1. Introduction

Near field optics (NFO) has spread in most scientific communities as the prominent tool to study dielectric properties of material at the micrometer and nanometer scale. NFO is a particularly matched technique to understand local optical interactions. In the last decades, NFO microscopes (SNOM) have been used in various range of the electromagnetic spectrum. Microwave[1], visible/IR[2] and THz[3, 4] extensions of SNOM microscopes has met great enthousiasm, especially because the nature of the electromagnetic contrast is well understood at bigger scale. For instance one can observe in the IR the molecular vibration offering a spectroscopic finger print to identify chemical composition[5]. But NFO studies in the long wave-length range can reveals unexpected behavior at the nanometer scale, for instance the existence of coherent thermal wave[6]. From a fondamental point of view, two different techniques exists to access optically near field information[7, 8]. The first one, called ‘aperture mode’, illuminates with a sub-wavelength source a sample at a distance smaller that the wavelength. The second, called ‘apertureless mode’, collects electromagnetic information of a sample with a sub-wavelength scatterer placed at a distance from the sample smaller than the wavelength. The resolution is then not limited by the wavelength but rather by geometrical parameters, mostly the size of the aperture in ‘aperture mode’ and the size of the scatterer in ‘apertureless mode’. In aperture mode however, the search for the best resolution has a major drawback: the best resolution is obtained with the lowest available power. Therefore a practical limit of resolution is λ/10 [9]. In the THz domain the main difficulty is to find a good broadband waveguide, one that can easily drive the THz light with a good coupling efficiency. Implementation in the THz of the optical fiber technology used in the visible is not easy because of the absorption of glass in the THz domain. Despite recent attempts to fabricate tip like terahertz waveguide[10, 11] or to overcome the difficulty using dynamic aperture[12, 13, 14], most successful near-field terahertz instruments works in apertureless configuration [15, 16, 17] in order to avoid the problem of aperture power limitation and glass absorption.

In this article a concept of aperture mode microscope working in the THz domain is presented, allowing sub-wavelength resolution better than λ/10. The originality lies in an in-situ THz/IR generation based on optical rectification. The concept was introduce earlier [18] without good control of the THz source. Instead, the THz/IR microscope presented here uses a perfectly control broadband source, allowing spectroscopic and polarisation studies[19]. With a simple diffraction model we show on dielectric samples that this microscope works like a classical microscope in scattering configuration. Taking advantage of known deconvolution technique we are able to improve the resolution down to λ/50.

2. Experimental setup

The experimental setup is an original illumination mode based SNOM arrangement[19]. A cw Nd:YVO₄ laser pumped mode-locked Ti:sapphire laser (Coherent MIRA^™) is used as the source of near-infrared (NIR) optical femtosecond pulses. The MIRA laser produces an output pulse energy ℰ_p≥10 nJ with a repetition rate of 76 MHz and a pulse duration Δτ≤150 fs at a wavelength around 800 nm. The laser output is mechanically chopped and focused with a ×10 microscope objective (N.A.=0.2) in a 200 µm thick nonlinear ZnTe crystal, cf. Fig. 1. THz and IR pulses are generated by optical rectification in the crystal. Collection of the emitted broadband source is performed with a ×50 mirror objective, i.e. Cassegrain objective (N.A.=0.4). Bolometer or HgCdTe detectors are used according to the desired spectral range. The availability of both detectors allows us to realize alternatively THz and IR images. When using the bolometer, THz images are obtained in the [150–1500 µm] wavelength range[19]. When using the HgCdTe detector IR images are obtained in the [8–15 µm] wavelength range. A lock-in amplifier with a 200 ms integration time extracts the modulated signal from the two detectors. Samples are deposited directly on the nonlinear cristal. This constitutes an originality of the system with respect to[18] because here the non-linear crystal gives a perfect control over the efficiency of the THz source and allows better physical interpretation of the images.

 

Fig. 1. Near-field microscopy set-up for THz and IR radiation.

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3. Characterization without samples

The abilities of our microscope depend on the quality and the homogeneity of the crystal, because images are obtained by a scan of the crystal with ultra precision motorized linear stages (1 nm resolution). Characterization of the imaging system without sample on the bare crystal provides a good estimation of the performance of the set-up, in order to understand the influence of the sample in the imaging process.

 

Fig. 2. Knife edge THz image with normalized intensity on a bare surface of ZnTe crystal. (a) 100×100µm ² image of the edge of the ZnTe crystal. (b) profile taken from a line parallel to the displacement of the crystal, as drawn in image (a). The profil gives access to the size of the THz sub-wavelength source.

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Figure 2(a) represents a knife edge experiment on the bare ZnTe crystal. The edge of the crystal is moved from bottom right to top left and THz signal is recorded. This image gives a good approximation of the size of the THz spot (see profile in Fig. 2(b)). For this image, the spot focalization waist is 30 µm, value given with the 10–90% criteria in Fig. 2(b). As expected, the waist of the THz beam is bigger than the waist w_NIR of the near infra-red laser focused on the crystal, estimated with a CCD camera (w^CCD_NIR<10µm) and by calculation with gaussian beam propagation and focalization (w^Cal_NIR~3µm) [20]. In Fig. 2(b) The signal to noise ratio is bigger than 50. For incident optical power P_laser≤60mW the noise has a poissonian statistic. Here the incident optical power refers to the average optical power of the NIR laser before focalization. However saturation of the THz power and deterioration of the quality of the THz signal has been detected at high NIR power (P_laser>60 mW). Therefore all the following images are obtained for incident power P_laser<50 mW.

Furthermore, the resolution of our microscope depends on the focus quality of the near-infrared pump laser into the ZnTe crystal. In the limit of subwavelength focusing, i.e. focusing spot with a diameter smaller than the average THz wavelength λ_THz≃300 µm, it has been shown [21] that when diffraction and optical rectification are combined the intensity of generated THz is independent on the size of the focusing area. This is indeed perfectly valid for very thin ZnTe crystals (width below 20 µm), as demonstrated recently by Yan et al. on a three-layer system[22]. However with thicker crystals other non linear effects become important, like two-photon absorption, second harmonic generation or third order non linear effects. They decrease the emitted power of THz for strong focusing, i.e. in the THz subwavelength limit. This decrease in the emitted power with crystal thickness have been observed by Zhang et al. with 500 µm thick GaAs crystals[23] and by Gaivoronskii et al. with ZnTe crystals[24]. But this decrease has still not been quantitatively demonstrated.

For THz generation, when the diameter of the beam inside the crystal is smaller than 100 µm and higher than 30 µm, no bulk crystal damage occurs and only two photon absorption diminishes the THz emitted power. For IR generation, smaller focusing area can be obtained (typically with diameter smaller than 10 µm). However destruction of the crystal surface may appear. This destruction of the crystal decreases the amount of generated IR and consequently limits the signal to noise ratio.

4. THz microscopy

In order to characterize a microscope, it is common to measure or calculate the point spread function (PSF)[25]. PSF is a function describing how a point source is imaged by an optical instrument. Experimentally, measure of PSF is implemented with a point like object. This model object has a distribution whose spatial contrast is like a Dirac distribution, i.e. the size of the model object must be smaller than the wavelength used to illuminate the sample. When an image of a point object is realized, both diffraction and optical aberration are taken into account. The final image is a transfert function of the microscope. It gives an indication of the degradation of an object by the process of image formation in the microscope. Except for the non linear origin of the local source of IR/THz, the emission microscope described here behaves as a linear imaging system. It is then possible to determine the PSF of our microscope. Estimation of the PSF is made by imaging sub-wavelength size dielectric beads.

4.1. In the THz range

For the THz domain, 30 µm diameter silicon dioxide beads have been imaged. Figure 3(a) shows one of them, with better focusing of the local source than in Fig. 2(b). Full width at half maximum (FWHM) of the imaged sphere is nearly 40 µm. It proves that our microscope is able to overcome the classical Abbe diffraction limit, and that the size of the THz local source which sets the resolution is at most equal to 30 µm, i.e. λ/10 (convolution of a THz gaussian beam with the 30 µm diameter bead). The resolution is there limited by the size of the focusing area. Unfortunately it was in this case impossible to focus below the value of 30 µm without losing too much in signal to noise ratio. There is a compromise to find for each image between the THz emitted power and the resolution. In order to get the best compromise between resolution and signal, the size of the focusing area at the surface of the crystal is measured by a knife edge experiment before each image (see figure 2(b)).

The THz emission microscope increases the amount of collected scattered light over the direct transmitted light. This is demonstrated in the following section where the physical origin of the contrast is explained. It leads to a positive contrast on the bead. The maximum to mean signal ratio is therefore a crucial parameter. For comparison, the negative contrast observed with metal wire in [19] is obtained with a configuration where the transmitted light is not blocked by the secondary mirror of the Cassegrain objective.

From an applicative point of view, PSF is used to realize deconvolution of more complex images, and allows better resolution of THz images.We used the deconvolution algorithm from the software imageJ and a Wiener filter [26]. In the case of a linear deterioration of images, when the deterioration is spatially homogeneous, measured image g(x,y) can be written as:

where * is the product of convolution, f is the real image, h is the PSF of the linear imaging system and n represent the additional noise. When there is no additional noise (n=0), it is possible to retrieve G by Fourier transfomation G=F·H where G (resp. F, H) is the Fourier transform of image g (resp. f, h). H is the linear transfer function which transforms the real image f into the deteriorated image g. If H can be inverted, F=H ^-1·G. Then return to the spatial image is obtained by inverse Fourier transform.With some restrictions on the nature of the noise, these calculations are also applied when n≠0.

This improvement is shown with THz image of human eyebrows on Fig. 4. The image is performed with 30 µm FWHM local source, as with Fig. 2(b). Resolution has been increased by a factor of two, and sets to 15 µm. Resolution can be further improved but with a strong reduction in the signal to noise ratio.

 

Fig. 3. (a) THz image of a 30 µm silicon dioxide bead. This image was obtained with the bolometer. (b) IR image of a 10 µm silicon dioxyde bead. This image was obtained with HgCdTe detector.

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Fig. 4. (a) THz image of a human eyebrow laid on the nonlinear ZnTe crystal. (b) THz image of the same human eyebrow, with deconvolution process, showing resolution improvement.

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4.2. in the IR range

In the IR domain, we realized images of silicon dioxide spheres of 5 µm diameter. The obtained images give a good approximation of the resolution of our IR microscope. But unfortunately it does not give the exact PSF because the mean IR wavelength and the size of the bead are of the same order. The bead cannot be considered as subwavelength anymore. Figure 3(b) shows an IR image obtained on a bead. Here also the contrast is positive, i.e. there is much more signal collected when the bead is on the optical axis of the IR beam. Moreover, like in the THz range, the microscope is working in the IR range according to a scattering configuration. Full Width at Half Maximum of the imaged sphere is nearly 5 µm and is entirely compatible with the real size of the sphere. Signal to noise ratio matches with the one obtained for the characterization of the microscope without samples. On the image 3(b), the Houston resolution criteria [27] gives a resolution of 5 µm. Nearly sub-wavelength resolution( $\frac{\lambda }{2}$ , where λ is between 8 and 15 µm) is reached without mechanic probes.

5. Mechanisms involved in the imaging process

As already mentioned, contrast with images of dielectric samples is positive. Moreover, the contrast on dielectrics increases with the illumination frequencies. In the IR domain, the peak level of the silicon dioxyde bead is equal to 10 times the signal far away from the bead on the bare crystal (what is later called ‘the mean signal’) r^IR_exp≃10, while in the THz domain this ratio becomes r^THz_exp≃3. In fact, the imaging contrast of the microscope comes first from the scattering of the subwavelength source by the sample, and then scattering combined with the collection angle of the microscope. More precisely, we explain this behavior with a model of the scattering of the beads based on Mie theory. The model provides an estimation of the ratio r^IR_th and r^THz_th of maximum to mean signal, obtained while imaging a sub-wavelength size silicon dioxide bead in the IR and THz domain respectively. In the two domains, the signal is estimated by the radiation of a sub-wavelength electromagnetic source using Mie scattering theory[28]. Mie theory is clearly justified in the THz domain by the order of magnitude of the average wavelength, the size of the source and the distance of observation. Experimentally, the collection angles are contained between 15° and 30° due to the numerical aperture of the Cassegrain objective used for the collection. Therefore in the angular emission scattering diagram only part of the emitted signal is collected by the microscope. In Fig. 5 this collected signal is shown by the dashed areas, and gives an evaluation of the maximum signal. Without bead, it gives an evaluation of the mean signal measured by our microscope.

For the evaluation of the maximum signal the scattering of the THz/IR light by the silicon bead and the induced changes in the angular scattering diagram are considered. The calculation hypothesis are as follow. In the IR and THz domains, for each emitted wavelength, the emission intensity is calculated from the diffusion matrix [28] and the experimental values of the refractive index extract from [29]. The resulting angular scattering diagram in intensity is shown in Fig. 5. As the experimental THz signal contains a broad spectrum, the model takes into account the polychromatism of the source. The resulting intensity is the sum of the intensities computed for each wavelength, see [19]. In the simulation the sum is limited to ten different wavelengths to simplify and to reduce the computation time. It is possible to evaluate the ratio r_th according to the two diagrams and therefore to calculate the amount of collected signal by the Cassegrain objective. The experimental value in the THz domain (r^THz_exp=3) is close to the calculated one (r^THz_th=1.95). The rather good match in the THz domain demonstrates that formation of images by our microscope is explained by the diffraction of the THz light by the sample and confirms previous results obtained on metallic samples [19]. Real shape of the THz gaussian beam and weak signal to noise in THz images could explain the slight difference between theoretical and experimental results.

In the IR domain however we found r^IR_exp=10 and r^IR_th=4. The increase of the IR signal compare to THz is clearly reproduced. But experimental and theoretical values do not match because the dipolar emission hypothesis (λ≫d, d being the diameter of the scattering particle) is not fulfilled in the IR domain (λ_IR≃10 µm, d=5 µm in the IR).

6. Conclusion

A near-field THz/IR microscope in illumination mode is presented where a local source is scanned below dielectric samples. This instrument works in a broad wavelength range, from 0.2 THz to 40 THz. Because there is no need for nanometric contact between the probe and the sample, this microscope is easier to use than the metal tip based SNOM. Thanks to in-situ THz generation and image formation, better resolution and higher contrast than usual microscopes techniques are obtained. Resolution of less than λ/10 has been reached, and better resolution can be achieved using thinner non linear crystal, leading to a more localized local source. Moreover the microscope gives a straightforward imaging contrast explained with a diffraction based model. This scattering configuration microscope is advantageous when imaging samples with weak THz/IR contrast. Furthermore improvement of the resolution of THz/IR images can be obtained by known microscopy techniques, like de-convolution process. Extension of this resolution to micrometer size objects, like biological cells or defaults in semiconductor or metal structures with coupling with local THz spectroscopy is underway.

 

Fig. 5. Scattering diagrams computed using Mie scattering for sub-wavelength size SiO ₂ beads in the THz (a) and IR (b) domain. The dashed areas correspond to the emitted angles collected by the Cassegrain objective.

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