Abstract

We propose and experimentally demonstrate a novel scheme to generate LP11/LP21 modes with tunable mode lobe orientation (MLO). Wherein, the MLOs have an excellent linear relationship with the linearly-polarized states of input fundamental modes. The proposed scheme is composed of a polarization controller (PC), a mode converter, a mode and polarization controller (PMC) which is twined with the few mode fiber (FMF) and a polarizer. Experimental results show that the deviations of MLOs between generated LP11/LP21 modes and simulated ones are less than 3.5 and 8 degrees over C band. Since polarization control up to nanosecond scale is available with GaAs or lithium based electro-optic modulator, the proposed scheme could enable nanosecond time scale MLO control, which would be immensely useful for optical trapping, fiber sensors and optical communications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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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] [PubMed]
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    [Crossref]
  18. X. Hong, X. Zeng, Y. Li, Q. Mo, Y. Tian, W. Li, Z. Liu, and J. Wu, “Tunable mode rotator for space-division multiplexing based on a few mode-polarization maintaining fiber,” Appl. Opt. 55(33), 9360–9364 (2016).
    [Crossref] [PubMed]
  19. Q. Mo, Z. Hong, D. Yu, S. Fu, L. Wang, K. Oh, M. Tang, and D. Liu, “All-fiber spatial rotation manipulation for radially asymmetric modes,” Sci. Rep. 7(1), 2539 (2017).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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2018 (1)

2017 (1)

Q. Mo, Z. Hong, D. Yu, S. Fu, L. Wang, K. Oh, M. Tang, and D. Liu, “All-fiber spatial rotation manipulation for radially asymmetric modes,” Sci. Rep. 7(1), 2539 (2017).
[Crossref] [PubMed]

2016 (5)

Z. Hong, S. Fu, D. Yu, M. Tang, and D. Liu, “All-fiber tunable LP11 mode rotator with 360° Range,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Y. Zhang, L. Zhao, Y. Chen, Z. Liu, Y. Zhang, E. Zhao, J. Yang, and L. Yuan, “Single optical tweezers based on elliptical core fiber,” Opt. Commun. 365, 103–107 (2016).
[Crossref]

S. G. Leon-Saval, N. K. Fontaine, and R. Amezcua-Correa, “Photonic lantern as mode multiplexer for multimode optical communications,” Opt. Fiber Technol. 35(6), 751–760 (2016).

R. D. Niederriter, M. E. Siemens, and J. T. Gopinath, “Continuously tunable orbital angular momentum generation using a polarization-maintaining fiber,” Opt. Lett. 41(14), 3213–3216 (2016).
[Crossref] [PubMed]

X. Hong, X. Zeng, Y. Li, Q. Mo, Y. Tian, W. Li, Z. Liu, and J. Wu, “Tunable mode rotator for space-division multiplexing based on a few mode-polarization maintaining fiber,” Appl. Opt. 55(33), 9360–9364 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (3)

2013 (1)

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

2012 (4)

1994 (1)

A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, and R. O. Claus, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12(1), 170–177 (1994).
[Crossref]

1987 (1)

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[Crossref] [PubMed]

1980 (1)

H. C. Lefevre, “Single-mode fibre fractional wave devices and polarisation controllers,” Electron. Lett. 16(20), 778–780 (1980).
[Crossref]

1979 (1)

Amezcua-Correa, R.

S. G. Leon-Saval, N. K. Fontaine, and R. Amezcua-Correa, “Photonic lantern as mode multiplexer for multimode optical communications,” Opt. Fiber Technol. 35(6), 751–760 (2016).

Ashkin, A.

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[Crossref] [PubMed]

Bai, N.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Bolle, C.

Burrows, E. C.

Chen, Y.

Y. Zhang, L. Zhao, Y. Chen, Z. Liu, Y. Zhang, E. Zhao, J. Yang, and L. Yuan, “Single optical tweezers based on elliptical core fiber,” Opt. Commun. 365, 103–107 (2016).
[Crossref]

Claus, R. O.

A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, and R. O. Claus, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12(1), 170–177 (1994).
[Crossref]

Culshaw, B.

A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, and R. O. Claus, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12(1), 170–177 (1994).
[Crossref]

Du, C.

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[Crossref] [PubMed]

Esmaeelpour, M.

Essiambre, R.

Fan, Y.

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Fontaine, N. K.

S. G. Leon-Saval, N. K. Fontaine, and R. Amezcua-Correa, “Photonic lantern as mode multiplexer for multimode optical communications,” Opt. Fiber Technol. 35(6), 751–760 (2016).

Fu, S.

Q. Mo, Z. Hong, D. Yu, S. Fu, L. Wang, K. Oh, M. Tang, and D. Liu, “All-fiber spatial rotation manipulation for radially asymmetric modes,” Sci. Rep. 7(1), 2539 (2017).
[Crossref] [PubMed]

Z. Hong, S. Fu, D. Yu, M. Tang, and D. Liu, “All-fiber tunable LP11 mode rotator with 360° Range,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Gnauck, A. H.

Gopinath, J. T.

Hanzawa, N.

He, Z.

Hong, X.

Hong, Z.

Q. Mo, Z. Hong, D. Yu, S. Fu, L. Wang, K. Oh, M. Tang, and D. Liu, “All-fiber spatial rotation manipulation for radially asymmetric modes,” Sci. Rep. 7(1), 2539 (2017).
[Crossref] [PubMed]

Z. Hong, S. Fu, D. Yu, M. Tang, and D. Liu, “All-fiber tunable LP11 mode rotator with 360° Range,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Hu, Q.

Hu, X.

Ip, E.

G. Milione, P. Ji, E. Ip, M. Li, J. Stone, and G. Peng, “Real-time Bi-directional 10GbE Transmission using MIMO-less Space-division-multiplexing with Spatial Modes,” Optical Fiber Communication Conference (Optical Society of America, 2016), paper W1F.2.
[Crossref]

Ishizaka, Y.

Jankovic, L.

A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, and R. O. Claus, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12(1), 170–177 (1994).
[Crossref]

Ji, P.

G. Milione, P. Ji, E. Ip, M. Li, J. Stone, and G. Peng, “Real-time Bi-directional 10GbE Transmission using MIMO-less Space-division-multiplexing with Spatial Modes,” Optical Fiber Communication Conference (Optical Society of America, 2016), paper W1F.2.
[Crossref]

Jiang, S.

Kogelnik, H.

Lefevre, H. C.

H. C. Lefevre, “Single-mode fibre fractional wave devices and polarisation controllers,” Electron. Lett. 16(20), 778–780 (1980).
[Crossref]

Lei, J.

Leon-Saval, S. G.

S. G. Leon-Saval, N. K. Fontaine, and R. Amezcua-Correa, “Photonic lantern as mode multiplexer for multimode optical communications,” Opt. Fiber Technol. 35(6), 751–760 (2016).

Li, A.

Li, G.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Li, M.

G. Milione, P. Ji, E. Ip, M. Li, J. Stone, and G. Peng, “Real-time Bi-directional 10GbE Transmission using MIMO-less Space-division-multiplexing with Spatial Modes,” Optical Fiber Communication Conference (Optical Society of America, 2016), paper W1F.2.
[Crossref]

Li, S.

Li, W.

Li, Y.

Liang, P.

Lin, F.

Lingle, R.

Liu, D.

Q. Mo, Z. Hong, D. Yu, S. Fu, L. Wang, K. Oh, M. Tang, and D. Liu, “All-fiber spatial rotation manipulation for radially asymmetric modes,” Sci. Rep. 7(1), 2539 (2017).
[Crossref] [PubMed]

Z. Hong, S. Fu, D. Yu, M. Tang, and D. Liu, “All-fiber tunable LP11 mode rotator with 360° Range,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Liu, Z.

Ma, L.

Ma, P.

Ma, Y.

Masumoto, K.

Matsui, T.

McCurdy, A. H.

Michie, W. C.

A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, and R. O. Claus, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12(1), 170–177 (1994).
[Crossref]

Milione, G.

G. Milione, P. Ji, E. Ip, M. Li, J. Stone, and G. Peng, “Real-time Bi-directional 10GbE Transmission using MIMO-less Space-division-multiplexing with Spatial Modes,” Optical Fiber Communication Conference (Optical Society of America, 2016), paper W1F.2.
[Crossref]

Mo, Q.

Mumtaz, S.

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Niederriter, R. D.

Oh, K.

Q. Mo, Z. Hong, D. Yu, S. Fu, L. Wang, K. Oh, M. Tang, and D. Liu, “All-fiber spatial rotation manipulation for radially asymmetric modes,” Sci. Rep. 7(1), 2539 (2017).
[Crossref] [PubMed]

Peckham, D. W.

Peng, G.

G. Milione, P. Ji, E. Ip, M. Li, J. Stone, and G. Peng, “Real-time Bi-directional 10GbE Transmission using MIMO-less Space-division-multiplexing with Spatial Modes,” Optical Fiber Communication Conference (Optical Society of America, 2016), paper W1F.2.
[Crossref]

Randel, S.

Richardson, D. J.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Ryf, R.

Saitoh, K.

Sakamoto, T.

Shieh, W.

Siemens, M. E.

Sierra, A.

Simon, A.

Stone, J.

G. Milione, P. Ji, E. Ip, M. Li, J. Stone, and G. Peng, “Real-time Bi-directional 10GbE Transmission using MIMO-less Space-division-multiplexing with Spatial Modes,” Optical Fiber Communication Conference (Optical Society of America, 2016), paper W1F.2.
[Crossref]

Su, R.

Tang, M.

Q. Mo, Z. Hong, D. Yu, S. Fu, L. Wang, K. Oh, M. Tang, and D. Liu, “All-fiber spatial rotation manipulation for radially asymmetric modes,” Sci. Rep. 7(1), 2539 (2017).
[Crossref] [PubMed]

Z. Hong, S. Fu, D. Yu, M. Tang, and D. Liu, “All-fiber tunable LP11 mode rotator with 360° Range,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Tian, Y.

Tsujikawa, K.

Uematsu, T.

Ulrich, R.

Vengsarkar, A. M.

A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, and R. O. Claus, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12(1), 170–177 (1994).
[Crossref]

Wang, J.

Wang, L.

Q. Mo, Z. Hong, D. Yu, S. Fu, L. Wang, K. Oh, M. Tang, and D. Liu, “All-fiber spatial rotation manipulation for radially asymmetric modes,” Sci. Rep. 7(1), 2539 (2017).
[Crossref] [PubMed]

Y. Zhang, P. Liang, J. Lei, L. Wang, Z. Liu, J. Yang, and L. Yuan, “Multi-Dimensional Manipulation of Yeast Cells Using an LP11 Mode Beam,” J. Lightwave Technol. 32(6), 1098–1103 (2014).
[Crossref]

Wang, X.

Wang, Y.

Wei, W.

Winzer, P. J.

Wu, G.

Wu, J.

Wu, X.

Xia, C.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Yamamoto, F.

Yang, J.

Y. Zhang, L. Zhao, Y. Chen, Z. Liu, Y. Zhang, E. Zhao, J. Yang, and L. Yuan, “Single optical tweezers based on elliptical core fiber,” Opt. Commun. 365, 103–107 (2016).
[Crossref]

Y. Zhang, P. Liang, J. Lei, L. Wang, Z. Liu, J. Yang, and L. Yuan, “Multi-Dimensional Manipulation of Yeast Cells Using an LP11 Mode Beam,” J. Lightwave Technol. 32(6), 1098–1103 (2014).
[Crossref]

Yu, D.

Q. Mo, Z. Hong, D. Yu, S. Fu, L. Wang, K. Oh, M. Tang, and D. Liu, “All-fiber spatial rotation manipulation for radially asymmetric modes,” Sci. Rep. 7(1), 2539 (2017).
[Crossref] [PubMed]

Z. Hong, S. Fu, D. Yu, M. Tang, and D. Liu, “All-fiber tunable LP11 mode rotator with 360° Range,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Yuan, L.

Y. Zhang, L. Zhao, Y. Chen, Z. Liu, Y. Zhang, E. Zhao, J. Yang, and L. Yuan, “Single optical tweezers based on elliptical core fiber,” Opt. Commun. 365, 103–107 (2016).
[Crossref]

Y. Zhang, P. Liang, J. Lei, L. Wang, Z. Liu, J. Yang, and L. Yuan, “Multi-Dimensional Manipulation of Yeast Cells Using an LP11 Mode Beam,” J. Lightwave Technol. 32(6), 1098–1103 (2014).
[Crossref]

Yuan, Y.

Zeng, X.

Zhang, Y.

Y. Zhang, L. Zhao, Y. Chen, Z. Liu, Y. Zhang, E. Zhao, J. Yang, and L. Yuan, “Single optical tweezers based on elliptical core fiber,” Opt. Commun. 365, 103–107 (2016).
[Crossref]

Y. Zhang, L. Zhao, Y. Chen, Z. Liu, Y. Zhang, E. Zhao, J. Yang, and L. Yuan, “Single optical tweezers based on elliptical core fiber,” Opt. Commun. 365, 103–107 (2016).
[Crossref]

Y. Zhang, P. Liang, J. Lei, L. Wang, Z. Liu, J. Yang, and L. Yuan, “Multi-Dimensional Manipulation of Yeast Cells Using an LP11 Mode Beam,” J. Lightwave Technol. 32(6), 1098–1103 (2014).
[Crossref]

Zhao, E.

Y. Zhang, L. Zhao, Y. Chen, Z. Liu, Y. Zhang, E. Zhao, J. Yang, and L. Yuan, “Single optical tweezers based on elliptical core fiber,” Opt. Commun. 365, 103–107 (2016).
[Crossref]

Zhao, L.

Y. Zhang, L. Zhao, Y. Chen, Z. Liu, Y. Zhang, E. Zhao, J. Yang, and L. Yuan, “Single optical tweezers based on elliptical core fiber,” Opt. Commun. 365, 103–107 (2016).
[Crossref]

Zhao, N.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Zhou, P.

Adv. Opt. Photonics (1)

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Appl. Opt. (2)

Electron. Lett. (1)

H. C. Lefevre, “Single-mode fibre fractional wave devices and polarisation controllers,” Electron. Lett. 16(20), 778–780 (1980).
[Crossref]

IEEE Photonics J. (1)

Z. Hong, S. Fu, D. Yu, M. Tang, and D. Liu, “All-fiber tunable LP11 mode rotator with 360° Range,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

J. Lightwave Technol. (4)

Nat. Photonics (1)

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Opt. Commun. (1)

Y. Zhang, L. Zhao, Y. Chen, Z. Liu, Y. Zhang, E. Zhao, J. Yang, and L. Yuan, “Single optical tweezers based on elliptical core fiber,” Opt. Commun. 365, 103–107 (2016).
[Crossref]

Opt. Express (4)

Opt. Fiber Technol. (1)

S. G. Leon-Saval, N. K. Fontaine, and R. Amezcua-Correa, “Photonic lantern as mode multiplexer for multimode optical communications,” Opt. Fiber Technol. 35(6), 751–760 (2016).

Opt. Lett. (3)

Sci. Rep. (1)

Q. Mo, Z. Hong, D. Yu, S. Fu, L. Wang, K. Oh, M. Tang, and D. Liu, “All-fiber spatial rotation manipulation for radially asymmetric modes,” Sci. Rep. 7(1), 2539 (2017).
[Crossref] [PubMed]

Science (1)

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[Crossref] [PubMed]

Other (3)

G. Milione, P. Ji, E. Ip, M. Li, J. Stone, and G. Peng, “Real-time Bi-directional 10GbE Transmission using MIMO-less Space-division-multiplexing with Spatial Modes,” Optical Fiber Communication Conference (Optical Society of America, 2016), paper W1F.2.
[Crossref]

F. Parmigiani, Y. Jung, L. GrünerNielsen, T. Geisler, P. Petropoulos and D. Richardson, “MIMO-less space division multiplexing transmission over 1 km elliptical core few mode fiber”. Laser science to Photonic Applications (Optical Society of America, 2017), paper SW1I.1.

For instance, http://versawave.com/products/polarizationmodulators/ .

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Figures (8)

Fig. 1
Fig. 1 (a) The schematic of LP11/LP21 mode generators with tunable MLO; (b) Mode profiles of LP11ax, LP11ay, LP11bx, LP11by and LP21ax, LP21ay,LP21bx, LP21by along H-V axes; (c) Left view of the PMC and mode base profiles of LP11a’x’, LP11a’y’, LP11b’x’, LP11b’y’ and LP21a’x’, LP21a’y’, LP21b’x’, LP21b’y’ along S-F axes.
Fig. 2
Fig. 2 The rotational way of rotation matrix R(α).
Fig. 3
Fig. 3 The relationship between the rotation angles of (a) LP11 and (b) LP21 mode with respect to the input polarization states after passing the polarizer under the conditions of β = 1/2π or 3/8π.
Fig. 4
Fig. 4 Experimental setup of the generator of LP11/LP21 modes with tunable mode lobe orientation.
Fig. 5
Fig. 5 (a) The phase differences δ11a’x’a’y’, δ11b’x’a’y’, δ11b’y’a’y’ and δ21a’x’a’y’, δ21b’x’a’y’, δ21b’y’a’y’ for the cases of 1-9 loops, respectively. (b) The phase differences over the C-band, for the cases of 8 loops.
Fig. 6
Fig. 6 (a) The experimental mode profiles of LP11 mode and (b) LP21 mode with the polarization angle θ varies from 0° to 180° at the wavelength of 1540nm, 1550nm and 1560nm, respectively.
Fig. 7
Fig. 7 Experimental MLOs and the Experimental MLO deviations with respect to the simulated MLOs as functions of polarization angle θ at 1540nm, 1550nm and 1560nm for (a) LP11 modes and (b) LP21 modes.
Fig. 8
Fig. 8 The correlation coefficients between experimental (a) LP11 mode and (b) LP21 mode profiles and the corresponding ideal ones with specific MLO when the polarization angle varies from 0° to 180° at the wavelength of 1540nm, 1550nm and 1560nm, respectively.

Equations (13)

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E i n l = E a x L P l m a x + E b x L P l m b x + E a y L P l m a y + E b y L P l m b y
L P l m a x = F l m ( r ) cos ( l Φ ) x L P l m a y = F l m ( r ) cos ( l Φ ) y L P l m b x = F l m ( r ) sin ( l Φ ) x L P l m b y = F l m ( r ) sin ( l Φ ) y
E = [ E a x E b x E a y E b y ] T
E i n l = [ cos θ 0 sin θ 0 ] T .
R ( α ) = [ cos ( l α ) cos ( α ) sin ( l α ) cos ( α ) cos ( l α ) sin ( α ) sin ( l α ) sin ( α ) sin ( l α ) cos ( α ) cos ( l α ) cos ( α ) sin ( l α ) sin ( α ) cos ( l α ) sin ( α ) cos ( l α ) sin ( α ) sin ( l α ) sin ( α ) cos ( l α ) cos ( α ) sin ( l α ) cos ( α ) sin ( l α ) sin ( α ) cos ( l α ) sin ( α ) sin ( l α ) cos ( α ) cos ( l α ) cos ( α ) ] .
r ( δ ) = [ e i δ a ' x ' a ' y ' 0 0 0 0 e i δ b ' x ' a ' y ' 0 0 0 0 e i δ a ' y ' a ' y ' 0 0 0 0 e i δ b ' y ' a ' y ' ]
H = R ( α ) × r ( δ ) × R ( α )
E o u t l = H × E i n l = [ sin 2 α cos θ cos α sin α sin θ cos 2 α cos θ cos α sin α sin θ cos α sin α cos θ + cos 2 α sin θ cos α sin α cos θ sin 2 α sin θ ]
E x = ( sin 2 α cos θ cos α sin α sin θ ) L P 11 a x ( cos 2 α cos θ + cos α sin α sin θ ) L P 11 b x = F l m [ ( sin 2 α cos θ cos α sin α sin θ ) cos ( l Φ ) ( cos 2 α cos θ + cos α sin α sin θ ) sin ( l Φ ) ]
E y = ( cos 2 α sin θ cos α sin α cos θ ) L P 11 a y ( cos α sin α cos θ + sin 2 α sin θ ) L P 11 b y = F l m [ ( cos 2 α sin θ cos α sin α cos θ ) cos ( l Φ ) ( cos α sin α cos θ + sin 2 α sin θ ) sin ( l Φ ) ]
P = [ cos 2 β sin β cos β cos β sin β sin 2 β ]
[ E 1 E 2 ] = P × [ E x E y ]
P o u t l = E 1 2 + E 2 2 = 1 2 F l m cos 2 ( l Φ ( θ + ( ( 2 l 1 ) π 4 l ) )

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