Abstract

The group index dispersion and birefringence of guided modes supported by straight photonic crystal (PhC) waveguides are theoretically and experimentally investigated as a function of the waveguide width within various reduced frequency domains. Within the photonic gap and far from the Brillouin zone edges, strongly confined modes supported by narrow PhC guides exhibit both a group index and a birefringence larger than those of a deep ridge. These two results evidence the contribution of the photonic gap to the guiding mechanism in the refractivelike domain.

© 2006 Optical Society of America

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  1. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef] [PubMed]
  2. T. Asano, K. Kiyota, D. Kumamoto, B. S. Song, and S. Noda, Appl. Phys. Lett. 84, 4690 (2004).
    [CrossRef]
  3. D. Mori and T. Baba, Appl. Phys. Lett. 85, 1101 (2004).
    [CrossRef]
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    [CrossRef]
  5. D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, Opt. Express 11, 125 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
  7. M. Mulot, S. Anand, M. Swillo, M. Qiu, B. Jaskorzynska, and A. Talneau, J. Vac. Sci. Technol. B 21, 900 (2003).
    [CrossRef]
  8. A. Talneau, L. Legouezigou, and N. Bouadma, Opt. Lett. 26, 1259 (2001).
    [CrossRef]
  9. A. S. Sudbø, Pure Appl. Opt. 2, 211 (1993).
    [CrossRef]
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    [CrossRef]
  11. S. Adachi, Physical Properties of III-V Semiconductor Compounds (Wiley, 1992).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. M. Qiu, B. Jaskorzynska, M. Swillo, and H. Benisty, Microwave Opt. Technol. Lett. 34, 387 (2002).
    [CrossRef]

2004 (2)

T. Asano, K. Kiyota, D. Kumamoto, B. S. Song, and S. Noda, Appl. Phys. Lett. 84, 4690 (2004).
[CrossRef]

D. Mori and T. Baba, Appl. Phys. Lett. 85, 1101 (2004).
[CrossRef]

2003 (3)

A. Talneau, M. Mulot, S. Anand, and Ph. Lalanne, Appl. Phys. Lett. 82, 2577 (2003).
[CrossRef]

M. Mulot, S. Anand, M. Swillo, M. Qiu, B. Jaskorzynska, and A. Talneau, J. Vac. Sci. Technol. B 21, 900 (2003).
[CrossRef]

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, Opt. Express 11, 125 (2003).
[CrossRef] [PubMed]

2002 (1)

M. Qiu, B. Jaskorzynska, M. Swillo, and H. Benisty, Microwave Opt. Technol. Lett. 34, 387 (2002).
[CrossRef]

2001 (3)

A. Talneau, L. Legouezigou, and N. Bouadma, Opt. Lett. 26, 1259 (2001).
[CrossRef]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, and P. Viktorovitch, Appl. Phys. Lett. 79, 2312 (2001).
[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

1999 (1)

Y. Ohtera, T. Sato, T. Kawashima, and S. Kawakami, Electron. Lett. 35, 1271 (1999).
[CrossRef]

1993 (1)

A. S. Sudbø, Pure Appl. Opt. 2, 211 (1993).
[CrossRef]

1984 (1)

B. Broberg and S. Lindgren, J. Appl. Phys. 55, 3376 (1984).
[CrossRef]

1976 (1)

F. L. Lederman and J. D. Dow, Phys. Rev. B 13, 1633 (1976).
[CrossRef]

Adachi, S.

S. Adachi, Physical Properties of III-V Semiconductor Compounds (Wiley, 1992).
[CrossRef]

Anand, S.

M. Mulot, S. Anand, M. Swillo, M. Qiu, B. Jaskorzynska, and A. Talneau, J. Vac. Sci. Technol. B 21, 900 (2003).
[CrossRef]

A. Talneau, M. Mulot, S. Anand, and Ph. Lalanne, Appl. Phys. Lett. 82, 2577 (2003).
[CrossRef]

Asano, T.

T. Asano, K. Kiyota, D. Kumamoto, B. S. Song, and S. Noda, Appl. Phys. Lett. 84, 4690 (2004).
[CrossRef]

Baba, T.

D. Mori and T. Baba, Appl. Phys. Lett. 85, 1101 (2004).
[CrossRef]

Benisty, H.

M. Qiu, B. Jaskorzynska, M. Swillo, and H. Benisty, Microwave Opt. Technol. Lett. 34, 387 (2002).
[CrossRef]

Bouadma, N.

Broberg, B.

B. Broberg and S. Lindgren, J. Appl. Phys. 55, 3376 (1984).
[CrossRef]

Chiao, R. Y.

Dow, J. D.

F. L. Lederman and J. D. Dow, Phys. Rev. B 13, 1633 (1976).
[CrossRef]

Grillet, C.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, and P. Viktorovitch, Appl. Phys. Lett. 79, 2312 (2001).
[CrossRef]

Hickmann, J. M.

Jaskorzynska, B.

M. Mulot, S. Anand, M. Swillo, M. Qiu, B. Jaskorzynska, and A. Talneau, J. Vac. Sci. Technol. B 21, 900 (2003).
[CrossRef]

M. Qiu, B. Jaskorzynska, M. Swillo, and H. Benisty, Microwave Opt. Technol. Lett. 34, 387 (2002).
[CrossRef]

Kawakami, S.

Y. Ohtera, T. Sato, T. Kawashima, and S. Kawakami, Electron. Lett. 35, 1271 (1999).
[CrossRef]

Kawashima, T.

Y. Ohtera, T. Sato, T. Kawashima, and S. Kawakami, Electron. Lett. 35, 1271 (1999).
[CrossRef]

Kiyota, K.

T. Asano, K. Kiyota, D. Kumamoto, B. S. Song, and S. Noda, Appl. Phys. Lett. 84, 4690 (2004).
[CrossRef]

Kumamoto, D.

T. Asano, K. Kiyota, D. Kumamoto, B. S. Song, and S. Noda, Appl. Phys. Lett. 84, 4690 (2004).
[CrossRef]

Lalanne, Ph.

A. Talneau, M. Mulot, S. Anand, and Ph. Lalanne, Appl. Phys. Lett. 82, 2577 (2003).
[CrossRef]

Lederman, F. L.

F. L. Lederman and J. D. Dow, Phys. Rev. B 13, 1633 (1976).
[CrossRef]

Legouezigou, L.

Letartre, X.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, and P. Viktorovitch, Appl. Phys. Lett. 79, 2312 (2001).
[CrossRef]

Lindgren, S.

B. Broberg and S. Lindgren, J. Appl. Phys. 55, 3376 (1984).
[CrossRef]

McCormick, C. F.

Mori, D.

D. Mori and T. Baba, Appl. Phys. Lett. 85, 1101 (2004).
[CrossRef]

Mulot, M.

M. Mulot, S. Anand, M. Swillo, M. Qiu, B. Jaskorzynska, and A. Talneau, J. Vac. Sci. Technol. B 21, 900 (2003).
[CrossRef]

A. Talneau, M. Mulot, S. Anand, and Ph. Lalanne, Appl. Phys. Lett. 82, 2577 (2003).
[CrossRef]

Noda, S.

T. Asano, K. Kiyota, D. Kumamoto, B. S. Song, and S. Noda, Appl. Phys. Lett. 84, 4690 (2004).
[CrossRef]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Ohtera, Y.

Y. Ohtera, T. Sato, T. Kawashima, and S. Kawakami, Electron. Lett. 35, 1271 (1999).
[CrossRef]

Qiu, M.

M. Mulot, S. Anand, M. Swillo, M. Qiu, B. Jaskorzynska, and A. Talneau, J. Vac. Sci. Technol. B 21, 900 (2003).
[CrossRef]

M. Qiu, B. Jaskorzynska, M. Swillo, and H. Benisty, Microwave Opt. Technol. Lett. 34, 387 (2002).
[CrossRef]

Rojo-Romeo, P.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, and P. Viktorovitch, Appl. Phys. Lett. 79, 2312 (2001).
[CrossRef]

Sato, T.

Y. Ohtera, T. Sato, T. Kawashima, and S. Kawakami, Electron. Lett. 35, 1271 (1999).
[CrossRef]

Seassal, C.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, and P. Viktorovitch, Appl. Phys. Lett. 79, 2312 (2001).
[CrossRef]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Solli, D. R.

Song, B. S.

T. Asano, K. Kiyota, D. Kumamoto, B. S. Song, and S. Noda, Appl. Phys. Lett. 84, 4690 (2004).
[CrossRef]

Sudbø, A. S.

A. S. Sudbø, Pure Appl. Opt. 2, 211 (1993).
[CrossRef]

Swillo, M.

M. Mulot, S. Anand, M. Swillo, M. Qiu, B. Jaskorzynska, and A. Talneau, J. Vac. Sci. Technol. B 21, 900 (2003).
[CrossRef]

M. Qiu, B. Jaskorzynska, M. Swillo, and H. Benisty, Microwave Opt. Technol. Lett. 34, 387 (2002).
[CrossRef]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Talneau, A.

M. Mulot, S. Anand, M. Swillo, M. Qiu, B. Jaskorzynska, and A. Talneau, J. Vac. Sci. Technol. B 21, 900 (2003).
[CrossRef]

A. Talneau, M. Mulot, S. Anand, and Ph. Lalanne, Appl. Phys. Lett. 82, 2577 (2003).
[CrossRef]

A. Talneau, L. Legouezigou, and N. Bouadma, Opt. Lett. 26, 1259 (2001).
[CrossRef]

Viktorovitch, P.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, and P. Viktorovitch, Appl. Phys. Lett. 79, 2312 (2001).
[CrossRef]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Appl. Phys. Lett. (4)

T. Asano, K. Kiyota, D. Kumamoto, B. S. Song, and S. Noda, Appl. Phys. Lett. 84, 4690 (2004).
[CrossRef]

D. Mori and T. Baba, Appl. Phys. Lett. 85, 1101 (2004).
[CrossRef]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, and P. Viktorovitch, Appl. Phys. Lett. 79, 2312 (2001).
[CrossRef]

A. Talneau, M. Mulot, S. Anand, and Ph. Lalanne, Appl. Phys. Lett. 82, 2577 (2003).
[CrossRef]

Electron. Lett. (1)

Y. Ohtera, T. Sato, T. Kawashima, and S. Kawakami, Electron. Lett. 35, 1271 (1999).
[CrossRef]

J. Appl. Phys. (1)

B. Broberg and S. Lindgren, J. Appl. Phys. 55, 3376 (1984).
[CrossRef]

J. Vac. Sci. Technol. B (1)

M. Mulot, S. Anand, M. Swillo, M. Qiu, B. Jaskorzynska, and A. Talneau, J. Vac. Sci. Technol. B 21, 900 (2003).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

M. Qiu, B. Jaskorzynska, M. Swillo, and H. Benisty, Microwave Opt. Technol. Lett. 34, 387 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

F. L. Lederman and J. D. Dow, Phys. Rev. B 13, 1633 (1976).
[CrossRef]

Phys. Rev. Lett. (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Pure Appl. Opt. (1)

A. S. Sudbø, Pure Appl. Opt. 2, 211 (1993).
[CrossRef]

Other (1)

S. Adachi, Physical Properties of III-V Semiconductor Compounds (Wiley, 1992).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of the three-section structures with a SEM top view of the ridge–W1 transition ( a = 450 nm ) . (b) Group index calculated and measured for a 1.2 μ m wide ridge (dashed curve and squares; the experimental error is smaller than the square size) and for the W1 (solid curve and circles). The calculated group index of a 0.5 μ m wide ridge is added (dotted curve). The W1 dispersion curve for TE polarization is added in the inset; the photonic gap is indicated between the dashed lines.

Fig. 2
Fig. 2

(a) Transmission spectrum of W2. The W2 TE dispersion curve is plotted in the inset; the photonic gap is indicated between the dashed lines. (b) Group index measured for W2 (circles). Group indices calculated for a 1 μ m wide deep ridge are plotted as a dashed curve.

Fig. 3
Fig. 3

(a) Birefringence measurement principle. Cross-polarized transmission measurements: (b) deep ridge (reference). In the u = 0.29 domain, (c) 60 row long W1, (d) 120 row long W1, (e) birefringence versus PhC guide width.

Fig. 4
Fig. 4

(a) FDTD simulation of transmission for both TE and TM polarizations. The photonic gap is indicated between the dashed lines. (b) Transmission spectra measured for both polarizations in the u = 0.24 domain.

Fig. 5
Fig. 5

Scanning electron microscope pictures (top view and cross-section view) of a W3 PhC guide, with a = 150 nm in the u = 0.1 reduced frequency domain.

Equations (6)

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n g = n eff λ ( d n eff d λ )
n g ( PhCW ) = peak ( L 3 ) [ peak ( L 2 ) + peak ( L 1 ) ] L ( PhCW ) ,
Δ Φ = { [ 2 π Δ ( n ) L ] λ } + Ψ ,
T ( λ ) 1 + cos [ ( 2 π λ ) Δ n L + Ψ ] .
Δ ( n ) L = λ 1 λ 2 ( λ 1 λ 2 ) .
Δ n L = Δ n ridge L ridge + Δ n PhCW L PhCW .

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