Abstract

Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate phase aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown, providing the first analysis of AO applied to high peak power laser beams. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere.

© 2016 Optical Society of America

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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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2016 (1)

2015 (2)

P. Panagiotopoulos, P. Whalen, M. Kolesik, and J. V. Moloney, “Super high power mid-infrared femtosecond light bullet,” Nat. Photonics 9(8), 543–548 (2015).
[Crossref]

W. Nelson, J. P. Palastro, C. Wu, and C. C. Davis, “Enhanced backscatter of optical beams reflected in turbulent air,” J. Opt. Soc. Am. A 32(7), 1371–1378 (2015).
[Crossref] [PubMed]

2014 (2)

2012 (1)

2009 (1)

2007 (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–190 (2007).
[Crossref]

2000 (1)

1999 (1)

O. Bang, D. Edmundson, and W. Krolikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83(26), 5479–5482 (1999).
[Crossref]

1998 (1)

1997 (1)

1982 (1)

V. P. Lukin and M. I. Charnotskii, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12(5), 602–605 (1982).
[Crossref]

1978 (1)

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

1975 (2)

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63(12), 1669–1692 (1975).
[Crossref]

J. H. Marburger, “Self-focusing: Theory,” Prog. Quantum Electron. 4, 35–110 (1975).
[Crossref]

Aksenov, V. P.

Atuchin, V. V.

Bang, O.

O. Bang, D. Edmundson, and W. Krolikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83(26), 5479–5482 (1999).
[Crossref]

Barnes, T. H.

Carhart, G. W.

Charnotskii, M. I.

V. P. Lukin and M. I. Charnotskii, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12(5), 602–605 (1982).
[Crossref]

Couairon, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–190 (2007).
[Crossref]

Davis, C. C.

DiComo, G.

B. Hafizi, J. R. Peñano, J. P. Palastro, R. P. Fischer, and G. DiComo, in preparation.

Edmundson, D.

O. Bang, D. Edmundson, and W. Krolikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83(26), 5479–5482 (1999).
[Crossref]

Fante, R. L.

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63(12), 1669–1692 (1975).
[Crossref]

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

Fischer, R. P.

B. Hafizi, J. R. Peñano, J. P. Palastro, R. P. Fischer, and G. DiComo, in preparation.

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

Giuliano, C. R.

Hafizi, B.

Haskell, T. G.

Helle, M.

Izmailov, I. V.

Kanev, F. Yu.

Kochemasov, G. G.

Kolesik, M.

P. Panagiotopoulos, P. Whalen, M. Kolesik, and J. V. Moloney, “Super high power mid-infrared femtosecond light bullet,” Nat. Photonics 9(8), 543–548 (2015).
[Crossref]

Koltygin, M. O.

Krolikowski, W.

O. Bang, D. Edmundson, and W. Krolikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83(26), 5479–5482 (1999).
[Crossref]

Kulikov, S. M.

Lee, D. J.

Lukin, V. P.

V. P. Lukin and M. I. Charnotskii, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12(5), 602–605 (1982).
[Crossref]

Manachinsky, A. N.

Marburger, J. H.

J. H. Marburger, “Self-focusing: Theory,” Prog. Quantum Electron. 4, 35–110 (1975).
[Crossref]

Maslov, N. V.

Moloney, J. V.

P. Panagiotopoulos, P. Whalen, M. Kolesik, and J. V. Moloney, “Super high power mid-infrared femtosecond light bullet,” Nat. Photonics 9(8), 543–548 (2015).
[Crossref]

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–190 (2007).
[Crossref]

Nelson, W.

Palastro, J. P.

Panagiotopoulos, P.

P. Panagiotopoulos, P. Whalen, M. Kolesik, and J. V. Moloney, “Super high power mid-infrared femtosecond light bullet,” Nat. Photonics 9(8), 543–548 (2015).
[Crossref]

Peñano, J.

Peñano, J. R.

B. Hafizi, J. R. Peñano, J. P. Palastro, R. P. Fischer, and G. DiComo, in preparation.

Puryear, A. L.

Ricklin, J. C.

Roggemann, M. C.

Shapiro, J. H.

Shirai, T.

Soldatenkov, I. S.

Sprangle, P.

Starikov, F. A.

Sukharev, S. A.

Ting, A.

Vorontsov, M. A.

Wang, V.

Whalen, P.

P. Panagiotopoulos, P. Whalen, M. Kolesik, and J. V. Moloney, “Super high power mid-infrared femtosecond light bullet,” Nat. Photonics 9(8), 543–548 (2015).
[Crossref]

Wu, C.

Appl. Opt. (1)

Appl. Phys. (Berl.) (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

J. Opt. Commun. Netw. (1)

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

J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

P. Panagiotopoulos, P. Whalen, M. Kolesik, and J. V. Moloney, “Super high power mid-infrared femtosecond light bullet,” Nat. Photonics 9(8), 543–548 (2015).
[Crossref]

Opt. Lett. (5)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–190 (2007).
[Crossref]

Phys. Rev. Lett. (1)

O. Bang, D. Edmundson, and W. Krolikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83(26), 5479–5482 (1999).
[Crossref]

Proc. IEEE (1)

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63(12), 1669–1692 (1975).
[Crossref]

Prog. Quantum Electron. (1)

J. H. Marburger, “Self-focusing: Theory,” Prog. Quantum Electron. 4, 35–110 (1975).
[Crossref]

Sov. J. Quantum Electron. (1)

V. P. Lukin and M. I. Charnotskii, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12(5), 602–605 (1982).
[Crossref]

Other (7)

V. P. Lukin, Atmospheric Adaptive Optics (SPIE, 1995).

G. Fibich, “Some Modern Aspects of Self-Focusing Theory,” in Self-focusing: Past and Present, R.W. Boyd, S. G. Lukishova, and Y. R. Shen, eds. (Springer 2009).
[Crossref]

J.P. Palastro, “Time-dependent polarization states of high-power, utrashort laser pulses during atmospheric propagation,” Phys. Rev. A 89, 013804 (2014).

B. Hafizi, J. R. Peñano, J. P. Palastro, R. P. Fischer, and G. DiComo, in preparation.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

G. Agrawal, Nonlinear Fiber Optics (Academic, 2013).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

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Figures (4)

Fig. 1
Fig. 1 A beacon located on a target embedded in a random medium informs the phase and amplitude of a laser beam incident on the target.
Fig. 2
Fig. 2 (a) Ensemble average of R( z T ) as a function of P L / P cr for σ r 2 =6.8 . The dots, squares, and triangles show the means of the magnitude, and real and imaginary components respectively, and the swathes +/- the standard deviation. (b) the initial on-target beacon intensity profile. (c) and (d) examples of low, |R|=0.28 , and high, |R|=0.96 , reciprocality, at P L = 1.5 P cr . The reciprocality drops with increasing power due to nonlinear refraction of the beam.
Fig. 3
Fig. 3 Ensemble average of ( P L / P cr ) 2 ReR( z T )1 and ( P L / P cr ) 1 ImR( z T ) as a function of σ r 2 for P L = 0.25 P cr red triangles, P L = 0.5 P cr green squares, and P L = 1.0 P cr blue dot. The initial drop and subsequent rise with turbulence strength is associated with the same behavior in the scintillation index.
Fig. 4
Fig. 4 Ensemble averages of |R( z T )| , blue dots, and | R I ( z T )| , red triangles, as a function of P L / P cr for σ r 2 =4.6 , top, and σ r 2 for P L / P cr =1.0 , bottom. The swathes indicate +/- the standard deviation. At the target, the drop in reciprocity is dominated by phase differences between the beacon and beam.

Equations (11)

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z E(x)=i 1 2k [ 2 +2 k 2 n 0 δn(x) ]E(x)
[ i z + 1 2k 2 +k n 0 δ n L (x) ] G + (r,z; r , z )=δ(x x )
[ i z + 1 2k 2 +k n 0 δ n L (x) ] G (r,z; r , z )=δ(x x ),
E(r,z)= H ± (r,z; r ,zΔz)E( r ,zΔz)d r ,
H ± (r,z; r ,zΔz)= G ± (r,z; r ,z Δz 2 ) e ikΔzδ n NL h G ± ( r ,z Δz 2 ; r ,zΔz)d r ,
R(z) 1 2 ε 0 c [ P B (z) P L (z)] 1/2 E B (r,z) E L (r,z) dr,
θ(r)= (2πΔ z s ) 1/2 k dκ e i κ r [ a r ( κ )+i a i ( κ ) ] Φ n 1/2 ( κ ,0) ,
Φ n (κ)=0.033 C n 2 e (κ 0 /2π) 2 ( κ 2 + L 0 2 ) 11/6 ,
R(z)1 4α π w 2 [ i I ^ R 2 (r) dr+α I ^ R 3 (r) dr ]
R I (z) 1 2 ε 0 c [ P B (z) P L (z)] 1/2 | E B (r,z) E L (r,z) | dr.
R( z T ) P R 1 I R exp[ik z T δ n NL ( η 2 I R )]dr ,

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