Abstract

We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite– Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering.

© 2011 Optical Society of America

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2010

2009

T. Ellenbogen, N. Voloch-Bloch, A. Gannay-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

2008

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef] [PubMed]

T. Ellenbogen, I. Dolev, and A. Arie, Opt. Lett. 33, 1207 (2008).
[CrossRef] [PubMed]

2007

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

2002

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. A. Fejer, IEEE J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

1998

1993

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
[CrossRef]

1979

1967

J. J. Burch, Proc. IEEE 55, 599 (1967).
[CrossRef]

1966

1948

D. A. Gabor, Nature 161, 777 (1948).
[CrossRef] [PubMed]

Arie, A.

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581 (2010).
[CrossRef] [PubMed]

I. Dolev and A. Arie, Appl. Phys. Lett. 97, 171102 (2010).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Gannay-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

T. Ellenbogen, I. Dolev, and A. Arie, Opt. Lett. 33, 1207 (2008).
[CrossRef] [PubMed]

Berger, V.

V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
[CrossRef]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Brown, B. R.

Burch, J. J.

J. J. Burch, Proc. IEEE 55, 599 (1967).
[CrossRef]

Christodoulides, D. N.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dolev, I.

I. Dolev and A. Arie, Appl. Phys. Lett. 97, 171102 (2010).
[CrossRef]

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581 (2010).
[CrossRef] [PubMed]

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

T. Ellenbogen, I. Dolev, and A. Arie, Opt. Lett. 33, 1207 (2008).
[CrossRef] [PubMed]

Ellenbogen, T.

Fejer, M. A.

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. A. Fejer, IEEE J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

Fejer, M. M.

Gabor, D. A.

D. A. Gabor, Nature 161, 777 (1948).
[CrossRef] [PubMed]

Gadret, G.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Ganany-Padowicz, A.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Gannay-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Gannay-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Gayer, O.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Hu, X.

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef] [PubMed]

Hum, D. S.

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. A. Fejer, IEEE J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

Imeshev, G.

Kurz, J. R.

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. A. Fejer, IEEE J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

Lee, W. H.

Lohmann, A. W.

Mangin, J.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Nada, N.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
[CrossRef]

Proctor, M.

Qin, Y.

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef] [PubMed]

Saitoh, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Saltzman, A. J.

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. A. Fejer, IEEE J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

Schober, A. M.

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. A. Fejer, IEEE J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Gannay-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Watanabe, K.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
[CrossRef]

Yamada, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
[CrossRef]

Zhang, C.

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef] [PubMed]

Zhao, G.

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef] [PubMed]

Zhu, Y.

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. B

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Appl. Phys. Lett.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
[CrossRef]

I. Dolev and A. Arie, Appl. Phys. Lett. 97, 171102 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. A. Fejer, IEEE J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

Nat. Photon.

T. Ellenbogen, N. Voloch-Bloch, A. Gannay-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Nature

D. A. Gabor, Nature 161, 777 (1948).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. Lett.

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
[CrossRef]

Proc. IEEE

J. J. Burch, Proc. IEEE 55, 599 (1967).
[CrossRef]

Other

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic illustration of the nonlinear CGH setup. Simulation results at the far field for (a)  HG 0 , (b)  HG 1 , and (c)  HG 2 .

Fig. 2
Fig. 2

Comparison between (a) theoretical and (b) measured beam profiles at the first diffraction order.

Fig. 3
Fig. 3

Comparison between measured (plus-sign curves) and predicted (solid curves) results: (a) total output power dependence on input power, (b) diffracted output power dependence on input power, and (c) diffracted output power dependence on temperature.

Fig. 4
Fig. 4

(a) Simulation of a one-dimensional Airy beam generation with a nonlinear CGH, normalized SH output power at the focal plane of a 125 mm lens placed after the crystal, (b) propagation of the generated Airy beam, and (c) schematic illustration of the modulation of the nonlinear coefficient in the suggested nonlinear CGH.

Tables (2)

Tables Icon

Table 1 Comparison between Predicted and Measured Conversion Efficiencies for the Total and the Diffracted Second Harmonic

Tables Icon

Table 2 Comparison between Theoretical and Measured M 2 for the Generated Modes

Equations (4)

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t ( x , y ) = 0.5 { 1 + A ( x , y ) cos [ 2 π f carrier x φ ( x , y ) ] } ,
χ ( 2 ) ( x , y ) = d i j sign { cos [ 2 π f QPM x + π t ( y ) ] } ,
t ( y ) = 0.5 { 1 + A ( y ) cos [ 2 π f carrier y φ ( y ) ] } .
U m ( y , x ) = A m W 0 W ( x ) G m [ 2 y W ( x ) ] × exp [ i k x i k y 2 2 R ( x ) + i ( m + 1 ) ξ ( x ) ] ,

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