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We present a polarization-insensitive subwavelength grating reflector based on a semiconductor-insulator-metal structure. The polarization-insensitive characteristic originates from the combined effect of the TM-polarized high-reflectivity high-index-contrast subwavelength grating and the TE-polarized metallic (Au) subwavelength grating with the addition of the insulator layer. The overlapped high reflectivity (>99.5%) bandwidth between the transverse electric polarization and the transverse magnetic polarization is 89 nm. This polarization-insensitive subwavelength grating reflector can be used in the applications without a preferred polarization.
©2012 Optical Society of America
1. Introduction
Optical gratings have a long history and have been extensively studied due to its wide applications. Recently subwavelength gratings with a period smaller than the incident wavelength have attracted much attention and have been widely studied. According to the grating equation, when light is incident normally onto a subwavelength grating surface, only the 0-th order diffraction exists, and many new properties with a wide rang of potential applications emerge. Therefore, subwavelength gratings can serve as waveplates [1,2], couplers [3], high-Q resonators [4], lenses [5,6], filters [7], and reflectors [8–11], and can be used to realize the polarization control and achieve single-fundamental-mode operation for vertical-cavity surface-emitting lasers (VCSELs) [12–15]. Particularly, the subwavelength grating surrounded by low-index media, called high-index-contrast subwavelength grating (HCG) [15] or photonic crystal mirror (PCM) [16], can function as reflectors. These subwavelength gratings have a thickness in the nanoscale range and a very high reflectivity over a broad wavelength range. Hence they can be used as mirrors to replace distributed Bragg reflectors (DBRs) and release the challenges in designing and fabricating DBRs for VCSELs, especially for long-wavelength VCSELs [17,18]. At the same time, HCG- or PCM-VCSELs can realize single-mode operation [15,16], high tuning speed [19], and high modulation speed because of the shortened cavity [20]. Unlike DBRs and two-dimensional photonic crystal reflectors [21], subwavelength gratings are asymmetrical in plane, and HCGs or PCMs are always polarization-sensitive. HCG- or PCM-VCSELs only select one polarization [15,16]. Because of the inherent polarization sensitivity, the above-mentioned reflectors cannot be used in applications such as unpolarized lasers, filters [22], and wavelength demultiplexing [23]. Recently, Wu et al. proposed and demonstrated a broadband and polarization-insensitive reflector based on a multilayered subwavelength grating structure with a multisubpart profile with the optimization based on the particle swarm optimization method [24]. Zhao et al. also reported a polarization independent broadband reflectors based on cross-stacked subwavelength gratings, with ~100% reflectance over a designed spectral range of 1.4 μm to 1.6 μm [25]. However, the cross-stacked subwavelength gratings may be difficult to fabricate practically.
Very recently, with the emergence of nanoscale fabrication and characterization, studies of the interaction of electromagnetic radiation with nanostructured metals (e.g., Au and Ag) have become an area of intense research driven by potential applications in optics and photonics. In the past few years, metallic subwavelength gratings (MSGs) have been widely researched for special optical applications, e.g., polarizers [26], biosensors [27], and couplers [28]. Generally, MSGs have a selection for the transverse magnetic (TM) polarization (the electric field is perpendicular to the grating stripe), because only the TM-polarized incident light can excite surface plasmons at the interface between the metal and the insulator. The excited surface plasmons are always considered to account for some anomalous optical characteristics of MSGs, for example, the enhanced optical transmission (EOT) [29–32]. Thus the EOT is always TM-selective. However, Crouse et al. [33] and Lu et al. [34] recently reported that the EOT of the transverse electric (TE) (the electric field is parallel to the grating stripe) and TM polarizations can be achieved simultaneously by tuning the groove with of the MSG.
In this paper, we propose a subwavelength grating based on a semiconductor-insulator-metal structure, called SIM-SG. The SIM-SG exhibits a broadband high reflectivity and polarization independence. The Rigorous Coupled-Wave Analysis (RCWA) is used to calculate the reflectivity spectra and optimize the structure parameters to realize the broadband high reflectivity and the polarization insensitivity. The two-dimensional Finite-Difference Time-Domain (2D-FDTD) method is used to calculate the field distribution in the SIM-SG. The characteristics of the broadband high reflectivity and the polarization independence are investigated.
2. Structures and simulation results
2.1 Simulation methods
In the past few decades, many grating theories and methods have been developed to deal with all kinds of grating problems. The RCWA [35,36] proposed by Moharam and Gaylord is the most popular method for accurate analysis of the diffraction of electromagnetic waves by periodic structures. Here the RCWA is used as one tool for spectral analysis of subwavelength gratings. Also, the 2D-FDTD method is used to calculate the reflectivity spectra and the field distributions of subwavelength gratings. The domain of 2-D FDTD simulation is shown in Fig. 1 . The periodic boundary condition is used at the left and right boundaries in the x direction, and perfectly matched layer (PML) absorbing boundary conditions are used at the top and bottom boundaries in the z direction. The grid sizes in the x and z directions are 2 nm. For simplicity, the subwavelength gratings are assumed to be transversely infinite and the semiconductor and insulator materials are lossless and dispersion free. In the SIM-SGs, the metal Au is used, and the Drude model [37] is used to describe the optical properties of the metal Au.
Fig. 1 Domain of 2-D FDTD simulation. Λ is the period, dn is the width of the subwavelength grating strip, and hn is the thickness of each layer (n = s, i, or m, denoting the semiconductor, insulator, and metal, respectively).
We first calculate the reflectivity spectra of a HCG which is shown in Fig. 2(a) . For comparison, the structure and parameters in the reference [38] are used. The semiconductor material is Al0.6Ga0.4As, with the refractive index ns = 3.2137, and the material surrounding the grating strips is air with n = 1. The period (Λ) of the HCG is 380 nm, the width (d) of grating strips is 250 nm, and the thickness (hs) is 235 nm (s denoting the semiconductor). The RCWA and 2-D FDTD method are separately used to calculate the reflectivity spectra for the surface-normal incident plane waves. As shown in Fig. 2(b), the HCG has a TM-polarized, broadband, and high reflectivity, and the calculated results for the TE and TM polarizations are consistent well with the results reported in the reference [38].This verifies that the calculation methods and procedures we use here are correct.
Fig. 2 (a) Schematic of a HCG. Λ is 380 nm, dis 250 nm, and hs is 235 nm. For the TM polarization, the electric field is perpendicular to the grating stripe (in the x direction). For the TE polarization, the electric field is parallel to the grating stripe (in the y direction). (b) Calculated reflectivity spectra for surface-normal incident plane waves with the parameters in Fig. 2(a).
2.3 Reflectivity spectra of the SIM-SG
As shown in Fig. 2(b), the HCG is polarization-selective. To realize the polarization independence, another two layers are added to the HCG, and the SIM-SG is formed, as shown in Fig. 3 . The parameters, Λ, d, and hs, are the same as Fig. 2(a). The thickness hm of Au is fixed at 100 nm, and the dependency of reflectivity spectrum on the thickness hi of the insulator is studied. Figure 4(a) is the calculated reflectivity spectra as a function of hi for the TM polarization. As shown in Fig. 4(a), with the thickness hi in the range of about 330 nm to 450 nm, the SIM-SG presents a wideband reflectivity. When the thickness hi is 400 nm, the largest reflectivity band is achieved and is 155 nm (0.713 μm to 0.868 μm). Then the thickness hi is set to 400 nm and the reflectivity spectra as a function of duty cycle (defined as d/Λ) for the TM polarization is calculated. The calculated result is shown in Fig. 4(b). When the duty cycle is 0.7, there is a widest reflectivity band of 170 nm (0.705 μm to 0.875 μm) for the TM polarization. We also calculate the reflectivity spectra as a function of the thickness hi and duty cycle for the TE polarization, respectively, as show in Figs. 5(a) and 5(b). When the thickness hi is set to 400 nm and the duty cycle is 0.7, there are two high reflectivity bands for the TE polarization, 0.749 μm to 0.794 μm and 0.831 μm to 0.944 μm, as shown in Fig. 6 . In total, there are two overlapped high reflectivity bands (>99.5%) between the TM polarization and the TE polarization, namely 0.749 μm to 0.794 μm, and 0.831 μm to 0.875 μm. Compared to the reflectivity band (TM polarization, >99.5%, 123 nm) in Fig. 2(b), the high reflectivity band of the SIM-SG for the TM polarization is enhanced by 38%.
Fig. 3 Schematic of the SIM-SG. hi is the thickness of the insulator layer and hm is the thickness of the metal layer. Subscripts i and m denote the insulator and the metal, respectively.
Fig. 4 (a) Calculated reflectivity spectra as a function of thickness hi for the TM polarization. (b) Calculated reflectivity spectra as a function of duty cycle (defined as d/Λ) for the TM polarization.
Fig. 5 (a) Reflectivity spectra as a function of the thickness hi for the TE polarization. (b) Reflectivity spectra as a function of duty cycle for the TE polarization.
When the duty cycle is 0.7, the reflectivity spectra of the HCG (other parameters are same as those shown in Fig. 2(a)) is similar to Fig. 2(b) for the TM and TE polarizations, which illustrates the polarization selectivity. With the same Λ, duty cycle, and thickness as the optimized SIM-SG, the reflectivity spectra of the MSG are shown in Fig. 7 . The reflectivity is less than 99.5%. Especially, the reflectivity of the TM polarization is less than 90%. Thus compared with both Figs. 2(a) and 7, the high reflectivity band of SIM-SG is greatly enhanced, and the polarization independence is also improved. We believe that compared to the HCG, the enhancement of reflectivity band is due to the addition of the insulator layer and the metal layer. The characteristic of polarization independence is the combined effect of the HCG and the Au subwavelength grating. As mentioned above, the HCG has the TM selectivity. In the Au subwavelength grating, the reflectivity of the TE polarization is much higher than that of the TM polarization, and reaches about 99%. Thus the combination of the HCG and the Au subwavelength grating demonstrates the polarization-insensitive property. However, this combination should involve the insulator layer. If the insulator layer is absent, the broadband and high reflectivity and polarization independence would not be realized.
Fig. 7 Reflectivity spectra of the MSG. Period Λ is 380 nm, strip width dis 250 nm, and thickness hmis100 nm (m denotes the metal). The inset is the MSG structure.
2.3 Field distributions in subwavelength gratings
To further understand the wide high-reflectivity band and the polarization-insensitive property, the 2D-FDTD method is used to calculate the field distributions in the MIS-SG. As shown in Fig. 2, the HCG has a wide high-reflectivity band for the TM polarization. The continuous-wave source is used to illuminate the MIS-SG, and the wavelength is 870 nm which is in the range of the high-reflectivity band. For the TM polarization, the reflectivity is 99.65% at 870 nm, as shown in Fig. 6. The field distribution of Ex component in the MIS-SG is shown in Fig. 8(a) . Also as shown in field distribution of Ez component (see Fig. 8(b)), there are very weak localized fields at the metal/air and metal/insulator interfaces. The localized fields at the semiconductor/insulator and semiconductor/air interfaces are very strong. The field is mainly confined in the semiconductor layer, and the field in the slit between grating strips is decayed from the entrance to the exit. Because the fields are mainly localized in the region of the semiconductor layer and the insulator layer, the loss induced by Au layer for the TM polarization is very low. In the high reflectivity band of 170 nm (0.705 μm to 0.875 μm), the loss is nearly zero. It should be noted again that if the insulator layer is absent, the characteristic of the broadband high reflectivity is not realized, as shown in Fig. 8(c). Compared Figs. 9(a) and 9(b) with Figs. 8(a) and 8(b), we find that the inserted insulator layer weakens the localized fields at the metal/air interface and enhances the reflectivity, because the localized fields at the metal/air interface play an important role in the reduced reflectivity for the TM polarization. On the other hand, the inserted insulator layer reduces the optical field strength inside the metal which increases the absorption by the metal and reduces the reflectivity.
Fig. 8 (a) Field distribution of Ex component in the SIM-SG for the TM polarization at the wavelength of 870 nm. (b) Field distribution of Ez component in the SIM-SG for the TM polarization at the wavelength of 870 nm. (c) Reflectivity spectra of the subwavelength grating based on the metal-semiconductor structure for the TM polarization.
Fig. 9 (a) Field distribution of Ex component in the metal-semiconductor structure for the TM polarization at the wavelength of 870 nm. (b) Field distribution of Ez component in the metal-semiconductor structure for the TM polarization at the wavelength of 870 nm.
For comparison, fields of the MIS-SG at the wavelength out of the high-reflectivity band are also calculated, as shown in Fig. 10 . The wavelength of 953.38 nm at the tip (see Fig. 6) of the reflectivity spectra of the TM polarization is used. With the illumination at this wavelength, a cavity mode is formed in the sit (see Fig. 10(a)). Also, surface plasmons occur at metal/insulator and metal/air interfaces. There are strong localized fields at semiconductor/insulator and semiconductor/air interfaces (see Fig. 10(b)). The combined effect of the cavity mode and the surface plasmons results in the EOT, causing the dip in the reflectivity spectra [29].
Fig. 10 (a) Field distribution of Ex component in the SIM-SG for the TM polarization at the wavelength of 953.38 nm. (b) Field distribution of Ez component in the SIM-SG for the TM polarization at the wavelength of 953.38 nm.
For the TE polarization, the HCG has a reflectivity of 55% at the wavelength of 870 nm (see Fig. 2). As shown in Fig. 11(a) , a considerable part of light is transmitted. However, the MSG has a reflectivity of 98.8% for the TE polarization (see Fig. 7). Also as shown in Fig. 11(b), the MSG blocks the light transmission, and almost no light is transmitted through the slit at the wavelength of 870 nm. When the HCG and the MSG are combined with the addition of the insulator layer, the SIM-SG has a reflectivity of 99.7% for the TE polarization, as shown in Fig. 6. The field distribution of Ey component in the SIM-SG for the TE polarization is shown in Fig. 11(c). The incident light transmits from the semiconductor layer to the insulator layer, and then is blocked by the metal layer. The reflected light by the metal layer is coupled with the incident light, and a standing wave is formed. A standing wave is also formed in the slit, resulting in the reduced light through the slit. Also if the insulator layer is not inserted between the semiconductor layer and the metal layer, the reflectivity of 99.7% is not achieved, as shown in Fig. 11(d). That is because the inserted insulator layer strengthens the standing wave in the slit and also reduces the absorption by the metal (compared Fig. 12 with Fig. 11(c)).
Fig. 11 (a) Field distribution of Ey component in the HCG for the TE polarization at the wavelength of 870 nm. (b) Field distribution of Ey component in the MSG for the TE polarization at the wavelength of 870 nm. (c) Field distribution of Ey component in the SIM-SG for the TE polarization at the wavelength of 870 nm. (d) Reflectivity spectra of the subwavelength grating based on the metal-semiconductor structure for the TE polarization.
Fig. 12 Field distribution of Ey component in the metal-semiconductor structure for the TE polarization at the wavelength of 870 nm.
3. Conclusions
In this work, the subwavelength grating based on the semiconductor-insulator-metal structure is demonstrated. The SIM-SG is designed by the RCWA method and the 2D-FDTD method. The SIM-SG possesses a reflectivity band of 170 nm (0.705 μm to 0.875 μm) for the TM polarization, and two high reflectivity bands for the TE polarization, 0.749μm to 0.794μm and 0.831μm to 0.944μm. There are two overlapped high reflectivity bands between the TM polarization and the TE polarization, 0.749μm to 0.794μm and 0.831μm to 0.875 μm. That indicates in the high reflectivity bandwidth of 89 nm, the SIM-SG is polarization-insensitive. The characteristics of the wide high reflectivity band and the polarization independence are the combined effect of the HCG and the Au subwavelength grating with the addition of the insulator layer. For the TM polarization, the reduced localized fields at the metal/air interfaces play an important role in the high reflectivity in the SIM-SG. For the TE polarization, standing waves are formed in the grating strips and the slit. The standing waves account for the high reflectivity. The SIM-SG can be more easily fabricated and used as polarization-insensitive reflectors, replacing the top DBR of single-mode unpolarized VCSELs [39,40]. Also with optimization, the SIM-SG can be used in the applications of filters and biosensor.
Acknowledgments
This work is supported by the Chinese National Key Basic Research Special Fund/CNKBRSF (Grant No. 2011CB922002 and 2012CB933501), the National Natural Science Foundation of China (Grant Nos. 61025025, 61137003 and 60838003).
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