Abstract

We demonstrate unpolarized wideband reflectors fashioned with orthogonal serial resonant reflectors. Unpolarized incident light generates internal TM- and TE-polarized reflections that are made to cooperate to extend the bandwidth of the composite spectral reflectance. The experimental results presented show ~42% band extension by a two-grating module. In addition, good angular tolerance is found because the orthogonal arrangement simultaneously supports classical and fully conic mountings at oblique angles. The resulting spectra form contiguous zero-order reflectance across wide spectral/angular regions. Furthermore, using a multimodule device with serial reflectors fabricated with silicon-on-quartz wafers with different device layer thicknesses, extreme band extension is achieved providing ~56% fractional bandwidth with reflectance exceeding 98%. These results imply potential for developing lossless unpolarized mirrors operating in diverse spectral regions of practical interest.

© 2017 Optical Society of America

1. Introduction

Mirrors are among the simplest of optical component. Metallic mirrors and dielectric thin-film mirrors find numerous practical applications in everyday life and in sophisticated optical systems. Not all mirrors are created equal. The quest for perfect mirrors that are wideband, polarization independent, and omnidirectional motivates substantial R&D efforts in photonics and optical communications [1–3]. Typically, distributed Bragg reflectors (DBRs) are used for high reflectivity and wide bandwidth by alternating sequential quarter-wave layers [4,5]. Such reflectors have multiple layers that require precise parametric control attained by well-established vacuum deposition methods. To reduce layer count while maintaining polarization independence and wide bandwidths, there is interest in developing alternatives to multilayer reflectors by various means including subwavelength gratings, photonic crystal structures and metamaterials [6–8]. Particularly, utilizing periodic subwavelength gratings imbued with guide-mode resonance (GMR) effects, wideband reflectance spectra are achieved by few layers with optimal grating parameters [9].

Two-dimensional (2D) spatial periodicity may be employed to obtain polarization-insensitive GMR reflectors owing to 90° rotational symmetry at normal incidence [10]. However, there is a bandwidth limitation associated with 2D GMR reflectors due to formation of intrinsic low-reflectance spectral loci where TM and TE leaky modes coexist [11]. To design a polarization independent reflector with 1D gratings, Zhao et al. theoretically investigated two cross-stacked 1D gratings exhibiting high reflection in the 1.4-1.6 µm band [3]. However, this embodiment is challenging in practical fabrication. Capitalizing on the wideband TM response of 1D resonant gratings, we decoupled two serial reflectors with orthogonal periodicities thus achieving unpolarized reflection with 44% fractional bandwidth [12]. The fabrication is straightforward [12]. Additionally, with proper design, the combination of TM and TE resonant reflections extends the bandwidth.

In this paper, we present analysis and experiments pertinent to multimodule serial reflectors with emphasis on attaining high unpolarized reflectance across wide bands. A formula for the spectral reflectance of a composite reflector based on the numerical reflectance R(λ) for a single reflector is provided. A single module with two GMR gratings is designed, fabricated, and tested with experimental spectra agreeing well with the reflectance formula. We show that the serial structure exhibits favorable angular tolerance by supporting classical and fully conic mountings simultaneously at oblique angles. Finally, we demonstrate a multimodule device that covers contiguous spectral domains enabling an efficient wideband reflector. Our design and experimental results will be useful for understanding and improving the performance of this class of resonant reflectors.

2. Serial 1D-grating model

Figure 1(a) illustrates the serial reflector concept treated here. Unlike previous design [12], this serial reflector is assembled by two inner-faced 1D gratings that is beneficial for packaging and protection from outer environment. The detail is discussed in Section 3. We use Si (nSi = 3.48) on a quartz (nquartz = 1.51) substrate and fashion constituent gratings of the zero-contrast variety (i.e., zero-contrast grating, ZCG) to have wideband reflection and robust design relative to fabrication variations [9,13]. Applying rigorous coupled-wave analysis (RCWA) [14], the TM and TE zero-order reflectance (R0) spectra are characterized for specific grating parameters namely the grating period (Λ), fill factor (F), grating depth (dg), and thickness of the homogeneous sublayer (dh). To obtain a polarization-independent reflector, two identical 1D GMR gratings are orthogonally faced with an air gap with subsequent TM and TE internal reflections for unpolarized incidence. Figure 1(b) explains the external reflections in the serial device when TM (left) and TE (right) polarized light propagates through the orthogonal gratings. Here, we define the TM and TE reflectance (RTM and RTE) having light polarized perpendicular and parallel to grooves. In case of TM polarized input, the external reflectance includes the primary RTM from the top grating as well as multiple reflectances arising from light transmitted into the cavity and bouncing around. For example, the secondary reflectance should be RTE(1- RTM)2 by transmitting twice through the top grating generating (1- RTM)2 and one reflection of the bottom grating with RTE. For TE-polarized input, the external reflectance can be found similarly; essentially TE and TM are exchanged.

 figure: Fig. 1

Fig. 1 (a) Schematic of serial 1D gratings where the parameters include the period (Λ), fill factor (F), grating depth (dg), and thickness of the homogeneous sublayer (dh). (b) Illustration of the external reflection processes in under TM (left) and TE (right) polarization.

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Assuming that unpolarized light is equivalent to the average of TM and TE inputs, we thus estimate total reflectance (Rtotal) by a simple formula:

Rtotal=12{RTM+RTE+[RTE(1RTM)2+RTM(1RTE)2]n=0(RTMRTE)n}
leading to
=12{RTM+RTE+RTE(1RTM)2+RTM(1RTE)21RTMRTE},
where RTM and RTE are obtained by numerical computations for a single GMR grating. Approximately, in Eq. (1), we neglect Fabry-Perot interference in the cavity between the gratings because the round-trip phase is generally not controllable on mechanical assembly of the device. As shown in Fig. 2, the Rtotal spectrum calculated for this serial device {Λ = 640 nm, F = 0.55, dh = 170 nm, dg = 350 nm} using Si-on-quartz (SOQ-520 denoting a device layer thickness of 520 nm) exhibits a spectrum without Fabry-Perot resonance which is similar to measured spectra in our assembled devices. For perfectly parallel gratings, the RCWA calculated R0 spectra are presented with varying air-gap distances of d = 5, 50, and 500 µm. As d increases, multiple Fabry-Perot resonances are distributed densely due to a decreased free spectral range. In comparison, the approximate numerical results using Eq. (2) are near the averaged R0 spectra for the case of d = 500 µm.

 figure: Fig. 2

Fig. 2 Computed spectra pertinent to a two-grating module. The parameters are Λ = 640 nm, F = 0.55, dh = 170 nm, and dg = 350 nm. For comparison, the R0 spectra are calculated by RCWA. Here, d is the air gap distance between the two gratings as depicted in the inset. It is seen that the value of d does not significantly affect the spectrum at the high reflection band.

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Figure 3 shows calculated results with varying dg = (a) 420, (b) 410, (c) 400, and (d) 390 nm using Eq. (2). To achieve wideband reflection encompassing the telecom optical wavelength bands (1260-1625 nm), the grating parameter set {Λ = 640 nm, F = 0.55, dg + dh = 520 nm} is chosen. For practical fabrication, we consider the SOQ platform with 520 nm device layer (SOQ-520). For the single 1D GMR reflector at dg = 420 nm, in Fig. 3(a), high RTM is widely distributed from the O-band to the S-band while high RTE remains in the S-band partially. With two identical gratings, the serial device provides wideband unpolarized reflection (bandwidth, BW = 318 nm for R0>0.95) in these bands. As dg decreases, in Figs. 3(b)-3(d), the high RTM band moves to shorter wavelengths while the high RTE band shifts oppositely. Therefore, the two polarized reflection bands shift to extend the unpolarized band. However, a dip in reflectance forms at the junction dropping lower with increased spacing as seen in the figures. With dg between 390 and 400 nm, the module maintains unpolarized high reflectance over the telecom bands. Comparing to the RCWA result (a dense gray spectrum) in Fig. 3(d), it is seen that the simplified numerical model yielding Eq. (2) (black curve) provides a good approximation.

 figure: Fig. 3

Fig. 3 Numerical R0 spectra for a two-grating module with dg = (a) 420, (b) 410, (c) 400, and (d) 390 nm where the grating parameters are Λ = 640 nm, F = 0.55, and dg + dh = 520 nm. The black curves represent the approximation in Eq. (2) for unpolarized input light. The gray dense curve in (d) is the rigorously calculated R0 spectrum for the serial reflector.

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3. Fabrication and packaging

The zero-contrast gratings reported here are fabricated with laser interference lithography. After spin coating a SOQ substrate, we expose the photoresist (SEPR-701) with laser interference fringes (λ = 266 nm) and form photoresist (PR) etch-mask patterns by chemical development. Then, we dry etch the Si layer by reactive-ion etching within an SF6 + CF4 ambient. The residual resist is removed by O2 ashing and PR stripper. With two identical 1D grating reflectors and thin polydimethylsiloxane (PDMS) frame (thickness ~1 mm) as a spacer, we package the serial device as displayed in Fig. 4(a). Due to van der Waals attractive interaction between the PDMS and Si surfaces [15], the two grating reflectors with orthogonal arrangement of grooves adhere to the PDMS spacer. For sealing, we use UV-cured optical adhesives. Therefore, the subwavelength gratings are embedded by the rigid quartz flat cover protecting the gratings against environmental contamination such as water molecules and dust. Figure 4(b) shows photographic images of the packaged serial device. Owing to semi-transparency of the SOQ substrate, we can see the rectangular grating cells in the center. The spectral response is characterized with a fiber optic spectrometer with a super-continuum light source and spectrum analyzer. Under visible light illumination, in the picture shown as Fig. 4(b), orthogonal diffraction spectra are observable.

 figure: Fig. 4

Fig. 4 (a) Schematic illustration indicating packing of serial 1D gratings to form a module and (b) photographs of a mounted module.

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4. Measurement results and discussion

We characterize the reflectance spectra by approximating R0 = 1–T0 since the device is composed of crystalline Si with a low extinction coefficient <10−6 [16] and the subwavelength grating is scatter-free. Figure 5(a) displays SEM images of the fabricated grating with SOQ substrate. As seen in cross-sectional view in the SEM image, the partially etched Si forms zero-contrast grating ridges to the homogenous sublayer of the same material [9]. From the SEM images, the experimental grating parameters are estimated as Λ = 632 nm, F = 0.57, dg = 395 nm, and dh = 125 nm. Comparing Figs. 5(b) and 5(c), the measured and calculated results match Eq. (2) well. The single GMR grating exhibits TM reflectance R0>95% in the spectral range of 1205-1501 nm (BW = 296 nm). Meanwhile, under unpolarized light, the fabricated device exhibits a high-reflection band with R0>95% over 1203-1625 nm (BW = 422 nm). Thus, the serial arrangement extends the bandwidth of a component 1D grating by ~42%. Consequently, polarization independent wideband resonant reflectors operating over all the telecom optical bands simultaneously are possible.

 figure: Fig. 5

Fig. 5 (a) SEM top and cross-sectional views of the Si grating on a quartz substrate. (b) Calculated and (c) measured R0 spectra of single (TE and TM polarized) and serial reflectors (unpolarized).

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We now address the angular tolerance of these devices. In Fig. 6(a) the plane of incidence (POI) includes the classical and fully conic mountings simultaneously at oblique angles where the POI is perpendicular (in classical mounting) or parallel (in fully conical mounting) to the grating grooves. Previously, we reported wideband 1D reflectors in these mountings [17]. In summary, in classical mounting, the reflection band spreads out with attendant band splitting as the incidence angle increases. Full conical incidence shows less spread and maintains a high reflection band under higher incident angles. These different angular properties appear together in the serial device. Figure 6(b) shows the measured R0 map as a function of the incident angle (θ) from 0° to 15° under unpolarized light illumination. Up to θ = 7°, the serial device maintains a wide bandwidth (BW = 430 nm, 1200-1630 nm) for R0>95%. Especially, in the range of 3.5°≤θ≤5.2°, high reflectance exceeding 97% distributes broadly from 1210 to 1620 nm (BW = 410 nm). It is notable that simultaneous incidence in both mountings as inherent in these reflector modules leads a good angular tolerance.

 figure: Fig. 6

Fig. 6 (a) Simultaneous incidence in classical and fully conic mountings and (b) a measured color-coded R0 map as a function of the angle of incidence (θ) under unpolarized light illumination for the device in Fig. 5.

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To understand how the orthogonally polarized spectra superimpose, in Fig. 7 we present R0(λ,θ) maps for a single grating under TM or TE polarization in classical or fully conic mounting as delineated therein. As the incident angle increases, in classic TM incidence in Fig. 7(a), the reflection band spreads and splits into three bands. Under fully conic mounting in Fig. 7(b), high reflectance R0>97% remains contiguous for wavelengths 1215-1400 nm compensating the degraded R0 in classical mounting under TM polarization. Additionally, in TE polarization in both mounting of Figs. 7(c) and 7(d), high reflection bands (i.e., R0>97%) appear where the TM reflectance falls, thus extending the total external reflectance of the serial device. Interestingly, in Fig. 7(c), the narrow reflection band in the 1460-1480 nm at higher incident angle partially fills up dips of the TM (R0<97%) reflectance of both the classical and fully conic mountings in Figs. 7(a) and 7(b).

 figure: Fig. 7

Fig. 7 Measured R0 maps of a single 1D resonant reflector under (a) TM at classical incidence, (b) TM at fully conic incidence, (c) TE at classical and (d) fully conic mounting.

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Now, we consider the feasibility of further band extension by additional modules. We design a dual-grating reflector of the type discussed above but operating in an adjacent spectral region. We fashion 1D ZCGs with a thicker device layer (900 nm) using an SOQ-900 wafer. The design parameter set is {Λ = 780 nm, F = 0.56, dg = 540 nm, dh = 360 nm} with the corresponding experimental set being {Λ = 783 nm, F = 0.59, dg = 527 nm, dh = 374 nm}. Figure 8(a) shows simulated and calculated R0 spectra for this device under unpolarized incidence. The measured spectra match computed results found using Eq. (2) well. From 1568 nm to 2122 nm, we measure unpolarized reflectance with R0>97% bandwidth of 554 nm. To estimate the total band of the concatenated SOQ-520 and SOQ-900 modules illustrated in Fig. 8(b), we approximate total reflectance as

Rtot={R1+R2(1R1)2/1R1R2}
where R1 and R2 are unpolarized reflectances of the modules as noted in the figure. This expression is deduced in the same way as Eqs. (1) and (2) above. Figure 8(c) displays theoretical and experimental multimodule spectra at normal incidence. The measured spectrum exhibits R0>98% spanning 1200-2133 nm yielding BW = 933 nm corresponding to ~56% fractional bandwidth.

 figure: Fig. 8

Fig. 8 Unpolarized spectra of a multimodule reflector prototype under normal incidence. (a) Spectrum of a component SOQ-900 module. (b) Embodiment and modeling of the multimodule device. (c) Spectra pertaining to the multimodule reflector.

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5. Conclusions

In this paper, we demonstrate unpolarized wideband reflectors designed and fabricated with orthogonal serial resonant reflectors. By arranging two identical 1D gratings with orthogonal periodicities, the unpolarized reflection band exceeds those of the individual TM and TE bands. For practical fabrication, we design Si-based 1D ZCG on SOQ platform using RCWA calculations and modeling of the multiple reflections in the serial architecture. As a result, under unpolarized light, the packaged serial device provides a high reflectance R0>95% covering a wide spectral band of 1203-1625 nm (BW = 422 nm) that is a 42.4% extension relative to the single 1D grating. Furthermore, the device possesses good angular tolerance because the orthogonal design includes classical and fully conic mountings simultaneously at oblique incident angles, which compensates for low reflection bands between both mountings. The resulting contiguous bands for up to θ = 7° exhibit high reflectance with R0>95% and bandwidth of 430 nm. The measurement results in the respective angle-dependent R0 map of the single device confirm the reflection compensation in the corresponding spectral regions. Using the multimodule device with different serial reflectors, we extend the band of unpolarized high reflectance R0>98% achieving a 56% fractional bandwidth. This concept can be extended to additional serial reflectors across multiple reflection bands. Consequently, all design wavelengths can be reflected with high efficiency by a multi-element GMR reflector. The design and packaging presented in this paper will be useful for various optical applications requiring wideband and efficient unpolarized reflectors.

6 Appendix

To explain the band extension with the formula of Eq. (2), we calculate the total reflectance spectra considering two polarized reflectance spectra. Each flattop curve for RTM and RTE is expressed by a 3rd order Gaussian function as approximated modeling

RTM(λ)=exp(((λλTM)22σTM2)3)andRTE(λ)=exp(((λλTE)22σTE2)3)
where the λTM, λTE are center wavelength positions, and the σTM, σTE are width-control factors. For a single 1D resonant reflector, usually each TM and TE stop band is localized in a different spectral region [12]. Figure 9(a) shows an example for the band extension with separated RTM and RTE bands that are expressed by Eq. (4)TM = 1500 nm, λTE = 1600 nm, σTM = 80 nm, σTE = 20 nm}. When there is a separation between two bands, the high reflectance of Rtotal will encompass both RTM and RTE bands but a reflectance depression forms at the cross point. The level of the depression affects the value of the final reflectance of the composite band. Figure 9(b) shows a color map for calculated Rtotal with different separation between RTM and RTE bands. As the separation is larger, the high reflectance band is extended but with a deeper interceding valley. To obtain wideband reflection with Rtotal > 95% we can control the optimal separation by proper choice of the grating parameters such as grating depth and homogenous layer thickness.

 figure: Fig. 9

Fig. 9 (a) Calculated the Rtotal spectrum considering two different RTM and RTE spectra where these polarized reflectances are numerically expressed by a 3rd order Gaussian function. The parameters are λTM = 1500 nm, λTE = 1600 nm, σTM = 80 nm, and σTE = 20 nm. To show a separation between the bands, we select a 100-nm difference of the center wavelengths (λTE - λTE). (b) A color map of the calculated Rtotal as function of the separation between the polarized reflectance bands.

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Funding

National Science Foundation (NSF) award no. IIP-1444922.

Acknowledgment

The authors thank Shin-Etsu Chemical Co, Ltd., Japan, for providing the SOQ wafers used in the experiments.

References and links

1. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998). [CrossRef]   [PubMed]  

2. T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nat. Photonics 6(11), 759–763 (2012). [CrossRef]   [PubMed]  

3. D. Zhao, H. Yang, Z. Ma, and W. Zhou, “Polarization independent broadband reflectors based on cross-stacked gratings,” Opt. Express 19(10), 9050–9055 (2011). [CrossRef]   [PubMed]  

4. A. F. Turner and P. W. Baumeister, “Multilayer mirrors with high reflectance over an extended spectral region,” Appl. Opt. 5(1), 69–76 (1966). [CrossRef]   [PubMed]  

5. M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, “Wide-bandwidth distributed Bragg reflectors using oxide/GaAs multilayers,” Electron. Lett. 30(14), 1147–1149 (1994). [CrossRef]  

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

7. V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12(8), 1575–1582 (2004). [CrossRef]   [PubMed]  

8. P. Moitra, B. A. Slovick, Z. G. Yu, S. Krishnamurthy, and J. Valentine, “Experimental demonstration of a broadband all-dielectric metamaterial perfect reflector,” Appl. Phys. Lett. 104(17), 171102 (2014). [CrossRef]  

9. R. Magnusson, “Wideband reflectors with zero-contrast gratings,” Opt. Lett. 39(15), 4337–4340 (2014). [CrossRef]   [PubMed]  

10. M. Shokooh-Saremi and R. Magnusson, “Properties of two-dimensional resonant reflectors with zero-contrast gratings,” Opt. Lett. 39(24), 6958–6961 (2014). [CrossRef]   [PubMed]  

11. Y. H. Ko, M. Shokooh-Saremi, and R. Magnusson, “Modal processes in two-dimensional resonant reflectors and their correlation with spectra of one-dimensional equivalents,” IEEE Photonics J. 7(5), 4900210 (2015). [CrossRef]  

12. M. Niraula and R. Magnusson, “Unpolarized resonance grating reflectors with 44% fractional bandwidth,” Opt. Lett. 41(11), 2482–2485 (2016). [CrossRef]   [PubMed]  

13. R. Magnusson, M. Niraula, J. W. Yoon, Y. H. Ko, and K. J. Lee, Guided-mode resonance nanophotonics in materially sparse architectures,” Proc. SPIE 9757, 975705 (2016). [CrossRef]  

14. M. G. Moharam, “Rigorous coupled-wave analysis of planar-grating diffraction,” Proc. SPIE 883, 8–11 (1988). [CrossRef]  

15. Y. Y. Huang, W. Zhou, K. J. Hsia, E. Menard, J.-U. Park, J. A. Rogers, and A. G. Alleyne, “Stamp collapse in soft lithography,” Langmuir 21(17), 8058–8068 (2005). [CrossRef]   [PubMed]  

16. M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008). [CrossRef]  

17. Y. H. Ko, M. Niraula, K. J. Lee, and R. Magnusson, “Properties of wideband resonant reflectors under fully conical light incidence,” Opt. Express 24(5), 4542–4551 (2016). [CrossRef]  

References

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  1. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
    [Crossref] [PubMed]
  2. T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nat. Photonics 6(11), 759–763 (2012).
    [Crossref] [PubMed]
  3. D. Zhao, H. Yang, Z. Ma, and W. Zhou, “Polarization independent broadband reflectors based on cross-stacked gratings,” Opt. Express 19(10), 9050–9055 (2011).
    [Crossref] [PubMed]
  4. A. F. Turner and P. W. Baumeister, “Multilayer mirrors with high reflectance over an extended spectral region,” Appl. Opt. 5(1), 69–76 (1966).
    [Crossref] [PubMed]
  5. M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, “Wide-bandwidth distributed Bragg reflectors using oxide/GaAs multilayers,” Electron. Lett. 30(14), 1147–1149 (1994).
    [Crossref]
  6. R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008).
    [Crossref] [PubMed]
  7. V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12(8), 1575–1582 (2004).
    [Crossref] [PubMed]
  8. P. Moitra, B. A. Slovick, Z. G. Yu, S. Krishnamurthy, and J. Valentine, “Experimental demonstration of a broadband all-dielectric metamaterial perfect reflector,” Appl. Phys. Lett. 104(17), 171102 (2014).
    [Crossref]
  9. R. Magnusson, “Wideband reflectors with zero-contrast gratings,” Opt. Lett. 39(15), 4337–4340 (2014).
    [Crossref] [PubMed]
  10. M. Shokooh-Saremi and R. Magnusson, “Properties of two-dimensional resonant reflectors with zero-contrast gratings,” Opt. Lett. 39(24), 6958–6961 (2014).
    [Crossref] [PubMed]
  11. Y. H. Ko, M. Shokooh-Saremi, and R. Magnusson, “Modal processes in two-dimensional resonant reflectors and their correlation with spectra of one-dimensional equivalents,” IEEE Photonics J. 7(5), 4900210 (2015).
    [Crossref]
  12. M. Niraula and R. Magnusson, “Unpolarized resonance grating reflectors with 44% fractional bandwidth,” Opt. Lett. 41(11), 2482–2485 (2016).
    [Crossref] [PubMed]
  13. R. Magnusson, M. Niraula, J. W. Yoon, Y. H. Ko, and K. J. Lee, Guided-mode resonance nanophotonics in materially sparse architectures,” Proc. SPIE 9757, 975705 (2016).
    [Crossref]
  14. M. G. Moharam, “Rigorous coupled-wave analysis of planar-grating diffraction,” Proc. SPIE 883, 8–11 (1988).
    [Crossref]
  15. Y. Y. Huang, W. Zhou, K. J. Hsia, E. Menard, J.-U. Park, J. A. Rogers, and A. G. Alleyne, “Stamp collapse in soft lithography,” Langmuir 21(17), 8058–8068 (2005).
    [Crossref] [PubMed]
  16. M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
    [Crossref]
  17. Y. H. Ko, M. Niraula, K. J. Lee, and R. Magnusson, “Properties of wideband resonant reflectors under fully conical light incidence,” Opt. Express 24(5), 4542–4551 (2016).
    [Crossref]

2016 (3)

2015 (1)

Y. H. Ko, M. Shokooh-Saremi, and R. Magnusson, “Modal processes in two-dimensional resonant reflectors and their correlation with spectra of one-dimensional equivalents,” IEEE Photonics J. 7(5), 4900210 (2015).
[Crossref]

2014 (3)

P. Moitra, B. A. Slovick, Z. G. Yu, S. Krishnamurthy, and J. Valentine, “Experimental demonstration of a broadband all-dielectric metamaterial perfect reflector,” Appl. Phys. Lett. 104(17), 171102 (2014).
[Crossref]

R. Magnusson, “Wideband reflectors with zero-contrast gratings,” Opt. Lett. 39(15), 4337–4340 (2014).
[Crossref] [PubMed]

M. Shokooh-Saremi and R. Magnusson, “Properties of two-dimensional resonant reflectors with zero-contrast gratings,” Opt. Lett. 39(24), 6958–6961 (2014).
[Crossref] [PubMed]

2012 (1)

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nat. Photonics 6(11), 759–763 (2012).
[Crossref] [PubMed]

2011 (1)

2008 (2)

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

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

2005 (1)

Y. Y. Huang, W. Zhou, K. J. Hsia, E. Menard, J.-U. Park, J. A. Rogers, and A. G. Alleyne, “Stamp collapse in soft lithography,” Langmuir 21(17), 8058–8068 (2005).
[Crossref] [PubMed]

2004 (1)

1998 (1)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

1994 (1)

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, “Wide-bandwidth distributed Bragg reflectors using oxide/GaAs multilayers,” Electron. Lett. 30(14), 1147–1149 (1994).
[Crossref]

1988 (1)

M. G. Moharam, “Rigorous coupled-wave analysis of planar-grating diffraction,” Proc. SPIE 883, 8–11 (1988).
[Crossref]

1966 (1)

Alleyne, A. G.

Y. Y. Huang, W. Zhou, K. J. Hsia, E. Menard, J.-U. Park, J. A. Rogers, and A. G. Alleyne, “Stamp collapse in soft lithography,” Langmuir 21(17), 8058–8068 (2005).
[Crossref] [PubMed]

Baumeister, P. W.

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Dapkus, P. D.

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, “Wide-bandwidth distributed Bragg reflectors using oxide/GaAs multilayers,” Electron. Lett. 30(14), 1147–1149 (1994).
[Crossref]

Fan, S.

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12(8), 1575–1582 (2004).
[Crossref] [PubMed]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Fink, Y.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Green, M. A.

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

Hsia, K. J.

Y. Y. Huang, W. Zhou, K. J. Hsia, E. Menard, J.-U. Park, J. A. Rogers, and A. G. Alleyne, “Stamp collapse in soft lithography,” Langmuir 21(17), 8058–8068 (2005).
[Crossref] [PubMed]

Huang, Y. Y.

Y. Y. Huang, W. Zhou, K. J. Hsia, E. Menard, J.-U. Park, J. A. Rogers, and A. G. Alleyne, “Stamp collapse in soft lithography,” Langmuir 21(17), 8058–8068 (2005).
[Crossref] [PubMed]

Joannopoulos, J. D.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Jordan, T. M.

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nat. Photonics 6(11), 759–763 (2012).
[Crossref] [PubMed]

Kilic, O.

Kim, S.

Ko, Y. H.

Y. H. Ko, M. Niraula, K. J. Lee, and R. Magnusson, “Properties of wideband resonant reflectors under fully conical light incidence,” Opt. Express 24(5), 4542–4551 (2016).
[Crossref]

R. Magnusson, M. Niraula, J. W. Yoon, Y. H. Ko, and K. J. Lee, Guided-mode resonance nanophotonics in materially sparse architectures,” Proc. SPIE 9757, 975705 (2016).
[Crossref]

Y. H. Ko, M. Shokooh-Saremi, and R. Magnusson, “Modal processes in two-dimensional resonant reflectors and their correlation with spectra of one-dimensional equivalents,” IEEE Photonics J. 7(5), 4900210 (2015).
[Crossref]

Krishnamurthy, S.

P. Moitra, B. A. Slovick, Z. G. Yu, S. Krishnamurthy, and J. Valentine, “Experimental demonstration of a broadband all-dielectric metamaterial perfect reflector,” Appl. Phys. Lett. 104(17), 171102 (2014).
[Crossref]

Lee, K. J.

R. Magnusson, M. Niraula, J. W. Yoon, Y. H. Ko, and K. J. Lee, Guided-mode resonance nanophotonics in materially sparse architectures,” Proc. SPIE 9757, 975705 (2016).
[Crossref]

Y. H. Ko, M. Niraula, K. J. Lee, and R. Magnusson, “Properties of wideband resonant reflectors under fully conical light incidence,” Opt. Express 24(5), 4542–4551 (2016).
[Crossref]

Lousse, V.

Ma, Z.

MacDougal, M. H.

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, “Wide-bandwidth distributed Bragg reflectors using oxide/GaAs multilayers,” Electron. Lett. 30(14), 1147–1149 (1994).
[Crossref]

Magnusson, R.

Menard, E.

Y. Y. Huang, W. Zhou, K. J. Hsia, E. Menard, J.-U. Park, J. A. Rogers, and A. G. Alleyne, “Stamp collapse in soft lithography,” Langmuir 21(17), 8058–8068 (2005).
[Crossref] [PubMed]

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Moharam, M. G.

M. G. Moharam, “Rigorous coupled-wave analysis of planar-grating diffraction,” Proc. SPIE 883, 8–11 (1988).
[Crossref]

Moitra, P.

P. Moitra, B. A. Slovick, Z. G. Yu, S. Krishnamurthy, and J. Valentine, “Experimental demonstration of a broadband all-dielectric metamaterial perfect reflector,” Appl. Phys. Lett. 104(17), 171102 (2014).
[Crossref]

Niraula, M.

Park, J.-U.

Y. Y. Huang, W. Zhou, K. J. Hsia, E. Menard, J.-U. Park, J. A. Rogers, and A. G. Alleyne, “Stamp collapse in soft lithography,” Langmuir 21(17), 8058–8068 (2005).
[Crossref] [PubMed]

Partridge, J. C.

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nat. Photonics 6(11), 759–763 (2012).
[Crossref] [PubMed]

Roberts, N. W.

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nat. Photonics 6(11), 759–763 (2012).
[Crossref] [PubMed]

Rogers, J. A.

Y. Y. Huang, W. Zhou, K. J. Hsia, E. Menard, J.-U. Park, J. A. Rogers, and A. G. Alleyne, “Stamp collapse in soft lithography,” Langmuir 21(17), 8058–8068 (2005).
[Crossref] [PubMed]

Shokooh-Saremi, M.

Slovick, B. A.

P. Moitra, B. A. Slovick, Z. G. Yu, S. Krishnamurthy, and J. Valentine, “Experimental demonstration of a broadband all-dielectric metamaterial perfect reflector,” Appl. Phys. Lett. 104(17), 171102 (2014).
[Crossref]

Solgaard, O.

Steier, W. H.

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, “Wide-bandwidth distributed Bragg reflectors using oxide/GaAs multilayers,” Electron. Lett. 30(14), 1147–1149 (1994).
[Crossref]

Suh, W.

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Turner, A. F.

Valentine, J.

P. Moitra, B. A. Slovick, Z. G. Yu, S. Krishnamurthy, and J. Valentine, “Experimental demonstration of a broadband all-dielectric metamaterial perfect reflector,” Appl. Phys. Lett. 104(17), 171102 (2014).
[Crossref]

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Yang, H.

Yoon, J. W.

R. Magnusson, M. Niraula, J. W. Yoon, Y. H. Ko, and K. J. Lee, Guided-mode resonance nanophotonics in materially sparse architectures,” Proc. SPIE 9757, 975705 (2016).
[Crossref]

Yu, Z. G.

P. Moitra, B. A. Slovick, Z. G. Yu, S. Krishnamurthy, and J. Valentine, “Experimental demonstration of a broadband all-dielectric metamaterial perfect reflector,” Appl. Phys. Lett. 104(17), 171102 (2014).
[Crossref]

Zhao, D.

Zhao, H.

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, “Wide-bandwidth distributed Bragg reflectors using oxide/GaAs multilayers,” Electron. Lett. 30(14), 1147–1149 (1994).
[Crossref]

Zhou, W.

D. Zhao, H. Yang, Z. Ma, and W. Zhou, “Polarization independent broadband reflectors based on cross-stacked gratings,” Opt. Express 19(10), 9050–9055 (2011).
[Crossref] [PubMed]

Y. Y. Huang, W. Zhou, K. J. Hsia, E. Menard, J.-U. Park, J. A. Rogers, and A. G. Alleyne, “Stamp collapse in soft lithography,” Langmuir 21(17), 8058–8068 (2005).
[Crossref] [PubMed]

Ziari, M.

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, “Wide-bandwidth distributed Bragg reflectors using oxide/GaAs multilayers,” Electron. Lett. 30(14), 1147–1149 (1994).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. Moitra, B. A. Slovick, Z. G. Yu, S. Krishnamurthy, and J. Valentine, “Experimental demonstration of a broadband all-dielectric metamaterial perfect reflector,” Appl. Phys. Lett. 104(17), 171102 (2014).
[Crossref]

Electron. Lett. (1)

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, “Wide-bandwidth distributed Bragg reflectors using oxide/GaAs multilayers,” Electron. Lett. 30(14), 1147–1149 (1994).
[Crossref]

IEEE Photonics J. (1)

Y. H. Ko, M. Shokooh-Saremi, and R. Magnusson, “Modal processes in two-dimensional resonant reflectors and their correlation with spectra of one-dimensional equivalents,” IEEE Photonics J. 7(5), 4900210 (2015).
[Crossref]

Langmuir (1)

Y. Y. Huang, W. Zhou, K. J. Hsia, E. Menard, J.-U. Park, J. A. Rogers, and A. G. Alleyne, “Stamp collapse in soft lithography,” Langmuir 21(17), 8058–8068 (2005).
[Crossref] [PubMed]

Nat. Photonics (1)

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nat. Photonics 6(11), 759–763 (2012).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (3)

Proc. SPIE (2)

R. Magnusson, M. Niraula, J. W. Yoon, Y. H. Ko, and K. J. Lee, Guided-mode resonance nanophotonics in materially sparse architectures,” Proc. SPIE 9757, 975705 (2016).
[Crossref]

M. G. Moharam, “Rigorous coupled-wave analysis of planar-grating diffraction,” Proc. SPIE 883, 8–11 (1988).
[Crossref]

Science (1)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Sol. Energy Mater. Sol. Cells (1)

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 (a) Schematic of serial 1D gratings where the parameters include the period (Λ), fill factor (F), grating depth (dg), and thickness of the homogeneous sublayer (dh). (b) Illustration of the external reflection processes in under TM (left) and TE (right) polarization.
Fig. 2
Fig. 2 Computed spectra pertinent to a two-grating module. The parameters are Λ = 640 nm, F = 0.55, dh = 170 nm, and dg = 350 nm. For comparison, the R0 spectra are calculated by RCWA. Here, d is the air gap distance between the two gratings as depicted in the inset. It is seen that the value of d does not significantly affect the spectrum at the high reflection band.
Fig. 3
Fig. 3 Numerical R0 spectra for a two-grating module with dg = (a) 420, (b) 410, (c) 400, and (d) 390 nm where the grating parameters are Λ = 640 nm, F = 0.55, and dg + dh = 520 nm. The black curves represent the approximation in Eq. (2) for unpolarized input light. The gray dense curve in (d) is the rigorously calculated R0 spectrum for the serial reflector.
Fig. 4
Fig. 4 (a) Schematic illustration indicating packing of serial 1D gratings to form a module and (b) photographs of a mounted module.
Fig. 5
Fig. 5 (a) SEM top and cross-sectional views of the Si grating on a quartz substrate. (b) Calculated and (c) measured R0 spectra of single (TE and TM polarized) and serial reflectors (unpolarized).
Fig. 6
Fig. 6 (a) Simultaneous incidence in classical and fully conic mountings and (b) a measured color-coded R0 map as a function of the angle of incidence (θ) under unpolarized light illumination for the device in Fig. 5.
Fig. 7
Fig. 7 Measured R0 maps of a single 1D resonant reflector under (a) TM at classical incidence, (b) TM at fully conic incidence, (c) TE at classical and (d) fully conic mounting.
Fig. 8
Fig. 8 Unpolarized spectra of a multimodule reflector prototype under normal incidence. (a) Spectrum of a component SOQ-900 module. (b) Embodiment and modeling of the multimodule device. (c) Spectra pertaining to the multimodule reflector.
Fig. 9
Fig. 9 (a) Calculated the Rtotal spectrum considering two different RTM and RTE spectra where these polarized reflectances are numerically expressed by a 3rd order Gaussian function. The parameters are λTM = 1500 nm, λTE = 1600 nm, σTM = 80 nm, and σTE = 20 nm. To show a separation between the bands, we select a 100-nm difference of the center wavelengths (λTE - λTE). (b) A color map of the calculated Rtotal as function of the separation between the polarized reflectance bands.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

R total = 1 2 { R TM + R TE +[ R TE ( 1 R TM ) 2 + R TM ( 1 R TE ) 2 ] n=0 ( R TM R TE ) n }
= 1 2 { R TM + R TE + R TE ( 1 R TM ) 2 + R TM ( 1 R TE ) 2 1 R TM R TE },
R tot ={ R 1 + R 2 ( 1 R 1 ) 2 / 1 R 1 R 2 }
R TM ( λ )=exp ( ( ( λ λ TM ) 2 2 σ TM 2 ) 3 ) an d R TE ( λ )=exp( ( ( λ λ TE ) 2 2 σ TE 2 ) 3 )

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