1. Introduction

THz technology has attracted a great interest in many different applications, ranging from biomedical imaging [1,2], to semiconductor device inspection [3] and security screening [4]. In particular, spectroscopy in the THz region can represent a non-destructive method and a valuable tool for molecular sensing or, alternatively, for retrieving information about the dielectric properties of the material. Near-Field Scanning Optical Microscopy (NSOM) in the THz range (corresponding to a wavelength λ between 30 µm and 300 µm) constitues a relevant technique to achieve imaging with sub-wavelength resolution, which is crucial for most of these applications, demanding a resolution of few micrometers or better. Although there are well known limits connected with conventional aperture-less NSOM, (collection of the total scattered field from the probe-sample system, the size of the scanning probe, etc …), near field THz imaging has already been successfully demonstrated with submicrometer resolution [5,6] using THz time-domain spectroscopy set-ups. Recently, by combining the strong concentration of the THz radiation on a metal tip with interferometric detection, imaging of the carriers in a semiconductor device has been achieved using a continuous-wave CH3OH gas laser with the impressive resolution of λ/3000 at a wavelength λ=118 µm [7]. On the other hand, THz NSOM has also been realized with sub-wavelength circular [8, 9] or square metallic aperture probes [10, 11], and a spatial resolution of 7 µm was obtained over the broad spectral range of λ=120-1500 µm.

Quantum cascade (QC) lasers have now become a very promising source of THz radiation, thanks to their high power output, spectral purity, compactness and reliability [12, 13]. A subwavelength imaging instrument based on QC lasers would permit to take advantage of the higher stability of these devices compared for example to gas lasers, or to the fs-pulse laser systems commonly used to generate THz radiation, reduce the power consumption of the whole system, and finally allow to perform the analysis with minimal changes at any chosen frequency in the 1-5 THz spectral range.

Lately, a new microscopy approach has been proposed named differential NSOM [14, 15]. This concept differs from conventional NSOM because the acquisition is carried out using square apertures with dimensions comparable to the wavelength, which ensure a much higher signal/noise ratio.

Here we adopted this new technique and developed a subwavelength resolution (⋍λ/10) differential NSOM with a QC laser source operating at a wavelength of 105 µm. The paper is structured as follows. In the next section, we describe the experimental set-up and the main features of our system. In the third section we discuss briefly the basical theoretical background and present the numerical simulations carried out to validate our approach and to analyze polarization effects. In the last section we then present measurements realized with a CO₂ gas laser emitting at a frequency ⋍30 THz to study the dependence on sample-aperture distance, and the measurements performed at a frequency of ⋍3 THz with the QC laser, comparing them with theoretical predictions. Finally, in the conclusions, we comment on the results and discuss possible future improvements.

2. Experimental set-up

In standard aperture NSOM the light is diffracted by an aperture with size much smaller than the wavelength, which limits drastically the signal-to-noise ratio achievable, since in first approximation the electric field amplitude, in the limit of apertures much smaller than the wavelength, scales as the 3rd power of the aperture size [9, 10, 16]. In our procedure, we follow the theoretical approach described in [14, 15], which involves diffracting square apertures with size comparable with the irradiating wavelength. The aperture, illuminated by a laser source, is scanned in the near field of the object of interest, which is mounted on a xy translational stage, perpendicular to the incident radiation, driven with piezo-actuators, as shown in Fig. 1. The total transmitted power is then recorded in the far-field for each scanning position by a suitable detector. Differently from NSOM, recovery of the sample image is accomplished by performing a numerical second order derivative ∂ ²/∂x∂y of the image acquired by the detector. The final result consists of four independent replica of the original object, two positive and two negative, originating from the diffraction at the aperture’s corners. In our measurements we have employed a THz QC laser emitting around 3 THz, operating at liquid Helium temperature. We fabricated, with standard photolithography, square apertures of different sizes varying from 70×70 µm² to 150×150 µm² in a Cr/Au metalization on a GaAs substrate, with typical thickness of 10/500 nm. The objects realized to test the system correspond to triangular or square metal shapes evaporated on quartz, with typical lateral size of 10→30 µm, and approximately the same thickness of the aperture, sufficient to screen completely the laser wavelength. The objects are placed carefully in the near field of the aperture using a charge-coupled device (CCD) camera, which allows to determine the relative distance with an indetermination of Δz ⋍3 µm, and a z-piezo translation stage. In the inset of Fig. 1 we show a top-view visible picture of the sample, a metal triangle evaporated on a quartz substrate, placed in the near-field of the square aperture (100 µm side). The THz signal passing through the aperture/sample system and collected by an off-axis parabolic mirror with numerical aperture ⋍0.7 is focused on a Pyrodetector 1000 from Infrared System and then recorded as a function of the sample-aperture relative position. In order to ensure the maximum signal/noise ratio, we have implemented a lock-in technique for the far-field detection, and we have placed the whole set-up in a closed environment filled with Nitrogen gas, to reduce water absorption.

3. Numerical simulations

The precision of these measurements in principle depends only on the sharpness of the corners, on the minimum step size, and on the relative distance Δz between object and aperture. In fact, the nonpropagating evanescent waves with high spatial frequency in the xy plane, originating at the corners of the aperture and carrying the subwavelength information, have an exponential decay in the z-direction [17]. The interaction of these high spatial frequencies with the object shifts the evanescent waves into oscillating waves that can be collected by the optical system in the far-field.

In order to investigate the limits of our approach, the resolution, and the effect of the polarized QC laser emission, we have performed accurate simulations with the Finite Difference Time Domain (FDTD) method using the commercial software Remcom XFdtd, version 6.5 to calculate the intensiy profile emitted from the aperture, while we have performed the convolution between aperture and samples, and the bi-dimensional derivative process, with a custom C ANSI code. In our simulations, we assumed a linearly polarized plane wave incident on a 200 µm thick GaAs substrate, and a square aperture with typical size of 100×100 µm² opened in a 400 nm thick Au layer evaporated on top of the GaAs substrate. The radiation frequency was kept fixed at 100 µm in all the simulations. In Fig. 2(a) we present the total calculated intensity transmitted throught the aperture when the polarization is along a side of the aperture and when it is tilted to 45° with respect to the aperture side. At the interface between a metal and a dielectric material, boundary conditions are strongly dependent on the polarization, and surface plasmons are also preferentially excited accordingly. These effects, that critically affect the intensity distribution in the aperture, as showed in Fig. 2(a) left, are partly compensated by tilting the polarization to 45°, so that all four sides of the square aperture are now almost equivalent, as presented in Fig. 2(a) right. Clearly, also the convolution of the intensity transmitted through the aperture with the sample (a 30 µm side totally opaque triangle similar to the one displayed in the inset of Fig. 1, placed at a distance Δz=4 µm from the aperture) presents a similar asymmetric response, as shown in Fig. 2(b). In turn, also the final recovery of the sample is affected, and the four images appear strongly altered in the parallel configuration, as seen in Fig. 2(c).

 

Fig. 1. Scheme of the experimental apparatus. The radiation of a cryogenically cooled QCL laser emitting at λ ~105 µm, is collected by a system of parabolic mirrors (not shown here) and then focused through a Winston cone on a square aperture in a metal evaporated on a GaAs substrate. The sample corresponds to a metallic layer with regular geometrical shape, a triangle in this case, on a quartz substrate, which is transparent in the THz range. The sample, mounted on a xyz piezoelectric traslational stage, is placed in the near-field of the aperture with the help of a CCD camera.

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4. Operation and measurements

In light of the simulation results described above, all our measurements have been carried out with the laser beam polarization positioned at 45° with respect to the aperture side. The minimum relative distance Δz=z₀ attainable between sample and aperture has been estimated to be ⋍3-4 µm. Once the total collected signal passing through the aperture/sample system has been focused on the detector, a scan of the sample is performed in the xy plane, with an extension in the xy directions equal to twice the aperture size to avoid spatial aliasing [14], and the signal is recorded as a function of the aperture position. First measurements have been carried out with a CO₂ gas laser emitting around λ ⋍10.6 µm in order to test the z-dependence of the system, which is obviously more sensitive at short wavelengths. We have recorded the same scan at different Δz between the sample, a 30 µm side triangular metal shape on quartz shown in Fig. 1, and a 50×50 µm² aperture in a ⋍5/400 nm thick Cr/Au layer evaporated on a GaAs substrate. The total signal measured is presented in Fig. 3(a) for each Δz, and the corresponding recovery of the original image arising from the upper corner of the aperture, is reported in Fig. 3(b). While the total collected signal registered exhibits minimal changes at different Δz, the image obtained after the derivative process is more sensitive to this parameter. In fact, the original object can be distinguished only for the minimum relative distance Δz=z₀. All the measurements in the THz frequency range have been carried out using square apertures as large as 100×100 µm², and a QC laser source emitting at λ ⋍105 µm [18]. As an example, we consider in Fig. 4 a sample composed of a square metallic layer with 28 µm long sides, placed in the near field of the aperture. Numerical simulations were carried out for comparison keeping the relative distance Δz fixed to 4 µm between the 100×100 µm² aperture and a completely opaque square with 30 µm side, representing the sample. According to theory, after having performed a numerical second order derivative ∂ ²/∂x∂y of the total collected signal, the four replicas of the original object, two positive and two negative, appear, as reported in Fig. 4(b). The data obtained from the measurements are shown in Fig. 4(c) and show a good agreement with the calculated images. The final recovery in 4(c), has been obtained averaging over 3–4 pixels (corresponding to 8–10 µm), in order to increase the signal/noise ratio, and using sharpening edge filters.

 

Fig. 2. Numerical simulations obtained with the FDTD method. The aperture has 100×100 µm² size, and is defined in a 400 nm thick metal layer on top of a GaAs substrate illuminated with linearly polarized radiation with a wavelength of 100 µm. The object is a metallic triangular shape completely opaque to the THz radiation, and the relative distance Δz has been kept fixed to 4 µm. If the polarization is along one axis of the square aperture, the intensity profile of the aperture transmission, shown in a), is not uniform, due to the boundary conditions at the metal/dielectric interface related to the polarization and to the excitation of surface plasmons. This, in turns, affects the convolution with the sample, as it is presented in b), where the integrated transmitted intensity in the presence of the sample is displayed as function of the aperture-sample displacement, and the final recovery of the original object reported in c).

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Fig. 3. a) Total signal acquired using a CO₂ laser source emitting at λ ⋍10.6 µm wavelength for different relative distance Δz between sample and aperture; b) Recovered image of the original sample (detail originating from one corner). The aperture, with size 50×50 µm², is defined in a 5/400 nm Cr/Au evaporation on a GaAs substrate, and the sample corresponds to the one shown in Fig. 1. The minimum relative distance z₀ between sample and aperture is estimated to be ⋍3-4 µm.

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Fig. 4. The visible image of a square metallic evaporation with 28×28 µm² size on a quartz substrate, placed in the near field of the aperture, is shown in a). The result of the theoretical simulations, carried out assuming a relative distance object/aperture Δ z=4 µm, an incident wavelength of 100 µm, a square opaque object of 30 µm and an aperture of 100 µm, are presented in b). The final recovery of the original sample, obtained from the measured THz signal after the second derivative process, is presented in c).

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Fig. 5. a) The THz image of a 30-µm square as recorded without further treatment from a single corner replica; b) the same for the object already presented in Fig. 4(a), but summing up the four replica originating from each corner of the aperture. For comparison a single simulated image is presented in c) selected among those shown in Fig. 4(b). The dashed lines indicate the chosen profiles extracted in the pictures below, yielding a resolution, respectively, of 16±2 µm in a), of 11±2 µm in b), and of 9±1 µm in c) (10 %-90 % criterion).

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In order to derive an estimate of the system resolution, we present instead in Fig. 5 untreated individual images. Panel a) displays the THz image of a 30-µm side square as recorded from a single aperture corner. Alternatively, we report in panel b) the image of a 28-µm side square obtained by summing the four independent replicas, appropriately cropped and considered with the right sign, originating from each aperture corner. The second procedure increases the signal/noise without altering the resolution of the image, provided that the aperture plane is parallel to the sample and that the four corners are identical. Figure 5(c) represents one of the replica selected from the simulation presented in Fig. 4. The intensity profiles extracted along the dashed lines are plotted below each corresponding image. The measured profiles are consistent with the simulated one, although there is no evident flat maximum plateau, which may again be the result of the coupling to the surface plasmons on the metal surfaces of aperture and object. This of course makes it difficult to define a proper resolution value; in any case, assuming conservatively the conventional 10%-90% criterion, we obtained a resolution of 16±2 µm for image a) and 11±2 µm for image b), with the theoretical case of panel c) only slightly better at 9±1 µm. The experimental values tend to vary over a few µm range as the resolution depends quite sensitively on alignment, distance, illumination uniformity, etc. The reasonable agreement between the values of panel b) and c) is a good indication that the estimate of a distance Δz between aperture and sample of ⋍4 µm is indeed fairly correct.

The resolution of ⋍10 µm, comparable to what was achieved by other aperture-based techniques [10,19], does not represent the final limit of this approach. According to our simulations, a relative distance sample-aperture of ⋍1 µm, still feasible without a closed servo-loop feedback system, would yield a resolution of ⋍2 µm. In our present experiment, the resolution is limited not only by the distance between sample and aperture, but also from the indetermination in the direction of the polarization with respect to the aperture position, from the aperture/ sample materials, from the intensity distribution impinging on the aperture, and from the signal/noise ratio. An optimization of these factors, improving the aperture/sample alignment and using for instance a cryogenically cooled bolometer instead of the pyro-electric detector, is necessary for further enhancements. Due to the versatility of our approach, the system can operate in a wide frequency range, just apporting minimal changes to the set-up, thus profiting of the whole operating frequency range of QC lasers. Furthermore, the achieved resolution is already enough for investigating biological samples, or DNA chips, allowing a non-destructive spectroscopic analysis.

5. Conclusions

In conclusion, we have experimentally realized a Differential Near-Field Scanning Optical Microscope, working in the THz spectral region with a resolution of ≈λ/10, and relying on QC lasers as light sources. The results, which have been obtained using a laser emitting at a wavelength of λ ⋍105 µm, can be easily extended to a wide frequency range and have been validated through FDTD numerical simulations. Future developments will aim at improving the system resolution, and the results should further stimulate the investigation of biological samples.