Abstract

Development of a 2D metamaterial that preferentially emits broadband circularly-polarized (CP) infrared radiation is hindered by the fact that orthogonal electric-field components are uncorrelated at the surface of the thermal emitter, a consequence of the fluctuation-dissipation theorem. We achieve broadband CP thermal emission by fabricating a meanderline quarter-wave retarder on a transparent thermal-isolation layer. Behind this isolation layer, in thermal contact with the emitter, is a wire-grid polarizer. Along with an unavoidable linear polarized radiation characteristic from the meanderline, we measured a degree of circular polarization (DOCP) of 28%, averaged over the 8- to 12 μm band.

© 2011 OSA

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2011 (3)

2010 (4)

2009 (1)

M. W. Kudenov, J. L. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[CrossRef]

2008 (4)

J.-H. Lee, J. C. W. Lee, W. Leung, M. Li, K. Constant, C. T. Chan, and K.-M. Ho, “Polarization engineering of thermal radiation using metallic photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(17), 3244–3247 (2008).
[CrossRef]

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, “Extraordinary coherent thermal emission from SiC due to coupled resonant cavities,” J. Heat Transfer 130(11), 112401 (2008).
[CrossRef]

W. R. Folks, J. C. Ginn, D. J. Shelton, J. S. Tharp, and G. D. Boreman, “Spectroscopic ellipsometry of materials for infrared micro-device fabrication,” Phys. Status Solidi 5(5), 1113–1116 (2008) (c).
[CrossRef]

F. Marquier, C. Arnold, M. Laroche, J. J. Greffet, and Y. Chen, “Degree of polarization of thermal light emitted by gratings supporting surface waves,” Opt. Express 16(8), 5305–5313 (2008).
[CrossRef] [PubMed]

2007 (3)

B. J. Lee and Z. M. Zhang, “Coherent thermal emission from modified periodic multilayer structures,” J. Heat Transfer 129(1), 17–26 (2007).
[CrossRef]

J. C. W. Lee and C. T. Chan, “Circularly polarized thermal radiation from layer-by-layer photonic crystal structures,” Appl. Phys. Lett. 90(5), 051912 (2007).
[CrossRef]

O. G. Kollyukh, A. I. Liptuga, V. Morozhenko, V. I. Pipa, and E. F. Venger, “Circular polarized coherent thermal radiation from semiconductor layers in an external magnetic field,” Opt. Commun. 276(1), 131–134 (2007).
[CrossRef]

2006 (3)

D. L. C. Chan, M. Soljacić, and J. D. Joannopoulos, “Thermal emission and design in one-dimensional periodic metallic photonic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(1), 016609 (2006).
[CrossRef] [PubMed]

M. Laroche, R. Carminati, and J.-J. Greffet, “Coherent thermal antenna using a photonic crystal slab,” Phys. Rev. Lett. 96(12), 123903 (2006).
[CrossRef] [PubMed]

J. S. Tharp, J. M. Lopez-Alonso, J. C. Ginn, C. F. Middleton, B. A. Lail, B. A. Munk, and G. D. Boreman, “Demonstration of a single-layer meanderline phase retarder at infrared,” Opt. Lett. 31(18), 2687–2689 (2006).
[CrossRef] [PubMed]

2005 (5)

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]

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86(19), 191102 (2005).
[CrossRef]

M. Florescu, H. Lee, A. J. Stimpson, and J. Dowling, “Thermal emission and absorption of radiation in finite inverted-opal photonic crystals,” Phys. Rev. A 72(3), 033821 (2005).
[CrossRef]

S. Enoch, J.-J. Simon, L. Escoubas, Z. Elalmy, F. Lemarquis, P. Torchio, and G. Albrand, “Simple layer-by-layer photonic crystal for the control of thermal emission,” Appl. Phys. Lett. 86(26), 261101 (2005).
[CrossRef]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
[CrossRef]

2002 (1)

T. Setälä, M. Kaivola, and A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett. 88(12), 123902 (2002).
[CrossRef] [PubMed]

2000 (3)

A. V. Shchegrov, K. Joulain, R. Carminati, and J.-J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85(7), 1548–1551 (2000).
[CrossRef] [PubMed]

S.-Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and suppression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[CrossRef]

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186(1-3), 57–67 (2000).
[CrossRef]

1999 (3)

1998 (3)

J. J. Greffet and M. Nieto-Vesperinas, “Field theory for generalized bidirectional reflectivity: derivation of Helmholtz’s reciprocity principle and Kirchhoff’s law,” J. Opt. Soc. Am. A 15(10), 2735–2744 (1998).
[CrossRef]

J. A. Ruffner, P. G. Clem, B. A. Tuttle, C. J. Brinker, C. S. Sriram, and J. A. Bullington, “Uncooled thin film infrared imaging device with aerogel thermal isolation: deposition and planarization techniques,” Thin Solid Films 332(1-2), 356–361 (1998).
[CrossRef]

M. Schmidt and F. Schwertfeger, “Applications for silica aerogel products,” J. Non-Cryst. Solids 225, 364–368 (1998).
[CrossRef]

1997 (1)

J. Le Gall, M. Olivier, and J.-J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emissionby a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55(15), 10105–10114 (1997).
[CrossRef]

1994 (1)

L. W. Hrubesh and R. W. Pekala, “Thermal properties of organic and inorganic aerogels,” J. Mater. Res. 9(3), 731–738 (1994).
[CrossRef]

1991 (1)

1988 (1)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II. Doped silicon: Angular variation,” Phys. Rev. B Condens. Matter 37(18), 10803–10813 (1988).
[CrossRef] [PubMed]

1975 (1)

G. S. Agarwal, “Quantum electrodynamics in the presence of dielectrics and conductors. I. Electromagnetic-field response functions and black-body fluctuations in finite geometries,” Phys. Rev. A 11(1), 230–242 (1975).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, “Quantum electrodynamics in the presence of dielectrics and conductors. I. Electromagnetic-field response functions and black-body fluctuations in finite geometries,” Phys. Rev. A 11(1), 230–242 (1975).
[CrossRef]

Albrand, G.

S. Enoch, J.-J. Simon, L. Escoubas, Z. Elalmy, F. Lemarquis, P. Torchio, and G. Albrand, “Simple layer-by-layer photonic crystal for the control of thermal emission,” Appl. Phys. Lett. 86(26), 261101 (2005).
[CrossRef]

Alcubilla, R.

Araci, I. E.

Arnold, C.

Bardou, N.

Biener, G.

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, “Extraordinary coherent thermal emission from SiC due to coupled resonant cavities,” J. Heat Transfer 130(11), 112401 (2008).
[CrossRef]

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86(19), 191102 (2005).
[CrossRef]

Boreman, G.

Boreman, G. D.

Brinker, C. J.

P. E. Hopkins, B. Kaehr, L. M. Phinney, T. P. Koehler, A. M. Grillet, D. Dunphy, F. Garcia, and C. J. Brinker, “Measuring the thermal conductivity of porous, transparent SiO2 films with time domain thermoreflectance,” J. Heat Transfer 133(6), 061601 (2011).
[CrossRef]

J. A. Ruffner, P. G. Clem, B. A. Tuttle, C. J. Brinker, C. S. Sriram, and J. A. Bullington, “Uncooled thin film infrared imaging device with aerogel thermal isolation: deposition and planarization techniques,” Thin Solid Films 332(1-2), 356–361 (1998).
[CrossRef]

Bullington, J. A.

J. A. Ruffner, P. G. Clem, B. A. Tuttle, C. J. Brinker, C. S. Sriram, and J. A. Bullington, “Uncooled thin film infrared imaging device with aerogel thermal isolation: deposition and planarization techniques,” Thin Solid Films 332(1-2), 356–361 (1998).
[CrossRef]

Bur, J.

S.-Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and suppression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[CrossRef]

Carminati, R.

M. Laroche, R. Carminati, and J.-J. Greffet, “Coherent thermal antenna using a photonic crystal slab,” Phys. Rev. Lett. 96(12), 123903 (2006).
[CrossRef] [PubMed]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
[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]

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186(1-3), 57–67 (2000).
[CrossRef]

A. V. Shchegrov, K. Joulain, R. Carminati, and J.-J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85(7), 1548–1551 (2000).
[CrossRef] [PubMed]

Chan, C. T.

J.-H. Lee, J. C. W. Lee, W. Leung, M. Li, K. Constant, C. T. Chan, and K.-M. Ho, “Polarization engineering of thermal radiation using metallic photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(17), 3244–3247 (2008).
[CrossRef]

J. C. W. Lee and C. T. Chan, “Circularly polarized thermal radiation from layer-by-layer photonic crystal structures,” Appl. Phys. Lett. 90(5), 051912 (2007).
[CrossRef]

Chan, D. L. C.

D. L. C. Chan, M. Soljacić, and J. D. Joannopoulos, “Thermal emission and design in one-dimensional periodic metallic photonic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(1), 016609 (2006).
[CrossRef] [PubMed]

Chen, Y.

Choi, K. K.

S.-Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and suppression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[CrossRef]

Chow, E.

S.-Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and suppression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[CrossRef]

Clem, P. G.

J. A. Ruffner, P. G. Clem, B. A. Tuttle, C. J. Brinker, C. S. Sriram, and J. A. Bullington, “Uncooled thin film infrared imaging device with aerogel thermal isolation: deposition and planarization techniques,” Thin Solid Films 332(1-2), 356–361 (1998).
[CrossRef]

Collin, S.

Constant, K.

J.-H. Lee, J. C. W. Lee, W. Leung, M. Li, K. Constant, C. T. Chan, and K.-M. Ho, “Polarization engineering of thermal radiation using metallic photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(17), 3244–3247 (2008).
[CrossRef]

Dahan, N.

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, “Extraordinary coherent thermal emission from SiC due to coupled resonant cavities,” J. Heat Transfer 130(11), 112401 (2008).
[CrossRef]

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86(19), 191102 (2005).
[CrossRef]

Dalcher, A.

Deguzman, P. C.

Demir, V.

Dowling, J.

M. Florescu, H. Lee, A. J. Stimpson, and J. Dowling, “Thermal emission and absorption of radiation in finite inverted-opal photonic crystals,” Phys. Rev. A 72(3), 033821 (2005).
[CrossRef]

Dunphy, D.

P. E. Hopkins, B. Kaehr, L. M. Phinney, T. P. Koehler, A. M. Grillet, D. Dunphy, F. Garcia, and C. J. Brinker, “Measuring the thermal conductivity of porous, transparent SiO2 films with time domain thermoreflectance,” J. Heat Transfer 133(6), 061601 (2011).
[CrossRef]

Elalmy, Z.

S. Enoch, J.-J. Simon, L. Escoubas, Z. Elalmy, F. Lemarquis, P. Torchio, and G. Albrand, “Simple layer-by-layer photonic crystal for the control of thermal emission,” Appl. Phys. Lett. 86(26), 261101 (2005).
[CrossRef]

Enoch, S.

S. Enoch, J.-J. Simon, L. Escoubas, Z. Elalmy, F. Lemarquis, P. Torchio, and G. Albrand, “Simple layer-by-layer photonic crystal for the control of thermal emission,” Appl. Phys. Lett. 86(26), 261101 (2005).
[CrossRef]

Escoubas, L.

S. Enoch, J.-J. Simon, L. Escoubas, Z. Elalmy, F. Lemarquis, P. Torchio, and G. Albrand, “Simple layer-by-layer photonic crystal for the control of thermal emission,” Appl. Phys. Lett. 86(26), 261101 (2005).
[CrossRef]

Fleming, J. G.

S.-Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and suppression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[CrossRef]

Florescu, M.

M. Florescu, H. Lee, A. J. Stimpson, and J. Dowling, “Thermal emission and absorption of radiation in finite inverted-opal photonic crystals,” Phys. Rev. A 72(3), 033821 (2005).
[CrossRef]

Folks, W. R.

W. R. Folks, J. C. Ginn, D. J. Shelton, J. S. Tharp, and G. D. Boreman, “Spectroscopic ellipsometry of materials for infrared micro-device fabrication,” Phys. Status Solidi 5(5), 1113–1116 (2008) (c).
[CrossRef]

Friberg, A. T.

T. Setälä, M. Kaivola, and A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett. 88(12), 123902 (2002).
[CrossRef] [PubMed]

Garcia, F.

P. E. Hopkins, B. Kaehr, L. M. Phinney, T. P. Koehler, A. M. Grillet, D. Dunphy, F. Garcia, and C. J. Brinker, “Measuring the thermal conductivity of porous, transparent SiO2 films with time domain thermoreflectance,” J. Heat Transfer 133(6), 061601 (2011).
[CrossRef]

Garín, M.

Gebhart, B.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II. Doped silicon: Angular variation,” Phys. Rev. B Condens. Matter 37(18), 10803–10813 (1988).
[CrossRef] [PubMed]

Gerhart, G. R.

M. W. Kudenov, J. L. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[CrossRef]

Ginn, J.

Ginn, J. C.

W. R. Folks, J. C. Ginn, D. J. Shelton, J. S. Tharp, and G. D. Boreman, “Spectroscopic ellipsometry of materials for infrared micro-device fabrication,” Phys. Status Solidi 5(5), 1113–1116 (2008) (c).
[CrossRef]

J. S. Tharp, J. M. Lopez-Alonso, J. C. Ginn, C. F. Middleton, B. A. Lail, B. A. Munk, and G. D. Boreman, “Demonstration of a single-layer meanderline phase retarder at infrared,” Opt. Lett. 31(18), 2687–2689 (2006).
[CrossRef] [PubMed]

Goldberg, A.

S.-Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and suppression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[CrossRef]

Gori, F.

Gorodetski, Y.

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, “Extraordinary coherent thermal emission from SiC due to coupled resonant cavities,” J. Heat Transfer 130(11), 112401 (2008).
[CrossRef]

Greffet, J. J.

Greffet, J.-J.

M. Laroche, R. Carminati, and J.-J. Greffet, “Coherent thermal antenna using a photonic crystal slab,” Phys. Rev. Lett. 96(12), 123903 (2006).
[CrossRef] [PubMed]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
[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]

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186(1-3), 57–67 (2000).
[CrossRef]

A. V. Shchegrov, K. Joulain, R. Carminati, and J.-J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85(7), 1548–1551 (2000).
[CrossRef] [PubMed]

J. Le Gall, M. Olivier, and J.-J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emissionby a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55(15), 10105–10114 (1997).
[CrossRef]

Grillet, A. M.

P. E. Hopkins, B. Kaehr, L. M. Phinney, T. P. Koehler, A. M. Grillet, D. Dunphy, F. Garcia, and C. J. Brinker, “Measuring the thermal conductivity of porous, transparent SiO2 films with time domain thermoreflectance,” J. Heat Transfer 133(6), 061601 (2011).
[CrossRef]

Hasman, E.

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, “Extraordinary coherent thermal emission from SiC due to coupled resonant cavities,” J. Heat Transfer 130(11), 112401 (2008).
[CrossRef]

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86(19), 191102 (2005).
[CrossRef]

Henkel, C.

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186(1-3), 57–67 (2000).
[CrossRef]

Hernández, D.

Hesketh, P. J.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II. Doped silicon: Angular variation,” Phys. Rev. B Condens. Matter 37(18), 10803–10813 (1988).
[CrossRef] [PubMed]

Ho, K.-M.

J.-H. Lee, J. C. W. Lee, W. Leung, M. Li, K. Constant, C. T. Chan, and K.-M. Ho, “Polarization engineering of thermal radiation using metallic photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(17), 3244–3247 (2008).
[CrossRef]

Hopkins, P. E.

P. E. Hopkins, B. Kaehr, L. M. Phinney, T. P. Koehler, A. M. Grillet, D. Dunphy, F. Garcia, and C. J. Brinker, “Measuring the thermal conductivity of porous, transparent SiO2 films with time domain thermoreflectance,” J. Heat Transfer 133(6), 061601 (2011).
[CrossRef]

Hrubesh, L. W.

L. W. Hrubesh and R. W. Pekala, “Thermal properties of organic and inorganic aerogels,” J. Mater. Res. 9(3), 731–738 (1994).
[CrossRef]

Joannopoulos, J. D.

D. L. C. Chan, M. Soljacić, and J. D. Joannopoulos, “Thermal emission and design in one-dimensional periodic metallic photonic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(1), 016609 (2006).
[CrossRef] [PubMed]

Jones, M. W.

Joulain, K.

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
[CrossRef]

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186(1-3), 57–67 (2000).
[CrossRef]

A. V. Shchegrov, K. Joulain, R. Carminati, and J.-J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85(7), 1548–1551 (2000).
[CrossRef] [PubMed]

Kaehr, B.

P. E. Hopkins, B. Kaehr, L. M. Phinney, T. P. Koehler, A. M. Grillet, D. Dunphy, F. Garcia, and C. J. Brinker, “Measuring the thermal conductivity of porous, transparent SiO2 films with time domain thermoreflectance,” J. Heat Transfer 133(6), 061601 (2011).
[CrossRef]

Kaivola, M.

T. Setälä, M. Kaivola, and A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett. 88(12), 123902 (2002).
[CrossRef] [PubMed]

Kleiner, V.

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, “Extraordinary coherent thermal emission from SiC due to coupled resonant cavities,” J. Heat Transfer 130(11), 112401 (2008).
[CrossRef]

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86(19), 191102 (2005).
[CrossRef]

Koehler, T. P.

P. E. Hopkins, B. Kaehr, L. M. Phinney, T. P. Koehler, A. M. Grillet, D. Dunphy, F. Garcia, and C. J. Brinker, “Measuring the thermal conductivity of porous, transparent SiO2 films with time domain thermoreflectance,” J. Heat Transfer 133(6), 061601 (2011).
[CrossRef]

Kollyukh, O. G.

O. G. Kollyukh, A. I. Liptuga, V. Morozhenko, V. I. Pipa, and E. F. Venger, “Circular polarized coherent thermal radiation from semiconductor layers in an external magnetic field,” Opt. Commun. 276(1), 131–134 (2007).
[CrossRef]

Krenz, P.

Kropachev, A.

Kudenov, M. W.

M. W. Kudenov, J. L. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[CrossRef]

Labadie, N. R.

N. R. Labadie and S. K. Sharma, “A novel compact volumetric metamaterial structure with asymmetric transmission and polarization conversion,” Metamaterials (Amst.) 4(1), 44–57 (2010).
[CrossRef]

Lail, B.

Lail, B. A.

Laroche, M.

Le Gall, J.

J. Le Gall, M. Olivier, and J.-J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emissionby a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55(15), 10105–10114 (1997).
[CrossRef]

Lee, B. J.

B. J. Lee and Z. M. Zhang, “Coherent thermal emission from modified periodic multilayer structures,” J. Heat Transfer 129(1), 17–26 (2007).
[CrossRef]

Lee, H.

M. Florescu, H. Lee, A. J. Stimpson, and J. Dowling, “Thermal emission and absorption of radiation in finite inverted-opal photonic crystals,” Phys. Rev. A 72(3), 033821 (2005).
[CrossRef]

Lee, J. C. W.

J.-H. Lee, J. C. W. Lee, W. Leung, M. Li, K. Constant, C. T. Chan, and K.-M. Ho, “Polarization engineering of thermal radiation using metallic photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(17), 3244–3247 (2008).
[CrossRef]

J. C. W. Lee and C. T. Chan, “Circularly polarized thermal radiation from layer-by-layer photonic crystal structures,” Appl. Phys. Lett. 90(5), 051912 (2007).
[CrossRef]

Lee, J.-H.

J.-H. Lee, J. C. W. Lee, W. Leung, M. Li, K. Constant, C. T. Chan, and K.-M. Ho, “Polarization engineering of thermal radiation using metallic photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(17), 3244–3247 (2008).
[CrossRef]

Lemarquis, F.

S. Enoch, J.-J. Simon, L. Escoubas, Z. Elalmy, F. Lemarquis, P. Torchio, and G. Albrand, “Simple layer-by-layer photonic crystal for the control of thermal emission,” Appl. Phys. Lett. 86(26), 261101 (2005).
[CrossRef]

Leung, W.

J.-H. Lee, J. C. W. Lee, W. Leung, M. Li, K. Constant, C. T. Chan, and K.-M. Ho, “Polarization engineering of thermal radiation using metallic photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(17), 3244–3247 (2008).
[CrossRef]

Li, M.

J.-H. Lee, J. C. W. Lee, W. Leung, M. Li, K. Constant, C. T. Chan, and K.-M. Ho, “Polarization engineering of thermal radiation using metallic photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(17), 3244–3247 (2008).
[CrossRef]

Lin, S.-Y.

S.-Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and suppression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[CrossRef]

Lindquist, G.

Liptuga, A. I.

O. G. Kollyukh, A. I. Liptuga, V. Morozhenko, V. I. Pipa, and E. F. Venger, “Circular polarized coherent thermal radiation from semiconductor layers in an external magnetic field,” Opt. Commun. 276(1), 131–134 (2007).
[CrossRef]

Lopez-Alonso, J. M.

Marquier, F.

Meier, J. T.

Middleton, C. F.

Morozhenko, V.

O. G. Kollyukh, A. I. Liptuga, V. Morozhenko, V. I. Pipa, and E. F. Venger, “Circular polarized coherent thermal radiation from semiconductor layers in an external magnetic field,” Opt. Commun. 276(1), 131–134 (2007).
[CrossRef]

Mulet, J.-P.

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
[CrossRef]

Munk, B. A.

Nagatsuma, T.

Nieto-Vesperinas, M.

Niv, A.

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, “Extraordinary coherent thermal emission from SiC due to coupled resonant cavities,” J. Heat Transfer 130(11), 112401 (2008).
[CrossRef]

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86(19), 191102 (2005).
[CrossRef]

Nordin, G. P.

Norwood, R. A.

Olivier, M.

J. Le Gall, M. Olivier, and J.-J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emissionby a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55(15), 10105–10114 (1997).
[CrossRef]

Pekala, R. W.

L. W. Hrubesh and R. W. Pekala, “Thermal properties of organic and inorganic aerogels,” J. Mater. Res. 9(3), 731–738 (1994).
[CrossRef]

Pelouard, J.-L.

Persons, C.

Peyghambarian, N.

Pezzaniti, J. L.

M. W. Kudenov, J. L. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[CrossRef]

Phinney, L. M.

P. E. Hopkins, B. Kaehr, L. M. Phinney, T. P. Koehler, A. M. Grillet, D. Dunphy, F. Garcia, and C. J. Brinker, “Measuring the thermal conductivity of porous, transparent SiO2 films with time domain thermoreflectance,” J. Heat Transfer 133(6), 061601 (2011).
[CrossRef]

Pipa, V. I.

O. G. Kollyukh, A. I. Liptuga, V. Morozhenko, V. I. Pipa, and E. F. Venger, “Circular polarized coherent thermal radiation from semiconductor layers in an external magnetic field,” Opt. Commun. 276(1), 131–134 (2007).
[CrossRef]

Resnick, A.

Rodriguez, A.

Ruffner, J. A.

J. A. Ruffner, P. G. Clem, B. A. Tuttle, C. J. Brinker, C. S. Sriram, and J. A. Bullington, “Uncooled thin film infrared imaging device with aerogel thermal isolation: deposition and planarization techniques,” Thin Solid Films 332(1-2), 356–361 (1998).
[CrossRef]

Schmidt, M.

M. Schmidt and F. Schwertfeger, “Applications for silica aerogel products,” J. Non-Cryst. Solids 225, 364–368 (1998).
[CrossRef]

Schwertfeger, F.

M. Schmidt and F. Schwertfeger, “Applications for silica aerogel products,” J. Non-Cryst. Solids 225, 364–368 (1998).
[CrossRef]

Setälä, T.

T. Setälä, M. Kaivola, and A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett. 88(12), 123902 (2002).
[CrossRef] [PubMed]

Sharma, S. K.

N. R. Labadie and S. K. Sharma, “A novel compact volumetric metamaterial structure with asymmetric transmission and polarization conversion,” Metamaterials (Amst.) 4(1), 44–57 (2010).
[CrossRef]

Shchegrov, A. V.

A. V. Shchegrov, K. Joulain, R. Carminati, and J.-J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85(7), 1548–1551 (2000).
[CrossRef] [PubMed]

Shelton, D.

Shelton, D. J.

W. R. Folks, J. C. Ginn, D. J. Shelton, J. S. Tharp, and G. D. Boreman, “Spectroscopic ellipsometry of materials for infrared micro-device fabrication,” Phys. Status Solidi 5(5), 1113–1116 (2008) (c).
[CrossRef]

Simon, J.-J.

S. Enoch, J.-J. Simon, L. Escoubas, Z. Elalmy, F. Lemarquis, P. Torchio, and G. Albrand, “Simple layer-by-layer photonic crystal for the control of thermal emission,” Appl. Phys. Lett. 86(26), 261101 (2005).
[CrossRef]

Skotheim, T.

Soljacic, M.

D. L. C. Chan, M. Soljacić, and J. D. Joannopoulos, “Thermal emission and design in one-dimensional periodic metallic photonic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(1), 016609 (2006).
[CrossRef] [PubMed]

Sriram, C. S.

J. A. Ruffner, P. G. Clem, B. A. Tuttle, C. J. Brinker, C. S. Sriram, and J. A. Bullington, “Uncooled thin film infrared imaging device with aerogel thermal isolation: deposition and planarization techniques,” Thin Solid Films 332(1-2), 356–361 (1998).
[CrossRef]

Stimpson, A. J.

M. Florescu, H. Lee, A. J. Stimpson, and J. Dowling, “Thermal emission and absorption of radiation in finite inverted-opal photonic crystals,” Phys. Rev. A 72(3), 033821 (2005).
[CrossRef]

Takahara, J.

Tharp, J. S.

W. R. Folks, J. C. Ginn, D. J. Shelton, J. S. Tharp, and G. D. Boreman, “Spectroscopic ellipsometry of materials for infrared micro-device fabrication,” Phys. Status Solidi 5(5), 1113–1116 (2008) (c).
[CrossRef]

J. S. Tharp, J. M. Lopez-Alonso, J. C. Ginn, C. F. Middleton, B. A. Lail, B. A. Munk, and G. D. Boreman, “Demonstration of a single-layer meanderline phase retarder at infrared,” Opt. Lett. 31(18), 2687–2689 (2006).
[CrossRef] [PubMed]

Torchio, P.

S. Enoch, J.-J. Simon, L. Escoubas, Z. Elalmy, F. Lemarquis, P. Torchio, and G. Albrand, “Simple layer-by-layer photonic crystal for the control of thermal emission,” Appl. Phys. Lett. 86(26), 261101 (2005).
[CrossRef]

Trifonov, T.

Tuttle, B. A.

J. A. Ruffner, P. G. Clem, B. A. Tuttle, C. J. Brinker, C. S. Sriram, and J. A. Bullington, “Uncooled thin film infrared imaging device with aerogel thermal isolation: deposition and planarization techniques,” Thin Solid Films 332(1-2), 356–361 (1998).
[CrossRef]

Ueba, Y.

Venger, E. F.

O. G. Kollyukh, A. I. Liptuga, V. Morozhenko, V. I. Pipa, and E. F. Venger, “Circular polarized coherent thermal radiation from semiconductor layers in an external magnetic field,” Opt. Commun. 276(1), 131–134 (2007).
[CrossRef]

Wadsworth, S. L.

Zemel, J. N.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II. Doped silicon: Angular variation,” Phys. Rev. B Condens. Matter 37(18), 10803–10813 (1988).
[CrossRef] [PubMed]

Zhang, Z. M.

B. J. Lee and Z. M. Zhang, “Coherent thermal emission from modified periodic multilayer structures,” J. Heat Transfer 129(1), 17–26 (2007).
[CrossRef]

Zimmermann, E. C.

Adv. Mater. (Deerfield Beach Fla.) (1)

J.-H. Lee, J. C. W. Lee, W. Leung, M. Li, K. Constant, C. T. Chan, and K.-M. Ho, “Polarization engineering of thermal radiation using metallic photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 20(17), 3244–3247 (2008).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

S. Enoch, J.-J. Simon, L. Escoubas, Z. Elalmy, F. Lemarquis, P. Torchio, and G. Albrand, “Simple layer-by-layer photonic crystal for the control of thermal emission,” Appl. Phys. Lett. 86(26), 261101 (2005).
[CrossRef]

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86(19), 191102 (2005).
[CrossRef]

J. C. W. Lee and C. T. Chan, “Circularly polarized thermal radiation from layer-by-layer photonic crystal structures,” Appl. Phys. Lett. 90(5), 051912 (2007).
[CrossRef]

J. Heat Transfer (3)

B. J. Lee and Z. M. Zhang, “Coherent thermal emission from modified periodic multilayer structures,” J. Heat Transfer 129(1), 17–26 (2007).
[CrossRef]

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, “Extraordinary coherent thermal emission from SiC due to coupled resonant cavities,” J. Heat Transfer 130(11), 112401 (2008).
[CrossRef]

P. E. Hopkins, B. Kaehr, L. M. Phinney, T. P. Koehler, A. M. Grillet, D. Dunphy, F. Garcia, and C. J. Brinker, “Measuring the thermal conductivity of porous, transparent SiO2 films with time domain thermoreflectance,” J. Heat Transfer 133(6), 061601 (2011).
[CrossRef]

J. Mater. Res. (1)

L. W. Hrubesh and R. W. Pekala, “Thermal properties of organic and inorganic aerogels,” J. Mater. Res. 9(3), 731–738 (1994).
[CrossRef]

J. Non-Cryst. Solids (1)

M. Schmidt and F. Schwertfeger, “Applications for silica aerogel products,” J. Non-Cryst. Solids 225, 364–368 (1998).
[CrossRef]

J. Opt. Soc. Am. A (3)

Metamaterials (Amst.) (1)

N. R. Labadie and S. K. Sharma, “A novel compact volumetric metamaterial structure with asymmetric transmission and polarization conversion,” Metamaterials (Amst.) 4(1), 44–57 (2010).
[CrossRef]

Opt. Commun. (2)

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186(1-3), 57–67 (2000).
[CrossRef]

O. G. Kollyukh, A. I. Liptuga, V. Morozhenko, V. I. Pipa, and E. F. Venger, “Circular polarized coherent thermal radiation from semiconductor layers in an external magnetic field,” Opt. Commun. 276(1), 131–134 (2007).
[CrossRef]

Opt. Eng. (1)

M. W. Kudenov, J. L. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[CrossRef]

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. A (2)

G. S. Agarwal, “Quantum electrodynamics in the presence of dielectrics and conductors. I. Electromagnetic-field response functions and black-body fluctuations in finite geometries,” Phys. Rev. A 11(1), 230–242 (1975).
[CrossRef]

M. Florescu, H. Lee, A. J. Stimpson, and J. Dowling, “Thermal emission and absorption of radiation in finite inverted-opal photonic crystals,” Phys. Rev. A 72(3), 033821 (2005).
[CrossRef]

Phys. Rev. B (2)

S.-Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and suppression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[CrossRef]

J. Le Gall, M. Olivier, and J.-J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emissionby a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55(15), 10105–10114 (1997).
[CrossRef]

Phys. Rev. B Condens. Matter (1)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II. Doped silicon: Angular variation,” Phys. Rev. B Condens. Matter 37(18), 10803–10813 (1988).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

D. L. C. Chan, M. Soljacić, and J. D. Joannopoulos, “Thermal emission and design in one-dimensional periodic metallic photonic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(1), 016609 (2006).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

T. Setälä, M. Kaivola, and A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett. 88(12), 123902 (2002).
[CrossRef] [PubMed]

A. V. Shchegrov, K. Joulain, R. Carminati, and J.-J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85(7), 1548–1551 (2000).
[CrossRef] [PubMed]

M. Laroche, R. Carminati, and J.-J. Greffet, “Coherent thermal antenna using a photonic crystal slab,” Phys. Rev. Lett. 96(12), 123903 (2006).
[CrossRef] [PubMed]

Phys. Status Solidi (1)

W. R. Folks, J. C. Ginn, D. J. Shelton, J. S. Tharp, and G. D. Boreman, “Spectroscopic ellipsometry of materials for infrared micro-device fabrication,” Phys. Status Solidi 5(5), 1113–1116 (2008) (c).
[CrossRef]

Surf. Sci. Rep. (1)

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
[CrossRef]

Thin Solid Films (1)

J. A. Ruffner, P. G. Clem, B. A. Tuttle, C. J. Brinker, C. S. Sriram, and J. A. Bullington, “Uncooled thin film infrared imaging device with aerogel thermal isolation: deposition and planarization techniques,” Thin Solid Films 332(1-2), 356–361 (1998).
[CrossRef]

Other (7)

P. E. Hopkins, B. Kaehr, E. S. Piekos, D. Dunphy, and C. J. Brinker, “Minimum thermal conductivity considerations in aerogel thin films,” manuscript in preparation (2011).

D. Goldstein, Polarized Light, (Marcel Dekker, 2003).

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves. Theories and Applications, (J. Wiley, 2000).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge, 1995).

L. Novotny and B. Hecht, Principles of Nano-Optics, (Cambridge, 2006).

S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics 3: Elements of Random Fields, (Springer-Verlag, 1989).

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, (Pergamon Press, 1960).

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Figures (10)

Fig. 1
Fig. 1

Unit cell profiles of a) circular spiral array, and b) L-shaped wedge array. Below c) is a cross-sectional profile of the emissive structures as simulated in HFSS.

Fig. 2
Fig. 2

Modeled Stokes parameters for a) circular spiral, and b) L-shaped wedge elements.

Fig. 3
Fig. 3

Depiction of a) cross-sectional profile of multilayer structure for generating CP thermal light. The silicon substrate is heated by an active thermal source (hotplate), which generates a linear-polarized signature upon thermal excitation of the wire-grid array. The wire-grid array (in grey) is rotated by 45°, as shown in b), so that the CP meanderline FSS structure (in orange) is able to generate circular polarization upon transmission of the 45°-tilted linear polarized emission. The aerogel helps to thermally isolate the CP meanderline layers from the effects of thermal conduction, and subsequently the consequences of the FDT.

Fig. 4
Fig. 4

Optical constants of silica aerogel measured by infrared ellipsometry [45].

Fig. 5
Fig. 5

SEM images of fabricated planar periodic FSS structures corresponding to a) L-shaped wedge elements, and b) circular spiral elements. Dimensions of the elements are given on the corresponding diagrams in Fig. 1.

Fig. 6
Fig. 6

Schematic of a) porous silica aerogel surface without any capping layer, and b) aerogel surface with a layer of BCB that effectively caps the aerogel film and planarizes the surface.

Fig. 7
Fig. 7

SEM micrograph of meanderline FSS QWP layer with corresponding array dimensions. The elements were fabricated via e-beam lithography and patterned with metallic Al.

Fig. 8
Fig. 8

Broadband imaging polarimetry setup with a) LWIR camera and polarization optics, and b) device under test (DUT) in direct contact with hotplate. The schematic represents the polarimetric system with the wire-grid linear polarizer (LP) and achromatic meanderline quarter-wave plate (QWP) as the analyzing polarization components.

Fig. 9
Fig. 9

Example image taken from polarimetric system with annotated boxes outlining the areas that were selected for noise averaging and the sample area.

Fig. 10
Fig. 10

Same image as Fig. 9, but with the baseline noise subtracted from the data. Part a) shows the sample area as before, with part b) as a zoomed-in image of the planar FSS area. Note the variation in local intensity of the thermally emitted fields over the area of the FSS.

Tables (1)

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Table 1 Measured Polarimetric Data for the Structures Investigated*

Equations (18)

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W ( x , y , t ) = [ E s ( x , y , t ) * E s ( x , y , t ) E s ( x , y , t ) * E p ( x , y , t ) E p ( x , y , t ) * E s ( x , y , t ) E p ( x , y , t ) * E p ( x , y , t ) ] ,
W ( x , y , t ) = [ ε s ( x , y , t ) * ε s ( x , y , t ) ε s ( x , y , t ) * ε p ( x , y , t ) ε p ( x , y , t ) * ε s ( x , y , t ) ε p ( x , y , t ) * ε p ( x , y , t ) ] ,
S ¯ ( x , y , t ) = [ S 0 S 1 S 2 S 3 ] = [ ε s ( x , y , t ) * ε s ( x , y , t ) + ε p ( x , y , t ) * ε p ( x , y , t ) ε s ( x , y , t ) * ε s ( x , y , t ) ε p ( x , y , t ) * ε p ( x , y , t ) ε s ( x , y , t ) * ε p ( x , y , t ) + ε p ( x , y , t ) * ε s ( x , y , t ) i ( ε p ( x , y , t ) * ε s ( x , y , t ) ε s ( x , y , t ) * ε p ( x , y , t ) ) ] ,
S ¯ = [ S 0 S 1 S 2 S 3 ] = [ ε s + ε p ε s ε p 2 ε s ε p cos ( δ ) 2 ε s ε p sin ( δ ) ] = [ ε s + ε p ε s ε p ε + 45 ε 45 ε R H C P ε L H C P ] ,
j s p = ε s ( x , y , t ) * ε p ( x , y , t ) ε s ( x , y , t ) * ε s ( x , y , t ) 1 / 2 ε p ( x , y , t ) * ε p ( x , y , t ) 1 / 2 ,
ε ( λ , Τ ) = A ( λ , Τ ) = 1 R ( λ , Τ ) ,
ε s , p = 1 R s , p ,
ε ± 45 ° = 1 R ± 45 ° ,
ε R H C P , L H C P = 1 R R H C P , L H C P .
S 0 = I ( θ = 0 , ϕ = 0 ) + I ( θ = 90 , ϕ = 0 ) ,
S 1 = I ( θ = 0 , ϕ = 0 ) I ( θ = 90 , ϕ = 0 ) ,
S 2 = I ( θ = 45 , ϕ = 0 ) I ( θ = 135 , ϕ = 0 ) ,
S 3 = ( I ( θ = 45 , ϕ = π / 2 ) I ( θ = 135 , ϕ = π / 2 ) ) / a 2 .
D O P = S 1 2 + S 2 2 + S 3 2 / S 0 ,
D O C P = | S 3 / S 0 | ,
D O L P = D O P 2 D O C P 2 = S 1 2 + S 2 2 / S 0 ,
D O U P = 1 D O P 2 .
D O C P = | ( I ( θ = 45 , ϕ = π / 2 ) I ( θ = 135 , ϕ = π / 2 ) ) ( I ( θ = 45 , ϕ = π / 2 ) + I ( θ = 135 , ϕ = π / 2 ) ) | .

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