Abstract

The performance of lithium niobate (LN) photonic crystals (PhCs) is theoretically analyzed with transmission spectra and band diagrams as calculated by the 3-D Finite-Difference Time Domain (FDTD) method. For a square lattice of holes fabricated in the top surface of an Annealed Proton-Exchange (APE) waveguide, we investigate the influence of both finite hole depth and non-cylindrical hole shape, using a full treatment of the birefringent gradient index profile. As expected, cylindrical holes which are sufficiently deep to overlap the APE waveguide mode (centered at 2.5µm below the surface) produce transmission spectra closely resembling those predicted by simple 2-D modeling. As the hole depth decreases without any change in the cylindrical shape, the contrast between the photonic pass- and stop-bands and the sharpness of the band-edge are slowly lost. We show that this loss of contrast is due to the portion of the buried APE waveguide mode that passes under the holes. However, conical holes of any depth fail to produce well-defined stop-bands in either the transmission spectra or band diagrams. Deep conical holes act as a broad-band attenuator due to refraction of the mode out of the APE region down into the bulk. Experimental results confirming this observation are shown. The impact of holes which are cylindrical at the top and conical at their bottom is also investigated. Given the difficulty of fabricating high aspect-ratio cylindrical holes in lithium niobate, we propose a partial solution to improve the overlap between shallow holes and the buried mode, in which the PhC holes are fabricated at the bottom of a wide, shallow trench previously introduced into the APE waveguide surface.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2007 (1)

2006 (2)

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, "Improving accuracy by subpixel smoothing in the finite-difference time domain," Opt. Lett. 31, 2972-2974 (2006).
[CrossRef] [PubMed]

M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, and F. Baida, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

2005 (3)

F. Lacour, N. Courjal, M. P. Bernal, A. Sabac, C. Bainier, and M. Spajer, "Nanostructuring lithium niobate substrates by focused ion beam milling," Opt. Mater. 27, 1421-1425 (2005).
[CrossRef]

S. G. Johnson, M. I. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

P. Rabiei and W. H. Steier, "Lithium niobate ridge waveguides and modulators fabricated using smart guide," Appl. Phys. Lett. 86, 161115 (2005).
[CrossRef]

2004 (2)

D. Gerace and L. C. Andreani, "Disorder-induced losses in photonic crystal waveguides with line defects," Opt. Lett. 29, 1897-1899 (2004).
[CrossRef] [PubMed]

R. Ferrini, A. Berrier, L. A. Dunbar, R. Houdre, M. Mulot, S. Anand, S. de Rossi, and A. Talneau, "Minimization of out-of-plane losses in planar photonic crystals by optimizing the vertical waveguide," Appl. Phys. Lett. 85, 3998-4000 (2004).
[CrossRef]

2003 (4)

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

R. Ferrini, B. Lombardet, B. Wild, R. Houdre, and G. H. Duan, "Hole depth- and shape-induced radiation losses in two-dimensional photonic crystals," Appl. Phys. Lett. 82, 1009-1011 (2003).
[CrossRef]

L. C. Andreani and M. Agio, "Intrinsic diffraction losses in photonic crystal waveguides with line defects," Appl. Phys. Lett. 82, 2011-2013 (2003).
[CrossRef]

R. Ferrini, R. Houdre, H. Benisty, M. Qiu, and J. Moosburger, "Radiation losses in planar photonic crystals: two-dimensional representation of hole depth and shape by an imaginary dielectric constant," J. Opt. Soc. Am. B 20, 469-478 (2003).
[CrossRef]

2002 (4)

A. M. Radojevic, R. M. Osgood, N. A. Roy, and H. Bakhru, "Prepatterned optical circuits in thin ion-sliced single-crystal films of LiNbO3," IEEE Photon. Technol. Lett. 14, 322-324 (2002).
[CrossRef]

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, "Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate," IEEE J. Quantum Electron. 38, 743-752 (2002).
[CrossRef]

T. Baba and M. Nakamura, "Photonic crystal light deflection devices using the superprism effect," IEEE J. Quantum Electron. 38, 909-914 (2002).
[CrossRef]

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, "Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals," Opt. Quantum Electron. 34, 205-215 (2002).
[CrossRef]

2001 (2)

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, "Out-of-plane scattering in photonic crystal slabs," IEEE Photon. Technol. Lett. 13, 565-567 (2001).
[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

2000 (2)

J. A. Roden and S. D. Gedney, "Convolution PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media," Microwave Opt. Technol. Lett. 27, 334-339 (2000).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

1999 (1)

1998 (3)

S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop filters in photonic crystals," Opt. Express 3, 4-11 (1998).
[CrossRef] [PubMed]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

M. Levy, R. M. Osgood, R. Liu, L. E. Cross, G. S. Cargill, A. Kumar, and H. Bakhru, "Fabrication of single-crystal lithium niobate films by crystal ion slicing," Appl. Phys. Lett. 73, 2293-2295 (1998).
[CrossRef]

1997 (1)

1982 (1)

J. L. Jackel, C. E. Rice, and J. J. Veselka, "Proton-Exchange for High-Index Waveguides in LiNbO3," Appl. Phys. Lett. 41, 607-608 (1982).
[CrossRef]

Agio, M.

L. C. Andreani and M. Agio, "Intrinsic diffraction losses in photonic crystal waveguides with line defects," Appl. Phys. Lett. 82, 2011-2013 (2003).
[CrossRef]

Akahane, Y.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Anand, S.

R. Ferrini, A. Berrier, L. A. Dunbar, R. Houdre, M. Mulot, S. Anand, S. de Rossi, and A. Talneau, "Minimization of out-of-plane losses in planar photonic crystals by optimizing the vertical waveguide," Appl. Phys. Lett. 85, 3998-4000 (2004).
[CrossRef]

Andreani, L. C.

D. Gerace and L. C. Andreani, "Disorder-induced losses in photonic crystal waveguides with line defects," Opt. Lett. 29, 1897-1899 (2004).
[CrossRef] [PubMed]

L. C. Andreani and M. Agio, "Intrinsic diffraction losses in photonic crystal waveguides with line defects," Appl. Phys. Lett. 82, 2011-2013 (2003).
[CrossRef]

Asano, T.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Baba, T.

T. Baba and M. Nakamura, "Photonic crystal light deflection devices using the superprism effect," IEEE J. Quantum Electron. 38, 909-914 (2002).
[CrossRef]

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, "Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate," IEEE J. Quantum Electron. 38, 743-752 (2002).
[CrossRef]

Baets, R.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, "Out-of-plane scattering in photonic crystal slabs," IEEE Photon. Technol. Lett. 13, 565-567 (2001).
[CrossRef]

Baida, F.

M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, and F. Baida, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Baida, F. I.

Bainier, C.

F. Lacour, N. Courjal, M. P. Bernal, A. Sabac, C. Bainier, and M. Spajer, "Nanostructuring lithium niobate substrates by focused ion beam milling," Opt. Mater. 27, 1421-1425 (2005).
[CrossRef]

Bakhru, H.

A. M. Radojevic, R. M. Osgood, N. A. Roy, and H. Bakhru, "Prepatterned optical circuits in thin ion-sliced single-crystal films of LiNbO3," IEEE Photon. Technol. Lett. 14, 322-324 (2002).
[CrossRef]

M. Levy, R. M. Osgood, R. Liu, L. E. Cross, G. S. Cargill, A. Kumar, and H. Bakhru, "Fabrication of single-crystal lithium niobate films by crystal ion slicing," Appl. Phys. Lett. 73, 2293-2295 (1998).
[CrossRef]

Benisty, H.

R. Ferrini, R. Houdre, H. Benisty, M. Qiu, and J. Moosburger, "Radiation losses in planar photonic crystals: two-dimensional representation of hole depth and shape by an imaginary dielectric constant," J. Opt. Soc. Am. B 20, 469-478 (2003).
[CrossRef]

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, "Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals," Opt. Quantum Electron. 34, 205-215 (2002).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

Beraud, A.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

Bermel, P.

Bernal, M. P.

F. Lacour, N. Courjal, M. P. Bernal, A. Sabac, C. Bainier, and M. Spajer, "Nanostructuring lithium niobate substrates by focused ion beam milling," Opt. Mater. 27, 1421-1425 (2005).
[CrossRef]

Bernal, M.-P.

M. Roussey, F. I. Baida, and M.-P. Bernal, "Experimental and theoretical observation of the slow light effect on a tunable photonic crystal," J. Opt. Soc. Am. B 24, 1416-1422 (2007).
[CrossRef]

M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, and F. Baida, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Berrier, A.

R. Ferrini, A. Berrier, L. A. Dunbar, R. Houdre, M. Mulot, S. Anand, S. de Rossi, and A. Talneau, "Minimization of out-of-plane losses in planar photonic crystals by optimizing the vertical waveguide," Appl. Phys. Lett. 85, 3998-4000 (2004).
[CrossRef]

Bienstman, P.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, "Out-of-plane scattering in photonic crystal slabs," IEEE Photon. Technol. Lett. 13, 565-567 (2001).
[CrossRef]

Bogaerts, W.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, "Out-of-plane scattering in photonic crystal slabs," IEEE Photon. Technol. Lett. 13, 565-567 (2001).
[CrossRef]

Burr, G. W.

Cargill, G. S.

M. Levy, R. M. Osgood, R. Liu, L. E. Cross, G. S. Cargill, A. Kumar, and H. Bakhru, "Fabrication of single-crystal lithium niobate films by crystal ion slicing," Appl. Phys. Lett. 73, 2293-2295 (1998).
[CrossRef]

Cassagne, D.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, "Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals," Opt. Quantum Electron. 34, 205-215 (2002).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

Courjal, N.

M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, and F. Baida, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

F. Lacour, N. Courjal, M. P. Bernal, A. Sabac, C. Bainier, and M. Spajer, "Nanostructuring lithium niobate substrates by focused ion beam milling," Opt. Mater. 27, 1421-1425 (2005).
[CrossRef]

Cross, L. E.

M. Levy, R. M. Osgood, R. Liu, L. E. Cross, G. S. Cargill, A. Kumar, and H. Bakhru, "Fabrication of single-crystal lithium niobate films by crystal ion slicing," Appl. Phys. Lett. 73, 2293-2295 (1998).
[CrossRef]

de Rossi, S.

R. Ferrini, A. Berrier, L. A. Dunbar, R. Houdre, M. Mulot, S. Anand, S. de Rossi, and A. Talneau, "Minimization of out-of-plane losses in planar photonic crystals by optimizing the vertical waveguide," Appl. Phys. Lett. 85, 3998-4000 (2004).
[CrossRef]

De Zutter, D.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, "Out-of-plane scattering in photonic crystal slabs," IEEE Photon. Technol. Lett. 13, 565-567 (2001).
[CrossRef]

Duan, G. H.

R. Ferrini, B. Lombardet, B. Wild, R. Houdre, and G. H. Duan, "Hole depth- and shape-induced radiation losses in two-dimensional photonic crystals," Appl. Phys. Lett. 82, 1009-1011 (2003).
[CrossRef]

Dunbar, L. A.

R. Ferrini, A. Berrier, L. A. Dunbar, R. Houdre, M. Mulot, S. Anand, S. de Rossi, and A. Talneau, "Minimization of out-of-plane losses in planar photonic crystals by optimizing the vertical waveguide," Appl. Phys. Lett. 85, 3998-4000 (2004).
[CrossRef]

Fan, S. H.

Farjadpour, A.

Ferrini, R.

R. Ferrini, A. Berrier, L. A. Dunbar, R. Houdre, M. Mulot, S. Anand, S. de Rossi, and A. Talneau, "Minimization of out-of-plane losses in planar photonic crystals by optimizing the vertical waveguide," Appl. Phys. Lett. 85, 3998-4000 (2004).
[CrossRef]

R. Ferrini, R. Houdre, H. Benisty, M. Qiu, and J. Moosburger, "Radiation losses in planar photonic crystals: two-dimensional representation of hole depth and shape by an imaginary dielectric constant," J. Opt. Soc. Am. B 20, 469-478 (2003).
[CrossRef]

R. Ferrini, B. Lombardet, B. Wild, R. Houdre, and G. H. Duan, "Hole depth- and shape-induced radiation losses in two-dimensional photonic crystals," Appl. Phys. Lett. 82, 1009-1011 (2003).
[CrossRef]

Fukaya, N.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, "Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate," IEEE J. Quantum Electron. 38, 743-752 (2002).
[CrossRef]

Gedney, S. D.

J. A. Roden and S. D. Gedney, "Convolution PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media," Microwave Opt. Technol. Lett. 27, 334-339 (2000).
[CrossRef]

Gerace, D.

Haus, H. A.

Houdre, R.

R. Ferrini, A. Berrier, L. A. Dunbar, R. Houdre, M. Mulot, S. Anand, S. de Rossi, and A. Talneau, "Minimization of out-of-plane losses in planar photonic crystals by optimizing the vertical waveguide," Appl. Phys. Lett. 85, 3998-4000 (2004).
[CrossRef]

R. Ferrini, R. Houdre, H. Benisty, M. Qiu, and J. Moosburger, "Radiation losses in planar photonic crystals: two-dimensional representation of hole depth and shape by an imaginary dielectric constant," J. Opt. Soc. Am. B 20, 469-478 (2003).
[CrossRef]

R. Ferrini, B. Lombardet, B. Wild, R. Houdre, and G. H. Duan, "Hole depth- and shape-induced radiation losses in two-dimensional photonic crystals," Appl. Phys. Lett. 82, 1009-1011 (2003).
[CrossRef]

Ibanescu, M.

Iwai, T.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, "Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate," IEEE J. Quantum Electron. 38, 743-752 (2002).
[CrossRef]

Jackel, J. L.

J. L. Jackel, C. E. Rice, and J. J. Veselka, "Proton-Exchange for High-Index Waveguides in LiNbO3," Appl. Phys. Lett. 41, 607-608 (1982).
[CrossRef]

Jacobs, S.

S. G. Johnson, M. I. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, "Improving accuracy by subpixel smoothing in the finite-difference time domain," Opt. Lett. 31, 2972-2974 (2006).
[CrossRef] [PubMed]

S. G. Johnson, M. I. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

Jouanin, C.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, "Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals," Opt. Quantum Electron. 34, 205-215 (2002).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

Karalis, A.

S. G. Johnson, M. I. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Krauss, T. F.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, "Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals," Opt. Quantum Electron. 34, 205-215 (2002).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

Kumar, A.

M. Levy, R. M. Osgood, R. Liu, L. E. Cross, G. S. Cargill, A. Kumar, and H. Bakhru, "Fabrication of single-crystal lithium niobate films by crystal ion slicing," Appl. Phys. Lett. 73, 2293-2295 (1998).
[CrossRef]

Labilloy, D.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

Lacour, F.

F. Lacour, N. Courjal, M. P. Bernal, A. Sabac, C. Bainier, and M. Spajer, "Nanostructuring lithium niobate substrates by focused ion beam milling," Opt. Mater. 27, 1421-1425 (2005).
[CrossRef]

Lalanne, P.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, "Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals," Opt. Quantum Electron. 34, 205-215 (2002).
[CrossRef]

Lee, R. K.

Levy, M.

M. Levy, R. M. Osgood, R. Liu, L. E. Cross, G. S. Cargill, A. Kumar, and H. Bakhru, "Fabrication of single-crystal lithium niobate films by crystal ion slicing," Appl. Phys. Lett. 73, 2293-2295 (1998).
[CrossRef]

Liang, T.

Liu, R.

M. Levy, R. M. Osgood, R. Liu, L. E. Cross, G. S. Cargill, A. Kumar, and H. Bakhru, "Fabrication of single-crystal lithium niobate films by crystal ion slicing," Appl. Phys. Lett. 73, 2293-2295 (1998).
[CrossRef]

Lombardet, B.

R. Ferrini, B. Lombardet, B. Wild, R. Houdre, and G. H. Duan, "Hole depth- and shape-induced radiation losses in two-dimensional photonic crystals," Appl. Phys. Lett. 82, 1009-1011 (2003).
[CrossRef]

Moosburger, J.

Motegi, A.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, "Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate," IEEE J. Quantum Electron. 38, 743-752 (2002).
[CrossRef]

Mulot, M.

R. Ferrini, A. Berrier, L. A. Dunbar, R. Houdre, M. Mulot, S. Anand, S. de Rossi, and A. Talneau, "Minimization of out-of-plane losses in planar photonic crystals by optimizing the vertical waveguide," Appl. Phys. Lett. 85, 3998-4000 (2004).
[CrossRef]

Nakamura, M.

T. Baba and M. Nakamura, "Photonic crystal light deflection devices using the superprism effect," IEEE J. Quantum Electron. 38, 909-914 (2002).
[CrossRef]

Noda, S.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Olivier, S.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, "Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals," Opt. Quantum Electron. 34, 205-215 (2002).
[CrossRef]

Osgood, R. M.

A. M. Radojevic, R. M. Osgood, N. A. Roy, and H. Bakhru, "Prepatterned optical circuits in thin ion-sliced single-crystal films of LiNbO3," IEEE Photon. Technol. Lett. 14, 322-324 (2002).
[CrossRef]

M. Levy, R. M. Osgood, R. Liu, L. E. Cross, G. S. Cargill, A. Kumar, and H. Bakhru, "Fabrication of single-crystal lithium niobate films by crystal ion slicing," Appl. Phys. Lett. 73, 2293-2295 (1998).
[CrossRef]

Povinelli, M. I.

S. G. Johnson, M. I. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

Qiu, M.

Rabiei, P.

P. Rabiei and W. H. Steier, "Lithium niobate ridge waveguides and modulators fabricated using smart guide," Appl. Phys. Lett. 86, 161115 (2005).
[CrossRef]

Radojevic, A. M.

A. M. Radojevic, R. M. Osgood, N. A. Roy, and H. Bakhru, "Prepatterned optical circuits in thin ion-sliced single-crystal films of LiNbO3," IEEE Photon. Technol. Lett. 14, 322-324 (2002).
[CrossRef]

Rattier, M.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, "Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals," Opt. Quantum Electron. 34, 205-215 (2002).
[CrossRef]

Rice, C. E.

J. L. Jackel, C. E. Rice, and J. J. Veselka, "Proton-Exchange for High-Index Waveguides in LiNbO3," Appl. Phys. Lett. 41, 607-608 (1982).
[CrossRef]

Roden, J. A.

J. A. Roden and S. D. Gedney, "Convolution PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media," Microwave Opt. Technol. Lett. 27, 334-339 (2000).
[CrossRef]

Rodriguez, A.

Roundy, D.

Roussey, M.

M. Roussey, F. I. Baida, and M.-P. Bernal, "Experimental and theoretical observation of the slow light effect on a tunable photonic crystal," J. Opt. Soc. Am. B 24, 1416-1422 (2007).
[CrossRef]

M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, and F. Baida, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Roy, N. A.

A. M. Radojevic, R. M. Osgood, N. A. Roy, and H. Bakhru, "Prepatterned optical circuits in thin ion-sliced single-crystal films of LiNbO3," IEEE Photon. Technol. Lett. 14, 322-324 (2002).
[CrossRef]

Sabac, A.

F. Lacour, N. Courjal, M. P. Bernal, A. Sabac, C. Bainier, and M. Spajer, "Nanostructuring lithium niobate substrates by focused ion beam milling," Opt. Mater. 27, 1421-1425 (2005).
[CrossRef]

Sakai, A.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, "Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate," IEEE J. Quantum Electron. 38, 743-752 (2002).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Scherer, A.

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Smith, C. J. M.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, "Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals," Opt. Quantum Electron. 34, 205-215 (2002).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

Soljacic, M.

S. G. Johnson, M. I. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

Song, B. S.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Spajer, M.

F. Lacour, N. Courjal, M. P. Bernal, A. Sabac, C. Bainier, and M. Spajer, "Nanostructuring lithium niobate substrates by focused ion beam milling," Opt. Mater. 27, 1421-1425 (2005).
[CrossRef]

Steier, W. H.

P. Rabiei and W. H. Steier, "Lithium niobate ridge waveguides and modulators fabricated using smart guide," Appl. Phys. Lett. 86, 161115 (2005).
[CrossRef]

Taillaert, D.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, "Out-of-plane scattering in photonic crystal slabs," IEEE Photon. Technol. Lett. 13, 565-567 (2001).
[CrossRef]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Talneau, A.

R. Ferrini, A. Berrier, L. A. Dunbar, R. Houdre, M. Mulot, S. Anand, S. de Rossi, and A. Talneau, "Minimization of out-of-plane losses in planar photonic crystals by optimizing the vertical waveguide," Appl. Phys. Lett. 85, 3998-4000 (2004).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Tanaka, Y.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Van Labeke, D.

M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, and F. Baida, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Veselka, J. J.

J. L. Jackel, C. E. Rice, and J. J. Veselka, "Proton-Exchange for High-Index Waveguides in LiNbO3," Appl. Phys. Lett. 41, 607-608 (1982).
[CrossRef]

Villeneuve, P. R.

Watanabe, Y.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, "Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate," IEEE J. Quantum Electron. 38, 743-752 (2002).
[CrossRef]

Weisbuch, C.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, "Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals," Opt. Quantum Electron. 34, 205-215 (2002).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

Wild, B.

R. Ferrini, B. Lombardet, B. Wild, R. Houdre, and G. H. Duan, "Hole depth- and shape-induced radiation losses in two-dimensional photonic crystals," Appl. Phys. Lett. 82, 1009-1011 (2003).
[CrossRef]

Xu, Y.

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Yariv, A.

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Ziolkowski, R. W.

Appl. Phys. B (1)

S. G. Johnson, M. I. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

Appl. Phys. Lett. (9)

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, and F. Baida, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

L. C. Andreani and M. Agio, "Intrinsic diffraction losses in photonic crystal waveguides with line defects," Appl. Phys. Lett. 82, 2011-2013 (2003).
[CrossRef]

J. L. Jackel, C. E. Rice, and J. J. Veselka, "Proton-Exchange for High-Index Waveguides in LiNbO3," Appl. Phys. Lett. 41, 607-608 (1982).
[CrossRef]

R. Ferrini, B. Lombardet, B. Wild, R. Houdre, and G. H. Duan, "Hole depth- and shape-induced radiation losses in two-dimensional photonic crystals," Appl. Phys. Lett. 82, 1009-1011 (2003).
[CrossRef]

R. Ferrini, A. Berrier, L. A. Dunbar, R. Houdre, M. Mulot, S. Anand, S. de Rossi, and A. Talneau, "Minimization of out-of-plane losses in planar photonic crystals by optimizing the vertical waveguide," Appl. Phys. Lett. 85, 3998-4000 (2004).
[CrossRef]

M. Levy, R. M. Osgood, R. Liu, L. E. Cross, G. S. Cargill, A. Kumar, and H. Bakhru, "Fabrication of single-crystal lithium niobate films by crystal ion slicing," Appl. Phys. Lett. 73, 2293-2295 (1998).
[CrossRef]

P. Rabiei and W. H. Steier, "Lithium niobate ridge waveguides and modulators fabricated using smart guide," Appl. Phys. Lett. 86, 161115 (2005).
[CrossRef]

IEEE J. Quantum Electron. (2)

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, "Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate," IEEE J. Quantum Electron. 38, 743-752 (2002).
[CrossRef]

T. Baba and M. Nakamura, "Photonic crystal light deflection devices using the superprism effect," IEEE J. Quantum Electron. 38, 909-914 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, "Out-of-plane scattering in photonic crystal slabs," IEEE Photon. Technol. Lett. 13, 565-567 (2001).
[CrossRef]

A. M. Radojevic, R. M. Osgood, N. A. Roy, and H. Bakhru, "Prepatterned optical circuits in thin ion-sliced single-crystal films of LiNbO3," IEEE Photon. Technol. Lett. 14, 322-324 (2002).
[CrossRef]

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

Microwave Opt. Technol. Lett. (1)

J. A. Roden and S. D. Gedney, "Convolution PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media," Microwave Opt. Technol. Lett. 27, 334-339 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Opt. Mater. (1)

F. Lacour, N. Courjal, M. P. Bernal, A. Sabac, C. Bainier, and M. Spajer, "Nanostructuring lithium niobate substrates by focused ion beam milling," Opt. Mater. 27, 1421-1425 (2005).
[CrossRef]

Opt. Quantum Electron. (1)

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. Weisbuch, C. J. M. Smith, T. F. Krauss, C. Jouanin, and D. Cassagne, "Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals," Opt. Quantum Electron. 34, 205-215 (2002).
[CrossRef]

Phys. Rev. B (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Other (3)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: molding the flow of light (Princeton University Press, Princeton, NJ, 1995).

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 3rd ed. (Artech House, Boston, 2005).

G. W. Burr, S. C. Hagness, and A. Taflove, "FDTD for Photonics," Chapter 16 of Ref. [10].

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Figures (12)

Fig. 1.
Fig. 1.

Scanning electron microscopy images of (a) square lattice and (b) triangular lattice photonic crystals fabricated on lithium niobate. The FIB cross-sections, although distorted by re-deposition during milling, provide qualitative information on the shape and depth of the fabricated holes.

Fig. 2.
Fig. 2.

(a) Theoretical spectra from 2-D FDTD simulations [23] compared with (b) experimentally measured spectra of a square lattice LN PhC [23].

Fig. 3.
Fig. 3.

(a) 3-D unit cell used for FDTD band-diagram computation, composed of a 2-D unit cell extruded vertically through the graded-index top surface of a lithium niobate APE waveguide. The coordinate system is chosen so that the crystal c axis intuitively corresponds to z and the vertical crystal a axis to x. (b) 3-D band diagram of a LN PhC with >8µm deep perfectly cylindrical holes (a=766 nm, r/a=0.27). (c) 2-D band diagram of the same LN PhC. (d) 3-D band diagram of un-patterned lithium niobate with the same APE gradient-index profile. The dotted box shows the span of frequencies corresponding to light between 1 and 2µm (top and bottom, respectively), propagating along the y axis (ΓY direction).

Fig. 4.
Fig. 4.

(a) 3-D unit cell used for FDTD simulations of transmission spectra, which occupies (na+12µm)×10µa for n rows of square-lattice photonic crystal at a spacing of a=766nm. (b) Transmission spectra of an infinitely-wide lithium niobate photonic crystal composed of 5, 10, 15, 30 and 45 rows of 10µm deep cylindrical holes.

Fig. 5.
Fig. 5.

(a) Transmission spectra of LN PhCs with 30 rows of 1, 2, 2.5, 3, 4, 5, 6 and 8µm deep cylindrical holes. 3-D band diagrams of LN PhCs with (b) 10 and (c) 2µm deep cylindrical holes corresponding to the ΓY direction in the Brillouin zone.

Fig. 6.
Fig. 6.

Transmission spectra of LN PhCs with 30 rows of 1, 2, 2.5, 3, 4, 5, 6 and 8µm deep conical holes. 3-D band diagrams of LN PhCs with (b) 10 and (c) 2µm deep conical holes corresponding to the ΓY direction in the Brillouin zone.

Fig. 7.
Fig. 7.

Transmission spectra of LN PhCs with 30 rows of 8, 10, 12, 16, 20, 30, and 40µm deep conical holes. Also shown are the associated half-cone or sidewall angles θ.

Fig. 8.
Fig. 8.

Continuous field (E z ) slices of LN APE waveguide photonic crystals with (a) deep (10µm) cylinders illuminated at λ=1.520µm, b) deep (10µm) cylinders illuminated at λ=1.570µm, (c) shallow (2µm) cylinders illuminated at λ=1.520µm, and (d) 6µm deep cones illuminated at λ=1.420µm

Fig. 9.
Fig. 9.

CCD images of the exit face of LN samples illuminated at a wavelength of 1.55µm, each containing an APE waveguide and a 15 by 15 square lattice photonic crystal fabricated with (a) cylindroconical holes located near the exit face, (b) conical holes located near the exit face, (c) cylindroconical holes located near the entrance face, and (d) conical holes near the entrance face. Not only do the cylindroconical holes (e.g., our best efforts at fabricating cylindrical holes) lead to noticeably better extinction, but conical holes deflect light downward into the substrate—just as predicted by simulation.

Fig. 10.
Fig. 10.

Transmission spectra of LN PhCs etched by 4µm deep holes that are cylindrical at the top (height d) and conical at the bottom (height (4µm -d)).

Fig. 11.
Fig. 11.

Transmission spectra of a LN APE planar waveguide with a wide trench of extent 15.3µm (20a) along the propagation direction, for depths varying from 0.5 to 3µm.

Fig. 12.
Fig. 12.

Transmission spectra of LN PhCs with holes etched into the bottom of a shallow trench. Parts (a) and (b) show the spectra for a 1µm deep trench (extending laterally only 1.5µm (2a) before and after the photonic crystal), for (a) cylindrical holes of depths ranging from 1 to 4µm, and for (a) cylindroconical holes of total depths ranging from 1 to 4µm, where the top 75% of the hole is cylindrical in shape followed by a conical shape over the bottom 25%. Similarly, but for a 1.5µm deep trench, spectra are also shown for (c) cylindrical holes, and for (d) holes which are 75% cylindrical and 25% conical.

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