Abstract

A model to analyze the interaction of the parametric fields being generated in a two-dimensional nonlinear photonic crystal has been developed. The analysis provides details of the interference of the generated wave(s) both inside and in the region just outside the crystal. The results are verified by second-harmonic generation in a LiNbO3 crystal that has been poled with a tetragonal inverted domain structure.

© 2007 Optical Society of America

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  1. V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
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  2. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
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  3. N. G. R. Broderick, G. W. Ross, H. L. Offenhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
    [Crossref] [PubMed]
  4. A. H. Norton and C. M. de Sterke, Opt. Lett. 28, 188 (2003).
    [Crossref] [PubMed]
  5. L.-H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, Appl. Phys. Lett. 84, 3250 (2004).
    [Crossref]
  6. N. G. R. Broderick, R. T. Bradfalean, T. M. Monro, D. J. Richardson, and C. M. de Sterke, J. Opt. Soc. Am. B 19, 2263 (2002).
    [Crossref]
  7. R. Lifshitz, A. Arie, and A. Bahabad, Phys. Rev. Lett. 95, 133901 (2005).
    [Crossref] [PubMed]
  8. J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Salzman, and M. M. Fejer, IEEE J. Sel. Top. Quantum Electron. 8, 660 (2002).
    [Crossref]
  9. G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
    [Crossref]
  10. J. W. Goodman, in Introduction to Fourier Optics (McGraw Hill, 1996), Chap. 3.
  11. L.-H. Peng, Chao-Ching Hsu, and A. H. Kung, IEEE J. Sel. Top. Quantum Electron. 10, 1142 (2004).
    [Crossref]
  12. C. S. Yu and A. H. Kung, J. Opt. Soc. Am. B 16, 2233 (1999).
    [Crossref]

2005 (1)

R. Lifshitz, A. Arie, and A. Bahabad, Phys. Rev. Lett. 95, 133901 (2005).
[Crossref] [PubMed]

2004 (2)

L.-H. Peng, Chao-Ching Hsu, and A. H. Kung, IEEE J. Sel. Top. Quantum Electron. 10, 1142 (2004).
[Crossref]

L.-H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, Appl. Phys. Lett. 84, 3250 (2004).
[Crossref]

2003 (1)

2002 (2)

N. G. R. Broderick, R. T. Bradfalean, T. M. Monro, D. J. Richardson, and C. M. de Sterke, J. Opt. Soc. Am. B 19, 2263 (2002).
[Crossref]

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

2000 (1)

N. G. R. Broderick, G. W. Ross, H. L. Offenhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[Crossref] [PubMed]

1999 (1)

1998 (1)

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

1996 (1)

J. W. Goodman, in Introduction to Fourier Optics (McGraw Hill, 1996), Chap. 3.

1968 (1)

G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[Crossref]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Arie, A.

R. Lifshitz, A. Arie, and A. Bahabad, Phys. Rev. Lett. 95, 133901 (2005).
[Crossref] [PubMed]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Bahabad, A.

R. Lifshitz, A. Arie, and A. Bahabad, Phys. Rev. Lett. 95, 133901 (2005).
[Crossref] [PubMed]

Berger, V.

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

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[Crossref]

Bradfalean, R. T.

Broderick, N. G. R.

N. G. R. Broderick, R. T. Bradfalean, T. M. Monro, D. J. Richardson, and C. M. de Sterke, J. Opt. Soc. Am. B 19, 2263 (2002).
[Crossref]

N. G. R. Broderick, G. W. Ross, H. L. Offenhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[Crossref] [PubMed]

de Sterke, C. M.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Fejer, M. M.

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

Goodman, J. W.

J. W. Goodman, in Introduction to Fourier Optics (McGraw Hill, 1996), Chap. 3.

Hanna, D. C.

N. G. R. Broderick, G. W. Ross, H. L. Offenhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[Crossref] [PubMed]

Hsu, C. C.

L.-H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, Appl. Phys. Lett. 84, 3250 (2004).
[Crossref]

Hsu, Chao-Ching

L.-H. Peng, Chao-Ching Hsu, and A. H. Kung, IEEE J. Sel. Top. Quantum Electron. 10, 1142 (2004).
[Crossref]

Hum, D. S.

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

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[Crossref]

Kung, A. H.

L.-H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, Appl. Phys. Lett. 84, 3250 (2004).
[Crossref]

L.-H. Peng, Chao-Ching Hsu, and A. H. Kung, IEEE J. Sel. Top. Quantum Electron. 10, 1142 (2004).
[Crossref]

C. S. Yu and A. H. Kung, J. Opt. Soc. Am. B 16, 2233 (1999).
[Crossref]

Kurz, J. R.

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

Lifshitz, R.

R. Lifshitz, A. Arie, and A. Bahabad, Phys. Rev. Lett. 95, 133901 (2005).
[Crossref] [PubMed]

Monro, T. M.

Ng, J.

L.-H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, Appl. Phys. Lett. 84, 3250 (2004).
[Crossref]

Norton, A. H.

Offenhaus, H. L.

N. G. R. Broderick, G. W. Ross, H. L. Offenhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[Crossref] [PubMed]

Peng, L.-H.

L.-H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, Appl. Phys. Lett. 84, 3250 (2004).
[Crossref]

L.-H. Peng, Chao-Ching Hsu, and A. H. Kung, IEEE J. Sel. Top. Quantum Electron. 10, 1142 (2004).
[Crossref]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Richardson, D. J.

N. G. R. Broderick, R. T. Bradfalean, T. M. Monro, D. J. Richardson, and C. M. de Sterke, J. Opt. Soc. Am. B 19, 2263 (2002).
[Crossref]

N. G. R. Broderick, G. W. Ross, H. L. Offenhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[Crossref] [PubMed]

Ross, G. W.

N. G. R. Broderick, G. W. Ross, H. L. Offenhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[Crossref] [PubMed]

Salzman, A. J.

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

Yu, C. S.

Appl. Phys. Lett. (1)

L.-H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, Appl. Phys. Lett. 84, 3250 (2004).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

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

L.-H. Peng, Chao-Ching Hsu, and A. H. Kung, IEEE J. Sel. Top. Quantum Electron. 10, 1142 (2004).
[Crossref]

J. Appl. Phys. (1)

G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[Crossref]

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

Opt. Lett. (1)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Phys. Rev. Lett. (3)

N. G. R. Broderick, G. W. Ross, H. L. Offenhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[Crossref] [PubMed]

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

R. Lifshitz, A. Arie, and A. Bahabad, Phys. Rev. Lett. 95, 133901 (2005).
[Crossref] [PubMed]

Other (1)

J. W. Goodman, in Introduction to Fourier Optics (McGraw Hill, 1996), Chap. 3.

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Figures (4)

Fig. 1
Fig. 1

Periodical 2D QPM crystal depicted as the combination of several 1D QPM channels separated by unpoled channels of the same width. Black squares represent inverted domains.

Fig. 2
Fig. 2

Simulated SH intensity distribution in the x y plane. x is the distance from the input face of a nonlinear photonic crystal. The dashed line indicates the exit end of the crystal.

Fig. 3
Fig. 3

Transverse SH intensity distribution at x = 1 , 2, 4 mm from the input end of the crystal. The black dots are experimental points and the solid curves are simulated result. The horizontal scale is for y in the image space, which is magnified four times by image relay relative to y in Fig. 2.

Fig. 4
Fig. 4

Experimental (circles and squares) and simulated (solid curve) SH intensity at a fixed y position when the crystal is translated a relative distance y 0 in the y direction. The lower trace is for a 1 mm long crystal. The upper trace is for a 2 mm long crystal. They share the same vertical axis. y 0 = 0 is chosen as the location where the simulated signal is largest from the 2 mm crystal.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

U 1 ( x , y , z ) U 0 ( 1 + x 2 b 2 ) 1 2 e ( y 2 + z 2 ) w 2 e i tan 1 ( x b ) e i k 1 x ,
d U 2 ( r ) = i μ 0 ( 2 ω ) 2 2 k 2 P 2 ( r ) d x ,
d U 2 ( r , r ) = i μ 0 ( 2 ω ) 2 2 k 2 d x F y exp [ i G y + i k 2 2 G y 2 ( x x ) ] d G y ,
F y 1 2 π P 2 ( r ) e i G y y d y
U 2 ( r ) = i 2 μ 0 ω 2 k 2 x F y ( G y , x ) exp [ i G y y + i k 2 2 G y 2 ( x x ) ] d G y d x .

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