1. Introduction

The coherent second harmonic generation (SHG) from nanoparticles can be efficiently detected in a nonlinear microscopy using standard femtosecond lasers producing pulses of 100 fs duration [1–5]. The study of these nonlinear nanoparticles constitutes a rapidly developing field of research, with establishing novel schemes of near-field microscopy [1], and leading to new markers for biology [2]. A single SHG-active nanoparticle is also a local probe of the electromagnetic field, with a response strongly dependent on the polarization of the excitation pulses and on the nanocrystal orientation [4]. Up to now, single inorganic nanoparticles with size down to 30 nm have been directly detected in the photon counting regime [5,6]. Downscaling the size by even a modest factor would be crucial for many applications in nano-optics or biology.

As a coherent process, the number of SHG photons emitted by a noncentrosymmetric nanoparticle scales as the square of the number of oscillators, i.e., as the sixth power of the nanoparticle average size. As a two-photon process the SHG intensity is also expected to scale, for a constant average laser power, as the inverse of the pulse time duration. It is therefore tempting to reduce the pulse duration from the standard 100 fs to 10 fs available from broadband ultrafast lasers in order to enhance the second harmonic photon emission rate thus reducing the limit size of detectable nanoparticles. Nevertheless, this downscaling has to be done with care since high-order phase dispersion of the microscope objective and other optical components induce temporal aberrations in the excitation pulse interacting with the nanoparticle at the focus of the microscope [7]. Using recently developed techniques for temporal characterization at the microscope focus and careful precompensation [8], SHG from large objects has indeed been shown to scale as the inverse of the pulse time duration [9]. Additionally, the broadband excitation corresponding to a 10-fs pulse offers the possibility of spectral manipulation for coherent control [10,11] of two-photon absorption and non-resonant second harmonic generation [12–14].

 

Fig. 1. (a) Experimental set-up; OSC- Ti:Sa femtosecond oscillator, DL – prism dispersion line for phase precompression, A – interferometric autocorrelator, PS – pulse shaper with spatial light modulator (SLM), OB – microscope objective, NP – SHG-active nanocrystals deposited on top of a glass plate, TS – translation stage with nanometric resolution, NF – notch filter for second harmonic detection, PCM – photon counting module. (b) Autocorrelation of the shortest precompensated pulse together with the corresponding calculated autocorrelation function. Inset: compensating phase retrieved by the genetic algorithm (GA).

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While it has been recently shown that a SHG-active nanoparticle of a size about a few hundreds of nanometers can be used for pulse detection in a nanoscopic version of the FROG technique [15], the effects of manipulation of the excitation beam on SHG emission, i.e., decreasing the time duration of a precompensated pulse as well as structuring its broadband spectrum, have not yet been investigated at the single nanoparticle level with a size well below the wavelength of light. Moreover in this size range phase matching conditions are automatically fulfilled, improving the coherent emission. Here we show that the use of broadband ultrashort laser pulses, precompensated using an automatic genetic algorithm, improves the second harmonic emission from a single nanoparticle of size about 100 nm. It results in a contrast enhancement of the SHG image obtained by raster scanning the sample. In this process, smaller nanoparticles are revealed for a given background. We also manipulate the broadband incident spectrum in a very simple manner to obtain a non-degenerate sum-frequency generation from a single nanoparticle.

2. Experiment

The experiment relies on a home-made titanium doped sapphire (Ti:Sa) femtosecond laser with a 100 nm bandwidth, and an inverted microscope with a high numerical aperture microscope objective (×100, N.A. = 1.4). The laser spectrum is sufficiently broad to support pulses of approximately 10 fs duration. While methods like MIIPS enable an accurate pulse precompensation [8], our goal was to optimize the pulse phase without performing any preliminary measurement of the phase distortion introduced by all dispersive optical components in the optical path. Since this can be achieved by a simple optimization of the total amount of SHG photons emitted by the nanocrystal, we applied a genetic algorithm [16], to search for the best phase correction on the incident pulse (see inset in Fig. 1).

The genetic algorithm search for the optimal spectral phase of the pulse, was performed with a reference sample, a bulk KTP crystal with one face polished, placed on the cover slip at the focus of the microscope. Under femtosecond beam illumination, the second harmonic signal emitted by the crystal and detected with an avalanche photodiode operated in photon counting regime served as the feedback information in the genetic algorithm procedure. The bulk crystal, instead of a nanocrystal, was selected because it provides a high signal to noise ratio, which speeds up the search for the optimal phase of the excitation pulse. The phase correction was achieved with two separate systems (Fig. 1.a): (1) a two-prism compressor used for the rough compensation of (mostly quadratic) phase, and (2) a compact pulse shaper using a diffraction grating and a spatial light modulator (SLM) [11]. The SLM-based pulse shaper was used for the genetic algorithm search for the optimal phase. To evaluate the result of this search we estimated the duration of the excitation pulse at the focus of the microscope by recording the interferometric autocorrelation of the pulse using the second harmonic field generated in the KTP nonlinear crystal. The result of the genetic algorithm search leads to a pulse of, approximately, 13 fs duration. (see Fig. 1(b)). Once the optimal pulse shape was found its duration can then be increased to any value by adding, with the SLM, a controlled amount of the second-order phase. The corresponding SHG photon number was then measured as a function of the corresponding pulse duration.

 

Fig. 2. Detected rate of the SHG from a 100 nm KTP nanocrystal as a function of pulse time duration showing the improvement of the SHG signal with the inverse of the pulse duration.

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For a constant average incident power, the SHG signal is expected to scale as the inverse of the duration of the pulse at the microscope focus. Indeed, we observed a linear increase of the SHG signal with the inverse of the time duration, as shown in Fig. 2. However, the measured average slope is approximately 0.7 instead of unity. This is due in part to the broadband spectrum which cannot be perfectly compressed by the SLM due to pixelization of the correction signal and imperfections in spectral wings compensation. Analysis of the data shown in Fig. 2 reveals that the slope is indeed close to unity for long pulses, while it decreases with the pulse duration. Such a behavior is consistent with imperfect phase compensation – even small phase errors become important when the pulse duration approaches the Fourier transform limit. Despite this imperfect phase compensation, the SH count rate is nevertheless improved by almost an order of magnitude, as compared to excitation by standard 100 fs pulses with the same average intensity.

With precompensated pulses, we recorded maps of the SH signal originating from well dispersed KTP nanoparticles (nanoKTP) deposited by spin-coating a colloidal solution on a glass cover-slip [5]. The maps were acquired by raster scanning the sample with a PZT-driven translation stage. Figure 3 shows maps of the same area of the sample recorded with different pulse durations ranging between 200 fs and 13 fs. Firstly, for nanoparticles already visible at 200 fs, a clear increase of the signal-to-noise ratio is observed for shorter pulses. Secondly, Fig. 3 reveals that a higher number of nanoparticles appear in the maps acquired with shorter pulses, since smaller objects can be detected due to enhanced second harmonic emission. This contrast enhancement is crucial for many practical applications of nonlinear microscopy.

We then focused on the study of an individual KTP nanocrystallite with a size of 120 nm independently measured by an in situ atomic force microscope (see Figs. 4(a) and 4(b))[5]. The associated SHG signal is shown in Fig. 4(c), corresponding to a diffraction-limited spot size. The pulse autocorrelation measured using the same nanocrystallite is shown in Fig. 4(d) proves that the 13-fs pulse in the focus of the microscope is close to the Fourier limit. This observation confirms the efficiency of the phase compensation and gives evidence that all spectral components of the precompensated pulse are converted by the nanoparticle. We note that the bandwidth of the SHG is, for bulk nonlinear crystal, limited by phase matching conditions [17]. However, because of the sub-wavelength dimension of the nanoparticle spectral filtering associated to phase-matching becomes negligible even for ultrashort femtosecond laser pulse.

 

Fig. 3. SHG maps of the same area of the nanoKTP sample. The maps correspond to excitation with pulse durations τ of (a) 200 fs (SNR=2.5), (b) 100 fs (SNR=4), (c) 65 fs (SNR=4.5) and (d) 13 fs (SNR=16). For each pulse duration both a three-dimensional graph of the SH intensity as well as a normalized two-dimensional map are shown.

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The broadband nonlinear response opens the way to the coherent control of the different spectral components of the single incident beam in order to manipulate the second-order nonlinear emission [18].

As a proof-of-principle of such spectral manipulation, we used a two-band incident spectrum, containing well-separated but coherent “red” and “blue” parts (see inset of Fig. 5), in order to excite and subsequently filter out a non-degenerate sum-frequency (SF) signal. If we simply assume two average excitation frequencies ω_R and ω_B in the single incident beam, the SF signal is due to a nonlinear polarization of the form [17]:

where i,j,k stands for x,y,z, the laboratory axes. With two well-separated spectral bands, Eq. (1) shows that we have access to the different polarizations j,k of the driving fields, then select a specific nonlinear coefficient χ_ijk ⁽²⁾, and thus control the direction i of the nonlinear dipole at the generated sum frequency. This can be applied e.g. to enhance the recognition of the nanoparticle-marker in a complex environment, and to investigate the shape dependence of the nonlinear optical response of an individual nanoparticle. Yet another possible future application concerns the measurement of the polarization properties of a femtosecond pulse in the focus of a microscope objective. In principle, the spatial resolution of such a measurement is limited by the minimum size of the nanocrystallite that produces a measurable signal. With sub 100-nm detection limit demonstrated in our experiment we hope to obtain in the future a detailed 3-D map of the polarization in the vicinity of the focus.

 

Fig. 4. (a) AFM raster scan of the nanoKTP sample (white bar is 1.4 micrometer long) and (b) associated cross section of the selected nanoparticle giving a size of ≈ 120 nm; (c) Associated second harmonic emission with a diffraction-limited spot; (d) Autocorrelation of the 13-fs pulse measured with the same nanoparticle, together with the theoretical autocorrelation of the Fourier limited pulses calculated from the measured laser spectrum.

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As an experimental proof of principle, we performed a simple two-band excitation by blocking a part of the incident pulse spectrum. A bandpass filter is then placed in the detection path to transmit ω_R + ω_B, and reject both 2ω_R and 2ω_B. We checked that excitation with any single spectral band, i.e., ω_R or ω_B, does not produce SF signal. Varying the power of the blue band of the spectrum while keeping fixed the intensity of the red band leads to a linear increase of SFG vs. blue band power (Fig. 5), as expected from Eq. (1). Due to the intrinsic absence of ensemble averaging, this result can be considered as an improved version of Kurtz powder method [19], now applied on a single 100-nm size nonlinear nanoparticle.

 

Fig. 5. Coherent sum frequency generation from a single nano-KTP vs the intensity of the blue band. Inset: corresponding pulse spectrum with two distinctive parts “red” and “blue”. The nonlinear response is detected in the sum-frequency band with an interference filter transmission (spectral transmission shown in red). Note that in the latter case the wavelength scale has been multiplied by two.

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3. Conclusion and prospects

We have shown that phase-compensated 13-fs infrared pulses generated through the application of a genetic algorithm allow one to gain about one order of magnitude (as compared to 100-fs pulses with the same average intensity) in the SHG emission rate of a noncentrosymmetric single KTP nanocrystal. This leads to efficient optical detection of smaller nanocrystals which appear only when shorter pulses are used. Since there is no phase matching limitation on the bandwidth of the excitation pulses, even shorter (sub-10 fs) pulses can be used to even further enhance the second harmonic signal. Autocorrelation from a nanocrystal with an AFM measured size of about 100 nm has been recorded, showing that pulse characterization can be obtained even on SHG-active nanoparticles of sub-wavelength size. This, coupled to amplitude and phase measurements based on nanoparticle nonlinear emission [15], opens the way to a full near-field characterization of ultra-short pulses.

The broad spectrum of 10-fs pulses can also be tailored to manipulate the non-resonant nonlinear second-order excitation process and extract e.g. a nondegenerate sum-frequency mixing signal generated in a single nanoparticle. In association with polarization spectral modulation [20], this will lead to direct measurement of each of the nanoparticle nonlinear coefficients. This work can be extended to the optical nonlinear response of other nanoparticles and specific single nanostructures [21], and to other nonlinear coherent processes such as four-wave mixing from nanometric-sized coupled gold nanospheres [22], or third-harmonic generation from silver nanoparticles used in cancer research [23]. More prospectively, tailored femtosecond excitation of nonlinear nanoparticles may lead to new insights on nonlinear localization at nanoscale [24,25].