Abstract

The possibility of beam combining and cleanup using orientational stimulated scattering in a nematic liquid crystal is considered. We numerically study the dynamics of the process and find that backconversion process tends to limit the effective interaction strength. The instability of the steady state of cross-phase modulation is demonstrated, during which both waves have the same frequency. We show that high conversion efficiency can be achieved and that the shape and wavefront of the amplified output signal are robust with respect to the amplitude and phase distortions of the input pump. © 2005 Optical Society of America

© 2005 Optical Society of America

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  1. T. Y. Chang, "Spatial-mode cleanup of a pulsed laser beam through mutually pumped phase conjugation with a cw reference," Opt. Lett. 15, 1342-1344 (1990).
    [CrossRef] [PubMed]
  2. A.Brignon and J.-P.Huignard eds., Phase Conjugate Laser Optics (Wiley, 2004).
  3. B. C Rodgers, T. H. Russell, and W. B. Roh, "Laser beam combining and cleanup by stimulated Brillouin scattering in a multimode optical fiber," Opt. Lett. 24, 1124-1126 (1999).
    [CrossRef]
  4. A. Flusberg and D. Korff, "Wave-front replication versus beam cleanup by stimulated scattering," J. Opt. Soc. Am. B 4, 687-690 (1987).
    [CrossRef]
  5. T. H. Russell, W. B. Roh, and J. R. Marciante, "Incoherent beam combining using stimulated Brillouin scattering in multimode fibers," Opt. Express 8, 246-254 (2001).
    [CrossRef] [PubMed]
  6. L. Schoulepnikoff and V. Mitev, "High-gain single-pass stimulated Raman scattering and four-wave mixing in a focused beam geometry: a numerical study," Pure Appl. Opt. 6, 277-302 (1997).
    [CrossRef]
  7. M. J. Shaw, G. Bialolenker, G. J. Hirst, C. J. Hooker, M. H. Key, A. K. Kidd, J. M. D. Lister, K. E. Hill, G. H. C. New, and D. C. Wilson, "Ultrahigh-brightness laser beams with low prepulse obtained by stimulated Raman scattering," Opt. Lett. 18, 1320-1322 (1993).
    [CrossRef] [PubMed]
  8. T. H. Russell, Sh. M. Willis, M. B. Crookston, and W. B. Roh, "Stimulated Raman scattering in multi-mode fibers and its application to beam cleanup and combining," J. Nonlinear Opt. Phys. Mater. 11, 303-316 (2002).
    [CrossRef]
  9. N. V. Tabirian, A. V. Sukhov, and B. Ya. Zeldovich, "High-efficiency energy transfer due to stimulated orientational scattering of light in nematic liquid crystals," J. Opt. Soc. Am. B 18, 1203-1205 (2001).
    [CrossRef]
  10. I. C. Khoo, and J. Ding, "All-optical cw laser polarization conversion at 1.55 µm by two-beam coupling in nematic liquid crystals," Appl. Phys. Lett. 81, 2496-2498 (2002).
    [CrossRef]
  11. I. C. Khoo, Yu Liang, and H. Li, "Observation of stimulated orientational scattering and cross-polarized self-starting phase conjugation in a nematic liquid-crystal film," Opt. Lett. 20, 130-132 (1995).
    [CrossRef] [PubMed]
  12. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995).
  13. N. V. Tabirian, B. Ya. Zel'dovich, and A. V. Sukhov, "The orientational optical nonlinearity of liquid crystals," Mol. Cryst. Liq. Cryst. 136, 1-140 (1986).
    [CrossRef]
  14. B. Ya Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).
    [CrossRef]
  15. R. W. Boyd, Nonlinear Optics (Academic 1992).
  16. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  17. B. Ya. Zeldovich, I. V. Ciapurin, L. B. Glebov, C. Tsai, and M. C. Stickley, "Beam clean-up and combining via stimulated scattering in liquid crystals," in Conference on Lasers and Electro-Optics, Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2004), paper CWJ4.
  18. J. M. Bernard, R. A. Chodzko, and J. G. Coffer, "Master oscillator with power amplifiers: performance of a two-element cw HF phased laser array," Appl. Opt. 28, 4543-4547 (1989).
    [CrossRef] [PubMed]
  19. N. B. Baranova, I. V. Goosev, V. A. Krivoschenkov, and B. Ya. Zeldovich, "Distortionless propagation of ordinary wave through inhomogeneous nematic (theory and experiment)," Mol. Cryst. Liq. Cryst. 210, 155-164 (1992).
    [CrossRef]
  20. N. B. Baranova and B. Ya. Zel'dovich, "High transparency of nonoriented mesophase of nematics for ordinary waves," Sov. Phys. JETP 32, 622 (1980).
  21. B. Ya. Zeldovich, A. V. Mamaev, and V. V. Shkunov, Speckle-Wave Interactions in Application to Holography and Nonlinear Optics (CRC Press, 1995).

2002 (2)

T. H. Russell, Sh. M. Willis, M. B. Crookston, and W. B. Roh, "Stimulated Raman scattering in multi-mode fibers and its application to beam cleanup and combining," J. Nonlinear Opt. Phys. Mater. 11, 303-316 (2002).
[CrossRef]

I. C. Khoo, and J. Ding, "All-optical cw laser polarization conversion at 1.55 µm by two-beam coupling in nematic liquid crystals," Appl. Phys. Lett. 81, 2496-2498 (2002).
[CrossRef]

2001 (2)

1999 (1)

1997 (1)

L. Schoulepnikoff and V. Mitev, "High-gain single-pass stimulated Raman scattering and four-wave mixing in a focused beam geometry: a numerical study," Pure Appl. Opt. 6, 277-302 (1997).
[CrossRef]

1995 (1)

1993 (1)

1992 (1)

N. B. Baranova, I. V. Goosev, V. A. Krivoschenkov, and B. Ya. Zeldovich, "Distortionless propagation of ordinary wave through inhomogeneous nematic (theory and experiment)," Mol. Cryst. Liq. Cryst. 210, 155-164 (1992).
[CrossRef]

1990 (1)

1989 (1)

1987 (1)

1986 (1)

N. V. Tabirian, B. Ya. Zel'dovich, and A. V. Sukhov, "The orientational optical nonlinearity of liquid crystals," Mol. Cryst. Liq. Cryst. 136, 1-140 (1986).
[CrossRef]

1980 (1)

N. B. Baranova and B. Ya. Zel'dovich, "High transparency of nonoriented mesophase of nematics for ordinary waves," Sov. Phys. JETP 32, 622 (1980).

Baranova, N. B.

N. B. Baranova, I. V. Goosev, V. A. Krivoschenkov, and B. Ya. Zeldovich, "Distortionless propagation of ordinary wave through inhomogeneous nematic (theory and experiment)," Mol. Cryst. Liq. Cryst. 210, 155-164 (1992).
[CrossRef]

N. B. Baranova and B. Ya. Zel'dovich, "High transparency of nonoriented mesophase of nematics for ordinary waves," Sov. Phys. JETP 32, 622 (1980).

Bernard, J. M.

Bialolenker, G.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic 1992).

Chang, T. Y.

Chodzko, R. A.

Ciapurin, I. V.

B. Ya. Zeldovich, I. V. Ciapurin, L. B. Glebov, C. Tsai, and M. C. Stickley, "Beam clean-up and combining via stimulated scattering in liquid crystals," in Conference on Lasers and Electro-Optics, Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2004), paper CWJ4.

Coffer, J. G.

Crookston, M. B.

T. H. Russell, Sh. M. Willis, M. B. Crookston, and W. B. Roh, "Stimulated Raman scattering in multi-mode fibers and its application to beam cleanup and combining," J. Nonlinear Opt. Phys. Mater. 11, 303-316 (2002).
[CrossRef]

Ding, J.

I. C. Khoo, and J. Ding, "All-optical cw laser polarization conversion at 1.55 µm by two-beam coupling in nematic liquid crystals," Appl. Phys. Lett. 81, 2496-2498 (2002).
[CrossRef]

Flusberg, A.

Glebov, L. B.

B. Ya. Zeldovich, I. V. Ciapurin, L. B. Glebov, C. Tsai, and M. C. Stickley, "Beam clean-up and combining via stimulated scattering in liquid crystals," in Conference on Lasers and Electro-Optics, Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2004), paper CWJ4.

Goosev, I. V.

N. B. Baranova, I. V. Goosev, V. A. Krivoschenkov, and B. Ya. Zeldovich, "Distortionless propagation of ordinary wave through inhomogeneous nematic (theory and experiment)," Mol. Cryst. Liq. Cryst. 210, 155-164 (1992).
[CrossRef]

Hill, K. E.

Hirst, G. J.

Hooker, C. J.

Key, M. H.

Khoo, I. C.

I. C. Khoo, and J. Ding, "All-optical cw laser polarization conversion at 1.55 µm by two-beam coupling in nematic liquid crystals," Appl. Phys. Lett. 81, 2496-2498 (2002).
[CrossRef]

I. C. Khoo, Yu Liang, and H. Li, "Observation of stimulated orientational scattering and cross-polarized self-starting phase conjugation in a nematic liquid-crystal film," Opt. Lett. 20, 130-132 (1995).
[CrossRef] [PubMed]

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995).

Kidd, A. K.

Korff, D.

Krivoschenkov, V. A.

N. B. Baranova, I. V. Goosev, V. A. Krivoschenkov, and B. Ya. Zeldovich, "Distortionless propagation of ordinary wave through inhomogeneous nematic (theory and experiment)," Mol. Cryst. Liq. Cryst. 210, 155-164 (1992).
[CrossRef]

Li, H.

Liang, Yu

Lister, J. M.

Mamaev, A. V.

B. Ya. Zeldovich, A. V. Mamaev, and V. V. Shkunov, Speckle-Wave Interactions in Application to Holography and Nonlinear Optics (CRC Press, 1995).

Marciante, J. R.

Mitev, V.

L. Schoulepnikoff and V. Mitev, "High-gain single-pass stimulated Raman scattering and four-wave mixing in a focused beam geometry: a numerical study," Pure Appl. Opt. 6, 277-302 (1997).
[CrossRef]

New, G. H.

Pilipetsky, N. F.

B. Ya Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).
[CrossRef]

Rodgers, B. C

Roh, W. B.

Russell, T. H.

Schoulepnikoff, L.

L. Schoulepnikoff and V. Mitev, "High-gain single-pass stimulated Raman scattering and four-wave mixing in a focused beam geometry: a numerical study," Pure Appl. Opt. 6, 277-302 (1997).
[CrossRef]

Shaw, M. J.

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Shkunov, V. V.

B. Ya. Zeldovich, A. V. Mamaev, and V. V. Shkunov, Speckle-Wave Interactions in Application to Holography and Nonlinear Optics (CRC Press, 1995).

B. Ya Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).
[CrossRef]

Stickley, M. C.

B. Ya. Zeldovich, I. V. Ciapurin, L. B. Glebov, C. Tsai, and M. C. Stickley, "Beam clean-up and combining via stimulated scattering in liquid crystals," in Conference on Lasers and Electro-Optics, Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2004), paper CWJ4.

Sukhov, A. V.

N. V. Tabirian, A. V. Sukhov, and B. Ya. Zeldovich, "High-efficiency energy transfer due to stimulated orientational scattering of light in nematic liquid crystals," J. Opt. Soc. Am. B 18, 1203-1205 (2001).
[CrossRef]

N. V. Tabirian, B. Ya. Zel'dovich, and A. V. Sukhov, "The orientational optical nonlinearity of liquid crystals," Mol. Cryst. Liq. Cryst. 136, 1-140 (1986).
[CrossRef]

Tabirian, N. V.

N. V. Tabirian, A. V. Sukhov, and B. Ya. Zeldovich, "High-efficiency energy transfer due to stimulated orientational scattering of light in nematic liquid crystals," J. Opt. Soc. Am. B 18, 1203-1205 (2001).
[CrossRef]

N. V. Tabirian, B. Ya. Zel'dovich, and A. V. Sukhov, "The orientational optical nonlinearity of liquid crystals," Mol. Cryst. Liq. Cryst. 136, 1-140 (1986).
[CrossRef]

Tsai, C.

B. Ya. Zeldovich, I. V. Ciapurin, L. B. Glebov, C. Tsai, and M. C. Stickley, "Beam clean-up and combining via stimulated scattering in liquid crystals," in Conference on Lasers and Electro-Optics, Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2004), paper CWJ4.

Willis, Sh. M.

T. H. Russell, Sh. M. Willis, M. B. Crookston, and W. B. Roh, "Stimulated Raman scattering in multi-mode fibers and its application to beam cleanup and combining," J. Nonlinear Opt. Phys. Mater. 11, 303-316 (2002).
[CrossRef]

Wilson, D. C.

Zeldovich, B. Ya

B. Ya Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).
[CrossRef]

Zeldovich, B. Ya.

N. V. Tabirian, A. V. Sukhov, and B. Ya. Zeldovich, "High-efficiency energy transfer due to stimulated orientational scattering of light in nematic liquid crystals," J. Opt. Soc. Am. B 18, 1203-1205 (2001).
[CrossRef]

N. B. Baranova, I. V. Goosev, V. A. Krivoschenkov, and B. Ya. Zeldovich, "Distortionless propagation of ordinary wave through inhomogeneous nematic (theory and experiment)," Mol. Cryst. Liq. Cryst. 210, 155-164 (1992).
[CrossRef]

B. Ya. Zeldovich, I. V. Ciapurin, L. B. Glebov, C. Tsai, and M. C. Stickley, "Beam clean-up and combining via stimulated scattering in liquid crystals," in Conference on Lasers and Electro-Optics, Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2004), paper CWJ4.

B. Ya. Zeldovich, A. V. Mamaev, and V. V. Shkunov, Speckle-Wave Interactions in Application to Holography and Nonlinear Optics (CRC Press, 1995).

Zel'dovich, B. Ya.

N. V. Tabirian, B. Ya. Zel'dovich, and A. V. Sukhov, "The orientational optical nonlinearity of liquid crystals," Mol. Cryst. Liq. Cryst. 136, 1-140 (1986).
[CrossRef]

N. B. Baranova and B. Ya. Zel'dovich, "High transparency of nonoriented mesophase of nematics for ordinary waves," Sov. Phys. JETP 32, 622 (1980).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

I. C. Khoo, and J. Ding, "All-optical cw laser polarization conversion at 1.55 µm by two-beam coupling in nematic liquid crystals," Appl. Phys. Lett. 81, 2496-2498 (2002).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

T. H. Russell, Sh. M. Willis, M. B. Crookston, and W. B. Roh, "Stimulated Raman scattering in multi-mode fibers and its application to beam cleanup and combining," J. Nonlinear Opt. Phys. Mater. 11, 303-316 (2002).
[CrossRef]

J. Opt. Soc. Am. B (2)

Mol. Cryst. Liq. Cryst. (2)

N. B. Baranova, I. V. Goosev, V. A. Krivoschenkov, and B. Ya. Zeldovich, "Distortionless propagation of ordinary wave through inhomogeneous nematic (theory and experiment)," Mol. Cryst. Liq. Cryst. 210, 155-164 (1992).
[CrossRef]

N. V. Tabirian, B. Ya. Zel'dovich, and A. V. Sukhov, "The orientational optical nonlinearity of liquid crystals," Mol. Cryst. Liq. Cryst. 136, 1-140 (1986).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Pure Appl. Opt. (1)

L. Schoulepnikoff and V. Mitev, "High-gain single-pass stimulated Raman scattering and four-wave mixing in a focused beam geometry: a numerical study," Pure Appl. Opt. 6, 277-302 (1997).
[CrossRef]

Sov. Phys. JETP (1)

N. B. Baranova and B. Ya. Zel'dovich, "High transparency of nonoriented mesophase of nematics for ordinary waves," Sov. Phys. JETP 32, 622 (1980).

Other (7)

B. Ya. Zeldovich, A. V. Mamaev, and V. V. Shkunov, Speckle-Wave Interactions in Application to Holography and Nonlinear Optics (CRC Press, 1995).

B. Ya Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic 1992).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

B. Ya. Zeldovich, I. V. Ciapurin, L. B. Glebov, C. Tsai, and M. C. Stickley, "Beam clean-up and combining via stimulated scattering in liquid crystals," in Conference on Lasers and Electro-Optics, Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2004), paper CWJ4.

A.Brignon and J.-P.Huignard eds., Phase Conjugate Laser Optics (Wiley, 2004).

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995).

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Figures (6)

Fig. 1
Fig. 1

Illustration of the operation principle of beam cleanup using OSS.

Fig. 2
Fig. 2

Dynamics of interaction of plane waves A ( z , t ) and B ( z , t ) through OSS. (a) intensity A ( z , t ) 2 of pump plane wave A, (b) phase arg [ A ( z , t ) ] of pump wave A, and (c) the grating amplitude θ ( z , t ) . The values of total interaction length and time are characterized by g max z = 50 , Γ t = 50 .

Fig. 3
Fig. 3

Self-similar character of reverse B A power transfer. Functions θ ( z , t 0 ) versus g z (solid curve) and θ ( z 0 , t ) versus Γ t 2.1 (dotted curve) very accurately coincide with each other.

Fig. 4
Fig. 4

Re [ κ 3 ( Ω ) ] (dashed curve), and Im [ κ 3 ( Ω ) ] (solid curve) for μ = 0.65 and ν = 0.35 .

Fig. 5
Fig. 5

Steady-state intensity distributions under the OSS in a 1 mm thick NLC cell. (a) Six overlapping and interfering pump beamlets; (b) amplified signal. Power-transfer coefficient P = 0.94 ; fidelity F = 0.96 .

Fig. 6
Fig. 6

Spatial x profiles for the following quantities: (a) input pump intensity, (b) amplified output signal intensity, (c) phase of input pump, and (d) phase of amplified output signal. Input signal was a super-Gaussian beam; i.e., it had a perfectly smooth amplitude profile and plane wavefront.

Equations (29)

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A z = i ( ω 0 n a c ) θ * B ,
B z = i ( ω 0 n a c ) θ A ,
θ t + Γ θ = ( 2 n n a ϵ vac η ) A * B .
θ real ( z , t ) = [ θ ( z , t ) exp ( i q z ) + θ * ( z , t ) exp ( i q z ) ] ,
q = ω 0 n a c , n a = n e n o ,
S z [ W m 2 ] S A + S B 0.5 c n ϵ vac [ A ( z , t ) 2 + B ( z , t ) 2 ] = const.
θ = ( 2 n n a ϵ vac η ) ( Γ + i Ω ) 1 A * B exp ( i Ω t ) .
d S A d z = ( G S B ) S A , d S B d z = + ( G S A ) S B ,
d φ A d z = ( G S B ) Γ Ω , d φ B d z = ( G S A ) Γ Ω .
G = G max 2 Ω Γ ( Ω 2 + Γ 2 ) , G max = 4 ω 0 K 22 = 2 λ vac π c K 22 ,
A ( z , t ) = C { 0.5 [ 1 tanh ( g z 2 ) ] } 1 2 exp ( i { g z 4 + 0.5 ln [ cosh ( g z 2 ) ] } i ω 0 t ) ,
B ( z , t ) = C { 0.5 [ 1 + tanh ( g z 2 ) ] } 1 2 exp ( i { g z 4 0.5 ln [ cosh ( g z 2 ) ] } i ( ω 0 Ω ) t ) ,
θ ( z , t ) = { 2 n n a ϵ vac [ η Γ ( l + i ) ] } [ A * ( z , t ) B ( z , t ) ] .
b z + [ i ρ A 0 2 ( Γ + i Ω ) 2 ] ( b t ) [ i ρ A 0 2 ( Γ + i Ω ) ] b ,
A ( z , t ) = A 0 exp [ i ν z i ω 0 t ] ,
B ( z , t ) = B 0 exp [ i μ z i ω 0 t ] ,
θ ( z , t ) = ( 2 n n a ϵ vac Γ η ) ( A 0 B 0 * ) exp [ i ( ν μ ) z ] .
A ( z , t ) = A 0 exp [ i ν z i ω 0 t ] [ 1 + α ( z , t ) ] ,
B ( z , t ) = B 0 exp [ i μ z i ω 0 t ] [ 1 + β ( z , t ) ] ,
θ ( z , t ) = ( 2 n n a ϵ vac Γ η ) ( A 0 B 0 * ) exp [ i ( ν μ ) z ] [ 1 + ψ ( z , t ) ] ,
det = ( κ D ) 2 [ κ 2 ( μ 2 + ν 2 ) ( 1 D ) 2 2 μ ν ( 1 D 2 ) ] = 0 , D ( Ω ) = 1 ( 1 + i Ω Γ ) .
κ 1 , 2 = 0 , κ 3 , 4 = ± { ( 1 D ) [ ( μ 2 + ν 2 ) ( 1 D ) + 2 μ ν ( 1 + D ) ] } 1 2 ,
A z ( i c 2 ω 0 n o ) ( 2 A x 2 ) = i ( ω 0 n a c ) θ * B ,
B z [ i c 2 ω 0 ( n o 2 n e ) ] ( 2 B x 2 ) = i ( ω 0 n a c ) θ A ,
θ t + Γ θ = ( 2 n n a ϵ vac η ) A * B .
A ( x , z = 0 , t ) = [ 2 S z ( 1 d ) c n ϵ 0 ] 0.5 exp [ ( x a ) 4 ] Σ ( m j M ) exp [ i ( ϕ j + ω n α j x c ) ] ,
B ( x , z = 0 , t ) = [ 2 S z d c n ϵ 0 ] 0.5 exp [ ( x b ) 4 ] exp [ i ω n β x c ] ,
P = [ B ( x , z = L z ) 2 d x B ( x , z = 0 ) 2 d x ] A ( x , z = 0 ) 2 d x ,
F = B ( x , z = L z ) B prop * ( x , z = L z ) d x 2 [ B ( x , z = L z ) 2 d x B prop ( x , z = L z ) 2 d x ] ,

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