Abstract

The design of a complete demultiplexer based on the k-vector superprism in a 1-D slab photonic crystal is proposed. This design scales to resolve 32 channels spaced by 0.8 nm (100 GHz) in the C band for a dense wavelength division multiplexing system. It is shown that a prism area of 0.017 mm2 is sufficient for the required wavelength resolution using typical silicon-on-insulator technology and that the total chip size would be 4×3 mm2. In order to achieve this, the modest angular dispersion of a 1-D slab photonic crystal is enhanced by considerably expanding the input beam through the superprism region and employing etched mirrors to collimate and focus the light into and out of the superprism. The plane wave expansion method is used to obtain the wave vector diagram and from this we develop design equations based on conventional ray tracing. We then present an optimization approach which minimizes the prism area whilst maintaining the necessary dispersion. Finally the non-uniformity of phase velocity dispersion across the desired spectral window is addressed.

© 2005 Optical Society of America

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References

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Appl. Phys. B (1)

Jafarpour, E. Chow, C. M. Reinke, J. Huang, A. Adibi, A. Grot, L. W. Mirkarimi, G. Girolami, R.K. Lee, and Y. Xu, �??Large-bandwidth ultra-low-loss guiding in bi-periodic crystal waveguides,�?? Appl. Phys. B 79, 409-414 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, �??Self-collimiating phenamena in photonic crystal,�?? Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Baba, A. Motegi, T. Iwai, N. Faoyuki, Y. Wantanabe nad A. Sakai, �??Light propagation characteristic of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on insulator substrate,�?? IEEE J. Quantum Electron. 38, 734-752 (2002).
[CrossRef]

IEEE Phot.onics Technol. Lett. (1)

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J.V. Campenhout, D. Taillaert, B. Luyssaert, P. bienstman, D. V. Thourhout, and R. Baets, �??Low-loss SOI photonic wires and ring resonators fabricated with deep uv lithography,�?? IEEE Phot.onics Technol. Lett. 16, 1328-1330 (2004).
[CrossRef]

IEEE Trans. Ant. Prop. (1)

S. Enoch, G. Tayeb and B. Gralak, �??The richness of the dispersion relation of electromagnetic band gap materials�??, IEEE Trans. Ant. Prop. 51, 2659-2666 (2003).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. (1)

LEOS 2004 (1)

A. G. Kirk and A. Bakhtazad, �??Dispersion optimization of a 1-D superprism based on phase velocities�?? LEOS 2004, 7-11 November 2004, 879-880 (2004).

Opt. Lett. (2)

Proc SPIE (1)

A. Bakhtazad, A. and A. G. Kirk, �??Superprism effect with planar 1-D photonic crystal�?? Proc. SPIE 5360, 364-372 (2004).
[CrossRef]

Proc. SPIE (1)

W. N. Ye, D. Xu, S. Janz, P. Cheben, A. Delage, M. Picard, B. Lamontage and N. G. Tarr, �??Stress-induced irefringence in silicon-on-insulator (SOI) waveguides, Proc. SPIE 5357, 57-66 (2004).
[CrossRef]

Other (3)

H. G. Unger, Planar Optical Waveguides and fibers, (Oxford, UK, Clarendon Press, Oxford Engineering Science Series, 1977).

K. Okamoto, Fundamentals of optical waveguides, (Academic press, ch. 9, 2000) p. 353. T. Baba and D. Ohsaki, �??Interface of photonic crystal for high efficiency light transmission,�?? Jpn. J. Appl. Phys. 40, 5920-5924 (2001).

P. St. Russell, T. A. Birks and F.D. Lloyd-Lucas, in Confined Electrons and Photons, edited by E. Burstein and C. Weisbuch (NATO, Plenum, New York, 1995), p. 585.
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Proposed 1-D slab photonic crystal demultiplexer

Fig. 2.
Fig. 2.

Typical normalized wave vector diagram (nxkx /k 0, n zkz /k 0) for a 1-D slab photonic crystal

Fig. 3.
Fig. 3.

The cross section of 1-D slab photonic crystal in SOI technology

Fig. 4.
Fig. 4.

Variation of propagation constant with wave number versus period at the band edge

Fig. 5.
Fig. 5.

The prism with slanted stratified media

Fig 6.
Fig 6.

Relationship between prism facets and beam size that results in a minimum prism area

Fig 7.
Fig 7.

Minimum prism surface and the corresponding angular dispersion versus slant angle for the structure of Fig. 3

Fig. 8.
Fig. 8.

Normalized wave vector diagram (nxkx /k 0, nzkz /k 0) for the superprism specified in Table 1

Fig. 9.
Fig. 9.

Angular dispersion and required output waveguide separation as a function of wavelength for the device specified in Table 1, assuming minimum output waveguide spacing of Λ i =1.75µm≈3.5 w 0.

Tables (1)

Tables Icon

Table 1. The optimum superprism slab 1-D superprism parameters

Equations (9)

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I ( r , θ , y ) = 2 I 0 π h 0 θ 0 r exp ( 2 θ 2 θ 0 2 ) exp ( 2 y 2 h 0 2 )
θ 0 = 0 π n eff ( slab ) w 0
f = Λ i 2 sin ( η δ 2 ) 3.5 w 0 η δ
L = 2 f sin θ 0
L min 7 0 ( η δ ) n eff ( slab ) π
l 2 l 1 = cos φ 2 cos ( ρ + φ 2 )
L 2 L 1 = cos φ 1 cos φ 4 · l 2 l 1
L 1 = L min m , L 2 = M m L min
l 1 = L 1 cos φ 1 , l 2 = L 2 cos φ 4 M

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