Abstract

We present the analysis and design of a superprism-based demultiplexer that employs both group and phase velocity dispersion of the photonic crystal (PhC). Simultaneous diffraction compensation and spatio-angular wavelength channel separation is realized in a slab region that divides the PhC. This avoids the excessive broadening of the beams inside the PhC and enhances the achievable angular dispersion of the conventional superprism topology. As a result, a compact demultiplexer with a relaxed requirement for low divergence input beams is attained. The dynamics of the beams envelops are considered based on the curvature of the band structure. Analysis shows at least 36-fold reduction of the PhC area and much smaller propagation length in slab compared to the preconditioned superprism, based on the same design model. PhC area scales as Δω-2.5 with Δω being the channel spacing.

©2010 Optical Society of America

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References

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  1. E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10(2), 283–295 (1993).
    [Crossref]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
    [Crossref] [PubMed]
  3. L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915–918 (2002).
    [Crossref]
  4. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096–R10099 (1998).
    [Crossref]
  5. T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81(13), 2325–2327 (2002).
    [Crossref]
  6. B. Momeni and A. Adibi, “Systematic design of superprism-based photonic crystal demultiplexers,” IEEE J. Sel. Areas Commun. 23(7), 1355–1364 (2005).
    [Crossref]
  7. A. Bakhtazad and A. G. Kirk, “First-band S-vector photonic-crystal superprism demultiplexer design and optimization,” J. Lightwave Technol. 25(5), 1322–1333 (2007).
    [Crossref]
  8. B. Momeni, M. Chamanzar, E. S. Hosseini, M. Askari, M. Soltani, and A. Adibi, “Implementation of high resolution planar wavelength demultiplexers using strong dispersion in photonic crystals,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, Technical Digest (CD) (Optical Society of America, 2008), paper CMY3.
  9. D. Bernier, X. Le Roux, A. Lupu, D. Marris-Morini, L. Vivien, and E. Cassan, “Compact, low cross-talk CWDM demultiplexer using photonic crystal superprism,” Opt. Express 16(22), 17209–17214 (2008).
    [Crossref] [PubMed]
  10. T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of Photonic crystal superprism and superlens,” Opt. Express 13(26), 10768–10776 (2005).
    [Crossref] [PubMed]
  11. J. Witzens, T. Baehr-Jones, and A. Scherer, “Hybrid superprism with low insertion losses and suppressed cross-talk,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(2), 026604 (2005).
    [Crossref] [PubMed]
  12. B. Momeni and A. Adibi, “Preconditioned superprism-based photonic crystal demultiplexers: analysis and design,” Appl. Opt. 45(33), 8466–8476 (2006).
    [Crossref] [PubMed]
  13. B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, M. Rakhshandehroo, and A. Adibi, “Compact wavelength demultiplexing using focusing negative index photonic crystal superprisms,” Opt. Express 14(6), 2413–2422 (2006).
    [Crossref] [PubMed]
  14. T. Matsumoto and T. Baba, “Photonic crystal κ-vector superprism,” J. Lightwave Technol. 22(3), 917–922 (2004).
    [Crossref]
  15. C. Luo, M. Soljacić, and J. D. Joannopoulos, “Superprism effect based on phase velocities,” Opt. Lett. 29(7), 745–747 (2004).
    [Crossref] [PubMed]
  16. A. Bakhtazad and A. G. Kirk, “1-D slab photonic crystal k-vector superprism demultiplexer: analysis, and design,” Opt. Express 13(14), 5472–5482 (2005).
    [Crossref] [PubMed]
  17. B. Momeni and A. Adibi, “An approximate effective index model for efficient analysis and control of beam propagation effects in photonic crystals,” J. Lightwave Technol. 23(3), 1522–1532 (2005).
    [Crossref]
  18. S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
    [Crossref] [PubMed]
  19. B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals,” Appl. Phys. Lett. 87(17), 171104 (2005).
    [Crossref]
  20. J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(4), 046609 (2004).
    [Crossref] [PubMed]
  21. T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. 40(Part 1, No. 10), 5920–5924 (2001).
    [Crossref]

2008 (1)

2007 (1)

2006 (2)

2005 (6)

B. Momeni and A. Adibi, “An approximate effective index model for efficient analysis and control of beam propagation effects in photonic crystals,” J. Lightwave Technol. 23(3), 1522–1532 (2005).
[Crossref]

A. Bakhtazad and A. G. Kirk, “1-D slab photonic crystal k-vector superprism demultiplexer: analysis, and design,” Opt. Express 13(14), 5472–5482 (2005).
[Crossref] [PubMed]

T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of Photonic crystal superprism and superlens,” Opt. Express 13(26), 10768–10776 (2005).
[Crossref] [PubMed]

B. Momeni and A. Adibi, “Systematic design of superprism-based photonic crystal demultiplexers,” IEEE J. Sel. Areas Commun. 23(7), 1355–1364 (2005).
[Crossref]

J. Witzens, T. Baehr-Jones, and A. Scherer, “Hybrid superprism with low insertion losses and suppressed cross-talk,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(2), 026604 (2005).
[Crossref] [PubMed]

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals,” Appl. Phys. Lett. 87(17), 171104 (2005).
[Crossref]

2004 (3)

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(4), 046609 (2004).
[Crossref] [PubMed]

C. Luo, M. Soljacić, and J. D. Joannopoulos, “Superprism effect based on phase velocities,” Opt. Lett. 29(7), 745–747 (2004).
[Crossref] [PubMed]

T. Matsumoto and T. Baba, “Photonic crystal κ-vector superprism,” J. Lightwave Technol. 22(3), 917–922 (2004).
[Crossref]

2002 (2)

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915–918 (2002).
[Crossref]

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81(13), 2325–2327 (2002).
[Crossref]

2001 (2)

T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. 40(Part 1, No. 10), 5920–5924 (2001).
[Crossref]

S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[Crossref] [PubMed]

1998 (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(16), R10096–R10099 (1998).
[Crossref]

1993 (1)

1987 (1)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

Adibi, A.

Askari, M.

Baba, T.

T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of Photonic crystal superprism and superlens,” Opt. Express 13(26), 10768–10776 (2005).
[Crossref] [PubMed]

T. Matsumoto and T. Baba, “Photonic crystal κ-vector superprism,” J. Lightwave Technol. 22(3), 917–922 (2004).
[Crossref]

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81(13), 2325–2327 (2002).
[Crossref]

T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. 40(Part 1, No. 10), 5920–5924 (2001).
[Crossref]

Baehr-Jones, T.

J. Witzens, T. Baehr-Jones, and A. Scherer, “Hybrid superprism with low insertion losses and suppressed cross-talk,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(2), 026604 (2005).
[Crossref] [PubMed]

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(4), 046609 (2004).
[Crossref] [PubMed]

Bakhtazad, A.

Bernier, D.

Cassan, E.

Fujita, S.

Hochberg, M.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(4), 046609 (2004).
[Crossref] [PubMed]

Huang, J.

Joannopoulos, J.

Joannopoulos, J. D.

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

Johnson, S.

Karle, T.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915–918 (2002).
[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(16), 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(16), R10096–R10099 (1998).
[Crossref]

Kirk, A. G.

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(16), R10096–R10099 (1998).
[Crossref]

Krauss, T. F.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915–918 (2002).
[Crossref]

Le Roux, X.

Luo, C.

Lupu, A.

Marris-Morini, D.

Matsumoto, T.

Mazilu, M.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915–918 (2002).
[Crossref]

Mohammadi, S.

Momeni, B.

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096–R10099 (1998).
[Crossref]

Ohsaki, D.

T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. 40(Part 1, No. 10), 5920–5924 (2001).
[Crossref]

Rakhshandehroo, M.

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(16), R10096–R10099 (1998).
[Crossref]

Scherer, A.

J. Witzens, T. Baehr-Jones, and A. Scherer, “Hybrid superprism with low insertion losses and suppressed cross-talk,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(2), 026604 (2005).
[Crossref] [PubMed]

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(4), 046609 (2004).
[Crossref] [PubMed]

Soljacic, M.

Soltani, M.

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(16), R10096–R10099 (1998).
[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(16), R10096–R10099 (1998).
[Crossref]

Vivien, L.

Witzens, J.

J. Witzens, T. Baehr-Jones, and A. Scherer, “Hybrid superprism with low insertion losses and suppressed cross-talk,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(2), 026604 (2005).
[Crossref] [PubMed]

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(4), 046609 (2004).
[Crossref] [PubMed]

Wu, L.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915–918 (2002).
[Crossref]

Yablonovitch, E.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81(13), 2325–2327 (2002).
[Crossref]

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals,” Appl. Phys. Lett. 87(17), 171104 (2005).
[Crossref]

IEEE J. Quantum Electron. (1)

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38(7), 915–918 (2002).
[Crossref]

IEEE J. Sel. Areas Commun. (1)

B. Momeni and A. Adibi, “Systematic design of superprism-based photonic crystal demultiplexers,” IEEE J. Sel. Areas Commun. 23(7), 1355–1364 (2005).
[Crossref]

J. Lightwave Technol. (3)

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

Jpn. J. Appl. Phys. (1)

T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. 40(Part 1, No. 10), 5920–5924 (2001).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

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(16), R10096–R10099 (1998).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

J. Witzens, T. Baehr-Jones, and A. Scherer, “Hybrid superprism with low insertion losses and suppressed cross-talk,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(2), 026604 (2005).
[Crossref] [PubMed]

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(4), 046609 (2004).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

Other (1)

B. Momeni, M. Chamanzar, E. S. Hosseini, M. Askari, M. Soltani, and A. Adibi, “Implementation of high resolution planar wavelength demultiplexers using strong dispersion in photonic crystals,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, Technical Digest (CD) (Optical Society of America, 2008), paper CMY3.

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Figures (4)

Fig. 1
Fig. 1 Schematic of the composite demultiplexer, i.e. properly scaled unit block defined in section 2.2, with the trajectory of two adjacent wavelength channels (not to scale). The actual beam envelope of a single channel and the corresponding profile considering only the higher order diffraction terms in the PhC are shown by light red and dark blue traces respectively; for perfect second order diffraction compensation, both profiles should match at the output. δ3 represents the equivalent divergence angle of the beam due to the dominant higher order (3rd order) diffraction inside the PhC.

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Fig. 2
Fig. 2 Path of two adjacent channels within the composite demultiplexer, determined by applying the continuity of the tangential wave-vector components along each interface using EFC representation of the band structure in 2D wave-vector plane. For an arbitrary point (Q) on the EFC, η (ζ) represents the direction parallel (perpendicular) to the beam propagation (i.e. the group velocity (Vg) direction).

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Fig. 3
Fig. 3 The path of two neighboring channels and the design parameters of the composite superprism. Solid trace represents the actual beam trajectory in the unit block whereas the light broken trace shows the equivalent virtual PhC model constructed for λ1 wavelength.

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Fig. 4
Fig. 4 Effective angular dispersion for (a) composite, (b) s-vector or preconditioned and (c) k-vector superprism configurations in °/nm at the center wavelength for candidates with negative effective diffractive index; lowest TM band of square lattice PhC in a 250nm slab with the input interface along ΓX axis is considered. For composite and k-vector superprisms the other PhC-slab interface is along the ΓM axis.

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Tables (1)

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Table 1 Optimum designs for 100GHZ channel spacing

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Equations (10)

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L S cos ( θ ​ ​ S ) × 1     ​ n e 2 , S w S 2 = L P h C | n e 2 , P h C | w P h C 2
w P h C = w 0 cos θ P h C / cos θ 0 w S = w P h C cos θ S / cos θ P h C *
Δ e f f = ( ∂ θ P h C ∂ λ ) Δ X Δ X 1 + | Δ X 22 − Δ X 21 |
L P h C = z 3 K η 3 − H
n e 3 , P h C = 2 3 w P h C ( k 0 d 3 k η d k ζ 3 ) − 1
L P h C = 2 K w P h C 3 Δ e f f ( min ) w P h C 2 − 2 3 H | d 3 k η / d k ζ 3 |
A P h C / C h = 1 2 ( w P h C z 2 L P h C ) L P h C = 4 K 2 w P h C 5 | d 2 k η / d k ζ 2 | ( Δ e f f ( min ) w P h C 2 − 2 3 H | d 3 k η / d k ζ 3 | ) 2
w P h C O p t = 10 3 H Δ e f f ( min ) | d 3 k η / d k ζ 3 |
L P h C O p t = K 125 3 2 Δ 3 e f f ( min ) H | d 3 k η / d k ζ 3 |
A P h C / C h O p t = 25 K 2 4 k 0 n e 2 , P h C 10 3 Δ 5 e f f ( min ) H | d 3 k η / d k ζ 3 |

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