Abstract

A self-consistent formalism is developed for treating propagation of beams in situations which include phase conjugation and nonreciprocal elements. Two equivalent field representations, the rectangular polarization and the circular polarization representation, are considered, and the rules for transforming between them are derived. An example involving a proposed new current fiber sensor is analyzed using the formalism.

© 1987 Optical Society of America

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Errata

Amnon Yariv, "Operator algebra for propagation problems involving phase conjugation and nonreciprocal elements: erratum," Appl. Opt. 27, 818-818 (1988)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-27-5-818

References

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  1. R. C. Jones, “New Calculus for the Treatment of Optical Systems,” J. Opt. Soc. Am. 31, 448 (1941).See also A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 121.
  2. A. Yariv, Quantum Electronics (Wiley, New York, 1968), p. 197.
  3. A. Yariv, K. Petermaun, E. Weidel, “Sensitivity of a Fiber-Optic Gyroscope to Environmental Magnetic Fields,” Opt. Lett. 7, 181, (1982).
  4. G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramskov-Hansen, “Faraday Rotation in Coiled Monomode Optical Fibers: Isolators, Filters, and Magnetic Sensors,” Opt. Lett. 7, 238 (1982).
    [CrossRef] [PubMed]
  5. K. Kyuma, A. Yariv, S. K. Kwong, “Polarization Recovery in Phase Conjugation by Modal Dispersal,” Appl. Phys. Lett. 49, 617 (1986).
    [CrossRef]
  6. S.-K. Kwong, R. Yahalom, K. Kyuma, A. Yariv, “Optical Phase Conjugation with Non-Reciprocal Media,” submitted for publication (1986).

1986

K. Kyuma, A. Yariv, S. K. Kwong, “Polarization Recovery in Phase Conjugation by Modal Dispersal,” Appl. Phys. Lett. 49, 617 (1986).
[CrossRef]

1982

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramskov-Hansen, “Faraday Rotation in Coiled Monomode Optical Fibers: Isolators, Filters, and Magnetic Sensors,” Opt. Lett. 7, 238 (1982).
[CrossRef] [PubMed]

A. Yariv, K. Petermaun, E. Weidel, “Sensitivity of a Fiber-Optic Gyroscope to Environmental Magnetic Fields,” Opt. Lett. 7, 181, (1982).

1941

Barlow, A. J.

Day, G. W.

Jones, R. C.

Kwong, S. K.

K. Kyuma, A. Yariv, S. K. Kwong, “Polarization Recovery in Phase Conjugation by Modal Dispersal,” Appl. Phys. Lett. 49, 617 (1986).
[CrossRef]

Kwong, S.-K.

S.-K. Kwong, R. Yahalom, K. Kyuma, A. Yariv, “Optical Phase Conjugation with Non-Reciprocal Media,” submitted for publication (1986).

Kyuma, K.

K. Kyuma, A. Yariv, S. K. Kwong, “Polarization Recovery in Phase Conjugation by Modal Dispersal,” Appl. Phys. Lett. 49, 617 (1986).
[CrossRef]

S.-K. Kwong, R. Yahalom, K. Kyuma, A. Yariv, “Optical Phase Conjugation with Non-Reciprocal Media,” submitted for publication (1986).

Payne, D. N.

Petermaun, K.

A. Yariv, K. Petermaun, E. Weidel, “Sensitivity of a Fiber-Optic Gyroscope to Environmental Magnetic Fields,” Opt. Lett. 7, 181, (1982).

Ramskov-Hansen, J. J.

Weidel, E.

A. Yariv, K. Petermaun, E. Weidel, “Sensitivity of a Fiber-Optic Gyroscope to Environmental Magnetic Fields,” Opt. Lett. 7, 181, (1982).

Yahalom, R.

S.-K. Kwong, R. Yahalom, K. Kyuma, A. Yariv, “Optical Phase Conjugation with Non-Reciprocal Media,” submitted for publication (1986).

Yariv, A.

K. Kyuma, A. Yariv, S. K. Kwong, “Polarization Recovery in Phase Conjugation by Modal Dispersal,” Appl. Phys. Lett. 49, 617 (1986).
[CrossRef]

A. Yariv, K. Petermaun, E. Weidel, “Sensitivity of a Fiber-Optic Gyroscope to Environmental Magnetic Fields,” Opt. Lett. 7, 181, (1982).

S.-K. Kwong, R. Yahalom, K. Kyuma, A. Yariv, “Optical Phase Conjugation with Non-Reciprocal Media,” submitted for publication (1986).

A. Yariv, Quantum Electronics (Wiley, New York, 1968), p. 197.

Appl. Phys. Lett.

K. Kyuma, A. Yariv, S. K. Kwong, “Polarization Recovery in Phase Conjugation by Modal Dispersal,” Appl. Phys. Lett. 49, 617 (1986).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

A. Yariv, K. Petermaun, E. Weidel, “Sensitivity of a Fiber-Optic Gyroscope to Environmental Magnetic Fields,” Opt. Lett. 7, 181, (1982).

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramskov-Hansen, “Faraday Rotation in Coiled Monomode Optical Fibers: Isolators, Filters, and Magnetic Sensors,” Opt. Lett. 7, 238 (1982).
[CrossRef] [PubMed]

Other

A. Yariv, Quantum Electronics (Wiley, New York, 1968), p. 197.

S.-K. Kwong, R. Yahalom, K. Kyuma, A. Yariv, “Optical Phase Conjugation with Non-Reciprocal Media,” submitted for publication (1986).

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Figures (1)

Fig. 1
Fig. 1

Schematic diagram of a wave propagating in sequence through an x polarizer P, a Faraday rotator F(θ), retardation plate γ(α). It is then reflected by a phase conjugate mirror (PCM) and retraces its path.

Equations (27)

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E t = { A B } in ( CP ) , E t = [ a b ] in ( RP ) .
{ A B } = 1 2 | 1 i 1 + i | [ a b ] T [ a b ] ,
[ a b ] = 1 2 | 1 1 i i | { A B } S { A B } ,
[ a b ] = | 1 0 0 1 | [ a b ] r [ a b ] = [ a b ] ,
{ A B } = { 0 1 1 0 } { A B } R { A B } = { B A } .
γ θ , α ( RP ) = | cos 2 θ exp ( i α / 2 ) + sin 2 θ exp ( i α / 2 ) i sin 2 θ sin α 2 i sin 2 θ sin α 2 sin 2 θ exp ( i α / 2 ) + cos 2 θ exp ( i α / 2 ) |
γ π / 4 , α ( RP ) = | cos α 2 i sin α 2 i sin α 2 cos α 2 | .
O = r O r 1 .
γ π / 4 , α ( RP ) = | cos α 2 i sin α 2 i sin α 2 cos α 2 | .
γ π / 4 , α ( CP ) = T γ π / 4 , α ( RP ) T 1 = { cos α 2 sin α 2 sin α 2 cos α 2 } ,
γ π / 4 , α ( CP ) = R γ π / 4 , α ( CP ) R 1 = { cos α 2 sin α 2 sin α 2 cos α 2 } .
γ π / 4 , α ( CP ) = T γ π / 4 , α ( RP ) T 1 .
F ( θ ) ( CP ) = { exp ( i θ ) 0 0 exp ( i θ ) } ,
F ( θ ) ( CP ) = R F ( CP ) R 1 = { exp ( i θ ) 0 0 exp ( i θ ) } ,
F ( RP ) = T 1 F ( CP ) T = | cos θ sin θ sin θ cos θ | ,
F ( RP ) = R F ( RP ) R 1 = | cos θ sin θ sin θ cos θ | .
P x ( CP ) = ½ { 1 1 1 1 }
P x ( RP ) = [ 1 0 0 0 ] ,
P y ( CP ) = ½ { 1 1 1 1 } ,
P y ( RP ) = ½ [ 0 0 0 1 ] ,
[ a b ] [ a * b * ] ,
ϕ * [ a b ] = [ a * b * ] .
ϕ * { A B } = T ϕ * [ S { A B } ] = { A * B * } .
[ a b ] refl . = T 1 P x F ( θ ) γ ( α ) F ( θ ) ϕ * [ F ( θ ) γ ( α ) F ( θ ) P x T [ a b ] incid . ] .
[ ( E x ) refl . ( E y ) refl . ] = [ + cos 2 α 2 cos 4 θ i sin α sin 2 θ + sin 2 α 2 0 0 0 ] [ ( E x ) incid . ( E y ) incid . ] ,
( E x ) out = [ cos 2 α 2 cos 4 θ sin 2 α 2 + i sin α sin 2 θ ] ( E x ) in ,
( E x ) out = ( E x ) in cos 4 θ ,

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