz near-field imaging employing synchrotron radiation,” Appl. Phys. Lett. 84, 1422 (2004). [CrossRef]  

20. Y. Ikemoto, T. Moriwaki, T. Kinoshita, M. Ishikawa, S. Nakashima, and H. Okamura, “Near-Field Spectroscopy with Infrared Synchrotron Radiation Source,” e-J. Surf. Sci. Nanotechnol. 9, 63–66 (2011). [CrossRef]  

21. D. A. Schmidt, E. Bründermann, and M. Havenith, “Combined far- and near-field chemical nanoscope at ANKA-IR2: applications and detection schemes,” J. Phys. Conf. Ser. 359, 12015 (2012). [CrossRef]  

22. P. Hermann, A. Hoehl, P. Patoka, F. Huth, E. Rühl, and G. Ulm, “Near-field imaging and nano-Fourier-transform infrared spectroscopy using broadband synchrotron radiation,” Opt. Express 21, 2913–2919 (2013). [CrossRef]   [PubMed]  

23. H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectro-scopic imaging,” Proc. Nat. Acad. Sci. U.S.A. 111, 7191–7196 (2014). [CrossRef]  

24. E. A. Muller, B. Pollard, and M. B. Raschke, “Infrared Chemical Nano-Imaging: Accessing Structure, Coupling, and Dynamics on Molecular Length Scales,” The Journal of Physical Chemistry Letters 7, 1275–1284 (2015). [CrossRef]  

25. P. Hermann, A. Hoehl, G. Ulrich, C. Fleischmann, A. Hermelink, B. Kästner, P. Patoka, A. Hornemann, B. Beckhoff, E. Rühl, and G. Ulm, “Characterization of semiconductor materials using synchrotron radiation-based near-field infrared microscopy and nano-FTIR spectroscopy,” Opt. Express 22, 17948–17958 (2014). [CrossRef]   [PubMed]  

26. F. Peragut, J.-B. Brubach, P. Roy, and Y. De Wilde, “Infrared near-field imaging and spectroscopy based on thermal or synchrotron radiation,” Appl. Phys. Lett. 104, 251118 (2014). [CrossRef]  

27. B. Pollard, F. C. B. Maia, M. B. Raschke, and R. O. Freitas, “Infrared Vibrational Nanospectroscopy by Self-Referenced Interferometry,” Nano Lett. 16, 55–61 (2016). [CrossRef]  

28. P. M. Donaldson, C. S. Kelley, M. D. Frogley, J. Filik, K. Wehbe, and C Gianfelice, “Broadband near-field infrared spectromicroscopy using photothermal probes and synchrotron radiation,” Opt. Express 24, 1852–1864 (2016). [CrossRef]   [PubMed]  

29. A. Gottwald, R. Klein, R. Müller, M. Richter, F. Scholze, R. Thornagel, and G. Ulm, “Current capabilities at the Metrology Light Source,” Metrologia 49, S146–S151 (2012). [CrossRef]  

30. R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85, 3029–3032 (2000). [CrossRef]   [PubMed]  

31. K. Yamamoto, R. Flesch, T. Ohigashi, S. Hedtrich, A. Klossek, P. Patoka, G. Ulrich, S. Ahlberg, F. Rancan, A. Vogt, U. Blume-Peytavi, P. Schrade, S. Bachmann, M. Schäfer-Korting, N. Kosugi, and E. Rühl, “Selective Probing of the Penetration of Dexamethasone into Human Skin by Soft X-ray Spectromicroscopy,” Anal. Chem. 87, 6173–6179 (2015). [CrossRef]   [PubMed]  

32. J. Feikes, M. von Hartrott, M. Ries, P. Schmid, G. Wüstefeld, A. Hoehl, R. Klein, R. Müller, and G. Ulm, “Metrology Light Source: The first electron storage ring optimized for generating coherent THz radiation,” Phys. Rev. S. T. 14, 030705 (2011).

33. F. Schäfers, “The BESSY Raytrace Program RAY,” in Modern Developments in X-Ray and Neutron Optics, A. Erko, M. Idir, T. Krist, and A. G. Michette, eds. (Springer, 2008). [CrossRef]  

34. E. Theocharous, J. Ishii, and N. P. Fox, “Absolute linearity measurements on HgCdTe detectors in the infrared region,” Applied Optics 43, 4182–4188 (2004). [CrossRef]   [PubMed]  

35. U. Schade, A. Röseler, E. H. Korte, M. Scheer, and W. B. Peatman, “Measured characteristics of infrared edge radiation from BESSY II,” Nucl. Instrum. Meth. A 455, 476–486 (2000). [CrossRef]  

36. G. Santoro, I. Yousef, F. Jamme, P. Dumas, and G. Ellis, “Infrared synchrotron radiation from bending magnet and edge radiation sources for the study of orientation and conformation in anisotropic materials,” Rev. Sci. Instrum. 82, 10–15 (2011). [CrossRef]  

37. A. Er, I. K. Öztürk, G. Baar, S. Kröger, A. Jarmola, R. Ferber, and M. Tamanis, “Hyperfine structure study of atomic niobium with enhanced sensitivity of Fourier transform spectroscopy,” J. Phys. B 44, 205001 (2011). [CrossRef]  

38. M. Kehrt, C. Monte, J. Beyer, and J. Hollandt, “A highly linear superconducting bolometer for quantitative THz Fourier transform spectroscopy,” Opt. Express 23, 11170–11182 (2015). [CrossRef]   [PubMed]  

39. Roman Klein, Guido Brandt, Rolf Fliegauf, Arne Hoehl, Ralph Müller, Reiner Thornagel, Gerhard Ulm, Michael Abo-Bakr, Jörg Feikes, Michael V. Hartrott, Karsten Holldack, and Godehard Wüstefeld, “Operation of the metrology light source as a primary radiation source standard,” Physical Review Special Topics - Accelerators and Beams 11, 110701 (2008). [CrossRef]  

40. S. Mastel, A. A. Govyadinov, T. V. A. G. de Oliveira, I. Amenabar, and R. Hillenbrand, “Nanoscale-resolved chemical identification of thin organic films using infrared near-field spectroscopy and standard Fourier transform infrared references,” Appl. Phys. Lett. 106, 023113 (2015). [CrossRef]  

41. K. Yamamoto, A. Klossek, R. Flesch, F. Rancan, M. Weigand, I. Bykova, M. Bechtel, S. Ahlberg, A. Vogt, U. Blume-Peytavi, P. Schrade, S. Bachmann, S. Hedtrich, M. Schäfer-Korting, and E. Rühl, “Influence of the skin barrier on the penetration of topically-applied dexamethasone probed by soft x-ray spectromicroscopy,” Eur. J. Pharm. Biopharm. (2017). [CrossRef]  , in press.

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Figures (10)

Fig. 1
Fig. 1 Schematic diagram of the experimental IR s-SNOM/nano-FTIR setup at the MLS, from [25]. The broadband IR synchrotron radiation is coupled out from a bending magnet and is directed by a set of mirrors (not shown in the image) to the nano-FTIR setup. The ZnSe beamsplitter separates the radiation into a reference beam and a second beam which is focused by a parabolic mirror on tip and sample. The reference mirror can be moved over a distance of up to 1500 µm. The signal is detected by a liquid nitrogen cooled MCT detector.
Fig. 2
Fig. 2 Summary of the different storage ring modes.
Fig. 3
Fig. 3 Comparison of beam size for different storage ring optics of the MLS facility. The scale bar corresponds to a length of 100 µm. By reducing the size of the electron bunches the focal spot of the emitted SR can also be significantly reduced. This is illustrated for three different storage ring optics: (a) standard user optics (electron bunch size: 380 µm (horizontal) and 260 µm (vertical)), (b) low-alpha optics (electron bunch size: 400 µm (horizontal) and 850 µm (vertical)), and (c) low-emittance optics (electron bunch size: 190 µm (horizontal) and 180 µm (vertical)). The images recorded with a focal plane array are normalized to the ring current.
Fig. 4
Fig. 4 Intensity distribution of the IR radiation focused onto the sample obtained from ray tracing calculations [33] for the three different storage ring optics illustrated in Fig. 3. The scale bar corresponds to a length of 100 µm. The electron bunch size for standard user optics is illustrated in (a). The lowest intensity values as well as the largest SR spot are obtained from low-alpha optics (b). For further decreasing electron bunch size the focused IR beam becomes increasingly asymmetric and the peak intensity increases as compared to standard user optics (c).
Fig. 5
Fig. 5 Influence of the storage ring optics and beam size on intensity of 6H-SiC nano-FTIR spectrum. The variation of the beam size compared to the standard user optics results in an enhanced signal intensity of about 200% for low-emittance optics and a signal decay of 50% for low-alpha optics. For a better comparison the spectra are normalized to a ring current of 90 mA.
Fig. 6
Fig. 6 Comparison of 6H-SiC near-field spectra recorded by the (a) standard and (b) the optimized low-emittance storage ring optics of MLS. Due to the relatively short life time in the low-emittance mode the signal amplitude in subsequently recorded near-field spectra decreases due to the decay of the storage ring current. This variation of the signal amplitude can be minimized by allowing a change of the electron bunch size with decreasing ring current thus providing an almost constant photon flux. The change in the peak intensity as function of ring current is shown in the inset of (b).
Fig. 7
Fig. 7 Dependence of MCT signal amplitude from storage ring current (a) and recorded nano-FTIR spectra from SiC recorded with and without a polarizer (b). For the measurements the number of electrons in the storage ring was gradually reduced so that the optical beam path remained unchanged. The amplitude shows a strong non-linear behavior for ring currents under which the MCT detector was typically operated (between 80 mA and 170 mA). A nearly linear increase in signal amplitude is observed only for ring current values below 10 mA. The incident SR contains to a certain portion also waves with a vertical polarization (perpendicular to tip axis). However, these waves do not contribute significantly to the electric field enhancement at the illuminated tip apex, but rather drive the detector more into the non-linear regime. By using a polarizer these waves can be removed from the incident SR beam resulting in a signal enhancement of about 100% in the recorded SiC near-field spectra (b) compared to the measurement without polarizer.
Fig. 8
Fig. 8 Influence of reduced spectral bandwidth on interferograms (a) and near-field IR spectra (b) recorded from bulk 6H-SiC (5th harmonic). The reduction of the spectral bandwidth of ultrabroadband synchrotron radiation by spectral filters to the wavelength range of interest has significant influence on the signal amplitude in the interferograms (a) and corresponding near-field spectra (b). The limitation of the spectral range by using edge filters in front of the asymmetric Michelson-Interferometer can significantly increase the intensity in the near-field spectra. The values in (b) indicate the upper limit of the wavenumber position above which the light intensity is reduced to almost zero, corresponding to the line color of the respective IR-spectrum and interferogram. A stepwise reduction of the spectral range by using different optical filters provides a signal enhancement of up to 2000% for the edge filter at 1818 cm−1.
Fig. 9
Fig. 9 Near-field spectra from poly(methyl methacrylate) (PMMA) (a) and polymethlysilox-ane (PDMS) (b) recorded using the optimized low-emittance optics of the MLS storage ring and a spectral bandwidth reduced to the wavenumber range from about 1820 cm−1 to 750 cm−1. The 40 nm PMMA layer was deposited on a Au substrate. The PDMS layer had a thickness of about 60 nm and was deposited on a Si substrate.
Fig. 10
Fig. 10 SR-based imaging and nano-FTIR spectroscopy on dexamethasone. Topography (a) and corresponding 3rd harm. near-field image (b) from a 5 µm × 5 µm large sample area. The optically dark wire-like structures are formed by dexamethasone crystals whereas the optically light regions indicate the exposed Au surface. Diagrams in (c) and (d) show the magnitude and phase of the near-field spectrum, respectively. The spectra corresponding to the red bar in (a) are shown as magnitude in (e) and phase in (f).

Equations (2)

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S ( ω ) = [ n 0 + e i ω Δ l / c n SNOM ( ω , t ) ] S 0 ( ω ) ,
P ( Δ l , t ) | S ( ω ) | 2 d ω = ( n 0 2 + 2 Re [ e i ω Δ l / c n SNOM ( ω , t ) ] + | n SNOM ( ω , t ) | 2 ) | S 0 ( ω ) | 2 d ω = n 0 2 | S 0 ( ω ) | 2 d ω + 2 Re [ n 0 e i ω Δ l / c n SNOM ( ω , t ) | S 0 ( ω ) | 2 d ω ] + | n SNOM ( ω , t ) | 2 | S 0 ( ω ) | 2 d ω .
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