Anti-reflection (AR) coating is a critical technology and an ongoing challenge for terahertz systems. The subwavelength structure (SWS) is an effective AR method, whereas the current manufacturing techniques, such as chemical etching and ultrafast laser processing, are low-efficient and low-quality for processing structures at the hundred-micron scale on hard brittle materials. We present a study of broadband SWSs directly ablated on the surface of quartz crystal by precisely controlled CO2 laser pulses, instead of commonly used ultra-fast lasers. The processing time of SWS can be shortened by two orders of magnitude compared with that by ultra-fast laser pulses. The SWS samples exhibit excellent AR properties with maximum transmittance of 97% at 0.71 THz, peak transmittance improvement of 13.5%, and optimal efficiency spectrum of 0.28–1.21 THz with transmittance >90%. The AR properties of SWS samples are in agreement with the simulated expectation and exist over a wide range of incidence angles up to ∼40°. The imaging of an object using SWS as the substrate shows an obvious improvement in imaging quality. We present an efficient and practical way to improve the transmission of optical components of materials, such as quartz crystal, alumina, and sapphire, in the terahertz band.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The terahertz (THz) wave has a series of excellent properties, such as penetrability of dielectric materials, non-ionization, and being in the frequency range of macromolecule's vibration and rotational levels. Thus, the wave is an attractive tool for a wide range of applications over the past few decades, including spectroscopy, imaging, chemical and biological sensing, medicine, security, and material characterizations [1,2]. In many THz systems, such as reflection imaging or holographic imaging for biological tissues [3–5], the signal-to-noise ratio (SNR) is not satisfactory due to the generally low power of the THz source . The electromagnetic waves are reflected at each interface of two media with different refractive indices, as described by Snell’s law and Fresnel equations. In addition to power loss, the Fabry-Perot interference fringes affect the accuracy of the detection system. A conventional antireflection (AR) technology is a mono- or multi-layer coating based on destructive interference [6–8]. However, finding appropriate coating materials that satisfy the index matching requirement over the entire THz spectrum is difficult. By contrast, mono-layered antireflection coatings require a quarter wavelength thickness, and the film is as thick as tens of micrometers or more. Fabricating such thick films is challenging and expensive. Moreover, the reflection of a multilayered structure strongly depends on the wavelength and incident angle. Many metallic coatings or microstructures, including thin metal films with precisely controlled thickness [9,10], metamaterials, or metasurface [11–14], and thin metallic lamellar gratings , achieve the AR effect. However, these artificial metallic structures continue to suffer from large insertion loss  and complex fabrication processes, such as photolithography.
An alternative approach obtain broadband antireflection coatings (ARC) is subwavelength structures (SWSs), which are often referred to as moth-eye surface relief structures and are widely explored in the visible , infrared , and microwave regions . Recently, AR by SWSs was implemented in the THz frequency band [20–34]. The difficulty of THz-SWSs is that traditional manufacturing techniques are not very suitable on the large structural scale. The THz-SWSs typically have periods and depths of tens to hundreds of microns. This feature sizes are relatively small for the traditional mechanical processing, that is, the dicing saw approach [20,22,24,26,29], and they are too large for the nanoscale of light waves. For the latter, common processing methods include nanoimprinting [17,18] and semiconductor fabrication techniques, such as lithography [13,25,33] and ion beam etching [21,23,30–32]. The most important problems based on chemical etching are complexity and inefficiency. Many hours are needed to fabricate SWSs with 100 μm depth at an etch rate of approximately hundreds of nanometers per minute . Although the deep reactive ion etching (DRIE) technique has advantages in processing SWSs with large aspect ratios, it cannot be easily applied to curved surfaces. 3-D printing has recently been applied to this field , but the accuracy of fabricating microstructures is still insufficient.
Laser direct writing (LDW) is a single-step, vacuum-free, and mask-free approach that does not use chemical etching or other post-processing procedures [35,36]; thus, it is a promising solution to the THz SWSs. Few attempts have been made to fabricate THz SWSs on the surface of silicon, alumina, and sapphire using picosecond or femtosecond laser ablation [24,27–29,36]. Although ultra-fast laser processing (<10 ps) is applicable to a variety of hard and brittle materials, the lower processing speed for long wavelength periodic structures and the quality degradation caused by surface debris and microcracks are major drawbacks.
Most of the reported THz SWSs are manufactured on the silicon wafer because of its high refractive index (3.42 at microwave and THz frequencies), low absorption, and relatively mature semiconductor process. For the first time, we report an excellent broadband THz antireflection effect of SWSs on quartz crystals. Quartz crystal (Z-cut) is a very good transmission material in the wide THz frequency band (0.1 THz–3.5 THz and 4.2 THz–7 THz ). Several advantages of quartz crystal windows or optical devices are found in THz systems, as follows: (i) opaqueness to infrared radiation to avoid noise; (ii) transparency to visible light for easily collimating beam path; and (iii) low Fresnel reflection loss because of the lower refractive index (approximately 2.1 in 0.1–2 THz). The largest AR bandwidth is 0.28–1.21 THz, in which the reflection loss of a double-surface is <10% (#S3 in Table 1), and the maximum transmittance is 97% at 0.71 THz (#S5 in Table 1). More importantly, a method for manufacturing microstructures on a glass surface by using mid-infrared laser ablation is proposed. Compared with the ultra-fast laser processing, the efficiency of our method is improved by approximately two orders of magnitude, and the surface quality is improved by producing less debris and microcracks. These THz AR optical elements and the manufacturing technique are desired in practical THz imaging applications. We designed an experiment to demonstrate the improvement.
The use of CO2 lasers to process silica glass, including damage repair , surface polishing [39,40], shape correction [39–41], and micro-lens array , has been reported. The thermal expansion during the CO2 laser process causes intensive stress in the heated region, and the value of thermal expansion coefficient plays a key role in stress. For quartz crystal, the thermal expansion coefficient is 14 × 10−6/K (perpendicular to the Z-axis) and 9 × 10−6/K (parallel to Z-axis) at 300 K and 26 × 10−6/K at 700 K, which is much higher than that of fused quartz (approximately 0.5 × 10−6/K in the range 293–1173 K). Therefore, the stress and strain of quartz crystal during CO2 laser heating is much larger than those of fused quartz. Although fused quartz can be processed by CO2 laser, quartz crystal tends to crack due to high stress and strain induced by excessive thermal expansion. Thus, general parameters of CO2 laser cannot be directly used to process quartz crystal. The heated region of quartz crystal must be more precisely suppressed during laser processing.
In this study, rectangular CO2 laser pulses are used to evaporate quartz crystal directly. Longer rising and falling edges of laser pulses cannot effectively ablate the material and just heat the substrate to incur stress and strain, whereas rectangular laser pulses with shorter rising and falling edges can directly ablate the materials without a large heated region in the substrate. The output pulses are from a CW 100 W commercial radio-frequency (RF) excited CO2 laser. The pulses are controlled by adjusting the repetition frequency and duty cycle of the RF source, and they have relatively long rising and falling times (~100 μs). The rectangular laser pulses were tailored by an external acousto-optic modulator (AOM), as shown in Fig. 1(a). The pulse duration ranged from 3 to 25 μs. The diffracted laser beam was expanded by a beam expander and then scanned by a two-axis galvanometer scanner. A scan lens with a focal length of 100 mm focused the laser beam onto the surface of the quartz crystal sample with a focal spot diameter of ~90 μm at 1/e. The quartz crystal at the focal spot was directly evaporated from the sample surface. The galvanometer scanner was used to produce rectangular or hexagonal arrays of local ablating zones. An overview of laser specifications and processing parameters used in the experiments are given in Table 2.
Under the control of the scanning galvanometer, a series of uniform distributed ablation craters with period Λ are formed on the surface of the quartz crystal, as shown in Fig. 1(c). Each unit cell naturally has a quasi-Gaussian profile due to the Gaussian distribution of the laser beam intensity. The SWS layer can be regarded as a gradually changing index of refraction that follows the effective medium theory (EMT). When Λ is closer to the specific wavelength λ, the effective index is determined by the second-order EMT , as follows:Fig. 1(b). An index step is found from the material to the air. For rectangular arrays, the setup is from 1.35 to 1, and for hexagonal arrays, the index step is from 1.16 to 1. Therefore, the Fresnel reflection loss could not be eliminated to zero. The transmittance of hexagonal SWS is better than rectangular SWS theoretically. These SWSs are consistently broad-bandpass filters , and the bandwidth is mainly determined by Λ and depth d . To avoid high order diffractions, Λ is constrained within Λ ≤ λ/(ni + ns) for a minimum wavelength λ for a given bandwidth under an arbitrary angle of incidence. For perpendicular incidence, the constraint becomes Λ ≤ λ/ns. The structural depth is specified by the largest wavelength of the spectrum. In this study, an AR bandwidth of 0.1–1.5 THz was expected, ns ≈2.1. Thus, we prepared six types of samples: rectangular and hexagonal SWS arrays with Λ = 80, 100, 120 μm; and double-sided fabricating on the surface of z-cut quartz crystal (φ36 mm and thickness of 2 mm), as labeled in Table 1.
The microstructures of the samples were characterized using a Helios Nanolab 650 scanning electron microscope (SEM). The SEM image of #S1 is shown in Fig. 2(a). The image of a single unit cell in Fig. 2(b) shows that each crater was ablated by 10 pulse trains, which is consistent with the processing parameters. The ablated surface has few residues and almost no microcracks, which is far superior to the processing quality of structures with femtosecond lasers. The cross-sectional profile was measured by a laser scanning confocal microscopy (KEYENCE, VK-X1000), as shown in Fig. 2(c). The ablating depth was approximately 130 μm, and the aspect ratio was approximately 1:1. Increasing SWS depth is important for improving the antireflection of long wavelengths. A higher aspect ratio could be optimized by techniques, such as beam shaping. For the area of SWS arrays of 10 × 10 mm, the minimum processing time was only 3 minutes. Compared with the manufacturing complexity of multi-layer stepped structures , this LDW method is more simple and effective. Compared with several hours of processing time by using picosecond or femtosecond lasers , the efficiency of the method in this study is improved by approximately two orders of magnitude.
3. Results and discussion
A THz time-domain (TDS) system (Zomega, Z-3), which was excited by a femtosecond laser (Spectra-Physics, MaiTai) with an average power of 150 mW, was used to measure the transmission spectra of the samples. The measurement was conducted in dry air with temperature fluctuations <3%, but the water vapor absorption was not completely avoided. The THz pulse generated by the photoconductive antenna was linearly polarized, and the polarization direction was parallel to the arrangement direction of SWSs. Figure 3 is the original transmission time-domain signal and frequency-domain spectrum of the air (background), substrate, and sample #S1. Figure 3(a) indicates that the transmittance of the main pulses of substrate and SWS to air was 84.6% and 87.2%, respectively. The main pulse energy of SWS was 3.1% higher than that of the substrate, and the secondary pulse energy of SWS was only 49% of the substrate, thereby showing a significant decrease in reflected energy. The main pulse at the samples appeared 7.42 ps after the main pulse of the air. This delayed time Δt1 = Δn·d/c is due to the increased optical path length of the sample, with Δn = ns-ni – the change of the refractive index, d – the thickness of the sample, and c – the velocity of light in vacuum. The secondary pulse at 28.07ps after the main pulse, which is theoretically Δt2 = 2d·ns/c, was due to Fresnel reflections between the two surfaces. By solving the two equations simultaneously under the condition of ni = 1, we can obtain d = 1.983mm and ns = 2.122. The accuracy of these values proves the reliability of the measured results of TDS.
The frequency-domain spectrum curves in Fig. 3(b) were obtained by applying the Fourier transform directly on the time-domain curves in Fig. 3(a). The transmission spectrum of air (background) shows that the TDS system has a fine SNR in the range 0.1–1.6 THz. The oscillations superimposed onto the transmission spectrum curves of the samples are caused mathematically by the superposition of reflection peaks of the time-domain spectrum and physically by the interference between two surfaces. The transmittance of binary SWSs is obviously better than that of the planar substrate in a wide frequency range.
The SEM images of the six samples of Table 1 are shown in Fig. 4(a)–(f). The surface morphology changes as the period Λ decreases from 120 μm to 80 μm because the overlap of laser ablation areas results in the material’s removal from the surface. Therefore, a single ablated crater is no longer a complete Gaussian profile when Λ becomes less than the maximum ablated diameter. The depth of SWSs for these three periods is 130, 100, and 75 μm, decreasing with Λ.
The transmission spectrum of each sample was plotted by dividing the original frequency-domain spectral line of each sample by that of the air, as shown in Fig. 4(g)–(i). The blue dot lines are transmittance curves of the planar substrate as a reference. The AR effectiveness can be defined as the transmittance of SWS being higher than that of the planar substrate. In this case, the AR spectra of samples #S1, #S3, and #S5 are 0.18–1.35, 0.22–1.5, and 0.32–1.9 THz, respectively, as marked by the black dashed vertical lines in Fig. 4(g)–(i). The blue dashed vertical lines indicate the zeroth-diffraction-order limit of rectangular SWSs, which are slightly lower than the upper limit of the AR spectra. This result is reasonable and shows that diffraction-order is higher when the wavelength exceeds the lower limit. As the wavelength decreases, the first-diffraction-order causes rapid energy loss.
The hexagonal SWSs have a relatively smaller index step from the air to the medium due to the larger filling factor, and thus, better AR property than rectangular SWSs. Theoretically, the zeroth-diffraction-order limit frequency of a hexagonal SWS is 15.5% larger than that for a rectangular SWS . The transmission spectra of hexagonal SWSs in Figs. 4(g) and 4(h) are in good agreement with this expectation. However, this phenomenon is abnormal in Fig. 4(i). The reasons for this situation are ascribed to (i) the decline in processing quality under Λ = 80 μm and (ii) worse SNR of the TDS system at relatively high frequencies (>1.8 THz).
We replace the reflected pulses of the time-domain spectrum with zero, as shown in the dashed square of Fig. 3(a), and use the Fourier transform again. The oscillations of the frequency-domain spectrum are removed, such that we can find the accurate cross point of AR spectra. This treatment is purely mathematical, although destructive interference is an important antireflection means in physics. We can obtain smooth spectrum curves and the measured results of all samples in Table 1. The largest AR bandwidth is 8.2:1 (#S2) and AR frequency range is 0.32–1.9 THz (#S5). These SWS samples also show a wide optimal efficiency spectrum (transmittance >90% of double-surface). The best result is 0.28–1.21 THz of #S3. The highest 97% transmittance is measured on sample #S5 at 0.71 THz, whereas the peak transmittance of all samples exceeds 95%.
Below, we verify and explain the validity of the experimental results by numerical simulation. We simulate structures with a one-dimensional instead of a full two-dimensional array for simplicity without loss of generality, by using rigorous coupled wave analysis (RCWA) . The simulated models were double-sided and single-sided SWSs with geometry of Gaussian profile and thickness of 2 mm. The incident wave was TE mode, with normal incidence. The direction of polarization was parallel to the period of the structure. The solid lines in Figs. 5(a) and 5(b) are the transmittance of zeroth-diffraction-order, in which the curves in Fig. 5(a) are cut off at the initial frequency of higher diffraction-order. We remove the reflection from the output surface and retain the loss caused by the thickness. Thus, we obtain smooth curves, as shown in Fig. 5(b). For the SWSs of three periods Λ = 120, 100, 80 μm, the cross points with substrates are located at 1.28, 1.56, and 1.91 THz, respectively, which are in fairly good agreement with the upper limit of AR spectrum measured above.
Compared with the commonly continuous surface-relief or moth-eye structures, a uniform AR property of our “crater arrays” SWS has been detected. Another concern is the profile of SWS. In , reflectance is investigated for several different profiles. Furthermore, we simulate the AR properties of different SWS profiles under Λ = 100 μm, including parabolic, trigonometric, and Gaussian. As shown in Fig. 5(c), the parabolic profile shows improved transmittance, whereas the difference is not significant, and the AR bandwidths of the three continuously profiles are roughly the same. Although achieving the optimal profile of SWS with laser ablation is not easy, the method in this study can be used for broadband AR applications.
An important feature of AR SWS is the ability to maintain effectiveness across a wide range of incident angles, which is useful for many practical applications. We selected #S2 as a test sample to measure the transmittance at the incidence angle θ (in Fig. 6(a)) from 0° to 40°. The TDS measured results are shown in Fig. 6(b). The AR bandwidth decreases with increasing θ, whereas the broadband antireflection effectiveness remains up to θ = 40°. Limited by the spot size of the THz wave, we did not measure the spectrum of θ>40°.
The effective index depends highly on the polarization of incidence wave, and thus, two-dimension structures are preferred. However, the projected period of SWS onto different coordinate axes will alter, theoretically resulting in slight differences in spectral characteristics of different polarization directions (α in Fig. 6(c)). A hexagonal SWS can also be described as a rectangular SWS (neff,x = neff,y) with two different periods in the x and y directions (Fig. 6(c)), but the effective indices in x and y direction are equal for rectangular arrays. Thus, the hexagonal SWS works also as a uniaxial medium with the optic axis perpendicular to the surface . Under the condition of the SNR of TDS in our experiments, we did not observe a significant difference in the AR bandwidth of incident wave with different α, as shown in Figs. 6(d) and 6(e).
One of the most important applications of the quartz crystal with SWS is as a substrate material or window in the THz imaging systems . The CO2 laser-manufactured SWS sample was tested for the imaging quality. We used an optically pumped THz gas laser (OPTL, FIR-100 of Edinburgh Instruments) as a source and an infrared camera (IRXCAM-THz-384 of INO, 384 × 288 pixel Uncooled Microbolometer, 35 μm pixel pitch) as a detector to receive the diffracted optical field. The output wavelength was λ = 433 μm (0.7 THz) with HCOOH as laser gas excited by a 9R20 line of CO2 laser. The object to be observed was a needle with a width of 0.7 mm, which was less than twice the THz wavelength. After subtracting the background of Fig. 7(b), the interference fringes seriously affect the quality of the diffraction pattern with a common planar substrate, as shown in Fig. 7(d). By contrast, the diffraction pattern in Fig. 7(f) that uses SWS as the substrate more clearly shows the shape of the needle. Therefore, the quartz crystal optics with AR-SWS are important in complex imaging systems.
We proposed a new method to fabricate anti-reflective subwavelength structures on the surface of quartz crystal in the THz band. A CO2 laser was used to fabricate the SWS structures on quartz crystals. In fabrication, the interaction time between CO2 laser pulses and materials was precisely controlled to achieve rapid ablation removal without negative thermal effects. The fabrication time of the SWS structures with a similar area is sharply reduced from some hours to only several minutes, and the surface quality is improved remarkably as compared with ultra-fast laser fabrication of SWS. The maximum AR bandwidth is 0.32–1.9 THz versus substrate and 0.28–1.21 THz of optimal efficiency spectrum with transmittance >90%. The fabricated samples are able to achieve a peak transmittance improvement between 9.5% and 13.5%, and a maximum transmittance of 97% @0.71 THz is been obtained. The experimental results agree well with theoretical expectations. For the hexagonal SWS sample with Λ = 120 μm, the broadband AR effect with a bandwidth of 0.3–1.4 THz is considerable at the incident angle up to 40°. Finally, an obvious improvement of imaging quality using SWS as the substrate of the object has shown the significance of this work. Our method will likely pave the way for faster, higher-quality, and more cost-effective THz AR surfaces directly onto optical passive components with materials such as crystalline quartz, alumina, and sapphire.
National Natural Science Foundation of China (61605184, 51505444); Outstanding Youth Talents Project (2017JCJQZQ024); Laser Fusion Research Center Funds for Young Talents (LFRC-CZ013, LFRC-PD013).
Authors acknowledge Hu Deng and Quancheng Liu, Southwest University of Science and Technology, for their kind assistance with the THz-TDS system.
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