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A multiple thin metal-film subwavelength grating is proposed for polarizers in the infrared wavelength region of 10–20 μm. The dependence of the transmission characteristics of the polarizers on structural parameters was obtained numerically, and the potential for high performance was confirmed experimentally. The measured TE-wave losses in a polarizer comprising a triangular triple Al-film grating are more than 45 and 35 dB for the wavelength ranges of 10–16 and 16–20 μm, respectively, while the net TM-wave losses are lower than 1.5 dB in the wavelength rage of 15–20 μm.
©2013 Optical Society of America
1. Introduction
There exist various types of polarizers [1–6] for the wavelength region from visible to near-infrared. Polarizers for this wavelength region have extinction ratios higher than 50dB with insertion losses lower than 0.5dB. In contrast, only the wire-grid type polarizer [7–14] is available for the mid- and far-infrared regions. Most of the wire-grid polarizers for mid-infrared employ patterned metal-film grids with subwavelength period on substrates. Since the width of each patterned metal wire is considerably larger than its thickness and the grid pattern is not perfect, extinction ratios are relatively low. Typical attainable extinction ratios do not exceed 25 dB and insertion losses are higher than 2 dB. A new scheme of polarizer for the mid-infrared region is needed.
Recently, a polarizer employing a sinusoidal or triangular thin metal-film grating with a subwavelength period was proposed [15], and an extinction ratio of higher than 50 dB together with insertion loss of lower than 1dB at the frequency range of 1−2.5 THz were experimentally demonstrated [16, 17]. The new scheme is expected to be applicable to the mid-infrared region. It is well known, however, that the absolute value, especially the imaginary part, of the complex refractive index of metals in the mid-infrared region is much smaller than that in the Terahertz region. As a result, the predicted optical characteristics of the polarizer are not so good. To overcome the problem, we propose an advanced version of the polarizer comprised of multiple metal-film subwavelength gratings. The potential for high performance was predicted numerically and confirmed experimentally.
2. Polarizer architecture and calculated characteristics
Figure 1 illustrates an example of the structure of the proposed polarizer, showing a double metal-film grating with a triangular cross section. Two thin metal films with a transparent intermediate layer between them are deposited on the subwavelength grating with a triangular or sinusoidal (not shown in the picture) cross section formed onto a suitable transparent substrate such as crystal silicon (c-Si) wafer. The period Λ of the grating is chosen to be considerably smaller than the wavelength λ, and thus no diffracted wave is excited. Furthermore, the aspect ratio of the grating (h/Λ) is set to the neighborhood of unity, where h is the height of the grating, and the thickness of the metal film (t) is chosen to be in the order of the skin-depth of the light wave in the metal. The material of the intermediate layer is, for example, assumed to be amorphous silicon (a-Si) that can be deposited by the conventional sputtering or vacuum evaporation method. Note that the thicknesses of each metal film t and intermediate layer T are measured in the Z-direction, rather than the surface normal. The basic principle of operation of the polarizer comprised of a single metal-film subwavelength grating was described in a previous paper [16]. The input TE-wave (polarized in the Y-direction) is strongly reflected by the metal gratings, whereas the TM-wave (polarized in the X-direction) excites surface plasmons on the input surface of the thin metal-film grating, and vice versa on the output surface of the film, and thus results in strong transmission.
Fig. 1 Schematic diagram of the polarizer comprised of the double triangular metallic-film subwavelength grating on silicon substrate.
Transmission characteristics of the multiple thin metal-film sub-wavelength grating for the TE-and TM-waves were analyzed numerically by using the rigorous coupled-wave analysis (RCWA) method [18]. In the calculation, grating profiles were approximated with segmented stair ones with the X- and Z-directional steps of Λ/8192 and h/250, respectively. It is recommended to employ a metal film with large absolute value of the complex refractive index (n ‒ jκ) for the polarizer to attain a high extinction ratio together with a low insertion loss [16]. Aluminum (Al) has the largest imaginary part of the complex index in the mid-infrared region [19], and thus we assume that Al is used as the metal for the grating. Unless specified otherwise, the following metal film, substrate, and intermediate layer are assumed: Al film with complex refractive index given by Ref. 19, a c-Si wafer of refractive index 3.42 [20], and intermediate of a-Si with the same refractive index of 3.42, respectively. The complex refractive-index of Al at the wavelength of λ = 10 μm, for example, is 25.3 – j89.8 and its wavelength dependence [19] is given in the subsequent section (dashed lines in Fig. 8).
Figure 2 shows the calculated transmission losses of the polarizer comprised of a single Al-film subwavelength grating as a function of the Al-film thickness. The structural parameters are given at the top of the figure. Both the triangular- and sinusoidal-grating profiles are considered. The TE-wave losses increase almost in proportion to the Al-film thickness, whereas the TM-wave losses increase rapidly for a thickness of larger than 15 nm. Thus the Al-film thickness must be less than 15 nm to secure a low insertion loss. When the thickness is less than 15 nm, however, the attainable TE-wave loss is lower than 30 dB, meaning that a high optical performance cannot be expected. Note that the TM-wave loss is considerably low for a metal-film thickness of less than 10 nm, suggesting that the transmission loss will not be so high even if multiple metal-film gratings are cascaded. In this case, a high TE-wave loss together with a relatively low TM-wave loss is expected.
Fig. 2 Calculated transmission losses as a function of the Al-film thickness for the polarizer comprised of a single Al-film subwavelength grating.
Figure 3 shows calculated transmission losses as a function of the intermediate-layer thickness T for the polarizer comprised of the double Al-film subwavelength grating. The Al-film thickness and the aspect ratio of the grating are assumed to be 9 nm and 1.0, respectively. Note that the origin (T = 0) of the horizontal axis corresponds to the polarizer comprised of the single Al-film grating with thickness of 18 nm. Clearly, TE-wave losses increase rapidly as the thickness T increases from 0 to 1.5 μm, while TM-wave losses decrease as the thickness of the layer increases, showing that an extinction ratio higher than 50 dB together with insertion loss lower than 0.5 dB can readily be obtained by introducing a 1.5 μm-thick intermediate layer. The TE-wave loss originates in absorption in each metallic film and reflection at the four surfaces of the Al films. The TM-wave loss is considered to decrease because it becomes possible for the wave to pass easily through each thin metal film via surface plasmons. Transmission losses are not sensitive to the input angle (in the X-Z plane), much the same as given by Fig. 11 in Ref. 16. For example, TE- and TM-wave losses of the polarizer with T = 1.5μm shown in Fig. 3 increase from 56.7 to 57.7dB and 0.44 to 0.77dB, respectively, by increasing the input angle from 0 to 30°.
Fig. 3 Calculated transmission losses as a function of the intermediate (a-Si)-layer thickness for the polarizer comprised of the double Al-film subwavelength grating.
Figure 4 shows calculated transmission losses of polarizers comprised of single, double, and triple triangular Al-film gratings as a function of the aspect ratio of the grating. The total thickness of Al films in each polarizer is fixed to be 18 nm. TE-wave losses increase rapidly for the aspect ratio higher than 0.3, while TM-losses drastically decrease for the aspect ratio of around 0.3. Similar transmission characteristics were obtained for the polarizer composed of sinusoidal Al-film gratings. A multiple Al-film grating having an aspect ratio of higher than 0.5 is recommended to obtain a high extinction ratio and a low insertion loss.
Fig. 4 Calculated transmission losses of the polarizers with single, double, and triple triangular Al-film gratings as a function of the aspect ratio of the grating.
Wavelength dependence of transmission losses for polarizers comprised of single- and multiple-triangular Al gratings are shown in Fig. 5 for the wavelength range of 10–30 μm, taking into account the wavelength dependence of the complex refractive index of Al [19]. The total thickness of Al films and each intermediate layer are assumed to be 20 nm and 1.5 μm, respectively. Clearly, TE-wave losses increase drastically over the wide wavelength region as the number of Al-film gratings is increased. Conversely, the TM-wave losses decrease by multiplying the grating, which is explicitly seen in the shorter wavelength range. Note that the optimum structural parameters giving the best optical characteristics depend on the wavelength, and hence a higher extinction ratio together with a lower insertion loss can be obtained at a specific wavelength by finding the best structural parameters at that wavelength. Similar transmission characteristics were obtained for polarizers with sinusoidal Al-film gratings.
Fig. 5 Calculated wavelength dependence of transmission losses of the polarizers composed of single, double, and triple triangular Al-film gratings.
3. Experimental results
A 0.5 mm-thick non-doped single-crystal Si wafer with the crystal surface of {100} was used as the substrate. Both sides of the substrate were polished to be mirror surfaces, and the electrical resistivity of the wafer was higher than 1 kΩcm. The transmittance of the substrate in the wavelength region of 5–25 μm was measured with an FTIR (Fourier transform infrared) spectrometer. The refractive index of the substrate was 3.42 in the wavelength range [20], and we estimated the absorption loss of the substrate from the measured transmittance by considering incoherent multiple reflections in the substrate. Dashed and dotted lines in Fig. 6 show the measured total transmission loss and the estimated absorption loss, respectively. There is an absorption-loss peak of 1.8 dB at the wavelength of 16.3 μm. The solid line represents the sum of the absorption loss and the Fresnel reflection loss (1.55 dB) at the reverse surface of the substrate, which will be deducted from measured total transmission losses of polarizers fabricated on the substrate surface to obtain net insertion losses of the polarizer. It is noteworthy that the reflection loss at the reverse side of the substrate would be considerably decreased by forming a subwavelength grating to prevent reflection [21]. According to Fig. 6 given in Ref. 21, the reflection loss decreases from 1.55 to 0.46dB, for example, by making the grating with Λ/λ = h/λ = 0.2 on the reverse side. Fabricating polarizers on both sides of the substrate will be another promising way to decrease the reflection loss. The peak absorption loss of the substrate could be decreased from 1.8 to 1.1dB by employing a thinner wafer, 0.3 mm for example, instead of the 0.5 mm-thick one used in the experiments.
Fig. 6 Transmission-loss spectra of the non-doped single-crystal Si substrate with the thickness of 0.5 mm.
Subwavelength gratings on substrates were fabricated by using of the conventional photolithography-patterning technique together with the preferential etching property of the single-crystal Si substrate. Figure 7 shows an SEM photomicrograph of the grating fabricated on the surface of the substrate. The grating has a triangular cross section with the period Λ = 2.40 μm and the height h = 1.55 μm, and thus the aspect ratio is 0.65. There exists a narrow flat facet of 0.15 μm width at the top of each triangular cross section.
Aluminum was chosen as the material for the metal-grating films because of its large absolute value of complex refractive index and the ease of depositing a uniform film thinner than 10 nm with the conventional rf sputtering method [22]. The refractive index of deposited Al film is usually different from that of bulk Al. The complex refractive index (n, κ) of the Al film in the mid-infrared wavelength region was thus estimated experimentally from a 100 nm-thick Al film deposited by rf sputtering by measuring complex reflectivity with a spectroscopic ellipsometer (IR-VASE, J. A. Woollam Co. Inc.), and is shown in Fig. 8 by the solid lines. Indices of bulk Al given by Ref. 19 are also shown by the dashed lines for comparison. Clearly, the absolute value, especially the imaginary part, of the index of the deposited Al film is much smaller than that of the bulk one, which will result in a decrease of TE-wave losses and increase of TM-wave losses of the polarizer [16].
Fig. 8 Measured complex refractive index (n - jκ) of the deposited Al film as a function of the wavelength. The dashed lines represent indices of bulk Al (after Ref. 19).
The a-Si was employed as the material of the intermediate, and the a-Si film was deposited by using the same rf-sputtering equipment. It is known that the refractive index of a-Si deposited with the method is sensitive to such deposition conditions as rf power, sputtering-gas pressure, substrate temperature, etc. In the experiments, the refractive index of the deposited a-Si film in the wavelength region of 10–25 μm was measured to be 3.68 with a negligibly small imaginary part, indicating that the index is higher than that of the Si substrate by 0.26. Al films and a-Si layers were deposited sequentially without opening the vacuum chamber of the sputtering equipment. After deposition of the top Al-film layer, a 10nm-thick a-Si film was deposited onto the top Al film as a passivation layer. An example of fabricated polarizers comprised of the double Al-film grating is shown in Fig. 9.
Transmission losses of the fabricated polarizers were measured with the FTIR spectrometer, which has a dynamic range of ~40 dB. In the TE-wave loss measurement, two identical polarizer samples were set perpendicular to each other, the crossed Nicols. In the following, the sum of the Fresnel reflection loss at the reverse surface of the substrate and the absorption loss in the substrate, namely the solid line given in Fig. 6, was deducted from the total transmission losses to investigate the net loss characteristics of the polarizer. Calculated transmission losses shown in the following figures were obtained by using the measured complex refractive index of Al given in Fig. 8, the measured refractive index of a-Si, and the measured grating profile given in Fig. 7.
Figure 10 shows measured and calculated transmission losses for the TE- and TM-waves versus wavelength for the polarizer comprised of a single layer of the 14 nm-thick Al-film grating. The maximum measurable transmission loss, the dynamic range, of the equipment used is also shown by the dotted line for comparison. Dynamic ranges are about 45 and 35 dB for the wavelength regions of 10–16 μm and 16–20 μm, respectively. Clearly, the dynamic ranges are much higher than the measured and calculated TE-wave losses, indicating that the polarizer does not have high TE-wave losses. Measured TE-wave losses are ~13 dB together with TM-wave losses of around 5 dB, indicating that the single Al-film subwavelength grating polarizer has poor optical performance. The discrepancy between the measured and calculated transmission losses is considered to be due to minute roughness on the etched surface of the Si wafer. The Y- and X-directional roughness of the Al film will result in a decrease of TE-wave losses and increase of TM-wave losses of the polarizer, respectively. The effect of roughness will be decreased by depositing a few-μm-thick a-Si film (a buffer layer) prior to deposit the Al layer.
Fig. 10 Measured and calculated transmission losses for the TE- and TM-waves for the polarizer comprised of a single Al-film grating as a function of wavelength. The dynamic range of the measurement system is shown by the dotted line.
Figure 11 shows measured and calculated transmission losses of the polarizer comprised of a double Al-film grating. The thickness t of each Al film is 10 nm and the intermediate-layer thickness T is set to 1.0 μm. Clearly, the TE-wave losses increase drastically and the TM-wave losses decrease considerably compared with those of the polarizer comprised of a single layer of Al grating. The TE-wave losses are higher than 40 and 30dB for the wavelength ranges of 10–15 and 15–20 μm, respectively. The net TM-wave losses of lower than 2 dB are obtained in the wavelength range of 15–20 μm.
Fig. 11 Measured and calculated transmission losses for the TE- and TM-waves for the polarizer comprised of the double Al-film grating as a function of wavelength.
Figure 12 shows measured and calculated transmission losses of the polarizer comprised of the triple Al-film grating. The thicknesses of each Al-film layer and each intermediate layer are 7 nm and 1.0 μm, respectively. The measured TE-wave losses are about 45 and 35 dB for the wavelength ranges of 10–16 and 16–20 μm, respectively, meaning that the losses obtained are the measurement limit of the system. The net TM-wave loss is lower than 1.5 dB in the wavelength range of 15–20 μm. The polarizer employing multiple metallic-film subwavelength gratings is experimentally confirmed to have high performance. However, it should be noted that the Fresnel reflection loss at the reverse side of the substrate and absorption loss in the substrate are not included in the losses shown here. For practical application, improvements such as using a thinner substrate, forming a subwavelength grating to prevent reverse-side reflection, and fabricating polarizers on both sides of the substrate would be required.
Fig. 12 Measured and calculated transmission losses for the TE- and TM-waves for the polarizer comprised of the triple Al-film grating as a function of wavelength.
4. Conclusion
A polarizer employing multiple thin metal-film subwavelength gratings has been proposed. The calculated extinction ratio between the TM- and TE-waves for the triple Al-film subwavelength grating (Λ = 2.4 μm) on a silicon substrate, for example, is greater than 80 dB for the wavelength range of 10−20 μm. Polarizers with single, double, and triple Al-film triangular subwavelength gratings were fabricated by using the conventional photolithography-patterning technique with the preferential etching property of the single-crystal Si substrate. The polarizer with a single Al-film grating showed low optical performance. By using multiple Al-film layers, the optical performance was dramatically improved. The measured transmission losses for the TE-wave in the polarizer with a triple Al-film grating were higher than 45 and 35 dB for the wavelength ranges of 10–16 and 16–20 μm, while the net TM-wave losses, insertion losses, were lower than 1.5 dB in the wavelength range of 15–20 μm. Thus, the potential of the multiple Al-film subwavelength grating structure to offer a high extinction ratio and low insertion loss in the mid-infrared region was demonstrated.
Acknowledgments
The authors would like to thank Y. Inagawa and T. Suzuki, Utsunomiya University, for their contributions to the experiments and numerical calculations in this work. This work was partially supported by the Ministry of Education, Science, Sports and Culture of Japan (MESSC-JP), Grant-in-Aid for Scientific Research 2365231.
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