Abstract

Heterodyne efficiency is referred as a measure of the quality for the coherent laser communication. The heterodyne efficiency not only reflects the matching of phase and amplitude between the received signal and the local oscillator, but also reveals the polarization matching between the two beams. Different from the common heterodyne efficiency, a revised heterodyne efficiency is proposed by considering the polarization aberrations of optical system. Based on the Polar and Pauli-Zernike decomposition algorithms, the effects of polarization aberrations on the output polarization states are analyzed and shown graphically. The variations of the heterodyne efficiency are investigated by including the separate component of polarization aberrations in mixing of two perfectly matched Gaussian beams. Depending on the modified heterodyne efficiency, an off-axis optical system with a periscopic scanner is modeled and used to discuss the variations of the heterodyne efficiency. A further investigation for three different coatings is accomplished to verify the effects the varied polarization aberrations have on the heterodyne efficiency. The analysis indicates that the modified heterodyne efficiency not only can provide a comprehensive description of the coherent detection system, but also can be used to evaluate and minimize the polarization aberrations of optical system.

© 2017 Optical Society of America

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References

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  1. K. Böhmer, M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Laser communication terminals for the European data relay system,” Proc. SPIE 8246, 82460D (2012).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  5. K. Tanaka and N. Ohta, “Effects of tilt and offset of signal field on heterodyne efficiency,” Appl. Opt. 26(4), 627–632 (1987).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  10. G. Yun, K. Crabtree, and R. A. Chipman, “Skew aberration: a form of polarization aberration,” Opt. Lett. 36(20), 4062–4064 (2011).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  20. W. S. Tiffany Lam, R. Chipman, and R. A. Chipman, “Balancing polarization aberrations in crossed fold mirrors,” Appl. Opt. 54(11), 3236–3245 (2015).
    [Crossref] [PubMed]
  21. Y. Yang and C. Yan, “Polarization property analysis of a periscopic scanner with three-dimensional polarization ray-tracing calculus,” Appl. Opt. 55(6), 1343–1350 (2016).
    [Crossref] [PubMed]
  22. G. Yun, K. Crabtree, and R. A. Chipman, “Three-dimensional polarization ray-tracing calculus I: definition and diattenuation,” Appl. Opt. 50(18), 2855–2865 (2011).
    [Crossref] [PubMed]
  23. G. Yun, S. C. McClain, and R. A. Chipman, “Three-dimensional polarization ray-tracing calculus II: retardance,” Appl. Opt. 50(18), 2866–2874 (2011).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2016 (2)

2015 (1)

2012 (2)

K. Böhmer, M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Laser communication terminals for the European data relay system,” Proc. SPIE 8246, 82460D (2012).
[Crossref]

M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Commercial optical inter-satellite communication at high data rates,” Opt. Eng. 51(3), 031202 (2012).
[Crossref]

2011 (3)

2009 (2)

J. Ruoff and M. Totzeck, “Orientation Zernike polynomials: a useful way to describe the polarization effects of optical imaging systems,” J. Micro/Nanolith. MEMS MOEMS 8(3), 031404 (2009).
[Crossref]

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, Y. Koyama, and H. Kunimori, “Polarization measurements through space-to-ground atmospheric propagation paths by using a highly polarized laser source in space,” Opt. Express 17(25), 22333–22340 (2009).
[Crossref] [PubMed]

2008 (2)

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16(2), 753–791 (2008).
[Crossref] [PubMed]

M. Salem and J. P. Rolland, “Effects of coherence and polarization changes on the heterodyne detection of stochastic beams propagating in free space,” Opt. Commun. 281(20), 5083–5091 (2008).
[Crossref]

2007 (2)

N. Yamamoto, J. Kye, and H. J. Levison, “Polarization aberration analysis using Pauli-Zernike representation,” Proc. SPIE 6520, 65200Y (2007).
[Crossref]

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

2006 (1)

G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, “Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations,” J. Microlith., Microfab., Microsyst. 5(3), 033001 (2006).

1999 (1)

D. Delautre, S. Breugnot, and V. Laude, “Measurement of the sensitivity of heterodyne detection to aberrations using programmable liquid-crystal modulator,” Opt. Commun. 160(1-3), 61–65 (1999).
[Crossref]

1997 (1)

1991 (1)

R. Garreis and C. Zeiss, “90° optical hybrid for coherent receivers,” Proc. SPIE 1522, 210–219 (1991).
[Crossref]

1987 (1)

1984 (1)

1978 (1)

1975 (2)

Barros, D. J. F.

Böhmer, K.

K. Böhmer, M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Laser communication terminals for the European data relay system,” Proc. SPIE 8246, 82460D (2012).
[Crossref]

Breugnot, S.

D. Delautre, S. Breugnot, and V. Laude, “Measurement of the sensitivity of heterodyne detection to aberrations using programmable liquid-crystal modulator,” Opt. Commun. 160(1-3), 61–65 (1999).
[Crossref]

Chambers, D.

Chipman, R.

Chipman, R. A.

Cohen, S. C.

Crabtree, K.

Delautre, D.

D. Delautre, S. Breugnot, and V. Laude, “Measurement of the sensitivity of heterodyne detection to aberrations using programmable liquid-crystal modulator,” Opt. Commun. 160(1-3), 61–65 (1999).
[Crossref]

Fink, D.

Fukumitsu, O.

Garreis, R.

R. Garreis and C. Zeiss, “90° optical hybrid for coherent receivers,” Proc. SPIE 1522, 210–219 (1991).
[Crossref]

Geh, B.

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Gräupner, P.

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Gregory, M.

K. Böhmer, M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Laser communication terminals for the European data relay system,” Proc. SPIE 8246, 82460D (2012).
[Crossref]

M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Commercial optical inter-satellite communication at high data rates,” Opt. Eng. 51(3), 031202 (2012).
[Crossref]

Hall, T. J.

Heine, F.

M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Commercial optical inter-satellite communication at high data rates,” Opt. Eng. 51(3), 031202 (2012).
[Crossref]

K. Böhmer, M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Laser communication terminals for the European data relay system,” Proc. SPIE 8246, 82460D (2012).
[Crossref]

Hempelmann, U.

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Ip, E.

Kahn, J. M.

Kämpfner, H.

K. Böhmer, M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Laser communication terminals for the European data relay system,” Proc. SPIE 8246, 82460D (2012).
[Crossref]

M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Commercial optical inter-satellite communication at high data rates,” Opt. Eng. 51(3), 031202 (2012).
[Crossref]

Koyama, Y.

Kunimori, H.

Kye, J.

N. Yamamoto, J. Kye, and H. J. Levison, “Polarization aberration analysis using Pauli-Zernike representation,” Proc. SPIE 6520, 65200Y (2007).
[Crossref]

G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, “Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations,” J. Microlith., Microfab., Microsyst. 5(3), 033001 (2006).

Lange, R.

M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Commercial optical inter-satellite communication at high data rates,” Opt. Eng. 51(3), 031202 (2012).
[Crossref]

K. Böhmer, M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Laser communication terminals for the European data relay system,” Proc. SPIE 8246, 82460D (2012).
[Crossref]

Lau, A. P. T.

Laude, V.

D. Delautre, S. Breugnot, and V. Laude, “Measurement of the sensitivity of heterodyne detection to aberrations using programmable liquid-crystal modulator,” Opt. Commun. 160(1-3), 61–65 (1999).
[Crossref]

Levinson, H.

G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, “Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations,” J. Microlith., Microfab., Microsyst. 5(3), 033001 (2006).

Levison, H. J.

N. Yamamoto, J. Kye, and H. J. Levison, “Polarization aberration analysis using Pauli-Zernike representation,” Proc. SPIE 6520, 65200Y (2007).
[Crossref]

Lutzer, M.

K. Böhmer, M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Laser communication terminals for the European data relay system,” Proc. SPIE 8246, 82460D (2012).
[Crossref]

M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Commercial optical inter-satellite communication at high data rates,” Opt. Eng. 51(3), 031202 (2012).
[Crossref]

McClain, S. C.

McIntyre, G. R.

G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, “Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations,” J. Microlith., Microfab., Microsyst. 5(3), 033001 (2006).

Mengel, M.

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Meyer, R.

M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Commercial optical inter-satellite communication at high data rates,” Opt. Eng. 51(3), 031202 (2012).
[Crossref]

K. Böhmer, M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Laser communication terminals for the European data relay system,” Proc. SPIE 8246, 82460D (2012).
[Crossref]

Nabavi, N.

Neureuther, A. R.

G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, “Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations,” J. Microlith., Microfab., Microsyst. 5(3), 033001 (2006).

Ohta, N.

Rolland, J. P.

M. Salem and J. P. Rolland, “Effects of coherence and polarization changes on the heterodyne detection of stochastic beams propagating in free space,” Opt. Commun. 281(20), 5083–5091 (2008).
[Crossref]

Ruoff, J.

J. Ruoff and M. Totzeck, “Orientation Zernike polynomials: a useful way to describe the polarization effects of optical imaging systems,” J. Micro/Nanolith. MEMS MOEMS 8(3), 031404 (2009).
[Crossref]

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Saga, N.

Salem, M.

M. Salem and J. P. Rolland, “Effects of coherence and polarization changes on the heterodyne detection of stochastic beams propagating in free space,” Opt. Commun. 281(20), 5083–5091 (2008).
[Crossref]

Schmitt-Weaver, E.

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Shoji, Y.

Takayama, Y.

Takenaka, H.

Takenaka, T.

Tanaka, K.

Tiffany Lam, W. S.

Totzeck, M.

J. Ruoff and M. Totzeck, “Orientation Zernike polynomials: a useful way to describe the polarization effects of optical imaging systems,” J. Micro/Nanolith. MEMS MOEMS 8(3), 031404 (2009).
[Crossref]

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Toyoshima, M.

Yamamoto, N.

N. Yamamoto, J. Kye, and H. J. Levison, “Polarization aberration analysis using Pauli-Zernike representation,” Proc. SPIE 6520, 65200Y (2007).
[Crossref]

Yan, C.

Yang, Y.

Yun, G.

Zeiss, C.

R. Garreis and C. Zeiss, “90° optical hybrid for coherent receivers,” Proc. SPIE 1522, 210–219 (1991).
[Crossref]

Zimmermann, J.

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Appl. Opt. (9)

D. Fink, “Coherent detection signal-to-noise,” Appl. Opt. 14(3), 689–690 (1975).
[Crossref] [PubMed]

T. Takenaka, K. Tanaka, and O. Fukumitsu, “Signal-to-noise ratio in optical heterodyne detection for Gaussian fields,” Appl. Opt. 17(21), 3466–3471 (1978).
[Crossref] [PubMed]

K. Tanaka and N. Ohta, “Effects of tilt and offset of signal field on heterodyne efficiency,” Appl. Opt. 26(4), 627–632 (1987).
[Crossref] [PubMed]

K. Tanaka and N. Saga, “Maximum heterodyne efficiency of optical heterodyne detection in the presence of background radiation,” Appl. Opt. 23(21), 3901–3904 (1984).
[Crossref] [PubMed]

S. C. Cohen, “Heterodyne detection: phase front alignment, beam spot size, and detector uniformity,” Appl. Opt. 14(8), 1953–1959 (1975).
[Crossref] [PubMed]

W. S. Tiffany Lam, R. Chipman, and R. A. Chipman, “Balancing polarization aberrations in crossed fold mirrors,” Appl. Opt. 54(11), 3236–3245 (2015).
[Crossref] [PubMed]

Y. Yang and C. Yan, “Polarization property analysis of a periscopic scanner with three-dimensional polarization ray-tracing calculus,” Appl. Opt. 55(6), 1343–1350 (2016).
[Crossref] [PubMed]

G. Yun, K. Crabtree, and R. A. Chipman, “Three-dimensional polarization ray-tracing calculus I: definition and diattenuation,” Appl. Opt. 50(18), 2855–2865 (2011).
[Crossref] [PubMed]

G. Yun, S. C. McClain, and R. A. Chipman, “Three-dimensional polarization ray-tracing calculus II: retardance,” Appl. Opt. 50(18), 2866–2874 (2011).
[Crossref] [PubMed]

J. Micro/Nanolith. MEMS MOEMS (1)

J. Ruoff and M. Totzeck, “Orientation Zernike polynomials: a useful way to describe the polarization effects of optical imaging systems,” J. Micro/Nanolith. MEMS MOEMS 8(3), 031404 (2009).
[Crossref]

J. Microlith., Microfab., Microsyst. (1)

G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, “Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations,” J. Microlith., Microfab., Microsyst. 5(3), 033001 (2006).

Opt. Commun. (2)

M. Salem and J. P. Rolland, “Effects of coherence and polarization changes on the heterodyne detection of stochastic beams propagating in free space,” Opt. Commun. 281(20), 5083–5091 (2008).
[Crossref]

D. Delautre, S. Breugnot, and V. Laude, “Measurement of the sensitivity of heterodyne detection to aberrations using programmable liquid-crystal modulator,” Opt. Commun. 160(1-3), 61–65 (1999).
[Crossref]

Opt. Eng. (1)

M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Commercial optical inter-satellite communication at high data rates,” Opt. Eng. 51(3), 031202 (2012).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Proc. SPIE (4)

K. Böhmer, M. Gregory, F. Heine, H. Kämpfner, R. Lange, M. Lutzer, and R. Meyer, “Laser communication terminals for the European data relay system,” Proc. SPIE 8246, 82460D (2012).
[Crossref]

R. Garreis and C. Zeiss, “90° optical hybrid for coherent receivers,” Proc. SPIE 1522, 210–219 (1991).
[Crossref]

N. Yamamoto, J. Kye, and H. J. Levison, “Polarization aberration analysis using Pauli-Zernike representation,” Proc. SPIE 6520, 65200Y (2007).
[Crossref]

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Other (1)

R. A. Chipman, “Polarization aberrations,” Ph.D. thesis (University of Arizona, 1987).

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Figures (18)

Fig. 1
Fig. 1 Schematic diagram of the coherent detection system, OA represents the optical antenna; RS represents the received signal; P represents the polarizer; OH represents the optical hybrid; LO represents the local oscillator.
Fig. 2
Fig. 2 Output polarization states with x/y linear diattenuation, the coefficients of each scalar Zernike polynomials are 0.5. d 1 > 0 represents the x-axis diattenuation, d 1 < 0 represents the y-axis diattenuation. The positive diattenuation corresponds to the clockwise rotation and the negative diattenuation corresponds to the counter-clock rotation.
Fig. 3
Fig. 3 Output polarization states with 45/135deg linear diattenuation, the coefficients of each scalar Zernike polynomials are 0.5. d 2 > 0 represents the 45deg diattenuation, d 2 < 0 represents the 135deg diattenuation. The output polarization states maintain 45deg polarized, and the lengths of the line segments are related to the magnitudes of 135deg diattenuation.
Fig. 4
Fig. 4 Output polarization states with x/y linear retardance, the coefficients of each scalar Zernike polynomials are 0.5. r 1 > 0 represents right-handed polarized, r 1 < 0 represents left-hand polarized. The ellipticity of each ellipse on the map represents the magnitude of the phase retardance. The ellipticities and orientation angles of these ellipses are related to the magnitudes and signs of the retardance.
Fig. 5
Fig. 5 Output polarization states with 45/135deg linear retardance, the coefficients of each scalar Zernike polynomials are 0.5. The output polarization states maintain 45deg polarized, and the lengths of the line segments are related to the magnitudes of the retardance.
Fig. 6
Fig. 6 Reduction of the polarization efficiency with the increment of the diattenuation and retardance. (a) linear diattenuation along the coordinate axes; (b) linear retardance along the coordinate axes; (c) linear diattenuation along the bisectors (45/135deg) to the coordinate axes; (d) linear retardance along the bisectors (45/135deg) to the coordinate axes.
Fig. 7
Fig. 7 Output polarization states with x/y linear diattenuation, the coefficients of each scalar Zernike polynomials are 0.5. d 1 > 0 represents the x-axis diattenuation, d 1 < 0 represents the y-axis diattenuation. The orientations of the ellipses are parallel to the coordinate axes. The ellipticities of the ellipses are related to the magnitudes of the diattenuation. The larger diattenuation corresponds to the smaller ellipticity.
Fig. 8
Fig. 8 Output polarization states with 45/135deg linear diattenuation, the coefficients of each scalar Zernike polynomials are 0.5. d 2 > 0 represents the 45deg diattenuation, d 2 < 0 represents the 135deg diattenuation. The orientations of the elliptical polarization are parallel to the 45/135deg diattenuation. The ellipticities of the elliptical polarization are related to the magnitudes of the diattenuation. The larger diattenuation corresponds to the smaller ellipticity.
Fig. 9
Fig. 9 Output polarization states with x/y linear retardance, the coefficients of each scalar Zernike polynomials are 0.5. r 1 > 0 corresponds to 135deg elliptical polarization, r 1 < 0 corresponds to 45deg elliptical polarization. The ellipticity of each ellipse on the map is related to the magnitude of the retardance. The larger retardance corresponds to the smaller ellipticity.
Fig. 10
Fig. 10 Output polarization states with 45/135deg linear retardance, the coefficients of each scalar Zernike polynomials are 0.5. r 2 > 0 corresponds to x-axis elliptical polarization, r 2 < 0 corresponds to y-axis elliptical polarization. The ellipticity of each ellipse on the map is related to the magnitude of the retardance. The larger retardance corresponds to the smaller ellipticity.
Fig. 11
Fig. 11 Reduction of the polarization efficiency with the increment of the diattenuation and retardance. (a) linear diattenuation along the coordinate axes; (b) linear retardance along the coordinate axes; (c) linear diattenuation along the bisectors (45/135deg) to the coordinate axes; (d) linear retardance along the bisectors (45/135deg) to the coordinate axes.
Fig. 12
Fig. 12 Schematic view of the optical system, together with the global coordinate system O; the layout in the red box is the simplified periscopic scanner.
Fig. 13
Fig. 13 The polarization efficiency of the Au-coated optical system; the incident signals are 45deg polarized. When α + β = 0 , 180 , 360 , the polarization efficiencies reach the maximum values, and the maximums are close to 100%; when α + β = 90 , 270 , the polarization efficiencies reach the minimum values, and the minimums are close to zero.
Fig. 14
Fig. 14 The polarization efficiency of the Au-coated optical system; the incident signals are right-handed circular polarized. The maximum polarization efficiencies are close to 0.66, and the maximums occur at β = 0 , 180 , 360 . The minimum polarization efficiencies are close to 0.49, and the minimums occur at β = 90 , 270 .
Fig. 15
Fig. 15 The Pauli-Zernike decomposition of the diattenuation (a) and retardance (b) when the rotation angles ( α , β ) = (0°, 0°); (c) is the ellipticities of the total diattenuation and retardance. The rotation angle ζ is 0deg.
Fig. 16
Fig. 16 The Pauli-Zernike decomposition of the diattenuation (a) and retardance (b) when the rotation angles ( α , β ) = (0°, 90°); (c) is the ellipticities of the total diattenuation and retardance. The rotation angle ζ is 90deg.
Fig. 17
Fig. 17 The Pauli-Zernike decomposition of the diattenuation (a) and retardance (a) when the rotation angles ( α , β ) = (45°, 45°); (c) is the ellipticities of total diattenuation and retardance. The rotation angle ζ is 90deg
Fig. 18
Fig. 18 The polarization efficiency of the Al-coated (a) and PM-coated (b) optical system; the incident signals are right-handed circular polarized. The maximum polarization efficiencies in figure (a) are close to 0.60, and the minimum values are close to 0.5. The maximums occur at β = 0 , 180 , 360 , and the minimums occur at β = 90 , 270 . In figure (b), the maximum polarization efficiencies are 0.51, and the minimum values are 0.49.

Tables (3)

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Table 1 Physical meanings of the decompositions of Jones matrix

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Table 2 Physical meanings of the Pauli coefficients

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Table 3 The optical prescription of the example system

Equations (23)

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( S / N ) i . f . = η P s h ν B i . f . [ ( A | U s | | U l | cos ϕ d A ) 2 + ( A | U s | | U l | sin ϕ d A ) 2 ] / ( | U s | 2 d A A | U l | 2 d A ) ,
γ i . f . = [ ( A | U s | | U l | cos ϕ d A ) 2 + ( A | U s | | U l | sin ϕ d A ) 2 ] ( | U s | 2 d A A | U l | 2 d A ) .
J P = 1 2 [ 1 1 1 1 ] ,
J s y s = [ J x x J x y J y x J y y ] ,
e ^ s = J s y s e ^ i n ,
e ^ s = J P e ^ s .
P s = P γ p o l ,
γ p o l = 1 z 0 A 1 2 Re ( E s E * s s * ) d A 1 z 0 A 1 2 Re ( E s E s * ) d A .
( S / N ) = η P h ν B i . f . A Re ( E s E s * ) d A A Re ( E s E s * ) d A × [ ( A | U s | | U l | cos ϕ d A ) 2 + ( A | U s | | U l | sin ϕ d A ) 2 ] ( | U s | 2 d A A | U l | 2 d A ) ,
γ = γ p o l γ i . f . = A Re ( E s E s * ) d A A Re ( E s E s * ) d A × [ ( A | U s | | U l | cos ϕ d A ) 2 + ( A | U s | | U l | sin ϕ d A ) 2 ] ( | U s | 2 d A A | U l | 2 d A ) .
J s y s = [ J x x J x y J y x J y y ] = J S J p o l ( d , ψ p , δ p ) J r o t ( ζ ) J r e t ( ϕ , ψ r , δ r ) ,
J p o l ( d , ψ p , δ p ) = [ 1 + d cos 2 ψ p d sin 2 ψ p e i δ p d sin 2 ψ p e i δ p 1 d cos 2 ψ p ] ,
J r e t ( ϕ , ψ r , δ r ) = [ cos ϕ i sin ϕ cos 2 ψ r sin ϕ sin 2 ψ r ( sin δ r + i cos δ r ) sin ϕ sin 2 ψ r ( sin δ r i cos δ r ) cos ϕ + i sin ϕ cos 2 ψ r ] ,
J r o t ( ζ ) = [ cos ζ sin ζ sin ζ cos ζ ] .
J p o l = d 0 σ 0 + d 1 σ 1 + d 2 σ 2 + d 3 σ 3 ,
J r e t = r 0 σ 0 + r 1 σ 1 + r 2 σ 2 + r 3 σ 3 ,
d 0 = 1 d 1 = d cos 2 ψ p d 2 = d sin 2 ψ p cos δ p , d 3 = d sin 2 ψ p sin δ p
r 0 = cos ϕ r 1 = i sin ϕ cos 2 ψ r r 2 = i sin ϕ sin 2 ψ r cos δ r r 3 = i sin ϕ sin 2 ψ r sin δ r .
d 1 ( ρ , θ ) = n = 0 9 d n 1 Z n ( ρ , θ ) d 2 ( ρ , θ ) = n = 0 9 d n 2 Z n ( ρ , θ ) d 3 ( ρ , θ ) = n = 0 9 d n 3 Z n ( ρ , θ )
r 1 ( ρ , θ ) = i ( n = 0 9 r n 1 Z n ( ρ , θ ) ) r 2 ( ρ , θ ) = i ( n = 0 9 r n 2 Z n ( ρ , θ ) ) r 3 ( ρ , θ ) = i ( n = 0 9 r n 3 Z n ( ρ , θ ) )
γ = γ p o l γ i . f . = γ p o l .
γ p o l = A | J x x + J x y + J y x + J y y | 2 | U s | 2 d A 2 A ( | J x x + J x y | 2 + | J y x + J y y | 2 ) | U s | 2 d A .
γ p o l = A | J x x + J y x + i ( J x y + J y y ) | 2 | U s | 2 d A 2 A ( | J x x | 2 + | J x y | 2 + | J y x | 2 + | J y y | 2 + i ( J * x x J x y J x x J * x y + J * y x J y y J y x J * y y ) ) | U s | 2 d A .

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