## Composite superprism photonic crystal demultiplexer: analysis and design |

Optics Express, Vol. 18, Issue 19, pp. 20518-20528 (2010)

http://dx.doi.org/10.1364/OE.18.020518

Acrobat PDF (1316 KB)

### 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 OSA

## 1. Introduction

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]

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]

12. B. Momeni and A. Adibi, “Preconditioned superprism-based photonic crystal demultiplexers: analysis and design,” Appl. Opt. **45**(33), 8466–8476 (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]

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]

^{-2.5}.

## 2. Composite superprism

### 2.1 Structure

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]

### 2.2 Design

12. B. Momeni and A. Adibi, “Preconditioned superprism-based photonic crystal demultiplexers: analysis and design,” Appl. Opt. **45**(33), 8466–8476 (2006). [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]

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]

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]

_{eff}) that captures the additional spatial separation gained in slab region. The effective dispersion is defined as: Equation (3) is simply the actual angular separation of the PhC (

*X*in Fig. 3) to the total contribution from propagation in both PhC sections (i.e.

## 3. Analysis

*L*in Eq. (6)), is obtained from Eq. (7).

_{PhC}^{α}with an α factor of −0.5, −1.5 and −2.5 respectively, where

*ω*) as

^{−4}scaling of the conventional s-vector superprism.

## 4. Results

**45**(33), 8466–8476 (2006). [CrossRef] [PubMed]

*X*symmetry point where

*k*the vacuum wave-number and

_{0}*a*the lattice period) at the longest wavelength.

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]

*X*or Γ

*Μ*orientation. Finally the diffraction compensation constraint (negative second order effective diffractive index for all the channels) that sets the range of incident angles for each candidate PhC completely defines the design platform.

*X*axis which results in minimum non-uniformity of the effective indices. Compared with the preconditioned counterparts, also given in the table, up to 6-fold reduction in the PhC length (4-channel) with at least 36 times reduced PhC area (8-channel), smaller incident beam waist and much shorter required slab propagation are achievable using the composite superprism.

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]

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]

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]

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]

## 5. Conclusion

## Acknowledgements

## References and links

1. | E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B |

2. | S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. |

3. | L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. |

4. | H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B |

5. | T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. |

6. | B. Momeni and A. Adibi, “Systematic design of superprism-based photonic crystal demultiplexers,” IEEE J. Sel. Areas Commun. |

7. | A. Bakhtazad and A. G. Kirk, “First-band S-vector photonic-crystal superprism demultiplexer design and optimization,” J. Lightwave Technol. |

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 |

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 |

10. | T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of Photonic crystal superprism and superlens,” Opt. Express |

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. |

12. | B. Momeni and A. Adibi, “Preconditioned superprism-based photonic crystal demultiplexers: analysis and design,” Appl. Opt. |

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. | T. Matsumoto and T. Baba, “Photonic crystal κ-vector superprism,” J. Lightwave Technol. |

15. | C. Luo, M. Soljacić, and J. D. Joannopoulos, “Superprism effect based on phase velocities,” Opt. Lett. |

16. | A. Bakhtazad and A. G. Kirk, “1-D slab photonic crystal k-vector superprism demultiplexer: analysis, and design,” Opt. Express |

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. |

18. | S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express |

19. | B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals,” Appl. Phys. Lett. |

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. |

21. | T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(230.5298) Optical devices : Photonic crystals

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: August 6, 2010

Revised Manuscript: September 3, 2010

Manuscript Accepted: September 3, 2010

Published: September 10, 2010

**Citation**

Amin Khorshidahmad and Andrew G. Kirk, "Composite superprism photonic crystal demultiplexer: analysis and design," Opt. Express **18**, 20518-20528 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-20518

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### References

- E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10(2), 283–295 (1993). [CrossRef]
- S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987). [CrossRef] [PubMed]
- 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]
- 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]
- T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81(13), 2325–2327 (2002). [CrossRef]
- B. Momeni and A. Adibi, “Systematic design of superprism-based photonic crystal demultiplexers,” IEEE J. Sel. Areas Commun. 23(7), 1355–1364 (2005). [CrossRef]
- 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]
- 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.
- 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]
- 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]
- 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, “Preconditioned superprism-based photonic crystal demultiplexers: analysis and design,” Appl. Opt. 45(33), 8466–8476 (2006). [CrossRef] [PubMed]
- 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]
- T. Matsumoto and T. Baba, “Photonic crystal κ-vector superprism,” J. Lightwave Technol. 22(3), 917–922 (2004). [CrossRef]
- C. Luo, M. Soljacić, and J. D. Joannopoulos, “Superprism effect based on phase velocities,” Opt. Lett. 29(7), 745–747 (2004). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]

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