Abstract

For spectral filters with subnanometer bandwidth, precise control of the device components’ dimensions (error<λ/1000, where λ is the center wavelength) is critical. Theoretical results from the transfer-matrix method show that an electro-optic thin-film filter can have a subnanometer bandwidth and still tolerate a root-mean-square error in the thickness of each layer up to λ/100. Illustrative examples of an electro-optic thin-film spectral filter with 0.05-nm (6-GHz), -3-dB bandwidth are presented.

© 2004 Optical Society of America

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References

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    [CrossRef]
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  4. B. A. Saleh and T. M. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, “Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape,” Science 288, 119–122 (2000).
    [CrossRef]
  9. M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
    [CrossRef]
  10. P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, “Integrated WDM polymer modulator,” in Optical Fiber Communications Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 31–33.

2001 (1)

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

2000 (1)

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, “Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape,” Science 288, 119–122 (2000).
[CrossRef]

1999 (1)

1993 (1)

1991 (1)

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Bechtel, J. H.

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, “Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape,” Science 288, 119–122 (2000).
[CrossRef]

Brommer, K. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Chang, D.

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Chang, Y.

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Dalton, L. R.

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, “Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape,” Science 288, 119–122 (2000).
[CrossRef]

Erlig, E.

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Fetterman, H. R.

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Gu, C.

Hauss, J.

Joannopoulos, J. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Kurizki, G.

Meade, R. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Oh, M.-Ch.

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Rapper, A. M.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Robinson, B. H.

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, “Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape,” Science 288, 119–122 (2000).
[CrossRef]

Shi, Y.

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, “Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape,” Science 288, 119–122 (2000).
[CrossRef]

Steier, W. H.

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, “Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape,” Science 288, 119–122 (2000).
[CrossRef]

Szep, A.

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Tsap, B.

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Yang, M.

Zhang, C.

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, “Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape,” Science 288, 119–122 (2000).
[CrossRef]

Zhang, H.

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, “Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape,” Science 288, 119–122 (2000).
[CrossRef]

Appl. Opt. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

M.-Ch. Oh, H. Zhang, C. Zhang, E. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electro-optic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001).
[CrossRef]

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

Phys. Rev. Lett. (1)

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Science (1)

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, “Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape,” Science 288, 119–122 (2000).
[CrossRef]

Other (5)

P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, “Integrated WDM polymer modulator,” in Optical Fiber Communications Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 31–33.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York, 1984).

B. A. Saleh and T. M. Teich, Fundamentals of Photonics (Wiley, New York, 1991).

G. Kurizki and J. Hauss, eds., “Photonic band structures,” J. Mod. Opt. 41 (1994), special issue.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Typical layout of a two-defect structure of the form XY, where X=A3 D A3 and Y=A2 D A2.

Fig. 2
Fig. 2

(a) Transmission spectrum of a 12-period reflector A12: A=[n1n2], n1=1.4, n2=1, n1d1=n2d2=λB/4; (b) field intensity inside the reflector at the upper wavelength band edge, λ=1790 nm; (c) transmission spectrum of a single-defect reflector A5 D A5, D=[n3n2], n3d3=1.06λB, λB=1550 nm; (d) field intensity inside the reflector at the defect transmission wavelength, λ=1593 nm.

Fig. 3
Fig. 3

(a) Comparison between the transmission spectra of 11-period and 13-period single-defect reflectors A5 D A5 and A6 D A6, respectively: A=[n1n2], D=[n3n2], n1=1.4, n2=1, n3=n1, n1d1=n2d2=λB/4, n3d3=1.06λB, λB=1550 nm; (b) field intensity inside the 11-period structure A5 D A5 at the transmission wavelength, λ=1592 nm; (c) field intensity inside the 13-period structure A6 D A6 at the transmission wavelength, λ=1592 nm.

Fig. 4
Fig. 4

(a) Transmission spectrum of a two-defect reflector XY, where X=A23 D A23 and Y=A22 D A22: A=[n1n2], D=[n3n2], n1=1.1891, n2=1, n3=1.1904, n1d1=n2d2=λB/4, n3d3=0.5λB, λB=1550 nm; (b) field intensity inside the reflector at the transmission wavelength.

Fig. 5
Fig. 5

(a) Transmission spectrum of three different five-defect reflectors of the form XY DY X, where X=Ax D Ax, Y=Ax-1 D Ax-1: A=[n1n2], D=[n3n2], n1=1.1891, n2=1, n3=1.1904, n1d1=n2d2=λB/4, n3d3=0.5λB. Values considered for the number of periods are x=15, 17, 20; (b) field intensity inside the reflector corresponding to x=17.

Fig. 6
Fig. 6

(a) Comparison between the transmission spectra of two-defect and five-defect reflectors XY and XY DY X, respectively, where X=A23 D A23, Y=A22 D A22: A=[n1n2], D=[n3n2], n1=1.1891, n2=1, n3=1.1904, n1d1=n2d2=λB/4, n3d3=0.5λB; (b) the refractive index of the second EO defect has been adjusted by a relative amount equal to Δn3/n3=3.5 10-3 to operate the device as a modulator. The adjusted substructure is denoted by a hat.

Fig. 7
Fig. 7

(a) Comparison between the transmission spectra of two-defect and five-defect reflectors XY and XY DY X, respectively, where X=A23 D A23, Y=A22 D A22: A=[n1n2], D=[n3n2], n1=1.1891, n2=1, n3=1.1904, n1d1=n2d2=λB/4, n3d3=0.5λB; (b) comparison between the transmission spectra of two-defect and five-defect reflectors, in which each layer has been randomly perturbed from its quarter-wave thickness by an rms absolute error equal to σ=δλB=10-2λB=15.5 nm. To counterbalance the error in each layer thickness, the refractive index of the EO defect layers in each substructure has been adjusted by a relative amount respectively equal to Δn3/n3=-5.4 10-3, -2.2 10-2, -1.6 10-2, and -10-2. Adjusted substructures are denoted by a hat.

Fig. 8
Fig. 8

Example of layer-thickness absolute error for the five-defect structure used in Fig. 7(b).

Fig. 9
Fig. 9

Same as Fig. 7 but with an absorption loss rate equal to 20 dB/cm: (a) transmission spectra of quarter-wave two-defect and five-defect reflectors without errors in layer thickness, (b) transmission spectra when each layer has been randomly perturbed from its quarter-wave thickness by an rms absolute error equal to σ=δλB=10-2λB=15.5 nm.

Equations (4)

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A(0)B(0)=TA(N+1)B(N+1),T=Q(0)Πl=1l=N P(l)Q(l),
Q(l)=121+α(l)1-α(l)1-α(l)1+α(l),α(l)=(l+1)/(l),
P(l)=eik(l)d(l)00e-ik(l)d(l),
T=T11T12T21T22,

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