Abstract

We present a new type of two-dimensional nonlinear structure for quasi-phase matching. This structure has continuous rotational symmetry, and in contrary to the commonly used periodic structures, is not lattice shaped and has no translation symmetry. It is shown that this annular symmetry structure possesses interesting phase matching attributes that are significantly different than those of periodic structures. In particular, it enables simultaneous phase-matched frequency doubling of the same pump into several different directions. Moreover, it has extremely wide phase-mismatch tolerance, since a change in the phase matching conditions does not change the second harmonic power, but only changes its propagation direction. Several structures were fabricated using either the indirect e-beam method in LiNbO3 or the electric field poling method in stoichiometric LiTaO3, and their conversion efficiencies, as well as angular and thermal dependencies, were characterized by second harmonic generation.

© 2006 Optical Society of America

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  1. M. M. Fejer, G. A. Magel, D. H. Jundt and R. L. Byer, "Quasi phase matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
    [CrossRef]
  2. V. Berger, "Nonlinear photonic crystals," Phys. Rev. Lett. 81, 4136-4139 (1998).
    [CrossRef]
  3. N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson and D. C. Hanna, "Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal," Phys. Rev. Lett. 84, 4345-4348 (2000).
    [CrossRef] [PubMed]
  4. S. M. Saltiel, A. A. Sukhorukov and Y. S. Kivshar, "Multistep parametric processes in nonlinear optics," Prog. Opt. 47, 1-73 (2005).
    [CrossRef]
  5. I. Amidror, "Fourier spectrum of radially periodic images," J. Opt. Soc. Am. A 14, 816-826 (1997).
    [CrossRef]
  6. Y. Glickman, E. Winebrand, A. Arie, and G. Rosenman, "Electron-beam-induced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion," Appl. Phys. Lett. 88, 011103 (2006).
    [CrossRef]
  7. M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase-matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
    [CrossRef]
  8. Y. Furukawa, K. Kitamura,E. Suzuki and K. Niwa, "Stoichiometric LiTaO3 single crystal growth by double-crucible Czochralski method using automatic powder supply system," J. Cryst. Growth 197, 889-895 (1999).
    [CrossRef]
  9. A. Bruner, D. Eger and S. Ruschin, "Second harmonic generation of green light in periodically-poled stoichiometric LiTaO3 doped with MgO," J. Appl. Phys. 96, 7445-7449 (2004).
    [CrossRef]
  10. R.W. Boyd, Nonlinear Optics, second edition, (Academic Press, 2002), Chap. 2.
  11. F. W. Byron and R. W. Fuller, Mathematics of classical and quantum physics, (Dover Publications, 1992), Chap. 7.
  12. D. H. Jundt, "Temperature-dependent Sellmeier equations for the index of refraction ne, in congruent lithium niobate," Opt. Lett. 22, 1553-1555 (1997).
    [CrossRef]

2006 (1)

Y. Glickman, E. Winebrand, A. Arie, and G. Rosenman, "Electron-beam-induced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion," Appl. Phys. Lett. 88, 011103 (2006).
[CrossRef]

2005 (1)

S. M. Saltiel, A. A. Sukhorukov and Y. S. Kivshar, "Multistep parametric processes in nonlinear optics," Prog. Opt. 47, 1-73 (2005).
[CrossRef]

2004 (1)

A. Bruner, D. Eger and S. Ruschin, "Second harmonic generation of green light in periodically-poled stoichiometric LiTaO3 doped with MgO," J. Appl. Phys. 96, 7445-7449 (2004).
[CrossRef]

2000 (1)

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson and D. C. Hanna, "Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal," Phys. Rev. Lett. 84, 4345-4348 (2000).
[CrossRef] [PubMed]

1999 (1)

Y. Furukawa, K. Kitamura,E. Suzuki and K. Niwa, "Stoichiometric LiTaO3 single crystal growth by double-crucible Czochralski method using automatic powder supply system," J. Cryst. Growth 197, 889-895 (1999).
[CrossRef]

1998 (1)

V. Berger, "Nonlinear photonic crystals," Phys. Rev. Lett. 81, 4136-4139 (1998).
[CrossRef]

1997 (2)

1993 (1)

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase-matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt and R. L. Byer, "Quasi phase matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Amidror, I.

Arie, A.

Y. Glickman, E. Winebrand, A. Arie, and G. Rosenman, "Electron-beam-induced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion," Appl. Phys. Lett. 88, 011103 (2006).
[CrossRef]

Berger, V.

V. Berger, "Nonlinear photonic crystals," Phys. Rev. Lett. 81, 4136-4139 (1998).
[CrossRef]

Broderick, N. G. R.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson and D. C. Hanna, "Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal," Phys. Rev. Lett. 84, 4345-4348 (2000).
[CrossRef] [PubMed]

Bruner, A.

A. Bruner, D. Eger and S. Ruschin, "Second harmonic generation of green light in periodically-poled stoichiometric LiTaO3 doped with MgO," J. Appl. Phys. 96, 7445-7449 (2004).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt and R. L. Byer, "Quasi phase matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Eger, D.

A. Bruner, D. Eger and S. Ruschin, "Second harmonic generation of green light in periodically-poled stoichiometric LiTaO3 doped with MgO," J. Appl. Phys. 96, 7445-7449 (2004).
[CrossRef]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt and R. L. Byer, "Quasi phase matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Furukawa, Y.

Y. Furukawa, K. Kitamura,E. Suzuki and K. Niwa, "Stoichiometric LiTaO3 single crystal growth by double-crucible Czochralski method using automatic powder supply system," J. Cryst. Growth 197, 889-895 (1999).
[CrossRef]

Glickman, Y.

Y. Glickman, E. Winebrand, A. Arie, and G. Rosenman, "Electron-beam-induced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion," Appl. Phys. Lett. 88, 011103 (2006).
[CrossRef]

Hanna, D. C.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson and D. C. Hanna, "Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal," Phys. Rev. Lett. 84, 4345-4348 (2000).
[CrossRef] [PubMed]

Jundt, D. H.

D. H. Jundt, "Temperature-dependent Sellmeier equations for the index of refraction ne, in congruent lithium niobate," Opt. Lett. 22, 1553-1555 (1997).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt and R. L. Byer, "Quasi phase matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Kitamura, K.

Y. Furukawa, K. Kitamura,E. Suzuki and K. Niwa, "Stoichiometric LiTaO3 single crystal growth by double-crucible Czochralski method using automatic powder supply system," J. Cryst. Growth 197, 889-895 (1999).
[CrossRef]

Kivshar, Y. S.

S. M. Saltiel, A. A. Sukhorukov and Y. S. Kivshar, "Multistep parametric processes in nonlinear optics," Prog. Opt. 47, 1-73 (2005).
[CrossRef]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt and R. L. Byer, "Quasi phase matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Nada, N.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase-matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

Niwa, K.

Y. Furukawa, K. Kitamura,E. Suzuki and K. Niwa, "Stoichiometric LiTaO3 single crystal growth by double-crucible Czochralski method using automatic powder supply system," J. Cryst. Growth 197, 889-895 (1999).
[CrossRef]

Offerhaus, H. L.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson and D. C. Hanna, "Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal," Phys. Rev. Lett. 84, 4345-4348 (2000).
[CrossRef] [PubMed]

Richardson, D. J.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson and D. C. Hanna, "Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal," Phys. Rev. Lett. 84, 4345-4348 (2000).
[CrossRef] [PubMed]

Rosenman, G.

Y. Glickman, E. Winebrand, A. Arie, and G. Rosenman, "Electron-beam-induced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion," Appl. Phys. Lett. 88, 011103 (2006).
[CrossRef]

Ross, G. W.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson and D. C. Hanna, "Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal," Phys. Rev. Lett. 84, 4345-4348 (2000).
[CrossRef] [PubMed]

Ruschin, S.

A. Bruner, D. Eger and S. Ruschin, "Second harmonic generation of green light in periodically-poled stoichiometric LiTaO3 doped with MgO," J. Appl. Phys. 96, 7445-7449 (2004).
[CrossRef]

Saitoh, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase-matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

Saltiel, S. M.

S. M. Saltiel, A. A. Sukhorukov and Y. S. Kivshar, "Multistep parametric processes in nonlinear optics," Prog. Opt. 47, 1-73 (2005).
[CrossRef]

Sukhorukov, A. A.

S. M. Saltiel, A. A. Sukhorukov and Y. S. Kivshar, "Multistep parametric processes in nonlinear optics," Prog. Opt. 47, 1-73 (2005).
[CrossRef]

Suzuki, E.

Y. Furukawa, K. Kitamura,E. Suzuki and K. Niwa, "Stoichiometric LiTaO3 single crystal growth by double-crucible Czochralski method using automatic powder supply system," J. Cryst. Growth 197, 889-895 (1999).
[CrossRef]

Watanabe, K.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase-matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

Winebrand, E.

Y. Glickman, E. Winebrand, A. Arie, and G. Rosenman, "Electron-beam-induced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion," Appl. Phys. Lett. 88, 011103 (2006).
[CrossRef]

Yamada, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase-matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

Appl. Phys. Lett. (2)

Y. Glickman, E. Winebrand, A. Arie, and G. Rosenman, "Electron-beam-induced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion," Appl. Phys. Lett. 88, 011103 (2006).
[CrossRef]

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase-matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt and R. L. Byer, "Quasi phase matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

J. Appl. Phys. (1)

A. Bruner, D. Eger and S. Ruschin, "Second harmonic generation of green light in periodically-poled stoichiometric LiTaO3 doped with MgO," J. Appl. Phys. 96, 7445-7449 (2004).
[CrossRef]

J. Cryst. Growth (1)

Y. Furukawa, K. Kitamura,E. Suzuki and K. Niwa, "Stoichiometric LiTaO3 single crystal growth by double-crucible Czochralski method using automatic powder supply system," J. Cryst. Growth 197, 889-895 (1999).
[CrossRef]

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

Opt. Lett. (1)

Phys. Rev. Lett. (2)

V. Berger, "Nonlinear photonic crystals," Phys. Rev. Lett. 81, 4136-4139 (1998).
[CrossRef]

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson and D. C. Hanna, "Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal," Phys. Rev. Lett. 84, 4345-4348 (2000).
[CrossRef] [PubMed]

Prog. Opt. (1)

S. M. Saltiel, A. A. Sukhorukov and Y. S. Kivshar, "Multistep parametric processes in nonlinear optics," Prog. Opt. 47, 1-73 (2005).
[CrossRef]

Other (2)

R.W. Boyd, Nonlinear Optics, second edition, (Academic Press, 2002), Chap. 2.

F. W. Byron and R. W. Fuller, Mathematics of classical and quantum physics, (Dover Publications, 1992), Chap. 7.

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Figures (4)

Fig. 1.
Fig. 1.

(a) — The binary annular grating with period Λ. (b) — Fourier transform of the binary annular grating and phase matching diagram for SHG. The second harmonic’s k-vector outlines a circle around the fundamental’s k-vectors giving all possible phase mismatches. Points of intersection between this circle and the structures Fourier space rings are the points of phase matching (represented by large grey dots).

Fig. 2.
Fig. 2.

Optical and AFM pictures of the e-beam poled lithium niobate - (a) and (b) respectively and of the electric field poled SLT - (c) and (d) respectively.

Fig. 3.
Fig. 3.

Diffraction pattern of the electric field poled structure.

Fig. 4.
Fig. 4.

Temperature dependence of the SHG efficiency in SLT. Solid and dashed lines: measurements of the 1st order (collinear) and 2nd order (non-collinear) interactions, respectively. Dash-dot line: Calculation of the co-linear 1st order. Inset: photo of the SHG signal on a screen. The central spot is the collinear SHG, whereas the side spots represent the non-collinear SHG

Tables (2)

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Table 1. Angular measurements in SHG experiments with annular structures

Tables Icon

Table 2. Normalized frequency doubling efficiencies

Equations (3)

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g ( r ) = sign ( cos ( 2 π r Λ ) )
cos θ n = ( 2 k ω ) 2 + ( k 2 ω ) 2 G n 2 4 k ω k 2 ω
E 2 ω ( r ) = G ( R ) ( 2 ω ) 2 c 2 2 d ( E ω ) 2 · d r ' .

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