Abstract

Developing controllable radiation sources in the mid-infrared spectral region is significant in photonics technology because of rare available resources. Based on the thermal emission from a one-dimensional shallow tungsten grating, we propose a two-dimensional orthogonally-crossed shallow grating to produce an orthogonally-polarized dual-wavelength radiation with the emissivity as high as 78% and 91% from a single surface. The simulation shows that the field is intensively concentrated in vicinity of the air-tungsten interface when surface plasmon polaritons are excited. In addition, by optimizing the geometric parameters of the grating, the field is found to be more concentrated which leads to higher emissivity. The two wavelengths can be produced independently or simultaneously, depending on the polarization of the picking-up polarizer. Our investigations can help us developing controllable multi-wavelength thermal radiation sources from a single surface.

© 2013 Optical Society of America

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2012

C. Arnold, F. Marquier, M. Garin, F. Pardo, S. Collin, N. Bardou, J.-L. Pelouard, and J.-J. Greffet, “Coherent thermal infrared emission by two-dimensional silicon carbide gratings,” Phys. Rev. B86(3), 035316 (2012).
[CrossRef]

N. Nguyen-Huu, Y. B. Chen, and Y. L. Lo, “Development of a polarization-insensitive thermophotovoltaic emitter with a binary grating,” Opt. Express20(6), 5882–5890 (2012).
[CrossRef] [PubMed]

2011

J.-J. Greffet, “Applied physics: Controlled incandescence,” Nature478(7368), 191–192 (2011).
[CrossRef] [PubMed]

K. Masuno, T. Sawada, S. Kumagai, and M. Sasaki, “Multiwavelength Selective IR Emission Using Surface Plasmon Polaritons for Gas Sensing,” IEEE Photon. Technol. Lett.23(22), 1661–1663 (2011).
[CrossRef]

2010

2009

2008

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett.92(14), 141114 (2008).
[CrossRef]

I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett.92(19), 193101 (2008).
[CrossRef]

E. Rephaeli and S. Fan, “Tungsten black absorber for solar light with wide angular operation range,” Appl. Phys. Lett.92(21), 211107 (2008).
[CrossRef]

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, “Confinement of infrared radiation to nanometer scales through metallic slit arrays,” J. Quant. Spectrosc. Radiat. Transf.109(4), 608–619 (2008).
[CrossRef]

2007

Y.-B. Chen and Z. M. Zhang, “Design of tungsten complex gratings for thermophotovoltaic radiators,” Opt. Commun.269(2), 411–417 (2007).
[CrossRef]

2006

J. T. Wan and C. T. Chan, “Thermal emission by metallic photonic crystal slabs,” Appl. Phys. Lett.89(4), 041915 (2006).
[CrossRef]

B. J. Lee and Z. M. Zhang, “Design and fabrication of planar multilayer structures with coherent thermal emission characteristics,” J. Appl. Phys.100(6), 063529 (2006).
[CrossRef]

D. L. C. Chan, M. Soljacić, and J. D. Joannopoulos, “Thermal emission and design in 2D-periodic metallic photonic crystal slabs,” Opt. Express14(19), 8785–8796 (2006).
[CrossRef] [PubMed]

2005

2004

C. Luo, A. Narayanaswamy, G. Chen, and J. D. Joannopoulos, “Thermal Radiation from Photonic Crystals: A Direct Calculation,” Phys. Rev. Lett.93(21), 213905 (2004).
[CrossRef] [PubMed]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

M. Kretschmann, T. A. Leskova, and A. A. Maradudin, “Conical Propagation of a Surface Polariton Across a Grating,” Opt. Commun.215(4-6), 205–223 (2003).
[CrossRef]

2002

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature417(6884), 52–55 (2002).
[CrossRef] [PubMed]

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature416(6876), 61–64 (2002).
[CrossRef] [PubMed]

2001

S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two-dimensionally confined modes in microcavities,” Appl. Phys. Lett.79(9), 1393 (2001).
[CrossRef]

1998

1986

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature324(6097), 549–551 (1986).
[CrossRef]

1975

J. H. Weaver, C. G. Olson, and D. W. Lynch, “Optical properties of crystalline tungsten,” Phys. Rev. B12(4), 1293–1297 (1975).
[CrossRef]

Arnold, C.

C. Arnold, F. Marquier, M. Garin, F. Pardo, S. Collin, N. Bardou, J.-L. Pelouard, and J.-J. Greffet, “Coherent thermal infrared emission by two-dimensional silicon carbide gratings,” Phys. Rev. B86(3), 035316 (2012).
[CrossRef]

M. Laroche, C. Arnold, F. Marquier, R. Carminati, J.-J. Greffet, S. Collin, N. Bardou, and J.-L. Pelouard, “Highly directional radiation generated by a tungsten thermal source,” Opt. Lett.30(19), 2623–2625 (2005).
[CrossRef] [PubMed]

Bardou, N.

C. Arnold, F. Marquier, M. Garin, F. Pardo, S. Collin, N. Bardou, J.-L. Pelouard, and J.-J. Greffet, “Coherent thermal infrared emission by two-dimensional silicon carbide gratings,” Phys. Rev. B86(3), 035316 (2012).
[CrossRef]

M. Laroche, C. Arnold, F. Marquier, R. Carminati, J.-J. Greffet, S. Collin, N. Bardou, and J.-L. Pelouard, “Highly directional radiation generated by a tungsten thermal source,” Opt. Lett.30(19), 2623–2625 (2005).
[CrossRef] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Biswas, R.

W. Zhao, R. Biswas, I. Puscasu, and E. Johnson, “Angular variation of absorption and thermal emission from photonic crystals,” J. Opt. Soc. Am. B26(9), 1808 (2009).
[CrossRef]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature417(6884), 52–55 (2002).
[CrossRef] [PubMed]

Carminati, R.

Celanovic, I.

I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett.92(19), 193101 (2008).
[CrossRef]

Chan, C. T.

J. T. Wan and C. T. Chan, “Thermal emission by metallic photonic crystal slabs,” Appl. Phys. Lett.89(4), 041915 (2006).
[CrossRef]

Chan, D. L. C.

Chen, G.

C. Luo, A. Narayanaswamy, G. Chen, and J. D. Joannopoulos, “Thermal Radiation from Photonic Crystals: A Direct Calculation,” Phys. Rev. Lett.93(21), 213905 (2004).
[CrossRef] [PubMed]

Chen, Y.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature416(6876), 61–64 (2002).
[CrossRef] [PubMed]

Chen, Y. B.

Chen, Y.-B.

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, “Confinement of infrared radiation to nanometer scales through metallic slit arrays,” J. Quant. Spectrosc. Radiat. Transf.109(4), 608–619 (2008).
[CrossRef]

Y.-B. Chen and Z. M. Zhang, “Design of tungsten complex gratings for thermophotovoltaic radiators,” Opt. Commun.269(2), 411–417 (2007).
[CrossRef]

Collin, S.

C. Arnold, F. Marquier, M. Garin, F. Pardo, S. Collin, N. Bardou, J.-L. Pelouard, and J.-J. Greffet, “Coherent thermal infrared emission by two-dimensional silicon carbide gratings,” Phys. Rev. B86(3), 035316 (2012).
[CrossRef]

M. Laroche, C. Arnold, F. Marquier, R. Carminati, J.-J. Greffet, S. Collin, N. Bardou, and J.-L. Pelouard, “Highly directional radiation generated by a tungsten thermal source,” Opt. Lett.30(19), 2623–2625 (2005).
[CrossRef] [PubMed]

Dai, Q.-F.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Djurisic, A. B.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Elazar, J. M.

El-Kady, I.

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature417(6884), 52–55 (2002).
[CrossRef] [PubMed]

Esashi, M.

S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two-dimensionally confined modes in microcavities,” Appl. Phys. Lett.79(9), 1393 (2001).
[CrossRef]

Fan, S.

E. Rephaeli and S. Fan, “Tungsten black absorber for solar light with wide angular operation range,” Appl. Phys. Lett.92(21), 211107 (2008).
[CrossRef]

Fleming, J. G.

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature417(6884), 52–55 (2002).
[CrossRef] [PubMed]

Fu, C. J.

B. J. Lee, C. J. Fu, and Z. M. Zhang, “Coherent thermal emission from one-dimensional photonic crystals,” Appl. Phys. Lett.87(7), 071904 (2005).
[CrossRef]

Fujimura, K.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett.92(14), 141114 (2008).
[CrossRef]

Garin, M.

C. Arnold, F. Marquier, M. Garin, F. Pardo, S. Collin, N. Bardou, J.-L. Pelouard, and J.-J. Greffet, “Coherent thermal infrared emission by two-dimensional silicon carbide gratings,” Phys. Rev. B86(3), 035316 (2012).
[CrossRef]

Gebhart, B.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature324(6097), 549–551 (1986).
[CrossRef]

Greffet, J.-J.

C. Arnold, F. Marquier, M. Garin, F. Pardo, S. Collin, N. Bardou, J.-L. Pelouard, and J.-J. Greffet, “Coherent thermal infrared emission by two-dimensional silicon carbide gratings,” Phys. Rev. B86(3), 035316 (2012).
[CrossRef]

J.-J. Greffet, “Applied physics: Controlled incandescence,” Nature478(7368), 191–192 (2011).
[CrossRef] [PubMed]

M. Laroche, C. Arnold, F. Marquier, R. Carminati, J.-J. Greffet, S. Collin, N. Bardou, and J.-L. Pelouard, “Highly directional radiation generated by a tungsten thermal source,” Opt. Lett.30(19), 2623–2625 (2005).
[CrossRef] [PubMed]

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature416(6876), 61–64 (2002).
[CrossRef] [PubMed]

Han, S. E.

Hatade, K.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett.92(14), 141114 (2008).
[CrossRef]

Hesketh, P. J.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature324(6097), 549–551 (1986).
[CrossRef]

Ho, K. M.

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature417(6884), 52–55 (2002).
[CrossRef] [PubMed]

Ikeda, K.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett.92(14), 141114 (2008).
[CrossRef]

Inoue, Y.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett.92(14), 141114 (2008).
[CrossRef]

Joannopoulos, J. D.

D. L. C. Chan, M. Soljacić, and J. D. Joannopoulos, “Thermal emission and design in 2D-periodic metallic photonic crystal slabs,” Opt. Express14(19), 8785–8796 (2006).
[CrossRef] [PubMed]

C. Luo, A. Narayanaswamy, G. Chen, and J. D. Joannopoulos, “Thermal Radiation from Photonic Crystals: A Direct Calculation,” Phys. Rev. Lett.93(21), 213905 (2004).
[CrossRef] [PubMed]

Johnson, E.

Joulain, K.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature416(6876), 61–64 (2002).
[CrossRef] [PubMed]

Jovanovic, N.

I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett.92(19), 193101 (2008).
[CrossRef]

Kanakugi, T.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett.92(14), 141114 (2008).
[CrossRef]

Kasaya, T.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett.92(14), 141114 (2008).
[CrossRef]

Kashiwa, T.

S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two-dimensionally confined modes in microcavities,” Appl. Phys. Lett.79(9), 1393 (2001).
[CrossRef]

Kassakian, J.

I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett.92(19), 193101 (2008).
[CrossRef]

Kitagawa, S.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett.92(14), 141114 (2008).
[CrossRef]

Kretschmann, M.

M. Kretschmann, T. A. Leskova, and A. A. Maradudin, “Conical Propagation of a Surface Polariton Across a Grating,” Opt. Commun.215(4-6), 205–223 (2003).
[CrossRef]

Kumagai, S.

K. Masuno, T. Sawada, S. Kumagai, and M. Sasaki, “Multiwavelength Selective IR Emission Using Surface Plasmon Polaritons for Gas Sensing,” IEEE Photon. Technol. Lett.23(22), 1661–1663 (2011).
[CrossRef]

Lan, S.

Laroche, M.

Lee, B. J.

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, “Confinement of infrared radiation to nanometer scales through metallic slit arrays,” J. Quant. Spectrosc. Radiat. Transf.109(4), 608–619 (2008).
[CrossRef]

B. J. Lee and Z. M. Zhang, “Design and fabrication of planar multilayer structures with coherent thermal emission characteristics,” J. Appl. Phys.100(6), 063529 (2006).
[CrossRef]

B. J. Lee, C. J. Fu, and Z. M. Zhang, “Coherent thermal emission from one-dimensional photonic crystals,” Appl. Phys. Lett.87(7), 071904 (2005).
[CrossRef]

Leskova, T. A.

M. Kretschmann, T. A. Leskova, and A. A. Maradudin, “Conical Propagation of a Surface Polariton Across a Grating,” Opt. Commun.215(4-6), 205–223 (2003).
[CrossRef]

Lin, S. Y.

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature417(6884), 52–55 (2002).
[CrossRef] [PubMed]

Lo, Y. L.

Luo, C.

C. Luo, A. Narayanaswamy, G. Chen, and J. D. Joannopoulos, “Thermal Radiation from Photonic Crystals: A Direct Calculation,” Phys. Rev. Lett.93(21), 213905 (2004).
[CrossRef] [PubMed]

Lynch, D. W.

J. H. Weaver, C. G. Olson, and D. W. Lynch, “Optical properties of crystalline tungsten,” Phys. Rev. B12(4), 1293–1297 (1975).
[CrossRef]

Mainguy, S.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature416(6876), 61–64 (2002).
[CrossRef] [PubMed]

Majewski, M. L.

Maradudin, A. A.

M. Kretschmann, T. A. Leskova, and A. A. Maradudin, “Conical Propagation of a Surface Polariton Across a Grating,” Opt. Commun.215(4-6), 205–223 (2003).
[CrossRef]

Marquier, F.

C. Arnold, F. Marquier, M. Garin, F. Pardo, S. Collin, N. Bardou, J.-L. Pelouard, and J.-J. Greffet, “Coherent thermal infrared emission by two-dimensional silicon carbide gratings,” Phys. Rev. B86(3), 035316 (2012).
[CrossRef]

M. Laroche, C. Arnold, F. Marquier, R. Carminati, J.-J. Greffet, S. Collin, N. Bardou, and J.-L. Pelouard, “Highly directional radiation generated by a tungsten thermal source,” Opt. Lett.30(19), 2623–2625 (2005).
[CrossRef] [PubMed]

Maruyama, S.

S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two-dimensionally confined modes in microcavities,” Appl. Phys. Lett.79(9), 1393 (2001).
[CrossRef]

Masuno, K.

K. Masuno, T. Sawada, S. Kumagai, and M. Sasaki, “Multiwavelength Selective IR Emission Using Surface Plasmon Polaritons for Gas Sensing,” IEEE Photon. Technol. Lett.23(22), 1661–1663 (2011).
[CrossRef]

Miyazaki, H. T.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett.92(14), 141114 (2008).
[CrossRef]

Mulet, J.-P.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature416(6876), 61–64 (2002).
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Supplementary Material (1)

» Media 1: MPG (413 KB)     

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic of the simulated 1D tungsten grating. The geometry of the grating is determined by its period (Λ), width of the ridge (d), and groove depth (h). (b) Emittance spectra of a 1D tungsten grating for TM waves at normal directions for periods 4 μm and 3.2 μm respectively. The filling factor f = 0.85, groove depth h = 0.3 μm. (c) E-field distribution in vicinity of the grating for different wavelengths corresponding to the zoomed-in spectrum of (b). At the wavelength of 4.10 μm, a standing surface wave is formed at the air-tungsten interface which evanescently penetrates air. The red lines plot the skeleton of the grating, similarly hereinafter in the field distribution map.

Fig. 2
Fig. 2

Emittance spectra of a 1D grating for TM waves at normal directions for period 4μm (left panel) and 3.2 μm (right panel) respectively with different filling factor and grating depth.

Fig. 3
Fig. 3

(a) E-field distributions at resonant wavelength for f = 0.85 and 0.4 respectively. (b) Corresponding E-field intensity (normalized to the highest value) versus the distance away from the air-tungsten interface for f = 0.85 and 0.4 along with the vertical magenta dotted line in the field distribution map as shown (a). The stars plot the calculated values and lines the fitting exponential functions. Obviously, the field decays to 1/e at a distance of 3.8 for f = 0.85 while 9.9 μm for f = 0.4, revealing that the field is more intensively concentrated in vicinity of the interface and more photons can be absorbed when f = 0.85.

Fig. 4
Fig. 4

Emittance spectra at various azimuthal angles between the incident plane and x direction.

Fig. 5
Fig. 5

(a) Schematic of the simulated orthogonally-crossed 2D tungsten grating. The geometry of the grating is determined by its periods (Λx and Λy). The definition of other geometric parameters is the same as in Fig. 1(a). Λx = Λy = 3.2 μm in (b)-(d). Emittance spectra of the 2D grating for TM waves at normal directions are shown in (b) for fx = fy = 0.3, h = 0.3 μm and (c) fx = fy = 0.3 with different h. Higher order mode (1,1) and (2,0) can be observed in (b) as expected. (d) Emittance spectra with fx = fy being varied from 0.1 to 0.6 when h = 0.3 μm. The dotted lines display the full width at half maximum (FWHM), which increases with the filling ratio.

Fig. 6
Fig. 6

(a) Emittance spectra of the orthogonally-crossed 2D grating for Λx = 3.2 and Λy = 4 μm with fx = fy = 0.3, h = 0.3 μm. Insets display E-field distributions at resonant for modes (1, 0) and (0, 1). (b)-(d) Emittance spectra at different f. Please note that in order to save simulating time, we only calculated the emittance near to the resonant wavelength corresponding to (1, 0) and (0, 1) modes respectively. (b) shows the emittance spectra of the 2D grating with different filling factors. fx and fy is varied simultaneously. (c) shows those with different fy when fx = 0.3 and (d) shows those with different fx when fy = 0.3. The results in the left panel are for x-direction (ϕ = 0°) and right panel for y-direction (ϕ = 90°).

Fig. 7
Fig. 7

(a) Emittance spectra at various azimuthal angles between the incident plane and x direction with Λx /Λy = 3.2/4 μm, h = 0.3μm and fx = fy = 0.3. (b) E-field distribution of the orthogonally-crossed 2D grating for Λx = 3.2 and Λy = 4 μm at a wavelength of 3.21 μm and 4.005 μm when ϕ = 45° (Media 1).

Tables (1)

Tables Icon

Table 1 The value of the emittance and resonant wavelength (in parenthesis) at different filling factor f and depth h (μm) for period 4 and 3.2 μm.

Equations (6)

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ε w (ω)=(1 Ω p 2 ω(ωi Γ 0 ) )+ I=1 k f I ω P 2 ( ω I 2 ω 2 )+iω Γ I ,
k sp,x = k 0 ε m (ω) 1+ ε m (ω) .
k sp,x = k ox ±j K x = k 0 sinθcosϕ + ¯ j 2π Λ ,
λ res =± Λ j ε w (ω) 1+ ε w (ω) .
λ res =± Λ j ε w eff (ω) 1+ ε w eff (ω) .
λ r e s , x = Λ x Λ y ( j x Λ y ) 2 + ( j y Λ x ) 2 ε w e f f , x ( ω ) 1 + ε w e f f , x ( ω ) λ r e s , y = Λ x Λ y ( j x Λ y ) 2 + ( j y Λ x ) 2 ε w e f f , y ( ω ) 1 + ε w e f f , y ( ω ) . }

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