1. Introduction

The overwhelming progress in far field super resolution (SR) microscopy relied on the ability to control the fluorescence of molecules or other fluorophores [1–10]. Only few attempts have been devoted to the developments of far-field label-free SR microscopy [11–14]. In a recent publication, we demonstrated a far field label-free SR methodology that relies on the nonlinear response of the reflectance to photo-modulation by a pump laser [15]. Nonlinear Photo-modulated Reflectivity (NPMR) depends 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. It is suitable for optical microscopy in reflection configuration (epi), does not require sample preparation and can operate in any environment.

In order to extract the components of NPMR (at ${\omega }_m$), we demodulate the reflection intensity at the corresponding harmonic frequencies $\left({\omega }_m, 2{\omega }_m,3{\omega }_m\dots \right)$ in a lock-in amplifier. The n^th harmonics components of the reflectivity scale with the n^th power of the excitation. Accordingly the related effective PSF scales as the √n^th power of the excitation PSF and effectively reduces spatial resolution below the diffraction limit. SAX [16], which records the nonlinear response of fluorescence, is a SR technique closely related in concept. In principle, by going to very high harmonics, resolution is not limited. In practice the ability to reach high harmonics is limited by the physical properties of the system and by the damage threshold since extremely high excitation energies are required for high order nonlinearities.

In this work we introduce two new methodologies aiming towards simplifying NPMR. The first is Single color photo-modulated reflectance. In this method a single laser pulse serves both as the pump and the probe, simplifying the experimental setup significantly. We demonstrate SR using a 392nm pulse and discuss the physical concepts of single pulse photo modulated reflectance. The second methodology introduces spatial overlap modulation (SPOM [17]) on top of our NPMR in order to enhance resolution using low orders of nonlinearity.

Additionally, since our approach is highly sensitive to the purity of the excitation wave and requires a pure sine excitation, we introduce here a method of achieving pure sinusoidal excitation based on acousto-optic modulator that will be reported in detail elsewhere.

The experimental setup is illustrated in Fig. 1. Briefly, a 785nm beam (probe) with 1ps pulse duration is frequency doubled to 392nm (pump). The beams are separated by a dichroic mirror. A variable delay line tunes the timing of the probe and a dichroic filter combines the beam into an epi-reflection microscope. The sample is mounted on a three axes scanning translator with 20nm step increment. The pump beam at 392nm is modulated using an acousto-optic modulator (AOM) driven by an arbitrary function generator. The replacement of our previous modulation chopper by an AOM was motivated by the need to provide a clean sinusoidal excitation. The driving waveform of the AOM, a distorted triangular function, is optimized to generate a pure sine-wave modulation of the pump at ω₁ = 10 KHz. With the AOM we reach, in excitation, 0.22% 0.2% and 0.04% for the 2nd 3rd and 4th harmonics respectively as compared to 3%, 2% and 0.2% for the corresponding harmonics using a chopper. The noise level reached~0.05% limiting the optimization for higher orders.

 

Fig. 1 Diagram of the optical setup.

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For spatial modulation of the probe beam, a galvanometer-mirror is stirred at ω₂ = 100Hz, resulting in spatial modulation of the focused beam in amplitude of about ~100nm at the sample. Reflectivity is monitored using a photodiode and a lock-in amplifier. The lock-in reference signal is tuned to ω_ref = nω₁ + mω₂, allowing the measurement of the system response in respected to the n^th order of optical reflectivity and to the m^th order of SPOM simultaneously.

2. Single color and new material – Au

A simplified version of NPMR requires only one laser beam, eliminating the need for temporal, spatial and focal depth adjustment of the pump and probe. The single beam is modulated at ω₁ and its reflectance is measured at high modulation harmonics in a lock-in amplifier, similarly to the pump-probe scheme. The interaction of the single pules can be described as follows: The pulse excites the sample and probes it at the same time. The measured change in reflectivity, $\Delta R$ due to a single pulse depends on the physical dynamics of the system and the pulse length and can be described as:

We tested the single color scheme and compared it with the two color method on a set of 100nm thick, 125nm wide pairs of gold stripes fabricated on Sapphire substrate. We inferred that the reflectivity changes due to electron excitation in Au are fast enough (approximately 100fs [18,19])to be detected by a single pulse in a duration of 2ps. On the other hand, in Silicon, the carrier excitation which leads to changes in reflectance is slower (~700fs) and the excited state of the system cannot be probed efficiently with our single pulse due to the delayed response. The results of two color and single color PM reflectivity on Au pattern are depicted in Fig. 2. Note that the resolution at the second harmonics of both detection schemes are equal and amount to 95 ± 5 nm.

 

Fig. 2 Super resolution Photo-modulated reflectivity using single color vs two color. The sample consists of Au double lines, 125 nm wide, with gaps of 370, 270 and 180 nm, respectively. a - line imaging of probe reflection (red) and pump reflection (purple) b - Two color Photo-modulated reflectivity line imaging using first (blue), and second (black) harmonics. c - Single color photo-modulated reflectivity using first (orange), and second (black) harmonics. Note the resolution enhancement (95 ± 5 nm) at 2ω₁ in both two and single color modalities.

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3. SPOM and NPMR

Spatial modulation microscopy (SMM) has been introduced as a technique for quantitative analysis of the optical extinction cross-section of small metal nanoparticles [20,21]. The method is based on the detection of a small modulation component in the reflected (or transmitted) light using lock-in detection. This spatial modulation is achieved by periodical displacement of a Gaussian laser focus on a specimen. A variation of this technique for nonlinear optical response such as sum frequency generation or stimulated Raman scattering was used for imaging with enhanced spatial resolution [17,22]. The method is based on spatial overlap modulation (SPOM) of one excitation beam in respect to a second beam which is involved in the nonlinear process. The resulting PSF formed by demodulating the 2nd harmonics of the SPOM is close to the second derivative of the PSF of the original beam. Consequently SPOM suffers from negative lobes in the second derivative image. We present here a variation of SPOM, in which detection of NPMR is combined with SPOM, resulting in improved resolution and major reduction of the negative lobes. In our experiments the probe beam was spatially modulated using a galvanometer mounted mirror, while the intensity of the spatially fixed pump beam was modulated using the AOM. The SPOM response of the system, demodulated at the second harmonics of ω₂ corresponds to the spatial second derivative of the probe beam, while the response at the n^th harmonics of ω₁ corresponds to the n^th nonlinearity of the reflectivity. The demodulated signal at ω_ref = nω₁ + 2ω₂ provides the integrated response of these two effects. Figure 3(a) depicts a simulation of the method using a pump beam at 392nm and a probe beam at 785nm, as in the experiment. We also present a simulation in which the probe beam is ~400nm to demonstrate the potential of the method in resolution enhancement. The improvement in resolution and the decrease of the negative lobes of SPOM by the response of NPMR is clearly demonstrated. In the simulation, we assumed that the PSFs of the pump and probe beams are Gaussians. The best fit of these simulation to the experimental results fits a situation in which the probe beam is 1.7 wider than the pump beam. This result implies that the pump beam is not diffraction limited. We note that the contribution of SPOM can be performed with large spatial modulation (up to 100nm) with high signal levels yet without resolution lose. Finally, our simulations indicate that 75 nm resolution can be achieved by combining SPOM and second order NPMR at 400nm.

 

Fig. 3 NPMR & SPOM, simulation vs experiment. a- Simulation of line scan using different imaging modalities. First modulation harmonic (Turquoise), Second harmonic (Blue), Second derivative (Black), and second derivative with second harmonic (Red).The Green curve depicts the second derivative with second harmonic using a probe at 400nm for improved resolution. b- Experimental results. Two color Line scans of silicon on sapphire samples using the various modalities.

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Our experiments were performed on 100nm thick silicon layers patterned on sapphire. Figure 3(b) depicts a scan of a single silicon 125nm wide stripe in different modalities. The results are in good correspondence to our simulations. Note that the introduction of SPOM improved the resolution of the 2nd harmonics NPMR by ~15%, down to 85 ± 5 nm, as indicated in the simulation. Theoretically, the incorporation of SPOM is equivalent to additional 1-2 higher harmonics in NPMR, yet with substantially better signal levels. Additionally, due to the increase in resolution in NPMR, the negative lobes, typical to the SPOM mode are significantly reduced.

4. Z sectioning

The nonlinear dependence of the reflectance signal provides inherent optical sectioning capability to NPMR. For examination of the cross section resolution in z direction, the double lines sample of silicon stripes on sapphire was scanned in the X-Z plane with 50 nm steps on the x axis and 100 nm steps on the z axis. The performance of different modalities of NPMR are depicted in Fig. 4. The FWHM of the 100 nm thick lines images in Z were 900nm, 650nm, 600nm, 450nm (without deconvolution) for the modalities of Two color 1st harmonic, Two color 2nd harmonic, single color 2nd harmonic and NPMR with SPOM with ω_ref = 2ω₁ + 2ω₂ respectively. For sectioning the introduction of SPOM has increased the sectioning resolution by about 30%.

 

Fig. 4 Enhanced cross sectioning of NPMR. a- SOS double line map in the X-Z plane using two color PM reflectance demodulated at the first harmonic of modulation, ω₁. X direction steps are 50nm and z direction steps are 100nm. b- Scan using two colors and demodulated at 2ω₁. c- Scan of Au on Sapphire sample using single color and demodulated at 2ω₁. d- Scan using spatial modulation demodulated at 2ω₁ + 2ω₂. e- Normalized cross sections of the a-d scans in the z plane. Resolution enhancement can be observed in the second harmonics and in particular in the spatial modulation.

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5. Dynamics of high harmonics in different materials

For investigating the source of the second order nonlinearity in silicon we have performed pump-probe delay experiment and compared the dynamics of the first and second modulation harmonics. Figure 5 shows that while the 1st harmonic that correlates to linear PM reflectance has a decay of ~10 ps, the second harmonic decays much faster and its dynamic curve practically follows the 2ps pulse envelope. Accordingly, it can be inferred that the nonlinear mechanism is an electronic one while the linear dynamics is composed of both electronic and lattice heating. Furthermore, we can assume that pulses in the femtosecond range would reveal richer electron dynamics and perhaps significant high order of non-linearity. Such nonlinearity have potential to further enhance the resolution and SNR of the method.

 

Fig. 5 Time-resolved change of reflectance of silicon on sapphire. Black- first harmonic of modulation. Blue- second harmonic of modulation. Note the fast decay of the 2nd harmonic component vs the 1st harmonic. Green- lock-in amplifier phase of the 2nd harmonic. Note the phase jump at 3ps.

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The sign change of the lock-in phase, depicted in Fig. 5 at 3ps, along with the change in the 2nd harmonic amplitude (lock-in amplifier R signal) could indicate depletion of decayed electrons or dielectric interference effects.

6. Summary

New modalities of NPMR were presented. The first is a simplified version of the super resolution method using a single pulse rather than pump and probe. Single pulse SR imaging was demonstrated in Au but the method could be applied to many materials once the pulse duration is optimized according to material specific timescales of its carrier dynamics. The second modality is an expansion of NPMR to include SPOM, to further enhance spatial resolution down to 85nm. We have also demonstrated the enhancement of sectioning with NPMR. The origins of the nonlinearity in reflectance was addressed in a series of pump-probe time delay experiments. The results indicate sub-picosecond charge carrier dynamics that governs the nonlinear reflectivity. Consequently, we intend to examine our two color method in the femtosecond regime, hoping to achieve higher nonlinear response for improved SR imaging.