Abstract

Designs of aperiodic photonic quantum-well (APQW) structures to achieve multiple channeled filtering at arbitrary preassigned frequencies are done by using the simulated annealing algorithm with a special merit function. The APQW structure consists of aperiodically stacked dielectric-layers sandwiched by two finite-length prototype photonic crystals (PCs). The insert of the APQWs can generate the specified defect states with predetermined frequencies. Numerical simulations show that the designed APQWs can achieve the desired specification.

© 2004 Optical Society of America

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References

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Appl. Phys. Lett. (1)

F. Qiao, C. Zhang, J. Wan, and J. Zi, �??Photonic quantum-well structures: Multiple channeled filtering phenomena,�?? Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

J. Opt. Soc. Am. B (3)

Micro. Opt. Tech. Lett. (1)

H. C. Huang, M. H. Hsu, K. L. Chen, and J. F. Huang, �??Simulated annealing algorithm applied in optimum design of optical thin-film filters,�?? Micro. Opt. Tech. Lett. 38, 423-428 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

E. Yablonovitch,�??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, �??Strong localization of photons in certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486- 2489 (1987).
[CrossRef] [PubMed]

Science (2)

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos,�??Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,�?? Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. Michel, J. D. Joannopoulos, and E. L. Thomas, �??A dielectric omnidirectional reflector,�?? Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the APQW structure. The APQWs are sandwiched by two finite-length prototype PCs.

Fig. 2.
Fig. 2.

Transmission spectrum of the designed APQW sample for two channeled filtering at the preset frequencies of ω1(o)=0.420 and ω2(o)=0.480(2πc/a).

Fig. 3.
Fig. 3.

Transmission spectrum of the designed APQW sample for two channeled filtering at the preset frequencies of ω1(o)=0.380 and ω2(o)=0.410(2πc/a)

Fig. 4.
Fig. 4.

Calculated results of the designed APQWs for four channeled filtering: (a) gray scaled diagram of the designed APQWs; (b) transmission spectrum.

Equations (8)

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M ̂ j = G ̂ j + 1 1 G ̂ j P ̂ j ,
P ̂ 1 = ( 1 0 0 1 ) , j = 1
P ̂ j = ( exp ( i k j d j ) 0 0 exp ( i k j d j ) ) , j = 2 , 3 , 4
G ̂ j = ( 1 1 ε j ε j ) ,
( t n r n ) = j M ̂ j ( t 1 r 1 ) ,
T = ε n ε 1 t n t 1 2 .
O = α s ω α ( o ) ω α ( s ) , ω α ( o ) , ω α ( s ) [ ω α 1 , ω α ] , α = 1 , 2 , 3
ω 0 ( = ω a ) < ω 1 o < ω 1 < < ω α 1 < ω α o < ω α ( = ω b ) ,

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