Enhancement of spatial resolution of terahertz imaging systems based on terajet generation by dielectric cube

In recent years, the terahertz (THz, 0.1–10 THz) region has attracted significant research attention, owing to the unique features of the electromagnetic waves in this frequency band, which show great promise in a lot of practical applications.^1–4 One of those unique features is the spectral fingerprint that many materials possess in these frequencies,^5,6 which can be exploited for nondestructive imaging applications such as biomedical, materials inspection, and security.^7–9 Therefore, high spatial resolution imaging at a specific frequency of interest is a highly desirable capability in THz imaging applications.^10,11

The resolution at a certain frequency or wavelength ( λ) is generally limited by the numerical aperture (NA) of the focusing device based on the diffraction limit described by the well-known Rayleigh¹² and Abbe criteria.¹³ The minimum full width at half maximum (FWHM) imposed by the diffraction limit in a coherent illumination system¹⁴ is given in the following equation:

where n, D, and f are the refractive index of the surrounding medium, the diameter of the collimated incident beam, and the focal length, respectively. Note that the FWHM is approximately 0.82 of the radius of the Airy disk first dark-ring and that the coefficient based on the Abbe criterion in Ref. 14 is 0.82, which leads to the 0.67 coefficient in Eq. (1) (⁠$0.82×0.82=0.67$⁠). Many research works addressing the issue of resolution enhancement to the subwavelength scale in the THz region have been published, such as near-field scanning dielectric probe,¹⁵ spoof surface plasmons,^16,17 and aspheric lenses.^18,19 Recently, the study of terajets—the generation of photonic jets^20–22 in the THz frequency band—has attracted considerable research interest because of its capability of obtaining a subwavelength hotspot with mesoscale dielectric particles.^23,24 The initial studies on terajet generation were based on spheroids and the well-known Mie scattering theory.^20,25,26 Later, researchers found out—both theoretically and experimentally—that cuboids can generate terajets²⁷ with some advantages over spheroid-generated terajets from the point of view of the imaging application, such as more symmetric hotspots.²³ The generation of terajets from the cuboid under planar illumination, which can be considered as an NA = 0 focusing device with the focal point at infinity, has been experimentally confirmed and verified in the THz frequency band; the obtained FWHM was 0.6λ.²⁸ The influence of the tangent losses in the cuboid’s dielectric material and the wide angular focusing capabilities has been studied numerically.^29,30

In this study, we establish, for the first time, that the mesoscale dielectric cube, the enhancer, can be exploited as a novel resolution enhancer by simply placing it at the focused imaging points of a continuous wave (CW)-THz imaging system of arbitrary types. First, we characterize the generated terajet at 125 GHz by placing the enhancer at the focal point of a mirror with the measured NA = 0.55 using our unique THz-wave visualization system based on a self-heterodyne nonpolarimetric electro-optic (EO) detection technique.^31–33 An FWHM of approximately 0.55λ (1.32 mm) is obtained, which is even superior to the FWHM obtained by conventional focusing devices with the ideal maximum NA = 1 in air (0.67λ). This result, when associated with the result previously reported in Ref. 28, indicates that this enhancer can enhance the spatial resolution into the subwavelength region by being placed at the focal point of the focusing device, regardless of its NA value. Subwavelength-resolution imaging based on the terajet generated by the enhancer is also demonstrated through nondestructive imaging of both an integrated-circuit (IC) card and an aluminum plate with subwavelength trenches. It should be noted that by simply using the enhancer in our 125 GHz imaging system, we successfully achieve the diffraction-limited spatial resolution of 275 GHz (1.32 mm), a 2.2 times higher frequency without increasing the frequency. The enhancement of spatial resolution without increasing the frequency of THz waves enabled by our technique is a far-reaching result and one of the figures of merit in THz imaging applications because an increase in frequency generally leads to a decrease in THz power and an increase in the materials’ absorption.^34–36 

This paper is organized as follows. Section II presents the experimental verification of terajet generation at 125 GHz and characterizes the generated terajet. In Section III, nondestructive subwavelength-resolution imaging based on the enhancer is demonstrated; two examples are used: an aluminum plate with subwavelength trenches and an IC card.

Figure 1 shows a schematic view of the THz imaging system in the reflection mode. THz waves at f₀ = 125 GHz (⁠$λ=2.4mm$⁠) emitted from an F-band (90–140 GHz) horn antenna were collimated by a lens and split by a beam splitter. The THz beam was widened by the next lens and Mirror1 (NA₁ = 0.5), and it was then compressed by Mirror2 with a larger NA (NA₂ = 0.75). Note that the values of the NA mentioned above are specification values. The actual NA₂ estimated by measuring the 1/e² beamwidth of the incident collimated beam and the focal length by our THz-wave visualization system was 0.55. The difference between the specification NA and the measured NA results from the fact that the diameter of the collimated beam entering the mirror is smaller than the diameter of the mirror. The actual measured value NA₂ = 0.55 is used in the discussion and evaluation presented in this study. A mesoscale cube of 2.4 mm × 2.4 mm × 2.4 mm (the size of the wavelength), made from Teflon (Polytetrafluoroethylene—PTFE), with a refractive index of 1.46, was placed at the position where the THz beam was compressed by Mirror2. The cubic structure, the dimensions, and the PTFE material were employed to obtain the optimal FWHM and terajet exploration range as reported in Refs. 23 and 27. The sample was placed behind and at the distance of about 0.5 mm (0.21λ) from the terajet-generating cube to demonstrate subwavelength-imaging applications in the reflection mode. The THz beam reflected from the sample propagated back to the beam splitter and was focused onto a detector (a photoconductive antenna—PCA), as shown by the orange arrows in Fig. 1. An absorber was placed on the opposite site of the PCA to eliminate unnecessary interference.

First, we verified the alignment of lenses and mirrors by directly visualizing the THz-wave distribution with our THz-wave visualization system.³¹ In this system, a low-invasiveness EO sensor was used as a detector. The accurate verification of the wave planarity and the focal lengths of the focusing devices in the THz imaging system was based on the observation of the wave-front distribution. The resolution of the electric-field visualization by the EO sensor was 0.2 mm (0.08λ), as determined by the diameter of the optical probe beam entering the EO crystal. Some additional details and the configuration of our THz-wave visualization system can be found in a previous study.³¹ 

The terajet obtained by placing the cube at the focal point of Mirror2 was then verified and characterized, using also our THz-wave visualization system. We note that visualizing the generated terajet is important because it directly relates to the point spread function (PSF), and all imaging results can be considered to be the convolution of the PSF with the real objects.^11,37 The EO sensor was moved in the near-field region to visualize the THz-wave distribution. The E-plane was parallel to the XZ-plane. Figure 2 shows the experimentally obtained results in XY-, XZ-, and YZ-plane of the beam focused by Mirror2 without using the cube, labeled as “without the enhancer,” and the generated terajet when the cube was placed at the focal point of Mirror2, labeled as “with the enhancer.” The amplitude values were normalized, in both cases with and without the enhancer, to the maximum value obtained with the enhancer. The measurement area was 18 mm × 18 mm, corresponding to 150 × 150 measurement points. The sampling interval was set at 0.12 mm (0.05λ). The signal-to-noise ratio (SNR) of the measurements was $33.8±0.4$ dB at the center and at approximately 0.5 mm (0.21λ) behind the enhancer. The SNR was calculated using the following equation:³⁸ 

where μ and σ are the mean value and standard deviation, respectively, of the detected amplitude values obtained during 1 min without moving the sensor. The terajet generated from the enhancer placed at the focal point of Mirror2 is clearly shown in all planes of the amplitude images in Fig. 2. The total THz power in the XY-plane (Fig. 2(a)) with the enhancer was about 88% of that without the enhancer. This slight degrade of the THz power is possibly due to the absorption and reflection of the dielectric cube.

The subwavelength hotspot property of the generated terajet was quantitatively characterized by evaluating the FWHM of the beam profiles with and without the enhancer in the XZ- and YZ-plane. The FWHM in each case, with and without the enhancer, was calculated based on the full width at position where the intensity is equal to half of the maximum intensity distribution in each case. Figure 3 shows the PSF of the imaging system in both cases. In this figure, the blue and orange dots represent the measured beam profiles with and without the enhancer, respectively. The THz power intensities with and without the enhancer (I_w and I_wo, respectively) were normalized to the maximum amplitude obtained without the enhancer on each plane (⁠$Amax_wo$⁠) as follows:

where A_w and A_wo are the measured amplitude distributions with and without the enhancer, respectively. Intensity enhancements of approximately 4.4 dB and 4.9 dB were obtained in the XZ- and YZ-plane, respectively. The slight difference in the observed intensity enhancement values in the two planes is probably caused by a slight misalignment in the horizontal and vertical directions (about 0.2λ) when placing the enhancer. The standard error was calculated from three measurements and Student’s t coefficient of 2.92, corresponding to a 90% confidence interval. The FWHMs obtained without the enhancer were $1.25±0.05λ$ (⁠$3.00±0.12$ mm) and $1.30±0.17λ$ (⁠$3.12±0.41$ mm) in the XZ- and YZ-plane, respectively. These FWHM values almost reached the diffraction limit (approximately 1.22λ), calculated by Eq. (1), of the focusing device with the actual NA = 0.55.

On the other hand, the FWHM obtained with the enhancer is $0.55±0.05λ$ (⁠$1.32±0.12$ mm), which is two times better than the one obtained without the enhancer in our experiment, in both the XZ-plane and YZ-plane. The FWHM obtained with the enhancer is even better than that obtained by a focusing device with an ideal maximum value of the NA in air (NA = 1, $FWHMlimit=0.67λ$⁠). Associating this result with the result previously obtained with terajets generated under planar incidence (FWHM $=0.6λ$⁠),²⁸ an NA = 0 focusing device, indicates that mesoscale dielectric cubes can enhance the spatial resolution to the subwavelength region by simply being placed at the focused imaging points of CW-THz imaging systems with different values of the NA. A slight misalignment of the enhancer position (about 0.2λ) when placing the enhancer at the focused imaging point shows no significant effect on the subwavelength FWHM of the hotspot. It should be noted that placing the enhancer at the focal point of focusing devices with small NAs leads to an inefficient use of THz power because the diameter of the imaging point of small NA focusing devices is much larger than the dimensions of the enhancer (a wavelength).

Figure 4 shows the simulated frequency characteristics of the subwavelength FWHM of the generated terajet from the enhancer under planar incidence. The dimensions of the enhancer (2.4 mm) are the same with the wavelength of the desired center frequency at f₀ = 125 GHz. The simulated results for both XZ-plane and YZ-plane in Fig. 4 indicate that the subwavelength FWHM better than 0.6λ was maintained for a wide bandwidth from 100 GHz to 250 GHz (0.8f₀–2f₀), located among F, D, and G bands. Moreover, the enhancer can be exploited in other frequency bands by scaling the dimensions of the enhancer accordingly to the wavelength of the frequency of interest.^27,30 It indicates a wide usability of this resolution enhancer in the THz region.

Figure 5 shows the intensity distributions along the z-axis, the propagation direction. The depth of field, $Δz(FWHM)$⁠, was defined as the beam length where the intensity is within 3 dB of the maximum intensity, and it is shown by the arrows in Fig. 5. As shown in the graphs, with the enhancer, the values of $Δz(FWHM)$ are $0.97±0.05λ$ (⁠$2.33±0.12$ mm) and $0.98±0.05λ$ (⁠$2.35±0.12$ mm) in the XZ- and YZ-plane, respectively; the corresponding values without the enhancer are $3.48±0.13λ$ (⁠$8.35±0.31$ mm) and $3.32±0.74λ$ (⁠$7.97±1.78$ mm) in the XZ- and YZ-plane, respectively. Therefore, the depth of field when using the enhancer is about 3.4 times smaller than that obtained without the enhancer. A small depth of field will be beneficial when imaging samples that have different reflectivity layers and the necessity of imaging those layers separately is required.

To demonstrate the subwavelength-resolution imaging capability obtained by placing the enhancer at the focused imaging point of the THz imaging system at 125 GHz, two demonstration samples were used: an aluminum plate with 1.5 mm (⁠$0.63λ$⁠) trenches and a 1.5 mm (⁠$0.63λ$⁠) diameter hole (Fig. 6(a)) and a Suica IC card, a common fare card used for trains in Japan (Fig. 6(b)). The thickness of both samples was 1 mm (⁠$0.42λ$⁠). The electronic circuitry inside the IC card includes four metal lines with an approximate width of 0.85 mm (⁠$0.35λ$⁠), placed around the border of the card.

The amplitude and phase images of the aluminum plate sample obtained with and without the enhancer are shown in Fig. 7(a). The measured area was 20 mm × 20 mm, and the sampling interval was 0.1 mm. Without the enhancer, the trenches and the hole were blurred because of the lack of resolution. In contrast, three trenches and the hole could be clearly observed when the enhancer was used. The cross sections at the center of the amplitude images are shown in Fig. 7(b), for both cases. The blue and orange dots represent the measured amplitudes with and without the enhancer, respectively. The amplitude values were normalized by their maximum value in each case, and the standard errors were calculated from three measured results. The dips in the graph correspond to the positions of the trenches and hole, where the reflected signal was smaller than that of the surrounding metal area. Four blue dips were clearly resolved when using the enhancer, whereas only three orange dips could be resolved without the enhancer. The image contrast is defined as $Amax−AminAmax+Amin$⁠, where A_max and A_min are the maximum and minimum detected amplitudes, respectively.³⁷ Without the enhancer, the obtained contrast was 0.14, and it increased by approximately 4.4 times up to 0.62 when the enhancer was used.

Figure 8 shows the results of nondestructive imaging of the IC card with and without the enhancer at 125 GHz. The measured area was 56 mm × 88 mm, and the sampling interval was set to 0.2 mm. The circuitry details were more clearly resolved with the enhancer because the resolution obtained in this case was two times better than that obtained without the enhancer. In particular, with the enhancer, we could observe the four vertical lines, corresponding to the four metal lines at the position indicated by the dashed-box. In contrast, without the enhancer, the image was blurred, and those four metal lines could not be resolved. These results clearly demonstrate the impact on subwavelength-resolution imaging obtained by simply placing the enhancer at the focused imaging point of the CW-THz imaging system.

We demonstrated, for the first time, that a mesoscale dielectric cube can be used as a novel resolution enhancer by simply placing it at the focused imaging point of a CW-THz imaging system, regardless of the value of the NA. This principle can be probably used both in reflection and transmission imaging systems. Using the enhancer at 125 GHz in our THz imaging system, we have successfully obtained a diffraction-limited FWHM corresponding to 275 GHz, a 2.2 times higher frequency. The terajet generated from the enhancer was experimentally characterized, and exhibited an FWHM of 0.55λ, which is even better than that obtained by using a focusing device with the ideal maximum value of NA = 1 in air (0.67λ). Nondestructive subwavelength-resolution imaging at 125 GHz exploiting the enhancer was demonstrated. With the enhancer, both the air-trenches on the aluminum plate and the electronic circuitry inside the IC card were clearly resolved, whereas without the enhancer the obtained images were blurred. An image contrast enhancement factor of approximately 4.4 times was also obtained by using the enhancer when imaging the aluminum plate sample.

This research was partially supported by MEXT KAKENHI Grant No. 15K13383, JSPS KAKENHI Grant No. 25709028, JSPS Research Fellow DC No. 16J05800, and Mendeleev scientific fund of Tomsk State University.