Abstract

We present the design and fabrication of guided-mode resonant broadband reflectors operating in transverse electric (TE) polarization. The structure consists of a subwavelength one-dimensional grating with a two-part period and a nanometric homogeneous layer of amorphous silicon on a quartz substrate. A representative reflector exhibits 99% reflectance over a 380-nm spectral range spanning 1440–1820 nm. The fabrication involves thin-film deposition, interferometric lithography, and reactive ion etching. Experimental reflectance greater than 90% is achieved over a ~360-nm bandwidth. The spectral bandwidths demonstrated exceed formerly reported results for two-part periodic resonators working in TE polarization.

© 2014 Optical Society of America

1. Introduction

Wideband reflectors based on photonic resonances are important because of their diverse design possibilities and integration compatibility for application in couplers, resonant cavity-enhanced photodetectors, and lasers [14]. These reflectors exhibit less material losses than metal mirrors and avoid multilayer depositions traditionally required for dielectric stack mirrors. These reflectors reveal guided- or leaky-mode resonances (GMRs or LMRs) and are most effectively fashioned as subwavelength waveguide grating structures. With proper parametric design, engineering the spectral, polarization, and phase attributes of GMR reflectors is achievable to match numerous applications.

Transverse electric (TE) and transverse magnetic (TM) resonant reflectors using subwavelength two-part or multipart periodic grating structures have been studied in the past [511]. Reviewing briefly, for TM polarization, Mateus et al. demonstrated a two-part device with a ~500-nm bandwidth [5] whereas Ding et al. reported four-part structures with a ~600-nm bandwidth [6]. For TE polarization, Ding et al. presented a four-part reflector with a ~600-nm bandwidth [6], and Wu et al. reported a ~630-nm bandwidth for a similar element [7]. Additionally, Wu et al. reported the fabrication results of a six-part TE device with reflectivity R > 97% over a 240-nm bandwidth [8], and Lee et al. fabricated a two-part TE structure with R ˃ 90% over a ~130-nm bandwidth [9]. We addressed the physical basis for GMR wideband reflectors in [10] and investigated the effects of added sublayers on the reflection response and bandwidth in [11]. In summary, TE-polarized wideband resonant reflectors with multipart periods have been achieved whereas the simpler two-part devices that are much easier to fabricate show markedly narrower bandwidths in the published literature. In this contribution, we aim at ameliorating this condition by designing and fabricating new resonant reflectors in this class.

Accordingly, in this paper, we present theoretical and experimental spectra pertaining to TE-polarized reflectors with two-part periods operating in the optical communication band. The structures consist of one-dimensional (1D) silicon grating patterns with integral nanometric silicon sublayers deposited on silica substrates. We find that the homogeneous layer plays a crucial role in extending the bandwidth. A similar resonant structure was recently reported and operated as a Rayleigh reflector [12]. This study elaborates the design approach with systematic parametric variations to tune the bandwidth. The fabrication and characterization processes are described in detail.

2. Device structure and design

The generic GMR element consists of a subwavelength periodic grating and a homogeneous layer on a substrate. Figure 1 shows the schematic view of a device model with the characteristic design parameters being period (Λ), fill factor (F), grating depth (dg), and homogeneous layer thickness (dh). The refractive indices of cover, device, and substrate are denoted as nc, n, and ns, respectively.

 figure: Fig. 1

Fig. 1 Wideband reflector model denoting the period Ʌ, fill factor F, grating thicknesses dg, homogeneous layer thickness dh, and refractive indices of cover nc, silicon n, and substrate ns. The incident (I), reflected (R), and transmitted (T) light waves are indicated. The TE-polarized incident light’s electric field vector is orthogonal to the plane of incidence and along the grating ridges in this case. We set nc = 1, n = 3.56, and substrate ns = 1.5 in this paper.

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We use a computer code based on rigorous coupled-wave analysis (RCWA) for the theoretical computations [13]. The detailed analysis of reflected and transmitted diffraction efficiencies of a basic GMR element is explained in [14]. Figure 2 shows the reflectance and transmittance spectra of a wideband reflector for normally incident TE-polarized light. The design parameters are Λ = 960 nm, F = 0.5, dg = 320 nm, and dh = 55 nm. The structure’s Rayleigh wavelength is λR = nsΛ = 1440 nm, where ns = 1.5 is the refractive index of the quartz substrate; the reflectance in Fig. 2(a) drops sharply at this wavelength. Beyond λ = 1440 nm, only zero-order diffraction prevails. The figure shows R0 > 99% over a ~380-nm bandwidth in the 1440-nm to 1820-nm wavelength range. Two transmission dips exist inside the reflection band at 1465 nm and 1771 nm as depicted on a logarithmic scale in Fig. 2(b); each dip corresponds to a GMR. Since 100% reflection is associated with GMRs, the interaction between these two side-by-side resonances yields wideband reflection. Varying the device parameters such as homogeneous layer thickness, grating depth, and fill factor changes the number and loci of resonances, which ultimately tunes the bandwidth. The effect of changing each of the parameters is described in successive sections. Among these variable parameters, tuning the homogeneous layer thickness is essential for making the reflector wideband in nature as reduced bandwidths are seen in its absence.

 figure: Fig. 2

Fig. 2 Zero-order reflectance and transmittance spectra; (a) linear and (b) logarithmic plots for normal incidence of TE-polarized light. Device parameters are Λ = 960 nm, F = 0.5, dg = 320 nm, and dh = 55 nm.

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2.1 Effect of homogeneous layer thickness

Figure 3 shows a zero-order reflectance (R0) map plotted against wavelength and homogeneous layer thickness with the parameters set as Λ = 960 nm, F = 0.5, and dg = 320 nm. With an increasing value of dh, the two GMRs separate correspondingly. Interaction between closely located resonances ensures high reflectivity but lowered bandwidth, whereas distantly located resonances yield a wider bandwidth with lowered reflectivity in the middle. For example, when dh = 45 nm, the two GMRs are located close together at 1491 nm and 1640 nm, resulting in a reflector with R0 > 99% over the 1440- to 1729-nm (289 nm) wavelength range as shown in Fig. 4(a); R0 is shown on a linear scale, and T0 is shown on a logarithmic scale. When dh = 75 nm, the GMRs locate farther apart at 1456 nm and 1940 nm, and the reflectance value drops to 96% at λ = 1700 nm. In this case, R0 > 95% in the 1440- to 1988–nm wavelength range, providing a 548-nm bandwidth as shown in Fig. 4(b). As evident in Fig. 3, the reflector’s bandwidth narrows when dh → 0. Hence, determining a proper value of the homogeneous layer thickness is essential to obtain a wideband TE reflector. When the thickness of the homogeneous layer exceeds ~100 nm, the reflectivity drops significantly because the GMRs are located too far apart to interact strongly as depicted in Fig. 3.

 figure: Fig. 3

Fig. 3 Map of zero-order reflectance in wavelength and homogeneous layer thickness. The reflectance is quantified according to the scale bar on the right.

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 figure: Fig. 4

Fig. 4 Zero-order reflectance (linear scale) and transmittance (log scale) spectra for (a) dh = 45 nm and (b) dh = 75 nm with Λ = 960 nm, F = 0.5, and dg = 320 nm.

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2.2 Effect of grating thickness

Figure 5 displays a zero-order reflectance map showing wavelength and grating thickness with the other parameters set as Λ = 960 nm, F = 0.5, and dh = 55 nm. The reflector’s bandwidth is determined by the grating depth as the spectral positioning of the GMRs varies with dg. In this example with an increasing value of dg, the two GMRs approach each other and the bandwidth of the reflector gradually decreases. When dg = 290 nm, the two transmission dips are located farther apart and the reflectivity drops to 96% at λ = 1700 nm as depicted in Fig. 6(a). Nevertheless, R0 > 95% is achieved over a ~450-nm bandwidth. Thus, a broadband reflector prevails with a lowered value of maximum reflectivity. When dg = 350 nm, R0 > 99% over a 340-nm bandwidth as shown in Fig. 6(b). In this particular example, when the grating thickness exceeds 400 nm, the flat band shifts to longer wavelengths and narrows as illustrated in Fig. 5. Charting R0 across a wider thickness range would bring in new regions of flat-band reflection as demonstrated in [10,11]; in this paper, we emphasize the minimal device for expedient fabrication.

 figure: Fig. 5

Fig. 5 Map of zero-order reflectance in wavelength and grating thickness. The reflectance is quantified according to the scale bar on the right.

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 figure: Fig. 6

Fig. 6 Zero-order reflectance (linear scale) and transmittance (log scale) spectra for (a) dg = 290 nm and (b) dg = 350 nm with Λ = 960 nm, F = 0.5, and dh = 55 nm.

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2.3 Effect of fill factor

Figure 7 shows R0 plotted against wavelength and fill factor for Λ = 960 nm, dg = 55 nm, and dg = 320 nm. A single GMR exists in the device up to F = 0.48, beyond which two GMRs prevail. When F = 0.45, the only transmission dip occurs at λ = 1683 nm, yielding R0 > 99% across a 316–nm bandwidth as shown in Fig. 8(a). When F = 0.55, the reflector produces R0 > 95% over a 438-nm bandwidth as depicted in Fig. 8(b).

 figure: Fig. 7

Fig. 7 Map of zero-order reflectance in wavelength and fill factor. The reflectance is quantified according to the scale bar on the right.

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 figure: Fig. 8

Fig. 8 Zero-order reflectance (linear scale) and transmittance (log scale) spectra for (a) F = 0.45 and (b) F = 0.55 with Λ = 960 nm, dg = 320 nm, and dh = 55 nm.

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3. Fabrication

A schematic of the step-by-step fabrication process is shown in Fig. 9. The fabrication commences with deposition of amorphous silicon (a-Si) on a clean quartz substrate by sputtering. The film thickness is 375 nm as verified with ellipsometry. A 400-nm-thick photoresist (PR) layer is then spin-coated on the a-Si film. A 1D grating pattern with a 960-nm period is recorded on the PR by laser interferometric lithography using a deep ultraviolet (UV) laser (λ = 266 nm). The exposed patterned area is 5 × 5 mm2. After developing the PR, reactive ion etching (RIE) using a gas mixture of trifluromethane (CHF3) and sulfur hexafluoride (SF6) is used to etch down the silicon to 320 nm leaving a ~55-nm sublayer. The residual PR is removed by RIE with oxygen plasma.

 figure: Fig. 9

Fig. 9 A schematic of the GMR reflector fabrication process.

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The device is characterized using an atomic force microscope (AFM) and a scanning electron microscope (SEM). Figure 10 shows the AFM image where Λ = 958 nm, F = 0.5, and dg = 320 nm, which are close to the design parameters. The top-view and cross-sectional SEM images of a similar device in Fig. 11 show acceptable fabrication uniformity as well as the etch profile and a nanometric homogeneous layer adjacent to the glass substrate. In Fig. 11, we use a device with the same a-Si film thickness and period as the measured device to save the measured wideband reflector reported in this study from the gold-coat and cross-sectional cut needed to take SEM images.

 figure: Fig. 10

Fig. 10 AFM image and profile of the fabricated a-Si grating. The parameters are Λ = 958 nm, F = 0.5, and dg = 320 nm.

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 figure: Fig. 11

Fig. 11 SEM top-view and cross-sectional images of a similar a-Si grating pattern on a glass substrate.

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4. Results and discussion

The spectral response is measured using a super-continuum source and an optical spectrum analyzer for a wavelength range of 1400–1900 nm. A polarizer is used to choose the TE polarization of the input light. After measuring the reflected light from the device, it is normalized with respect to light intensity from a reference gold mirror. The schematic diagram of the measurement setup at normal incidence of light is given in Fig. 12.

 figure: Fig. 12

Fig. 12 Schematic diagram of the optical measurement setup.

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Figure 13 gives the theoretical and experimental spectra of the fabricated resonant reflector. The parameters obtained from AFM and SEM images are used for simulation. The theoretical bandwidth is 380 nm with R0 > 99%, which is 255 nm larger than the result reported by Shokooh-Saremi et al. in [11] for a two-part grating structure for TE polarization. Measured performance of the fabricated device shows R0 > 90% over ~360 nm ranging from 1478 nm to 1838 nm. The reduced efficiency obtained in experiments compared to the simulated results can be attributed to the combined effect of scattering from surface roughness, absorption associated with the a-Si material, and differences in the experimental device profiles relative to the simulation model. A piecewise linear fitting is used to eliminate ripples in the measured data. The experimental bandwidth is 230 nm higher than the result published by Lee et al. in [9].

 figure: Fig. 13

Fig. 13 Calculated and experimental spectra associated with a resonant reflector with TE-polarized light at normal incidence. The parameters used for computation are Λ = 960 nm, F = 0.5, dg = 320 nm, dh = 55 nm, n = 3.56, nc = 1, and ns = 1.5.

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Figure 14 shows theoretical and experimental spectra of a similar wideband GMR reflector with different parametric values, namely Λ = 960 nm, dg = 330 nm, dh = 45 nm and F = 0.49. Since this device has a larger grating depth and smaller homogeneous layer thickness than the former design, it exhibits a lower computed bandwidth of 260 nm with R0 > 99%. It has an experimental R0 > 90% for a bandwidth of 315 nm ranging from 1437 to 1752 nm. The theoretical and experimental data for both devices are summarized in Table 1.

 figure: Fig. 14

Fig. 14 Calculated and experimental spectra for a reflector for TE-polarized light at normal incidence. The parameters used for computation are Λ = 960 nm, F = 0.49, dg = 330 nm, dh = 45 nm, n = 3.56, nc = 1, and ns = 1.5.

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Tables Icon

Table 1. Comparison of Theoretical and Experimental Results

5. Conclusion

We design and fabricate wideband GMR reflectors operating in TE polarization for normally incident light in the telecommunication spectral region. The device consists of a simple 1D grating along with a nanometric homogeneous layer of a-Si on a quartz substrate. The bandwidth and the efficiency of reflectors in this class can be tuned by properly selecting the values of grating depth, fill factor, and homogeneous layer thickness as demonstrated herein via extensive numerical simulations. Experimentally, a ~360-nm bandwidth wide reflector with R > 90% over the 1478- to 1838-nm wavelength range is achieved. The bandwidths demonstrated for these two-part devices in TE polarization exceed those previously reported in the literature.

Acknowledgments

This research was supported in part by the UT System Texas Nanoelectronics Research Superiority Award funded by the State of Texas Emerging Technology Fund as well as by the Texas Instruments Distinguished University Chair in Nanoelectronics Endowment.

References and links

1. P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, and S. Tanev, “A broad-band waveguide grating coupler with a subwavelength grating mirror,” IEEE Photon. Technol. Lett. 18(1), 13–15 (2006). [CrossRef]  

2. C. C. Wang and S. D. Lin, “Resonant cavity-enhanced quantum-dot infrared photodetectors with sub-wavelength grating mirror,” J. Appl. Phys. 113(21), 213108 (2013). [CrossRef]  

3. M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007). [CrossRef]  

4. M. A. Ahmed, M. Rumpel, A. Voss, and T. Graf, “Applications of sub-wavelength grating mirrors in high-power lasers,” Adv. Opt. Technol. 1, 381–388 (2012).

5. C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004). [CrossRef]  

6. Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004). [CrossRef]   [PubMed]  

7. H. Wu, L. Huang, Y. Xiao, C. Zhang, S. Li, N. Luo, X. He, and Y. Gao, “A wideband reflector realized by a subwavelength multi-subpart profile grating structure,” J. Opt. 15(3), 035703 (2013). [CrossRef]  

8. H. Wu, J. Hou, W. Mo, D. Gao, and Z. Zhou, “A multilayer-based high-performance multisubpart profile grating reflector,” IEEE Photon. Technol. Lett. 22(4), 203–205 (2010). [CrossRef]  

9. K. J. Lee and R. Magnusson, “Single-layer resonant high reflector in TE polarization: Theory and experiment,” IEEE Photon. J. 3(1), 123–129 (2011). [CrossRef]  

10. R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008). [CrossRef]   [PubMed]  

11. M. Shokooh-Saremi and R. Magnusson, “Wideband leaky-mode resonance reflectors: Influence of grating profile and sublayers,” Opt. Express 16(22), 18249–18263 (2008). [CrossRef]   [PubMed]  

12. R. Magnusson, “Flat-top resonant reflectors with sharply delimited angular spectra: an application of the Rayleigh anomaly,” Opt. Lett. 38(6), 989–991 (2013). [CrossRef]   [PubMed]  

13. T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985). [CrossRef]  

14. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993). [CrossRef]   [PubMed]  

References

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  1. P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, S. Tanev, “A broad-band waveguide grating coupler with a subwavelength grating mirror,” IEEE Photon. Technol. Lett. 18(1), 13–15 (2006).
    [Crossref]
  2. C. C. Wang, S. D. Lin, “Resonant cavity-enhanced quantum-dot infrared photodetectors with sub-wavelength grating mirror,” J. Appl. Phys. 113(21), 213108 (2013).
    [Crossref]
  3. M. C. Y. Huang, Y. Zhou, C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
    [Crossref]
  4. M. A. Ahmed, M. Rumpel, A. Voss, T. Graf, “Applications of sub-wavelength grating mirrors in high-power lasers,” Adv. Opt. Technol. 1, 381–388 (2012).
  5. C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
    [Crossref]
  6. Y. Ding, R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004).
    [Crossref] [PubMed]
  7. H. Wu, L. Huang, Y. Xiao, C. Zhang, S. Li, N. Luo, X. He, Y. Gao, “A wideband reflector realized by a subwavelength multi-subpart profile grating structure,” J. Opt. 15(3), 035703 (2013).
    [Crossref]
  8. H. Wu, J. Hou, W. Mo, D. Gao, Z. Zhou, “A multilayer-based high-performance multisubpart profile grating reflector,” IEEE Photon. Technol. Lett. 22(4), 203–205 (2010).
    [Crossref]
  9. K. J. Lee, R. Magnusson, “Single-layer resonant high reflector in TE polarization: Theory and experiment,” IEEE Photon. J. 3(1), 123–129 (2011).
    [Crossref]
  10. R. Magnusson, M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008).
    [Crossref] [PubMed]
  11. M. Shokooh-Saremi, R. Magnusson, “Wideband leaky-mode resonance reflectors: Influence of grating profile and sublayers,” Opt. Express 16(22), 18249–18263 (2008).
    [Crossref] [PubMed]
  12. R. Magnusson, “Flat-top resonant reflectors with sharply delimited angular spectra: an application of the Rayleigh anomaly,” Opt. Lett. 38(6), 989–991 (2013).
    [Crossref] [PubMed]
  13. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985).
    [Crossref]
  14. S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993).
    [Crossref] [PubMed]

2013 (3)

C. C. Wang, S. D. Lin, “Resonant cavity-enhanced quantum-dot infrared photodetectors with sub-wavelength grating mirror,” J. Appl. Phys. 113(21), 213108 (2013).
[Crossref]

H. Wu, L. Huang, Y. Xiao, C. Zhang, S. Li, N. Luo, X. He, Y. Gao, “A wideband reflector realized by a subwavelength multi-subpart profile grating structure,” J. Opt. 15(3), 035703 (2013).
[Crossref]

R. Magnusson, “Flat-top resonant reflectors with sharply delimited angular spectra: an application of the Rayleigh anomaly,” Opt. Lett. 38(6), 989–991 (2013).
[Crossref] [PubMed]

2012 (1)

M. A. Ahmed, M. Rumpel, A. Voss, T. Graf, “Applications of sub-wavelength grating mirrors in high-power lasers,” Adv. Opt. Technol. 1, 381–388 (2012).

2011 (1)

K. J. Lee, R. Magnusson, “Single-layer resonant high reflector in TE polarization: Theory and experiment,” IEEE Photon. J. 3(1), 123–129 (2011).
[Crossref]

2010 (1)

H. Wu, J. Hou, W. Mo, D. Gao, Z. Zhou, “A multilayer-based high-performance multisubpart profile grating reflector,” IEEE Photon. Technol. Lett. 22(4), 203–205 (2010).
[Crossref]

2008 (2)

2007 (1)

M. C. Y. Huang, Y. Zhou, C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

2006 (1)

P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, S. Tanev, “A broad-band waveguide grating coupler with a subwavelength grating mirror,” IEEE Photon. Technol. Lett. 18(1), 13–15 (2006).
[Crossref]

2004 (2)

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Y. Ding, R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004).
[Crossref] [PubMed]

1993 (1)

1985 (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985).
[Crossref]

Ahmed, M. A.

M. A. Ahmed, M. Rumpel, A. Voss, T. Graf, “Applications of sub-wavelength grating mirrors in high-power lasers,” Adv. Opt. Technol. 1, 381–388 (2012).

Chang-Hasnain, C. J.

M. C. Y. Huang, Y. Zhou, C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Cheben, P.

P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, S. Tanev, “A broad-band waveguide grating coupler with a subwavelength grating mirror,” IEEE Photon. Technol. Lett. 18(1), 13–15 (2006).
[Crossref]

Delâge, A.

P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, S. Tanev, “A broad-band waveguide grating coupler with a subwavelength grating mirror,” IEEE Photon. Technol. Lett. 18(1), 13–15 (2006).
[Crossref]

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Ding, Y.

Gao, D.

H. Wu, J. Hou, W. Mo, D. Gao, Z. Zhou, “A multilayer-based high-performance multisubpart profile grating reflector,” IEEE Photon. Technol. Lett. 22(4), 203–205 (2010).
[Crossref]

Gao, Y.

H. Wu, L. Huang, Y. Xiao, C. Zhang, S. Li, N. Luo, X. He, Y. Gao, “A wideband reflector realized by a subwavelength multi-subpart profile grating structure,” J. Opt. 15(3), 035703 (2013).
[Crossref]

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985).
[Crossref]

Graf, T.

M. A. Ahmed, M. Rumpel, A. Voss, T. Graf, “Applications of sub-wavelength grating mirrors in high-power lasers,” Adv. Opt. Technol. 1, 381–388 (2012).

He, X.

H. Wu, L. Huang, Y. Xiao, C. Zhang, S. Li, N. Luo, X. He, Y. Gao, “A wideband reflector realized by a subwavelength multi-subpart profile grating structure,” J. Opt. 15(3), 035703 (2013).
[Crossref]

Hou, J.

H. Wu, J. Hou, W. Mo, D. Gao, Z. Zhou, “A multilayer-based high-performance multisubpart profile grating reflector,” IEEE Photon. Technol. Lett. 22(4), 203–205 (2010).
[Crossref]

Huang, L.

H. Wu, L. Huang, Y. Xiao, C. Zhang, S. Li, N. Luo, X. He, Y. Gao, “A wideband reflector realized by a subwavelength multi-subpart profile grating structure,” J. Opt. 15(3), 035703 (2013).
[Crossref]

Huang, M. C. Y.

M. C. Y. Huang, Y. Zhou, C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Janz, S.

P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, S. Tanev, “A broad-band waveguide grating coupler with a subwavelength grating mirror,” IEEE Photon. Technol. Lett. 18(1), 13–15 (2006).
[Crossref]

Lamontagne, B.

P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, S. Tanev, “A broad-band waveguide grating coupler with a subwavelength grating mirror,” IEEE Photon. Technol. Lett. 18(1), 13–15 (2006).
[Crossref]

Lee, K. J.

K. J. Lee, R. Magnusson, “Single-layer resonant high reflector in TE polarization: Theory and experiment,” IEEE Photon. J. 3(1), 123–129 (2011).
[Crossref]

Li, S.

H. Wu, L. Huang, Y. Xiao, C. Zhang, S. Li, N. Luo, X. He, Y. Gao, “A wideband reflector realized by a subwavelength multi-subpart profile grating structure,” J. Opt. 15(3), 035703 (2013).
[Crossref]

Lin, S. D.

C. C. Wang, S. D. Lin, “Resonant cavity-enhanced quantum-dot infrared photodetectors with sub-wavelength grating mirror,” J. Appl. Phys. 113(21), 213108 (2013).
[Crossref]

Luo, N.

H. Wu, L. Huang, Y. Xiao, C. Zhang, S. Li, N. Luo, X. He, Y. Gao, “A wideband reflector realized by a subwavelength multi-subpart profile grating structure,” J. Opt. 15(3), 035703 (2013).
[Crossref]

Magnusson, R.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Mo, W.

H. Wu, J. Hou, W. Mo, D. Gao, Z. Zhou, “A multilayer-based high-performance multisubpart profile grating reflector,” IEEE Photon. Technol. Lett. 22(4), 203–205 (2010).
[Crossref]

Moharam, M. G.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985).
[Crossref]

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Rumpel, M.

M. A. Ahmed, M. Rumpel, A. Voss, T. Graf, “Applications of sub-wavelength grating mirrors in high-power lasers,” Adv. Opt. Technol. 1, 381–388 (2012).

Shokooh-Saremi, M.

Tanev, S.

P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, S. Tanev, “A broad-band waveguide grating coupler with a subwavelength grating mirror,” IEEE Photon. Technol. Lett. 18(1), 13–15 (2006).
[Crossref]

Voss, A.

M. A. Ahmed, M. Rumpel, A. Voss, T. Graf, “Applications of sub-wavelength grating mirrors in high-power lasers,” Adv. Opt. Technol. 1, 381–388 (2012).

Wang, C. C.

C. C. Wang, S. D. Lin, “Resonant cavity-enhanced quantum-dot infrared photodetectors with sub-wavelength grating mirror,” J. Appl. Phys. 113(21), 213108 (2013).
[Crossref]

Wang, S. S.

Wu, H.

H. Wu, L. Huang, Y. Xiao, C. Zhang, S. Li, N. Luo, X. He, Y. Gao, “A wideband reflector realized by a subwavelength multi-subpart profile grating structure,” J. Opt. 15(3), 035703 (2013).
[Crossref]

H. Wu, J. Hou, W. Mo, D. Gao, Z. Zhou, “A multilayer-based high-performance multisubpart profile grating reflector,” IEEE Photon. Technol. Lett. 22(4), 203–205 (2010).
[Crossref]

Xiao, Y.

H. Wu, L. Huang, Y. Xiao, C. Zhang, S. Li, N. Luo, X. He, Y. Gao, “A wideband reflector realized by a subwavelength multi-subpart profile grating structure,” J. Opt. 15(3), 035703 (2013).
[Crossref]

Xu, D.-X.

P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, S. Tanev, “A broad-band waveguide grating coupler with a subwavelength grating mirror,” IEEE Photon. Technol. Lett. 18(1), 13–15 (2006).
[Crossref]

Zhang, C.

H. Wu, L. Huang, Y. Xiao, C. Zhang, S. Li, N. Luo, X. He, Y. Gao, “A wideband reflector realized by a subwavelength multi-subpart profile grating structure,” J. Opt. 15(3), 035703 (2013).
[Crossref]

Zhou, Y.

M. C. Y. Huang, Y. Zhou, C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

Zhou, Z.

H. Wu, J. Hou, W. Mo, D. Gao, Z. Zhou, “A multilayer-based high-performance multisubpart profile grating reflector,” IEEE Photon. Technol. Lett. 22(4), 203–205 (2010).
[Crossref]

Adv. Opt. Technol. (1)

M. A. Ahmed, M. Rumpel, A. Voss, T. Graf, “Applications of sub-wavelength grating mirrors in high-power lasers,” Adv. Opt. Technol. 1, 381–388 (2012).

Appl. Opt. (1)

IEEE Photon. J. (1)

K. J. Lee, R. Magnusson, “Single-layer resonant high reflector in TE polarization: Theory and experiment,” IEEE Photon. J. 3(1), 123–129 (2011).
[Crossref]

IEEE Photon. Technol. Lett. (3)

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, S. Tanev, “A broad-band waveguide grating coupler with a subwavelength grating mirror,” IEEE Photon. Technol. Lett. 18(1), 13–15 (2006).
[Crossref]

H. Wu, J. Hou, W. Mo, D. Gao, Z. Zhou, “A multilayer-based high-performance multisubpart profile grating reflector,” IEEE Photon. Technol. Lett. 22(4), 203–205 (2010).
[Crossref]

J. Appl. Phys. (1)

C. C. Wang, S. D. Lin, “Resonant cavity-enhanced quantum-dot infrared photodetectors with sub-wavelength grating mirror,” J. Appl. Phys. 113(21), 213108 (2013).
[Crossref]

J. Opt. (1)

H. Wu, L. Huang, Y. Xiao, C. Zhang, S. Li, N. Luo, X. He, Y. Gao, “A wideband reflector realized by a subwavelength multi-subpart profile grating structure,” J. Opt. 15(3), 035703 (2013).
[Crossref]

Nat. Photonics (1)

M. C. Y. Huang, Y. Zhou, C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Proc. IEEE (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985).
[Crossref]

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Figures (14)

Fig. 1
Fig. 1 Wideband reflector model denoting the period Ʌ, fill factor F, grating thicknesses dg, homogeneous layer thickness dh, and refractive indices of cover nc, silicon n, and substrate ns. The incident (I), reflected (R), and transmitted (T) light waves are indicated. The TE-polarized incident light’s electric field vector is orthogonal to the plane of incidence and along the grating ridges in this case. We set nc = 1, n = 3.56, and substrate ns = 1.5 in this paper.
Fig. 2
Fig. 2 Zero-order reflectance and transmittance spectra; (a) linear and (b) logarithmic plots for normal incidence of TE-polarized light. Device parameters are Λ = 960 nm, F = 0.5, dg = 320 nm, and dh = 55 nm.
Fig. 3
Fig. 3 Map of zero-order reflectance in wavelength and homogeneous layer thickness. The reflectance is quantified according to the scale bar on the right.
Fig. 4
Fig. 4 Zero-order reflectance (linear scale) and transmittance (log scale) spectra for (a) dh = 45 nm and (b) dh = 75 nm with Λ = 960 nm, F = 0.5, and dg = 320 nm.
Fig. 5
Fig. 5 Map of zero-order reflectance in wavelength and grating thickness. The reflectance is quantified according to the scale bar on the right.
Fig. 6
Fig. 6 Zero-order reflectance (linear scale) and transmittance (log scale) spectra for (a) dg = 290 nm and (b) dg = 350 nm with Λ = 960 nm, F = 0.5, and dh = 55 nm.
Fig. 7
Fig. 7 Map of zero-order reflectance in wavelength and fill factor. The reflectance is quantified according to the scale bar on the right.
Fig. 8
Fig. 8 Zero-order reflectance (linear scale) and transmittance (log scale) spectra for (a) F = 0.45 and (b) F = 0.55 with Λ = 960 nm, dg = 320 nm, and dh = 55 nm.
Fig. 9
Fig. 9 A schematic of the GMR reflector fabrication process.
Fig. 10
Fig. 10 AFM image and profile of the fabricated a-Si grating. The parameters are Λ = 958 nm, F = 0.5, and dg = 320 nm.
Fig. 11
Fig. 11 SEM top-view and cross-sectional images of a similar a-Si grating pattern on a glass substrate.
Fig. 12
Fig. 12 Schematic diagram of the optical measurement setup.
Fig. 13
Fig. 13 Calculated and experimental spectra associated with a resonant reflector with TE-polarized light at normal incidence. The parameters used for computation are Λ = 960 nm, F = 0.5, dg = 320 nm, dh = 55 nm, n = 3.56, nc = 1, and ns = 1.5.
Fig. 14
Fig. 14 Calculated and experimental spectra for a reflector for TE-polarized light at normal incidence. The parameters used for computation are Λ = 960 nm, F = 0.49, dg = 330 nm, dh = 45 nm, n = 3.56, nc = 1, and ns = 1.5.

Tables (1)

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Table 1 Comparison of Theoretical and Experimental Results

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