1. Introduction

The terahertz (THz) frequency range, situated between the microwave and optical frequencies, has long been considered a difficult spectrum range to utilize due to a lack of emitter and detector technologies. However, in recent years, extensive efforts of researchers worldwide have dramatically increased THz usability to the point where the so-called “THz gap” may soon become an obsolete concept. In addition to the usual uses in spectroscopy and sensing, this maturation has manifested itself in the drastic growth of THz high-power [1], high-sensitivity [2], and communications applications [3], in which the extraordinary properties of the THz waves are expected to open avenues towards new devices and technologies.

While the drastic progress in THz emission and detection during the last decade has been a major enabler of recent advances, further refinements are necessary to continue this trend. In particular, progress in the development of non-perturbative high-power THz sources and ultra-sensitive and/or single-photon detectors still require suppression of losses.

Specifically, the generally large refractive indices of materials at THz frequencies give rise to a strong Fresnel reflection at every air-material interface. This makes the reduction of reflectivity a critical issue at THz frequencies. In particular, high-resistivity silicon is one of the most important optical materials to make optical components such as lenses, windows, and beam splitters, due to its high transparency from the far-infrared to microwave frequencies, including the THz region. It is used not only in traditional table-top systems, but also in state-of-the-art high-sensitivity telescopes [4,5]. However, since its refractive index in the THz range is about 3.4, 30% of the incident radiation is lost at every air-silicon interface. As a result, about half of the incident power will be lost for every passive THz silicon component, regardless of absorption. Importantly, the unique mixture of time and frequency domain measurements used in the THz regime often requires a very broad spectral range in which reflection should be suppressed.

Traditionally, broadband anti-reflection (AR) functionality has been realized in mainly two ways: by utilizing various coatings, or else by creating sub-wavelength structures [6]. The moth-eye structure falls into the second category: a structure consisting of arrayed sub-wavelength tapered protrusions of the substrate material [7]. As the spatial filling fraction of the subwavelength protrusions changes with the distance from the substrate surface, the effective refractive index changes gradually along with it; the structure thus smooths-out the refractive index discontinuity that gives rise to the Fresnel loss. The structure has several distinct advantages compared with other solutions, such as a wide bandwidth, high acceptance angle, and the ability to be used at cryogenic temperatures, all of which are difficult to realize with other AR methods, such as planar metamaterials or dielectric coatings. For the structure to function, the main design constraints are that the period of the arrayed protrusions must be smaller than the shortest wavelength to control, while the height must be larger than approximately half the longest wavelength in the target bandwidth [7].

While moth-eye structures are used widely in both optical and microwave spectral ranges as a broadband AR solution, it is still relatively difficult to realize this structure in the THz regime. This is due to the spatial scales required for moth-eye structures in the THz regime, where the moth-eye protrusions should have periods of tens of microns and heights near a hundred microns. Such micro-3D structures are difficult to produce with conventional micro-fabrication techniques, such as lithography, as well as too small to realize with macroscopic machining, such as with dicing saws. Correspondingly, the cutting edge of these techniques are often limited to the higher THz frequencies (>2 THz) for the lithography approaches [6], while the latter machining approaches are bound to lower frequencies (<1 THz) [5]. However, in many THz applications, such as THz time-domain spectroscopy (THz-TDS), the range between 1-2 THz becomes important as well. Furthermore, peak THz emission is often in this range for many commonly used nonlinear crystal-based sources, such as emission from zinc telluride or lithium niobate [8]. Thus, extending the AR frequency of the moth-eye structures to this frequency range is a very important issue.

As a new way to fabricate moth-eyes, laser processing has gained attention in recent years [5,9,10]. Such studies have utilized a picosecond laser to directly machine these structures onto the surface of silicon. The spatial scales of laser processing are, in general, well suited for the resolutions required for moth-eye fabrication; this makes a strong candidate to realize moth-eye structures covering the 1-2 THz range. However, in these previous studies, the moth-eye structures fabricated were either designed for frequencies below approximately 0.7 THz [5], or else were found to have only marginal improvements for higher frequencies, despite having apparent moth-eye morphology capable of higher-frequency performance [9].

Here, we demonstrate the creation of moth-eye structures for AR in the THz region by using femtosecond-laser micro-processing. The femtosecond laser source was chosen for fabrication of the microstructures for its high-precision and non-thermal nature [11,12], which may be key to enabling high-frequency performance. We create moth-eye structures on the surface of high-resistivity silicon, which is, as aforementioned, a key optical material in the THz regime. We evaluate the performance of such structures by THz-TDS, finding an increase of transmissivity across 0.3 - 2.5 THz, successfully extending the bandwidth of previous works [5,9]. We furthermore characterize and reproduce the spectral properties of the transmission by numerical calculations. As an application of such structures for this frequency range, we demonstrate the use of the structure as an output enhancer for THz light generated from magnesium doped lithium niobate (Mg:LN) crystals, used in conventional THz-TDS systems. This is realized by simply attaching the moth-eye structure to the THz output surface of the crystal, and despite its simplicity, we were able to increase the total THz output intensity by 40%. The methods introduced here should be important for applications where the reduction of losses is critical, such as astronomy and THz quantum optics.

2. Experimental setup

The light source used for the fabrication is a Yb:KGW based regenerative amplifier (PHAROS-SP-1.5, Light Conversion Ltd.). The central wavelength is 1028 nm, the pulse duration is 190 fs, and the repetition rate is 6 kHz. Laser intensity from the amplifier is tuned to 70 mW with a pair of Glan-laser prisms. Light from the amplifier is focused by a plano-convex lens with focal length of 50 mm onto the sample surface. The spot size at the focus is approximately 16 micrometers in $1/e^2$ diameter, measured by standard knife-edge beam characterization methods.

The processing procedure is as follows. A high-resistivity (>10 k$\Omega$cm), lossless in the THz regime, single-crystalline silicon plate is mounted onto a mechanical stage and scanned relative to the laser beam in a grid pattern. Plates are 700 $\mu$m thick to allow for double-side processing. A schematic representation of the stage grid-scan pattern is shown in Fig. 1. The areas where the laser is not irradiated (grey square areas in the figure) remain to form the moth-eye protrusions. Each line in the grid (black) consists of multiple parallel-offset linear passes, as denoted in the microscopic grid inset in the figure. In the current experiment, one macroscopic groove is made with 4 parallel linear scans, each spaced $\Delta _1$ = 3 $\mu$m apart. A gap of $\Delta _2$ = 23 $\mu$m is placed between these four line scans, to create macroscopic grooves with $3\Delta _1 + \Delta _2$ = 32 $\mu$m period, which in turn corresponds to the final moth-eye period.

 

Fig. 1. Overview of the fabrication process. Moth-eye structures are fabricated by linearly scanning the sample in a microscopic grid pattern against a focused laser.

Download Full Size | PDF

The stage is scanned at a speed of $v_{scan}$ = 1 mm/s across a total process area of 6.4 $\mathrm {mm}^2$, corresponding to a total of 200 macroscopic grid lines in each direction. To increase the protrusion aspect ratio, we performed 5 grid scans. The laser grooving process is known to create naturally slanted structures. In each pass, the rate of ablation becomes slower as the projected fluence on the material surface becomes smaller, resulting in uniform pyramid-shaped protrusions [5,9,10]. To process both sides, the sample is flipped within its mount and realigned by eye, after which processing is repeated. After laser processing is finished, the final created structure is cleaned of processing debris in an ultrasonic water bath for 3 minutes.

3. Results and discussions

Figure 2(a) shows the fabricated sample. The dark, 6.4 mm square region is the moth-eye processed area. A 3-D profile of the structure, measured by laser scanning microscope (Keyence, VK-X260), is shown in Fig. 2(b). Uniform processing over a broad area can be observed. A line profile is also shown in 2(c). Structure heights are around 80 $\mu$m measured from midpoint to the nearest neighbor (parallel to the groove lattice), and around 140 $\mu$m from the deepest point, located at the midpoint to the next nearest neighbor (diagonal to the groove lattice). The period was confirmed to be 32 $\mu$m, as designed.

 

Fig. 2. (a) A photograph of the fabricated moth-eye structured plate and (b) its 3-D profile image, taken by laser scanning microscope. (c) A representative line profile.

Download Full Size | PDF

To verify the THz transmission properties of the fabricated samples, we conducted standard THz time-domain spectroscopy (THz-TDS) measurements [13,14]. We utilized surface THz emission from an indium arsenide crystal for the broadband terahertz source [15], and used a 1 mm thick gallium phosphide crystal as the electro-optical detection crystal [16,17].

The results of the THz-TDS measurement for a double-side processed silicon plate is shown in Fig. 3(a). The black trace is the time-domain signal of THz wave passing through a bare silicon plate, while the red represents that through the moth-eye structured plate. A slight time delay between the two signals can be seen. This is due to material removal by laser ablation, which alters the effective optical path length between the two samples. In the case of the bare silicon, a clear duplicate of the main pulse can be observed approximately 15 ps behind the main pulse. The origin of this pulse is due to multiple reflections within the silicon plate, and likewise, the time delay corresponds well to what would be predicted from the optical path length of the silicon plate (15.9 ps). For the AR structured silicon, this reflection pulse is clearly absent; signal strength of the main pulse is also higher due to the reduction of the Fresnel loss. Both are strong indications of the anti-reflection properties of the sample.

 

Fig. 3. THz-TDS measurements of the double-side moth-eye structured silicon plate in (a) time and (b) frequency domain compared with a bare silicon plate.

Download Full Size | PDF

To understand the spectral properties of the moth-eye, we can take a Fourier transform of the THz-TDS waveform. The result is shown in Fig. 3(b). For clarity, Fabry-Perot fringes are removed by selecting a time window of 20 ps for the Fourier transform (6.7 ps before and 13.3 ps after the positive peak), corresponding to a time range where multiple-reflection pulses are not included. A clear increase in transmission can be observed from 0.3 to 2.5 THz, peaking at around 90% transmission at 0.6 THz. The decrease in THz transmission at lower frequencies is caused by the heights becoming comparable to the THz wavelength. The high-frequency decrease in THz transmissivity is, however, unexpected as a property of an ideal moth-eye structure. We return to this point later.

To better understand the results, we calculated transmittance at normal incidence by using rigorous coupled-wave analysis (RCWA) [18] and commercially available software (DiffractMOD; Cybernet Systems Co. Ltd.). In the numerical simulation, we considered a 650 $\mu$m thick structure, which was composed of two moth-eye layers of 120 $\mu$m height (characterized by microscope measurements) sandwiching a bulk silicon layer. The structure unit is shown in Fig. 4(a); these structures were aligned in a square lattice with period of 32 $\mu$m.

 

Fig. 4. Using the model shown in (a), the calculated transmissivity (b) is shown. The decrease in transmissivity in the higher frequency was well reproduced with the inclusion of an imaginary term $n_i=0.032$ to the silicon refractive index for the material in the moth-eye portion (red, solid) compared to when only the morphology was considered (blue, dashed).

Download Full Size | PDF

Calculated results compared with the Fourier transform spectrum of the full time-range of Fig. 3 (with Fabry-Perot fringes) are shown in Fig. 4(b). Results calculated for the moth-eye structure made with lossless silicon with $n=3.4$ is shown in dashed blue. Fabry-Perot fringes at low frequencies are confirmed to be due to incomplete AR functionality of the moth-eye structure. Differences in fringe depths suggest an underestimation of the moth-eye height, which is considered mainly to be due to limits in the spatial and depth resolution of the laser scanning microscope. At higher frequency, while both calculation and data show no fringes, suggesting complete AR functionality, the transmission for the experiment is notably decreased. It was found that the inclusion of an imaginary part to the refractive index of the silicon material in the moth-eye portion of the calculated region ($n=3.4+0.032i$) well reproduced the high-frequency decrease in transmission (red, solid line). It should be noted that the original high-resistivity silicon plate has no such imaginary part. The origin of this absorption is unclear, however it may be caused by amorphization of silicon under irradiation of femtosecond laser pulses [19]. Similar laser-induced changes may be responsible for changes in optical properties in the sample. Despite this setback to its performance, it should be noted that the peak transmission properties of the current structure are still significant. The peak transmission values are improved from previous laser fabricated structures [9], and nearly equivalent to that achievable by the commercially available paralyene coating, while having a larger bandwidth [20]. Further tuning of processing parameters, or appropriate post-processing of the processed material, may see further improvement to the already significant AR characteristic.

The fabricated AR plates may be used as effective filters of shorter-wavelength pulses in THz setups, or else as efficient THz beam-splitters. Here, as a an application of the fabricated moth-eye plate useful to conventional THz-TDS systems, we propose and demonstrate a THz output coupler for Mg:LN crystals, currently one of the most commonly used nonlinear crystal for the generation of intense THz light from NIR pulsed laser sources [21]. Mg:LN, while valued for its high nonlinear coefficients, is also known to have a high refractive index in the THz regime of 5.2 [22]. Due to this high refractive index, close to half of THz light generated within the crystal is reflected back within the crystal. This power is subsequently absorbed by the crystal and is effectively wasted. However, by refractive-index matching the interfaces crystal-air interface, it should be possible to couple out a greater portion of this power.

As directly processing and creating moth-eye structures on the crystal is both costly and may yield unwanted artifacts in the THz generation process, we propose the use of moth-eye structured silicon plates as an output coupler for the Mg:LN crystals. The high refractive index of silicon, combined with an ideal AR performance surface should be enough to couple a theoretical maximum of 96% of the generated THz out of the crystal.

The schematic for proposed output coupling configuration is shown in Fig. 5(a). A moth-eye processed silicon plate is mechanically attached to the surface of a Mg:LN plate. While such an attachment will lead to micrometer level gaps between the silicon and the crystal, this is in fact beneficial to the current setup. This gap allows generated THz, with wavelengths on the order of a couple hundreds of micrometers to pass evanescently into the silicon, while the pump NIR pulse is totally internally reflected from interface. Were the NIR pulse to enter the silicon plate, it would be able to excite free carriers in the silicon resulting in free-carrier absorption of THz light.

 

Fig. 5. (a) THz output coupled LN schematic. THz-TDS measurements of generated THz light in the (b) time and (c) frequency domains compared with the bare LN crystal.

Download Full Size | PDF

In Fig. 5(b), we show THz-TDS measurements of the generated THz light from both the bare Mg:LN crystal, and one with the same crystal in the proposed output-coupling setup realized by single-side processing a 350 $\mu$m thick silicon plate. We see clear increase in the THz generation, as evidenced by the greater peak values in the electric field. Figure 5(c) shows the Fourier transformed data. We see broadband increase in the THz intensity yield across the whole emission spectrum of Mg:LN. Altogether, we observed a 40% increase in the total THz intensity. Although still below the theoretical maximum, mainly due to imperfection in the AR functionality of the moth-eye, the obtained results offer a practical and cost-efficient solution to increasing THz yields.

4. Conclusion

In summary, we have fabricated THz broadband AR moth-eye structures onto the surface of high-resistivity silicon by femtosecond laser processing. We measured the THz transmission spectrum of the fabricated moth-eye plates by THz-TDS, finding broadband increase of the THz transmission spectrum. We also demonstrated a novel use of such plates as efficient THz output couplers for Mg:LN crystals. THz light generated by using the output coupled setup was demonstrated to have a 1.4 times increased THz intensity yield. Such a setup allows for practical and cost-effective scaling of THz powers currently required for high-field experiments.