Abstract

Abstract

We report here far infrared photonic crystals comprised of a lattice-matched pair of semiconductor materials: GaP and Si, or GaAs and Ge, or AlAs and GaAs. The crystals operate in a wavelength range where the real refractive index of one material undergoes a major dispersion associated with the LO and TO phonon absorption peaks. Using electromagnetic theory, we investigated the photonic-bandgap response for both TE and TM polarizations. Propagation losses for two types of crystals are estimated in this paper. These structures offer promise for the integration of III–V materials (GaP, GaAs) on group IV (Si, or Ge) for practical, active, far infrared photonic devices, such as light sources, amplifiers, modulators, reconfigurable waveguides and switches.

© 2007 Optical Society of America

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  1. E. Yablonovitch, "Photonic band-gap crystals," J. Phys. 5, 2443-2460 (1993).
  2. M. Tokushima, H. Yamada, and Y. Arakawa, "1.5um-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
    [CrossRef]
  3. W. D. Zhou, "Encapsulation for efficient electrical injection of photonic crystal surface emitting lasers," Appl. Phys. Lett. 88,051106 (2006).
    [CrossRef]
  4. W. Zhou, V. Nair, and G. Thiruvengadam, "The impact of high dielectric constant on photonic bandgaps in PbSe nanocrystal-based photonic crystal slabs," Proc. SPIE 6128, 61280B (2006).
    [CrossRef]
  5. E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, 1985) Vol. I.
  6. M. Wakaki, K. Kudo, and T. Shibuya, Physical Properties and Data of Optical Materials (CRC Press, 2007).
    [CrossRef]
  7. M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).
  8. R. Leiten, "Germanium-a surprise base for high-quality nitrides," Compd. Semicond. 13, 14-17 (2007).
  9. C. G. Ribbing, "Reststrahlen material bilayers- An option for tailoring in the infrared," Appl. Opt. 32, 5531-5534 (1993).
    [CrossRef] [PubMed]
  10. J. A. Dobrowolski, Y. Guo, T. Tiwald, P. Ma, and D. Poitras, "Toward perfect antireflection coatings. 3. Experimental results obtained with the use of Reststrahlen materials," Appl. Opt. 45, 1555-1562 (2006).
    [CrossRef] [PubMed]
  11. A. Rung and C. G. Ribbing, "Polaritonic and Photonic Gap Interactions in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 92, 123901 (2004).
    [CrossRef] [PubMed]
  12. A. Rung, C. G. Ribbing, and M. Qiu, "Gap maps for triangular photonic crystals with a dispersive and absorbing component," Phys. Rev. B 72, 205120 (2005).
  13. M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, "Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials," Phys. Rev. B 49, 11080 (1994).
  14. V. Kuzmiak and A. A. Maradudin, "Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation," Phys. Rev. B 55, 7427 (1997).
  15. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method (Artech House, 2000).
  16. J. B. Pendry, "Photonic Band Structures," J. Mod. Opt. 41, 209-229 (1994).
    [CrossRef]
  17. G. Veronis, R. W. Dutton, and S. Fan, "Metallic photonic crystals with strong broadband absorption at optical frequencies over wide angular range," J. Appl. Phys. 97, 093104 (2005).
    [CrossRef]
  18. M. Qiu and S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. Appl. Phys. 87, 8268 (2000).
    [CrossRef]
  19. E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, 1991) Vol. II.
  20. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, Princeton, 1995).

2007 (1)

R. Leiten, "Germanium-a surprise base for high-quality nitrides," Compd. Semicond. 13, 14-17 (2007).

2006 (3)

J. A. Dobrowolski, Y. Guo, T. Tiwald, P. Ma, and D. Poitras, "Toward perfect antireflection coatings. 3. Experimental results obtained with the use of Reststrahlen materials," Appl. Opt. 45, 1555-1562 (2006).
[CrossRef] [PubMed]

W. D. Zhou, "Encapsulation for efficient electrical injection of photonic crystal surface emitting lasers," Appl. Phys. Lett. 88,051106 (2006).
[CrossRef]

W. Zhou, V. Nair, and G. Thiruvengadam, "The impact of high dielectric constant on photonic bandgaps in PbSe nanocrystal-based photonic crystal slabs," Proc. SPIE 6128, 61280B (2006).
[CrossRef]

2005 (2)

A. Rung, C. G. Ribbing, and M. Qiu, "Gap maps for triangular photonic crystals with a dispersive and absorbing component," Phys. Rev. B 72, 205120 (2005).

G. Veronis, R. W. Dutton, and S. Fan, "Metallic photonic crystals with strong broadband absorption at optical frequencies over wide angular range," J. Appl. Phys. 97, 093104 (2005).
[CrossRef]

2004 (2)

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5um-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

A. Rung and C. G. Ribbing, "Polaritonic and Photonic Gap Interactions in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 92, 123901 (2004).
[CrossRef] [PubMed]

2000 (1)

M. Qiu and S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. Appl. Phys. 87, 8268 (2000).
[CrossRef]

1997 (1)

V. Kuzmiak and A. A. Maradudin, "Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation," Phys. Rev. B 55, 7427 (1997).

1994 (2)

J. B. Pendry, "Photonic Band Structures," J. Mod. Opt. 41, 209-229 (1994).
[CrossRef]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, "Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials," Phys. Rev. B 49, 11080 (1994).

1993 (2)

1991 (1)

M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).

Arakawa, Y.

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5um-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

Chan, C. T.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, "Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials," Phys. Rev. B 49, 11080 (1994).

Dobrowolski, J. A.

Dutton, R. W.

G. Veronis, R. W. Dutton, and S. Fan, "Metallic photonic crystals with strong broadband absorption at optical frequencies over wide angular range," J. Appl. Phys. 97, 093104 (2005).
[CrossRef]

Fan, S.

G. Veronis, R. W. Dutton, and S. Fan, "Metallic photonic crystals with strong broadband absorption at optical frequencies over wide angular range," J. Appl. Phys. 97, 093104 (2005).
[CrossRef]

Guo, Y.

He, S.

M. Qiu and S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. Appl. Phys. 87, 8268 (2000).
[CrossRef]

Ho, K. M.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, "Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials," Phys. Rev. B 49, 11080 (1994).

Kuzmiak, V.

V. Kuzmiak and A. A. Maradudin, "Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation," Phys. Rev. B 55, 7427 (1997).

Leiten, R.

R. Leiten, "Germanium-a surprise base for high-quality nitrides," Compd. Semicond. 13, 14-17 (2007).

Ma, P.

Maradudin, A. A.

V. Kuzmiak and A. A. Maradudin, "Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation," Phys. Rev. B 55, 7427 (1997).

M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).

Nair, V.

W. Zhou, V. Nair, and G. Thiruvengadam, "The impact of high dielectric constant on photonic bandgaps in PbSe nanocrystal-based photonic crystal slabs," Proc. SPIE 6128, 61280B (2006).
[CrossRef]

Pendry, J. B.

J. B. Pendry, "Photonic Band Structures," J. Mod. Opt. 41, 209-229 (1994).
[CrossRef]

Plihal, M.

M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).

Poitras, D.

Qiu, M.

A. Rung, C. G. Ribbing, and M. Qiu, "Gap maps for triangular photonic crystals with a dispersive and absorbing component," Phys. Rev. B 72, 205120 (2005).

M. Qiu and S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. Appl. Phys. 87, 8268 (2000).
[CrossRef]

Ribbing, C. G.

A. Rung, C. G. Ribbing, and M. Qiu, "Gap maps for triangular photonic crystals with a dispersive and absorbing component," Phys. Rev. B 72, 205120 (2005).

A. Rung and C. G. Ribbing, "Polaritonic and Photonic Gap Interactions in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 92, 123901 (2004).
[CrossRef] [PubMed]

C. G. Ribbing, "Reststrahlen material bilayers- An option for tailoring in the infrared," Appl. Opt. 32, 5531-5534 (1993).
[CrossRef] [PubMed]

Rung, A.

A. Rung, C. G. Ribbing, and M. Qiu, "Gap maps for triangular photonic crystals with a dispersive and absorbing component," Phys. Rev. B 72, 205120 (2005).

A. Rung and C. G. Ribbing, "Polaritonic and Photonic Gap Interactions in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 92, 123901 (2004).
[CrossRef] [PubMed]

Sigalas, M. M.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, "Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials," Phys. Rev. B 49, 11080 (1994).

Soukoulis, C. M.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, "Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials," Phys. Rev. B 49, 11080 (1994).

Thiruvengadam, G.

W. Zhou, V. Nair, and G. Thiruvengadam, "The impact of high dielectric constant on photonic bandgaps in PbSe nanocrystal-based photonic crystal slabs," Proc. SPIE 6128, 61280B (2006).
[CrossRef]

Tiwald, T.

Tokushima, M.

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5um-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

Veronis, G.

G. Veronis, R. W. Dutton, and S. Fan, "Metallic photonic crystals with strong broadband absorption at optical frequencies over wide angular range," J. Appl. Phys. 97, 093104 (2005).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, "Photonic band-gap crystals," J. Phys. 5, 2443-2460 (1993).

Yamada, H.

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5um-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

Zhou, W.

W. Zhou, V. Nair, and G. Thiruvengadam, "The impact of high dielectric constant on photonic bandgaps in PbSe nanocrystal-based photonic crystal slabs," Proc. SPIE 6128, 61280B (2006).
[CrossRef]

Zhou, W. D.

W. D. Zhou, "Encapsulation for efficient electrical injection of photonic crystal surface emitting lasers," Appl. Phys. Lett. 88,051106 (2006).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5um-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

W. D. Zhou, "Encapsulation for efficient electrical injection of photonic crystal surface emitting lasers," Appl. Phys. Lett. 88,051106 (2006).
[CrossRef]

Compd. Semicond. (1)

R. Leiten, "Germanium-a surprise base for high-quality nitrides," Compd. Semicond. 13, 14-17 (2007).

J. Appl. Phys. (2)

G. Veronis, R. W. Dutton, and S. Fan, "Metallic photonic crystals with strong broadband absorption at optical frequencies over wide angular range," J. Appl. Phys. 97, 093104 (2005).
[CrossRef]

M. Qiu and S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. Appl. Phys. 87, 8268 (2000).
[CrossRef]

J. Mod. Opt. (1)

J. B. Pendry, "Photonic Band Structures," J. Mod. Opt. 41, 209-229 (1994).
[CrossRef]

J. Phys. (1)

E. Yablonovitch, "Photonic band-gap crystals," J. Phys. 5, 2443-2460 (1993).

Phys. Rev. B (4)

M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).

A. Rung, C. G. Ribbing, and M. Qiu, "Gap maps for triangular photonic crystals with a dispersive and absorbing component," Phys. Rev. B 72, 205120 (2005).

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, "Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials," Phys. Rev. B 49, 11080 (1994).

V. Kuzmiak and A. A. Maradudin, "Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation," Phys. Rev. B 55, 7427 (1997).

Phys. Rev. Lett. (1)

A. Rung and C. G. Ribbing, "Polaritonic and Photonic Gap Interactions in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 92, 123901 (2004).
[CrossRef] [PubMed]

Proc. SPIE (1)

W. Zhou, V. Nair, and G. Thiruvengadam, "The impact of high dielectric constant on photonic bandgaps in PbSe nanocrystal-based photonic crystal slabs," Proc. SPIE 6128, 61280B (2006).
[CrossRef]

Other (5)

E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, 1985) Vol. I.

M. Wakaki, K. Kudo, and T. Shibuya, Physical Properties and Data of Optical Materials (CRC Press, 2007).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method (Artech House, 2000).

E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, 1991) Vol. II.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, Princeton, 1995).

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Figures (12)

Fig. 1.
Fig. 1.

Schematic of proposed (a) type 1 and (b) type 2 photonic crystals consisting of two types of semiconductor materials; (c) the hexagonal lattice and the corresponding first Brillouin zone with the high symmetry points Γ, M and K.

Fig. 2.
Fig. 2.

Index of GaAs and Ge in the long wave and far-infrared spectral regime: (a) real part of index, (b) imaginary part of index, (c) refractive index difference between GaAs and Ge, and (d) the propagation loss of GaAs and Ge.

Fig. 3.
Fig. 3.

Index of GaP and Si in the long wave and far-infrared spectral regime: (a) real part of index, (b) imaginary part of index, (c) refractive index difference between GaP and Si, and (d) propagation loss of GaP and Si.

Fig. 4.
Fig. 4.

(a). Index difference between GaAs and Ge, and absorption of GaAs and Ge in the spectral windows 1 and 2 that are situated within the GaAs Reststrahl-dispersion region; (b). Index difference between GaP and Si, and absorption of GaP and Si in the spectral windows 1 and 2 that are situated within the GaP Reststrahl-dispersion region.

Fig. 5.
Fig. 5.

Photonic bandgap for Type 1 photonic crystals (Ge column in GaAs slab): Gap maps at different r/a values for (a) TE and (b) TM polarizations; Bandgap plots at r/a=0.4 for (c) TE and (b) TM polarizations.

Fig. 6.
Fig. 6.

Photonic bandgap for Type 2 photonic crystals (GaAs column in Ge slab): Gap maps at different r/a values for (a) TE and (b) TM polarizations; Bandgap plots at r/a=0.2 for (c) TE and (b) TM polarizations.

Fig. 7.
Fig. 7.

Photonic bandgap for Type 1 photonic crystals (Si column in GaP slab): Gap maps at different r/a values for (a) TE and (b) TM polarizations; Bandgap plots at r/a=0.4 for (c) TE and (b) TM polarizations.

Fig. 8.
Fig. 8.

Photonic bandgap for Type 2 photonic crystals (GaP column in Si slab): Gap maps at different r/a values for (a) TE and (b) TM polarizations; Bandgap plots at r/a=0.2 for (c) TE and (b) TM polarizations.

Fig. 9.
Fig. 9.

Bandgap maps of photonic crystals in the low-index portion of the dispersion region: Ge/GaAs at λ=34.50 µm and Si/GaP at λ=25.58 µm.

Fig. 10.
Fig. 10.

Schematic of the simulation setup used for the propagation loss analysis associated with the material absorption.

Fig. 11.
Fig. 11.

The propagation field profile shown in the line-defect region is corresponding the the case shown in Table 1 for GaP/Si case with index of 2.0/3.42, r/a=0.40 and wavelength of 23.06 µm. Note the intensity difference for two cases without and with absorption.

Fig. 12.
Fig. 12.

Maximum infrared path vs attenuation for 3 dB and 10 dB total insertion loss

Tables (2)

Tables Icon

Table 1. Si/GaP photonic-crystal bandgap and propagation losses: the first six examples are in Window 1; the last four are in Window 2

Tables Icon

Table 2. Ge/GaAs photonic-crystal bandgap and propagation losses: the first six examples are in Window 1, the last four are in Window 2.

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