Abstract

We present the design, fabrication, and characterization of guided-mode resonance (GMR) linear polarizers that operate in the optical communications C-band near a wavelength of 1550 nm. We provide theoretical and experimental spectra using resonant elements fashioned in three material systems. In particular, we investigate silicon nitride resonant gratings and titanium dioxide gratings on glass substrates as well as silicon-on-quartz gratings. These materials exhibit very low losses and are capable of high diffraction efficiencies and extinction ratios; thus, high-power laser applications may be enabled. We present the methods applied to fabricate these GMR devices as well as means to ascertain their fabricated physical parameters. We quantify increased polarizer bandwidth with increased grating refractive-index modulation. The numerical results obtained with the fabricated-device parameters agree well with the experimental measured spectra.

© 2014 Optical Society of America

1. Introduction

Polarizers are important components for many engineered optical systems. They can filter light with random polarization components to a state of desired polarization. The wire-grid polarizer (WGP) is based on the one-dimensional subwavelength grating and has been of wide interest as reported during the past several decades due to its compact size and integration capability [15]. However, because WGPs comprise metals, they are absorptive and can only be used in low-power applications. For high-power applications with lossy device materials, optical absorption causes the material’s temperature to increase and thermal damage can occur. This increase in temperature also changes the material’s refractive index [6,7], which may change the functionality of the device. Therefore, lossless materials are preferred in high-power applications. Multilayer, all-dielectric polarizers are widely used in optics and can be fabricated using thin-film technology; however, these dielectric multilayer polarizers work only under oblique incidence [8].

In this paper, we report new types of polarizers that employ nanophotonic resonance effects, which enable the polarizers to operate at arbitrary input angles and, notably, at normal incidence. We utilize quasi-guided, or leaky, waveguide modes arising on subwavelength periodic films. The attendant guided-mode resonance (GMR) occurs as the input light couples to leaky eigenmodes [9,10]. GMR devices are advantageous because they are relatively simple and applicable for fabrication using low-loss materials. Previously, we reported GMR polarizers consisting of an amorphous silicon (a-Si) 1-D grating on a glass substrate [11,12]. At a wavelength of 1550 nm, a-Si has an extinction coefficient of ~10−2 [13], which is relatively high compared to typical dielectric materials. Nevertheless, successful polarizers are achievable in this medium.

Here, we present GMR polarizers operating at normal incidence based on nearly lossless dielectric materials such as silicon nitride (Si3N4) and titanium dioxide (TiO2). In addition, we demonstrate the bandwidth dependency of GMR polarizers on the refractive indices of the device materials with three different values. To realize a wide-bandwidth polarizer, we apply a silicon thin film, which has a high refractive index and relatively low loss at a wavelength of ~1550 nm.

2. Design of GMR polarizers

To find the polarizer design parameters, we use a metaheuristic optimization algorithm known as particle swarm optimization (PSO), which is an effective method in electromagnetic design problems [14,15]. We use PSO in conjunction with rigorous coupled-wave analysis to find the optimal design parameters [16]. Since Si3N4 and TiO2 are nearly lossless materials, we apply them as thin-film materials during the design step. Additionally, we apply Si for a wideband polarizer application.

2.1 GMR polarizers designed with Si3N4 thin films

Figure 1 illustrates the resultant Si3N4 GMR polarizer design configuration and parameters as well as its calculated transmittance spectra for TE and TM polarizations. The Si3N4 thin film can be prepared by plasma-enhanced chemical vapor deposition (PECVD), and its refractive index is 1.80 at a wavelength of 1550 nm. This design has only a single Si3N4 layer (Si3N4 will be partially etched) and a two-part grating profile with a grating ridge width of 433 nm. The polarizer has high transmittance for TM polarization and low transmittance for TE polarization in the 1550-nm wavelength band. It has a ~4-nm bandwidth (T>97% for TM, and T<3% for TE) and a theoretical extinction ratio TTM/TTE ~7 × 106 at a wavelength of 1550 nm.

 figure: Fig. 1

Fig. 1 Calculated spectral response of the PECVD-prepared Si3N4 GMR polarizer for TE and TM polarizations. Inset shows a schematic of a resonance polarizer. Parameters: thickness d1 = 324 nm, d2 = 270 nm; refractive index nH = 1.80, nL = 1.00, nC = 1.00, nS = 1.50; grating period Λ = 1006 nm; fill factor F = 0.43; incident angle θin = 0° Πnormal incidence|.

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In addition, we can attain Si3N4 thin film by applying the sputtering method. At a wavelength of 1550 nm, the Si3N4 GMR polarizer prepared by sputtering has a measured refractive index of 1.98 which is higher than the measured refractive index of the polarizer prepared by PECVD as the sputtered film is denser. Figure 2 illustrates the sputter-prepared Si3N4 GMR polarizer design and its calculated transmittance spectra for TE and TM polarizations. This design also has a single Si3N4 layer and a two-part grating profile with a grating-ridge feature size of 449 nm. The polarizer has high transmittance for TM polarization and low transmittance for TE polarization in the 1550-nm wavelength band. It has a ~9-nm bandwidth and a theoretical extinction ratio of ~4 × 106 at a wavelength of 1550 nm. Generally, the bandwidth of GMR devices is highly dependent on the degree of grating modulation (nH-nL). The GMR polarizer design with sputter-prepared Si3N4 thin film has a relatively wide bandwidth compared to the GMR polarizer design with PECVD-prepared Si3N4 thin film.

 figure: Fig. 2

Fig. 2 Calculated spectral response of the sputter-prepared Si3N4 GMR polarizer for TE and TM polarizations. Inset shows a schematic of a resonance polarizer. Parameters: thickness d1 = 302 nm, d2 = 162 nm; refractive index nH = 1.98, nL = 1.00, nC = 1.00, nS = 1.50; grating period Λ = 997 nm; fill factor F = 0.45; incident angle θin = 0° Πnormal incidence|.

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Figure 3 shows the calculated transmittance spectra for TE polarization when the values of the device parameters are changed from their original values. The resonance wavelengths and the bandwidths are presented in Table 1.Clearly, the grating modulation is the dominant parameter affecting the bandwidth. The effect of a 20% difference in fill factor is negligible. A 5% difference in etch depth does not change the bandwidth much, but the resonance wavelength red-shifts because of the increased residual layer thickness (d2) caused by under-etching.

 figure: Fig. 3

Fig. 3 Calculated spectral response of the sputter-prepared Si3N4 GMR polarizer for TE polarizations when values of the device parameters are changed from their original values.

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Tables Icon

Table 1. Resonance Wavelengths and Bandwidths

2.2 GMR polarizer designed with TiO2 thin film

The TiO2 GMR polarizer design and its calculated transmittance spectra for TE and TM modes are illustrated in Fig. 4. The TiO2 thin film can be prepared by the sputtering method, and its measured refractive index is 2.24. This design includes a single TiO2 layer and a two-part grating profile with a grating ridge width of 427 nm. The polarizer has high transmittance for TM polarization and low transmittance for TE polarization in the 1550-nm wavelength band. It has a ~17-nm bandwidth and a theoretical extinction ratio of ~2.9 × 105 at a wavelength of 1550 nm. The TiO2 GMR polarizer design has a relatively wide bandwidth compared to the Si3N4 GMR polarizer designs in Figs. 1 and 2.

 figure: Fig. 4

Fig. 4 Calculated spectral response of the TiO2 GMR polarizer for TE and TM polarizations. Inset shows a schematic of a resonance polarizer. Parameters: thickness d1 = 300 nm, d2 = 83 nm; refractive index nH = 2.24, nL = 1.00, nC = 1.00, nS = 1.50; grating period Λ = 994 nm; fill factor F = 0.43; incident angle θin = 0° Πnormal incidence|;

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2.3 GMR polarizer designed with Si thin film

Figure 5 shows the Silicon (Si) GMR polarizer design and its calculated transmittance spectra for TE and TM polarizations. In contrast to the previous Si3N4 and TiO2 polarizer designs, the configuration of this Si GMR polarizer is based on a thin conformal Si layer on a patterned quartz substrate. Moreover, this device differs in its configuration and response from Si-based polarizers we have reported in the past [11,12]. This Si-based GMR polarizer has high transmittance for TM polarization and low transmittance for TE polarization in the 1550-nm wavelength band. It has a ~200-nm bandwidth and a theoretical extinction ratio of ~2.5 × 104 at a wavelength of 1550 nm. Compared to the previous Si-based GMR polarizer reported in [12], this design provides a simple fabrication process. Particularly, it enables fabrication by nanoimprint methods, e.g., in polymers, which avoids the etch step altogether.

 figure: Fig. 5

Fig. 5 Calculated spectral response of the Si GMR polarizer for TE and TM polarizations. Inset shows a schematic of a resonance polarizer. Parameters: thickness d1 = 123 nm, d2 = 258 nm, d3 = 123 nm; refractive index nH(Si) = 3.48, nL = 1.44, nC = 1.00, nS = 1.44; grating period Λ = 766 nm; fill factor F1 = 0.061, F2 = 0.393, F3 = 0.061, F4 = 0.484; incident angle θin = 0° Πnormal incidence|.

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3. Fabrication

The fabrication process of the GMR polarizers is shown in Fig. 6(a) and summarized as follows. Si3N4 (or TiO2) is deposited on a 1 inch x 1 inch glass substrate. Positive photoresist (PR) is distributed evenly onto the substrate and spin-coated for 60 seconds at 1000 rpm. After the sample is soft-baked for 90 seconds on a hot plate at 110 C°, it is ready for patterning. A holographic interferometer with a deep UV laser (λ = 266 nm) is used to create the grating structure in the PR layer. Nine 5x5 mm2 devices are fabricated on the 1 square inch sample as depicted in Fig. 6(b). After PR patterning, the sample undergoes a post-exposure bake for 90 seconds on a hot plate at 110 C°.

 figure: Fig. 6

Fig. 6 (a) Fabrication process of the Si3N4 and TiO2 GMR polarizers. Fabrication process of the Si GMR polarizer slightly differs as the substrate is etched first. (b) Physical dimensions for a fabricated device.

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Then the sample is developed, rinsed with deionized water, and air blown with Nitrogen gas. Using a reactive-ion etching machine (RIE, Oxford Instruments, Plasmalab 80 Plus), the sample is descummed for 10 seconds and the PR grating pattern is transferred into the Si3N4 thin film with 22.5 sccm of CHF3 and 5.0 sccm of O2. For TiO2 etching, we apply a CHF3/CF4/Ar gas mixture with 25/25/25 sccm. The sample is then immersed in PR stripper in an ultrasonic cleaner to remove the residual PR layer. After the PR is removed, the single-layer Si3N4 polarizer is obtained.

For the Si GMR polarizer, a PR grating is patterned on the quartz substrate and then etched into it with a combination of 36 sccm of CHF3 and 14 sccm of SF6 gas. After patterning, the Si thin film is deposited on the top of the patterned quartz grating structure.

4. Characterization and results

After completing the thin-film deposition on the substrate, we measure the thickness and the complex refractive index of the deposited thin films using a spectroscopic ellipsometer (J.A. Woollam Co. Inc., V-VASE). The dispersion of the measured refractive index is very small. The difference of the refractive index between 1500 nm and 1600 nm is less than 0.001 and 0.003 for Si3N4 and TiO2 thin film, respectively. For the Si film, the difference in the refractive index between 1400 nm and 1700 nm is less than 0.05. To characterize the fabricated device, we use an atomic force microscope (AFM, Park XE-70). The AFM images and profiles permit comparison of the parameters of the fabricated device with the original design. Figure 7 shows AFM images of the fabricated Si3N4 GMR polarizer prepared by PECVD. These images show that the grating period is 1017 nm, the thickness of the Si3N4 grating is 310 nm, and the width of the grating layer is 428 nm; therefore, the experimental fill factor is 0.42. The sidewall profile obtained by AFM is not perfectly vertical. The slope of resulting trapezoid is a common effect influenced by the shape of the AFM tip during the surface scanning. This artifact of the AFM measurement can be verified by comparison between the AFM and SEM images shown in Figs. 13 and 14. Figures 10 and 14 obtained by SEM show that the fabricated GMR devices have vertical profiles.

 figure: Fig. 7

Fig. 7 AFM image and corresponding profile of the fabricated PECVD-prepared Si3N4 GMR polarizer. By using a cross-section image, the grating period and the etching depth of the fabricated GMR polarizer can be measured. The image shows that the depth is 310 nm.

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To measure the spectral response of the GMR polarizer, we employ a supercontinuum white light source (Koheras A/S, SuperK Compact) to illuminate broadband light through a collimating lens toward the device at normal incidence (θin = 0°). The polarizer (Thorlabs, Glan-Thompson polarizer) is used to set either the TE or TM polarization state. Both TE and TM spectra of the transmitted beam are measured with an optical spectrum analyzer for a wavelength range of 1450 nm–1650 nm (or 1800 nm).

4.1 GMR polarizers made in Si3N4

Figure 8 shows the measured transmittance spectra of the fabricated PECVD-prepared Si3N4 GMR polarizer for TE and TM polarizations. The fabricated polarizer indicates that the central wavelength (i.e., location of minimum transmittance) for TE occurs at λc ~1565 nm. The polarizer has high transmittance (~97%) for TM polarization and low transmittance (~2%) for TE polarization at the 1565-nm wavelength. The experimental data exhibits a central wavelength of 1565 nm versus that of the theoretical data at 1550 nm. This variation is due to the discrepancy of the grating period between the theoretical and experimental results; for the design and measured data, respectively, the grating period is 1006 nm and 1017 nm, the grating depth (d1) is 324 nm and 310 nm, the thickness of the homogeneous layer (d2) is 270 nm and 260 nm, and the fill factor is 0.43 and 0.42. Figure 7 also shows the comparison between the theoretical and experimental transmittance spectra of the PECVD-prepared Si3N4 GMR polarizer for TE and TM polarizations. The device parameters for the theoretical calculation are extracted from the AFM images. As elucidated in the figure, experimental and theoretical results are in good agreement.

 figure: Fig. 8

Fig. 8 Theoretical and experimental spectral response of the fabricated PECVD-prepared Si3N4 GMR polarizer for both TE and TM polarizations. The resonance wavelength for TE polarization is ~1565 nm. The device parameters for the theoretical calculation are extracted from the AFM images. The experimental data is corrected for a ~4% reflection at the backside of the substrate.

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Figure 9 shows the measured transmittance spectra of the fabricated sputter-prepared Si3N4 GMR polarizer for TE and TM polarizations. The fabricated polarizer shows that the central wavelength for TE occurs at λc~1584 nm. The polarizer has high transmittance (>95%) for TE polarization and low transmittance (<3%) for TM polarization over a ~9-nm wavelength range (~1580–1589 nm).

 figure: Fig. 9

Fig. 9 Theoretical and experimental spectral response of the fabricated sputter-prepared Si3N4 GMR polarizer for TE and TM polarizations. The resonance wavelength for TE polarization is ~1584 nm. The device parameters for the theoretical calculation are extracted from the AFM images.

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Its experimental extinction ratio is 160:1 at 1584 nm. The experimental data exhibits a central wavelength of 1584 nm versus that of the theoretical data at 1550 nm. This variance is due to the discrepancy of the grating period between the theoretical and experimental results; for the design and measured data, respectively, the grating period is 997 nm and 1021 nm, the grating depth (d1) is 302 nm and 302 nm, the thickness of the homogeneous layer (d2) is 162 nm and 155 nm, and the fill factor is 0.45 and 0.45. Figure 9 also shows the comparison between the theoretical and experimental transmittance spectra of the sputter-prepared Si3N4 GMR polarizer for TE and TM polarizations. As seen in the figure, experimental and theoretical results are in good agreement.

4.2 GMR polarizers made in TiO2

Figure 10 shows the fabricated TiO2 GMR polarizer; the cross-sectional view we obtained with a scanning electron microscope (SEM) indicates that the profile of the sidewall is vertical. Moreover, the SEM images confirm the parameters of the fabricated TiO2 GMR polarizer are as follows: the grating period is 974 nm, the thickness of the TiO2 grating (d1) is 238 nm, and the thickness of the TiO2 homogeneous layer (d2) is 150 nm. By using an etch recipe for PR/TiO2 layers, a selectivity of ~1:0.5 is obtained, which reveals that our PR layer is not thick enough to etch a ~300-nm TiO2 thin-film grating. After ~240 nm of TiO2 etching, SEM images show a ~60-nm PR layer remaining on the etched TiO2.

 figure: Fig. 10

Fig. 10 SEM images after PR/TiO2 etching. The PR layer remains on the etched TiO2 grating. After removing this PR residual layer, the TiO2 GMR polarizer is obtained. (a) Magnification = 10,000; (b) Magnification = 40,000.

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Figure 11 shows the measured transmittance spectra of the fabricated TiO2 GMR polarizer for TE and TM polarizations. The fabricated polarizer shows the central wavelength for TE occurs at λc~1711 nm. The polarizer has high transmittance (~86%) for TM polarization and low transmittance (~1%) for TE polarization at the 1711-nm wavelength. The measured central wavelength deviates significantly from the theoretical central wavelength of 1550 nm. This shift results from the under-etched TiO2 homogeneous layer (d2) caused by the thin PR layer. The thickness of the TiO2 homogeneous layer (d2) for design and measured data is 89 nm and 150 nm, respectively. However, this fabricated TiO2 GMR polarizer still exhibits polarizing property at the 1547-nm and 1711-nm wavelengths, which reveals the possibility of a dual-function polarizer. Figure 11 shows that the fabricated TiO2 GMR polarizer works as a TE-pass/TM-block polarizer at the 1547-nm wavelength and a TM-pass/TE-block polarizer at the 1711-nm wavelength. The comparison between the theoretical and experimental transmittance spectra of the TiO2 GMR polarizers for TE and TM polarizations are also shown in Fig. 11.

 figure: Fig. 11

Fig. 11 Measured spectral responses of the fabricated TiO2 GMR polarizer. The resonance wavelength for TE polarization is ~1711 nm due to the under-etched, much thicker TiO2 homogeneous layer (d2). The device parameters for the theoretical calculation are extracted from the AFM images.

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4.3. GMR polarizer made in Si

Figure 12 shows the measured transmittance spectra of the fabricated Si GMR polarizer for TE and TM polarizations. For TM polarization, the fabricated polarizer shows T>97% over a ~260-nm wavelength range (~1445–1700 nm). For TE polarization, the polarizer shows T<3% over a ~160-nm wavelength range (~1415–1572 nm). Therefore, the overlapping area (T>97% and T<3%) extends over a ~130-nm wavelength range (~1445–1575 nm). The fabricated polarizer shows that the central wavelength for TE occurs at λc~1499 nm, which is blue-shifted compared to that of the theoretical data at the 1550-nm wavelength. Its experimental extinction ratio is 360:1 at 1499 nm.

 figure: Fig. 12

Fig. 12 Measured spectral responses of the fabricated Si GMR polarizer. The resonance wavelength for TE polarization is ~1500 nm due to the thin Si layer (d3). The device parameters for the theoretical calculation are extracted from the AFM images.

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Figure 13 shows AFM images of the Si GMR polarizer before and after Si thin-film deposition. These AFM images show that the grating depth (d2) is 256 nm before and 286 nm after Si thin-film deposition. This implies that the thickness of the Si thin film on top of the quartz grating (d1) and in the trench (d3) differs, which the SEM image shown in Fig. 14 verifies. The SEM measurement shows that the Si thin film in the trench (d3 = 88 nm) is thinner than the Si thin film on top of the quartz grating (d1 = 117 nm). This variation in thickness is due to the configuration of the sputtering system because the material target lies in the vacuum chamber at a slight angle. The discrepancy between d1 and d3 can be reduced by applying directional thin-film deposition. In addition, the central wavelength of the polarizing bandwidth can be red-shifted by additional thin-film deposition.

 figure: Fig. 13

Fig. 13 AFM image and corresponding profile of the fabricated Si GMR polarizer (a) before Si thin-film deposition and (b) after Si thin-film deposition.

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 figure: Fig. 14

Fig. 14 SEM image of the fabricated Si GMR polarizer, which shows that thickness d1 and d3 are different. The fabricated thickness of d3 is thinner than its designed thickness.

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5. Conclusions

Subwavelength GMR polarizers implemented with a single deposited layer have been designed with inverse numerical mathematical methods conjoined with rigorous forward electromagnetic analysis. Applying expedient patterning by holographic lithography, we fabricate and characterize a variety of these relatively simple devices. In particular, we demonstrate GMR polarizers with three different, nearly lossless materials, namely Si3N4, TiO2, and Si, which have different refractive indices and operate at normal incidence. Comparison between the theoretical and experimental transmittance spectra of the GMR polarizers reveals good quantitative agreement.

Acknowledgments

This work was supported in part by the United States Air Force Office of Scientific Research under Agreement Number FA9550-10-1-0543 as well as by the National Science Foundation (NSF) under Award No. ECCS-0925774. L. Ajayi and J. Giese acknowledge support from the NSF under REU Supplement Award No. ECCS-0925774. J. Giese also acknowledges support from the University of Texas–Arlington College of Engineering’s Undergraduate Research Opportunity Program as well as by the NSF under REU Site Award No. EEC-1156801.

References and links

1. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989).

2. X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93(8), 4407–4412 (2003). [CrossRef]  

3. H. Tamada, T. Doumuki, T. Yamaguchi, and S. Matsumoto, “Al wire-grid polarizer using the s-polarization resonance effect at the 0.8-microm-wavelength band,” Opt. Lett. 22(6), 419–421 (1997). [CrossRef]   [PubMed]  

4. Y. Ekinci, H. H. Solak, C. David, and H. Sigg, “Bilayer Al wire-grids as broadband and high-performance polarizers,” Opt. Express 14(6), 2323–2334 (2006). [CrossRef]   [PubMed]  

5. J. J. Wang, W. Zhang, X. Deng, J. Deng, F. Liu, P. Sciortino, and L. Chen, “High-performance nanowire-grid polarizers,” Opt. Lett. 30(2), 195–197 (2005). [CrossRef]   [PubMed]  

6. G. E. Jellison Jr and H. H. Burke, “The temperature dependence of the refractive index of silicon at elevated temperatures at several laser wavelengths,” J. Appl. Phys. 60(2), 841–843 (1986). [CrossRef]  

7. H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(3), 561–658 (1980). [CrossRef]  

8. H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Institute of Physics Pub., 2001).

9. I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989). [CrossRef]  

10. R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992). [CrossRef]  

11. K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008). [CrossRef]  

12. K. J. Lee, J. Curzan, M. Shokooh-Saremi, and R. Magnusson, “Resonant wideband polarizer with single silicon layer,” Appl. Phys. Lett. 98(21), 211112 (2011). [CrossRef]  

13. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

14. J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of IEEE Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 1942–1948.

15. M. Shokooh-Saremi and R. Magnusson, “Particle swarm optimization and its application to the design of diffraction grating filters,” Opt. Lett. 32(8), 894–896 (2007). [CrossRef]   [PubMed]  

16. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: Enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 (1995). [CrossRef]  

References

  • View by:

  1. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989).
  2. X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93(8), 4407–4412 (2003).
    [Crossref]
  3. H. Tamada, T. Doumuki, T. Yamaguchi, and S. Matsumoto, “Al wire-grid polarizer using the s-polarization resonance effect at the 0.8-microm-wavelength band,” Opt. Lett. 22(6), 419–421 (1997).
    [Crossref] [PubMed]
  4. Y. Ekinci, H. H. Solak, C. David, and H. Sigg, “Bilayer Al wire-grids as broadband and high-performance polarizers,” Opt. Express 14(6), 2323–2334 (2006).
    [Crossref] [PubMed]
  5. J. J. Wang, W. Zhang, X. Deng, J. Deng, F. Liu, P. Sciortino, and L. Chen, “High-performance nanowire-grid polarizers,” Opt. Lett. 30(2), 195–197 (2005).
    [Crossref] [PubMed]
  6. G. E. Jellison and H. H. Burke, “The temperature dependence of the refractive index of silicon at elevated temperatures at several laser wavelengths,” J. Appl. Phys. 60(2), 841–843 (1986).
    [Crossref]
  7. H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(3), 561–658 (1980).
    [Crossref]
  8. H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Institute of Physics Pub., 2001).
  9. I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
    [Crossref]
  10. R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
    [Crossref]
  11. K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
    [Crossref]
  12. K. J. Lee, J. Curzan, M. Shokooh-Saremi, and R. Magnusson, “Resonant wideband polarizer with single silicon layer,” Appl. Phys. Lett. 98(21), 211112 (2011).
    [Crossref]
  13. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).
  14. J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of IEEE Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 1942–1948.
  15. M. Shokooh-Saremi and R. Magnusson, “Particle swarm optimization and its application to the design of diffraction grating filters,” Opt. Lett. 32(8), 894–896 (2007).
    [Crossref] [PubMed]
  16. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: Enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 (1995).
    [Crossref]

2011 (1)

K. J. Lee, J. Curzan, M. Shokooh-Saremi, and R. Magnusson, “Resonant wideband polarizer with single silicon layer,” Appl. Phys. Lett. 98(21), 211112 (2011).
[Crossref]

2008 (1)

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[Crossref]

2007 (1)

2006 (1)

2005 (1)

2003 (1)

X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93(8), 4407–4412 (2003).
[Crossref]

1997 (1)

1995 (1)

1992 (1)

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[Crossref]

1989 (1)

I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[Crossref]

1986 (1)

G. E. Jellison and H. H. Burke, “The temperature dependence of the refractive index of silicon at elevated temperatures at several laser wavelengths,” J. Appl. Phys. 60(2), 841–843 (1986).
[Crossref]

1980 (1)

H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(3), 561–658 (1980).
[Crossref]

Avrutsky, I. A.

I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[Crossref]

Britton, B.

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[Crossref]

Burke, H. H.

G. E. Jellison and H. H. Burke, “The temperature dependence of the refractive index of silicon at elevated temperatures at several laser wavelengths,” J. Appl. Phys. 60(2), 841–843 (1986).
[Crossref]

Chen, L.

Curzan, J.

K. J. Lee, J. Curzan, M. Shokooh-Saremi, and R. Magnusson, “Resonant wideband polarizer with single silicon layer,” Appl. Phys. Lett. 98(21), 211112 (2011).
[Crossref]

David, C.

Deng, J.

Deng, X.

Ding, Y.

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[Crossref]

Donkor, E.

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[Crossref]

Doumuki, T.

Ekinci, Y.

Gaylord, T. K.

Grann, E. B.

Jellison, G. E.

G. E. Jellison and H. H. Burke, “The temperature dependence of the refractive index of silicon at elevated temperatures at several laser wavelengths,” J. Appl. Phys. 60(2), 841–843 (1986).
[Crossref]

Kwok, H. S.

X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93(8), 4407–4412 (2003).
[Crossref]

LaComb, R.

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[Crossref]

Lee, K. J.

K. J. Lee, J. Curzan, M. Shokooh-Saremi, and R. Magnusson, “Resonant wideband polarizer with single silicon layer,” Appl. Phys. Lett. 98(21), 211112 (2011).
[Crossref]

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[Crossref]

Li, H. H.

H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(3), 561–658 (1980).
[Crossref]

Liu, F.

Magnusson, R.

K. J. Lee, J. Curzan, M. Shokooh-Saremi, and R. Magnusson, “Resonant wideband polarizer with single silicon layer,” Appl. Phys. Lett. 98(21), 211112 (2011).
[Crossref]

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[Crossref]

M. Shokooh-Saremi and R. Magnusson, “Particle swarm optimization and its application to the design of diffraction grating filters,” Opt. Lett. 32(8), 894–896 (2007).
[Crossref] [PubMed]

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[Crossref]

Matsumoto, S.

Moharam, M. G.

Pommet, D. A.

Sciortino, P.

Shokooh-Saremi, M.

K. J. Lee, J. Curzan, M. Shokooh-Saremi, and R. Magnusson, “Resonant wideband polarizer with single silicon layer,” Appl. Phys. Lett. 98(21), 211112 (2011).
[Crossref]

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[Crossref]

M. Shokooh-Saremi and R. Magnusson, “Particle swarm optimization and its application to the design of diffraction grating filters,” Opt. Lett. 32(8), 894–896 (2007).
[Crossref] [PubMed]

Sigg, H.

Silva, H.

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[Crossref]

Solak, H. H.

Sychugov, V. A.

I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[Crossref]

Tamada, H.

Wang, J. J.

Wang, S. S.

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[Crossref]

Yamaguchi, T.

Yu, X. J.

X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93(8), 4407–4412 (2003).
[Crossref]

Zhang, W.

Appl. Phys. Lett. (2)

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[Crossref]

K. J. Lee, J. Curzan, M. Shokooh-Saremi, and R. Magnusson, “Resonant wideband polarizer with single silicon layer,” Appl. Phys. Lett. 98(21), 211112 (2011).
[Crossref]

IEEE Photon. Technol. Lett. (1)

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[Crossref]

J. Appl. Phys. (2)

X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93(8), 4407–4412 (2003).
[Crossref]

G. E. Jellison and H. H. Burke, “The temperature dependence of the refractive index of silicon at elevated temperatures at several laser wavelengths,” J. Appl. Phys. 60(2), 841–843 (1986).
[Crossref]

J. Mod. Opt. (1)

I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Phys. Chem. Ref. Data (1)

H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(3), 561–658 (1980).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Other (4)

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Figures (14)

Fig. 1
Fig. 1 Calculated spectral response of the PECVD-prepared Si3N4 GMR polarizer for TE and TM polarizations. Inset shows a schematic of a resonance polarizer. Parameters: thickness d1 = 324 nm, d2 = 270 nm; refractive index nH = 1.80, nL = 1.00, nC = 1.00, nS = 1.50; grating period Λ = 1006 nm; fill factor F = 0.43; incident angle θin = 0° Πnormal incidence|.
Fig. 2
Fig. 2 Calculated spectral response of the sputter-prepared Si3N4 GMR polarizer for TE and TM polarizations. Inset shows a schematic of a resonance polarizer. Parameters: thickness d1 = 302 nm, d2 = 162 nm; refractive index nH = 1.98, nL = 1.00, nC = 1.00, nS = 1.50; grating period Λ = 997 nm; fill factor F = 0.45; incident angle θin = 0° Πnormal incidence|.
Fig. 3
Fig. 3 Calculated spectral response of the sputter-prepared Si3N4 GMR polarizer for TE polarizations when values of the device parameters are changed from their original values.
Fig. 4
Fig. 4 Calculated spectral response of the TiO2 GMR polarizer for TE and TM polarizations. Inset shows a schematic of a resonance polarizer. Parameters: thickness d1 = 300 nm, d2 = 83 nm; refractive index nH = 2.24, nL = 1.00, nC = 1.00, nS = 1.50; grating period Λ = 994 nm; fill factor F = 0.43; incident angle θin = 0° Πnormal incidence|;
Fig. 5
Fig. 5 Calculated spectral response of the Si GMR polarizer for TE and TM polarizations. Inset shows a schematic of a resonance polarizer. Parameters: thickness d1 = 123 nm, d2 = 258 nm, d3 = 123 nm; refractive index nH(Si) = 3.48, nL = 1.44, nC = 1.00, nS = 1.44; grating period Λ = 766 nm; fill factor F1 = 0.061, F2 = 0.393, F3 = 0.061, F4 = 0.484; incident angle θin = 0° Πnormal incidence|.
Fig. 6
Fig. 6 (a) Fabrication process of the Si3N4 and TiO2 GMR polarizers. Fabrication process of the Si GMR polarizer slightly differs as the substrate is etched first. (b) Physical dimensions for a fabricated device.
Fig. 7
Fig. 7 AFM image and corresponding profile of the fabricated PECVD-prepared Si3N4 GMR polarizer. By using a cross-section image, the grating period and the etching depth of the fabricated GMR polarizer can be measured. The image shows that the depth is 310 nm.
Fig. 8
Fig. 8 Theoretical and experimental spectral response of the fabricated PECVD-prepared Si3N4 GMR polarizer for both TE and TM polarizations. The resonance wavelength for TE polarization is ~1565 nm. The device parameters for the theoretical calculation are extracted from the AFM images. The experimental data is corrected for a ~4% reflection at the backside of the substrate.
Fig. 9
Fig. 9 Theoretical and experimental spectral response of the fabricated sputter-prepared Si3N4 GMR polarizer for TE and TM polarizations. The resonance wavelength for TE polarization is ~1584 nm. The device parameters for the theoretical calculation are extracted from the AFM images.
Fig. 10
Fig. 10 SEM images after PR/TiO2 etching. The PR layer remains on the etched TiO2 grating. After removing this PR residual layer, the TiO2 GMR polarizer is obtained. (a) Magnification = 10,000; (b) Magnification = 40,000.
Fig. 11
Fig. 11 Measured spectral responses of the fabricated TiO2 GMR polarizer. The resonance wavelength for TE polarization is ~1711 nm due to the under-etched, much thicker TiO2 homogeneous layer (d2). The device parameters for the theoretical calculation are extracted from the AFM images.
Fig. 12
Fig. 12 Measured spectral responses of the fabricated Si GMR polarizer. The resonance wavelength for TE polarization is ~1500 nm due to the thin Si layer (d3). The device parameters for the theoretical calculation are extracted from the AFM images.
Fig. 13
Fig. 13 AFM image and corresponding profile of the fabricated Si GMR polarizer (a) before Si thin-film deposition and (b) after Si thin-film deposition.
Fig. 14
Fig. 14 SEM image of the fabricated Si GMR polarizer, which shows that thickness d1 and d3 are different. The fabricated thickness of d3 is thinner than its designed thickness.

Tables (1)

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Table 1 Resonance Wavelengths and Bandwidths

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