International Research Journal of Applied and Basic Sciences 2014 Available online at www.irjabs.com ISSN 2251-838X / Vol, 8 (9): 1180-1186 Science Explorer Publications Design, Simulation and optimization of Midinfrared Ultra broadband HCG mirrors for 2.3µm VCSELs M.M. Sheikhey, A. Rostami, H. Baghban * School of Engineering-Emerging Technologies, University of Tabriz, Tabriz 5166614761, Iran, Corresponding author: Mohammad Mohsen Sheikhey ABSTRACT: We present the design of two Si/SiO 2 subwavelength high contrast grating mirrors. These mirrors are optimized for integration in mid-infrared VCSEL. We tried to optimize these structures for having an ultrabroadband mirror which has the polarization selection ability. We have proposed two structures. The first one, we optimized the structure to provide the largest bandwidth as possible for reflections above 99% and 99.9% respectively. Then, in second one, we optimized the structure for better TE mode suppression and better stability in design parameters changes. Finally higher order modes suppression verified and results shows very good mode suppression for degrees above 5 and 13 for both structures respectively. Keywords: vertical cavity surface emitting laser (VCSEL), subwavelength high contrast grating, Midinfrared, Tm and TE polarization INTRODUCTION Midinfrared single mode laser diodes are in high interest for trace gas spectroscopy due to the presence of the strong absorption lines of numerous polluting gases in this spectral region. Vertical cavity surface emitting lasers (VCSELs) appear particularly well suited to be used as laser sources for absorption spectroscopy due to several advantages that they offer, such as small beam divergence, single-mode operation, fast and wide wavelength tunability without mode hops, low threshold, and less susceptibility to optical feedback [1] Ducanchez et al., 2008 Room-Temperature Continuous-Wave Operation of 2.3µm GaSb-Based Electrically Pumped Monolithic Vertical-Cavity Lasers. Microcavity VCSELs traditionally include two distributed Bragg mirrors (DBR), which can be fabricated with semiconductor or dielectric materials. By low index contrast in this wavelength range (Δn 0.5), we need 20 pairs of layers to reach minimum reflectivity of 99% which lead to thickness about 11µm causes impairing the electro-thermo-optical properties of the device and epitaxial problems [1]-[2] Chevallier et al., 2011 Optimized subwavelength grating mirror design for mid-infrared wavelength range. Recently broadband high reflectivity Si/SiO 2 hybrid Bragg mirrors with Δn 2 and reflectivity above 99% with 4 pairs and thickness of 2.2µm realized [3] Bachmann et al., 2009 GaSb-Based VCSEL With Buried Tunnel Junction for Emission Around 2.3 µm but due to two dimensional symmetry, DBRs have no sensitivity to polarization [4] Ouvrard et al., 2004 Singlefrequency tunable sb-based VCSELs emitting at 2.3 µm. In an isotropic cavity, the dominant mode is random and cannot be controlled, but polarization control of VCSEL is possible using HCGs which means we can select the operation mode of laser [5] Wang et al., 2010 Optimization design of an ultrabroadband, high-efficiency, alldielectric grating. Many structures designed and proposed for different wavelength range with different polarization selectivity. HCG mirrors are easier to realization for less epitaxial stages, they are polarization selective, scalable, broadband high reflectivity mirrors which all provided ideal choose for top mirrors in VCSELs. In addition, They can suppress higher order modes [6] Mateus et al., 2004 Ultrabroadband mirror using low-index cladded subwavelength grating, [7] Hofmann et al., 2010 Long-Wavelength High-Contrast Grating Vertical-Cavity Surface- Emitting Laser, [8] Chase et al., 2011 High Contrast Grating VCSELs: Properties and Implementation on InPbased VCSELs. In this work, we have designed two optimized Si/SiO2 HCG with no Bragg mirror for a VCSEL application at 2.3 µm as top mirrors. First, we optimized the structure for the largest bandwidth as possible for TM polarization. Second, we optimized the structure for better TE mode suppression in reflection band and better stability in design parameters changes and have calculated reflection spectra of each structure for TE and TM polarization and change in design parameters. Finally we evaluate the higher mode suppression in this structure.
Duty Cycle Period Si T g T l SiO 2 GaSb-Substrate Figure 1. Scheme of the reflector. Structure designed to reach 99.9% reflectivity. Grating thickness Tg, low index material thickness Tl, period and duty cycle are free parameters have searched to optimize the structure. Design process The high contrast grating structure which had designed and studied in this work and showed in Figure 1 is based on Si/SiO 2 materials which properties and fabrication process are well known. The grating is made of Si (n = 3.48) on top of a low index layer of SiO 2 (n = 1.49) used to achieved high reflectivity and allowing the use of a selective etching method for the fabrication of the grating [2]. In many works Bragg mirrors combined with grating in order to increase the reflectivity and broadening the stopband [2] and [9] Schablitsky et al., 1996 Controlling polarization of vertical-cavity surface-emitting lasers using amorphous silicon subwavelength transmission gratings, but there is no Bragg mirror in this structure causes more sensitivity to polarization. The substrate is chosen as the VCSEL cavity material with an optical index of n gasb = 3.9. The refractive index becomes n sio2 = 1.49 + 2.1e -4 j, which results in a 0.1 % fall of the HCG reflectivity [2]. We can control the VCSEL polarization. In order to be well suitable for a VCSEL application, HCGs have to exhibit optical properties as we have defined with at least 99% transverse magnetic reflectivity for the largest possible bandwidth [5]. For these issues, we choose 99.9% reflectivity for ensuring lasing operation. Moreover, to ensure a polarization stability of the emitted beam, the reflectivity of the transverse electric mode has been chosen to be kept as low as possible. Such mirrors operate by excitation and reflection of transverse modes which propagate in the grating direction [10] Brückner et al., 2010 Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal. Their reflectivity is not straightforward like Bragg mirrors [11] and must be numerically computed by methods such as Rigorous Coupled- Wave Analysis (RCWA) which we had used in this paper [12] Moharam et al., 1995 Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings and [13] Moharam et al., 1995 Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings. We have used the optimization method for TM mode ultrabroadband design discussed in [6]. In first case, the aim was the largest bandwidth as possible, we sweep all design parameters for achieving ultrabroadband mirror. In second design, we sweep parameters for best suppression of TE mode in reflection band and stability of reflection by change in parameters. RESULTS AND DISCUSSION Figure 2 shows the first design calculated reflectivity for a TM HCG for 2.3µm. The goal was the largest bandwidth as possible. The best values achieves for this structure, were period 1066nm, grating thickness 688nm, semiconductor duty cycle 74.5% and the SiO 2 thickness of 1100 nm. Bandwidth for reflections upper than 99%, 99.5% and 99.9% are shown in Figure 2 (a)-(d) and TABLE I. The TE reflection is 20% in target wavelength of 2.3µm. For single mode operation, we choose a bandwidth which TE reflectivity is less than 90% (2000-2470nm) [9]. Results are shown in TABLE II. For ensuring of more than 99% reflection during fabrication process and system losses, we choose 99.9% reflection. So, the bandwidth for situations that device is single mode and has reflectivity more than 99.9% is around 350nm. Results indicate very good performance of the device as a VCSEL top mirror and also the operation of the device around the wavelength is guaranteed and we can have a flexible structure. Figure 3 describe the stability of the design by change in design parameters as a fabrication tolerant. For this purpose, we sweep all parameters individually and measure the reflectivity for 2.3µm wavelength. Results gathered in table III. The amounts of fabrication tolerant are acceptable for today technology makes this approach a good choice for VCSEL fabrication. 1181
Figure2.(a) Total Reflection spectra of TM and TE modes. Figure2.(b) Reflection spectra for reflection above 99%. Figure2.(c) Reflection spectra for reflection above 99.5%. Figure2.(d) Reflection spectra for reflection above 99.9%. Figure 2. Reflection spectra of TM (solid blue) and TE (dashed red) modes. Results show more than 700nm broadband reflection spectra for TM polarization, and more than 300nm bandwidth for totally single mode reflection. Table 1. Simulation results for different reflectivities for TM-HCG for first proposed structure. Reflectivity 99% 99.5% 99.9% Bandwidth(nm) 2000-2712 2045-2648 2120-2536 Δλ/λ 30.2% 25.6% 25.6% Table 2. Simulation results for different reflectivity for totally single mode TM-HCG for first proposed structure. Reflectivity 99% 99.5% 99.9% Bandwidth(nm) 2000-2470 2045-2470 2120-2470 Δλ/λ 21% 18.8% 15.2% Results show tolerant about 5% for duty cycle, 55nm for grating period, 55nm for grating period. So, for designing a lower sensitive structure, we sweep all design parameters to achieve the most stable structure that have TE polarization reflectivity lower than 80% in all of its bandwidth. The results described in Table V. Figure3.(a) Duty cycle tolerant for TM (solid-blue) and Figure3.(b) Acceptable tolerant for grating thickness. TE(red-dashed) polarization 1182
Figure3.(c) Acceptable tolerant for SiO 2 thickness. Figure3.(d) Acceptable tolerant for grating period. Figure 3. Acceptable tolerant for ultrabroadband design. We sweep all design parameters individually which means the other parameters have been kept constant. The results are indicated in Table III. Table 3. Maximum Acceptable tolerant for reflectivity above 99%. Parameter Designed Range Duty Cycle 74.5% 69.4-76.2% Grating Thickness 688nm 644-699nm SiO2 Thickness 1100nm 654nm> Period 1066nm 1044-1099nm As we can see in Figure 4, we tried to keep TE reflection lower than 80% in all of desired bandwidth where the TM reflection is more than 99%. Results and range of different reflections have been indicated in table IV. We see that the bandwidth is decreased from 700nm to 400nm that is more than enough for VCSEL applications. Figure 4. Reflection spectra of TM (solid blue) and TE (dashed red) modes. Results show more than 400nm reflection spectra for TM polarization, bandwidth is totally single mode. Although the bandwidth is deduced in second design, the tolerant of design parameters enhanced greatly. Figure 5, shows the change of reflectivity by changing the design parameters for 2.3µm wavelength. Results show tolerant about 25% for duty cycle, 137nm for grating period, 194nm for grating thickness which are around 3 time larger than the first design. In addition, we can deduce the SiO 2 thickness to 400nm enable us to have a very good mirror in this range by a thickness around 1µm. for example we change SiO 2 thickness to 500 with no change in other parameters. The results described in Figure 6 and shows the bandwidth around 370nm for TM reflection above 99% and TE reflection under 75%. Table 4. Simulation results for different reflectivity for TM-HCG for second proposed structure Reflectivity 99% 99.5% 99.9% Bandwidth(nm) 2078-2478 2088-2448 2115-2395 Δλ/λ 17.4% 15.6% 12.1% If all design parameters change together in their allowed range base on Table V, it is obvious that the reflection may be lower than desired value. In other hand, today s fabrication technology is able to do deposition by very high accuracy (less than nanometer). So, we can fix grating and SiO 2 thicknesses, vary the grating period and duty cycle together. The result is shown in Figure 7. We sweep grating period and duty cycle together. Central 1183
rectangular by grating period range of 926 to 1020 and duty cycle between 53% and 77% is allowed region for TM reflection above 99% and any value for grating period and duty cycle lead to TM reflection above 99%. Arrows junction is our central values and bright light is a duty cycle in which TM reflection is high.so we have 94nm tolerant for grating period and 24% duty cycle one. Figure5.(a) Duty cycle tolerant for TM (solid-blue) and Figure5.(b) Acceptable tolerant for grating thickness. TE(red-dashed) polarization Figure5.(c) Acceptable tolerant for SiO 2 thickness. Figure5.(d) Acceptable tolerant for grating period. Figure 5.Acceptable tolerant for second design. We sweep all design parameters individually. The results are indicated in Table III and show better stability of structure. Table 5. Maximum Acceptable tolerant for reflectivity above 99%. Parameter Designed Range Duty Cycle 62% 48-73.5% Grating Thickness 620nm 644-699nm SiO2 Thickness 1100nm 400nm> Period 962nm 886-1023nm Figure6.(a) Total Reflection spectra of TM and TE mod Figure 6. Reflection spectra of TM (solid blue) and TE (dashed red) modes for structure by 500nm SiO 2 thickness. Results Figure6.(b) above 99% Reflection spectra of TM 1184
show around 380nm bandwidth for reflection above 99%, bandwidth is totally single mode Figure7. we sweep grating period and duty cycle together. Central rectangular by grating period range of 926 to 1020 and duty cycle between 53% and 77% is allowed region for TM reflection above 99%. Arrows junction is our central values and bright light is a duty cycle in which TM reflection is high. For describing TM higher order modes suppression, we can model these higher modes by increase in incoming light angle and calculating the TM reflection spectra by change in this angle [8]. Figure 8 shows the reflectivity for TM-HCG (solid blue for first design and dashed green for second) and DBRs (dashed red). The DBRs consisted of four pairs Si/SiO 2 layers. DBRs show an extremely weak angular dependence, so they cannot be used for this type of approach. On the other hand, The HCG shows a much stronger angular dependence. In second design, the TE reflectivity is greater than first one for 2.3µm wavelength, so we have to expect the first one must be more sensitive to other modes than the first one. The reflectivity falling down drastically at angles greater than 5º for first design and around 13º for second one. Figure 8. angle sensitivity of Si/SiO2 DBRs (dashed red) and TM-HCG 1 (solid blue) and 2 (dashed green). The reflectivity is falling off drastically at angles greater than 5º for first structure and around 13º for second one showing good higher order mode supression. CONCLUSION In this paper, we have presented two different TM-HCG that are very good alternatives for conventional DBRs as top mirrors of VCSELs. There is no DBR in structure, causes good polarization selecting and higher mode suppression. In first design, we focused on an ultrabroadband design which lead to around 700nm above 99% TM reflectivity. But there was two problems. First the TE reflection spectra had a large peak in TM reflection bandwidth and the second, the range of parameters tolerant was a little low. So, we designed the second one base on TE reflection lower than 80% and more parameters tolerant. The results were around 400nm above 99% TM reflation and under 75% in all of reflection band. Then, we introduce a good structure by thickness around 1.1µm that can be used as top mirror in this rang. These dimensions are at least three times lower than DBRs for this wavelength 1185
range. Finally, we have evaluated both structures for TM higher mode suppression. Results show falling of reflectivity for angles above 5 0 and 13 0 for first and second design respectively. The mirror can be easily scaled by simply multiplying the dimensions by a constant value, and can be used in any wavelength range by using low absorbing materials on that wavelength range. In addition, we can optimize this structure for TE mode and these enable us to choose the output beam polarization of laser that was not realizable by DBRs. REFERENCES Bachmann A, Kashani-Shirazi K, Arafin S, Amann MC. 2009. GaSb-Based VCSEL With Buried Tunnel Junction for Emission Around 2.3 µm, Selected Topics in Quantum Electronics, IEEE Journal of, vol.15, no.3, pp.933-940, May-june Brückner F, Friedrich D, Clausnitzer T, Britzger M, Burmeister O, Danzmann K, Kley EB, Tünnermann A, Schnabel R. 2010. Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal, Phys. Rev. Lett. 104(16), 163903 Chevallier C, Fressengeas N, Genty F, Jacquet J. 2011. Optimized subwavelength grating mirror design for mid-infrared wavelength range, Applied physics Journal, Springer, vol.103, no.3, pp.1139-1144, 0947-8396 Christopher Ch.2011. High Contrast Grating VCSELs: Properties and Implementation on InP-based VCSELs, Ph.D. dissertation, Dept. electr comput Eng., Univ. California, Berkeley, Ducanchez A, Cerutti L, Grech P, Genty F. 2008. Room-Temperature Continuous-Wave Operation of 2.3µm Sb-Based Electrically Pumped Monolithic Vertical-Cavity Lasers, Photonics Technology Letters, IEEE, vol.20, no.20, pp.1745-1747, Oct.15, Hofmann W, Chase C, Müller M, Rao Y, Grasse C, Bo hm G, Amann MC, Chang-Hasnain CJ.2010. Long-Wavelength High-Contrast Grating Vertical-Cavity Surface-Emitting Laser, Photonics Journal, IEEE, vol.2, no.3, pp.415-422, June Magnusson R, Shokooh-Saremi M. 1995. Physical basis for wideband resonant reflectors, Opt. Express 16(5), 3456 3462 (2008). Mateus CFR, Huang MCY, Yunfei D, Neureuther AR, Chang-Hasnain CJ. 2004. Ultrabroadband mirror using low-index cladded subwavelength grating, Photonics Technology Letters, IEEE, vol.16, no.2, pp.518-520, Feb. Moharam MG, Da Pommet EB, Grann TK. Gaylord.1995. Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach, Journal of the Optical Society of America A. Moharam MG, Grann EB, Pommet DA, Gaylord TK. Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings, J. Opt. Soc. Am. A. Ouvrard A, Garnache A, Cerutti L, Genty F, Romanini D. 2005. Single-frequency tunable sb-based VCSELs emitting at 2.3 µm, IEEE Photon. Technol. Lett. 17(10), 2020 2022 Steven J. Schablitsky, Lei Zhuang, Rick C. Shi, Stephen Y Chou. 1996. Controlling polarization of vertical-cavity surface-emitting lasers using amorphous silicon subwavelength transmission gratings, Appl. Phys. Lett. 69, 7 Wang J, Jin Y, Shao J, Fan Z.2010. Optimization design of an ultrabroadband, high-efficiency, all-dielectric grating, Opt. Lett. 35, 187-189 1186