Abstract

We analyze the intensity-dependent optical response of the passive optical limiters realized with distributed-feedback structures, which consist of alternating layers of materials possessing opposite Kerr nonlinearities. By elaborating an analytical model and employing numerical simulations, we explore device performance with respect to key requirements for passive optical-limiter deployment. We prove that the proposed limiting mechanism results in complete clamping of transmitted intensity to a sensor-safe limiting value, independent of incident intensity. We provide a direct analytical result of this limiting intensity in terms of structural and material parameters.

© 2000 Optical Society of America

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1999 (2)

1998 (5)

N. S. Pate, L. Hall, L. Katherine, and K. A. Raushenbach, “Interferometric all-optical switches for ultrafast signal processing,” Appl. Opt. 27, 2831–2842 (1998).
[CrossRef]

H. B. Lin, R. J. Tonucci, and A. J. Campillo, “Two-dimensional photonic bandgap optical limiters in the visible,” Opt. Lett. 23, 94–96 (1998).
[CrossRef]

R. Rangel-Rojo, S. Yamada, S. Matsuda, and H. D. Yankelevich, “Large near-resonance third-order nonlinearity in an azobenzene-functionalized polymer film,” Appl. Phys. Lett. 72, 1021–1023 (1998).
[CrossRef]

K. Ishizu, T. Ikemoto, and A. Ichimure, “Architecture of polymeric superstructures formed by locking cubic lattices of core-shell polymer microspheres,” Polymer 39, 449–454 (1998).
[CrossRef]

C. R. Mendoca, M. M. Costa, J. A. Giacometti, F. D. Nunes, and S. C. Zilio, “Nonlinear refractive indices of polyesterene films doped with azobenzene dye Disperse Red 1,” Electron. Lett. 34, 116–117 (1998).
[CrossRef]

1997 (2)

1996 (3)

R. Bozio, M. Meneghetti, R. Signorini, M. Maggini, G. Scorrano, M. Prato, G. Brusatin, M. Guglielmi, “Optical limiting of fullerene derivatives embedded in sol-gel materials,” in Photoactive Organic Materials Science and Applications, F. Kajzer, ed., NATO ASI Ser. B 572, 159–174 (1996).
[CrossRef]

Z. X. Zhang, W. Qiu, E. Y. B. Pun, P. S. Chang, and Y. Q. Shen, “Doped polymer films with high nonlinear refractive indices,” Electron. Lett. 32, 129–130 (1996).
[CrossRef]

M. Bertolotti, P. Masciulli, P. Ranieri, and C. Sibilia, “Optical bistability in nonlinear Cantor corrugated waveguide,” J. Opt. Soc. Am. B 13, 1517–1525 (1996).
[CrossRef]

1995 (1)

C.-X. Shi, “Optical bistability in reflective fiber grating,” IEEE J. Quantum Electron. 31, 2037–2043 (1995).
[CrossRef]

1994 (3)

J. A. Hermann, P. B. Chapple, J. Staromlynska, and P. J. Wilson, “Design criteria for optical power limiters,” in Nonlinear Optical Materials for Switching and Limiting, M. J. Soileau, ed., Proc. SPIE 2229, 167–178 (1994).
[CrossRef]

K. Ishizu, F. Naruse, and R. Saito, “The aggregation behavior of core-shell type polymer microspheres,” Polymer 35, 2329–2334 (1994).
[CrossRef]

M. Scolara, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic bandgap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef]

1992 (2)

J. He and M. Cada, “Combined distributed feedback and Fabry–Perot structures with a phase-matching layer for bistable devices,” Appl. Phys. Lett. 61, 2150–2152 (1992).
[CrossRef]

S. Dubovitsky and W. H. Steier, “Analysis of optical bistability in a nonlinear coupled resonator,” IEEE J. Quantum Electron. 28, 585–589 (1992).
[CrossRef]

1991 (1)

J. S. Werner, “Children’s sunglasses: caveat emptor,” Optom. Vision Sci. 68, 318–320 (1991).
[CrossRef]

1989 (1)

G. L. Wood, W. W. Clark III, M. J. Miller, G. J. Salamo, and E. J. Sharp, “Evaluation of passive optical limiters and switches,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE 1105, 154–181 (1989).
[CrossRef]

1988 (1)

R. C. Hollins, “Overview of research on nonlinear optical limiters at DERA (Defence Evaluation & Research Agency),” in Photosensitive Optical Materials and Devices II, M. P. Andrews, ed., Proc. SPIE 3282, 2–8 (1988).
[CrossRef]

1984 (1)

S. M. Luria, “Preferred density of sunglasses,” Am. J. Optom. Physiol. Opt. 61, 397–402 (1984).
[CrossRef] [PubMed]

1982 (1)

H. G. Winful and G. D. Cooperman, “Self-pulsing and chaos in distributed feedback bistable optical devices,” Appl. Phys. Lett. 40, 298–300 (1982).
[CrossRef]

1979 (1)

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structure,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Bertlotti, M.

Bertolotti, M.

Bloemer, M. J.

M. Scolara, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic bandgap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef]

Bowden, C. M.

M. Scolara, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic bandgap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef]

Bozio, R.

R. Bozio, M. Meneghetti, R. Signorini, M. Maggini, G. Scorrano, M. Prato, G. Brusatin, M. Guglielmi, “Optical limiting of fullerene derivatives embedded in sol-gel materials,” in Photoactive Organic Materials Science and Applications, F. Kajzer, ed., NATO ASI Ser. B 572, 159–174 (1996).
[CrossRef]

Brusatin, G.

R. Bozio, M. Meneghetti, R. Signorini, M. Maggini, G. Scorrano, M. Prato, G. Brusatin, M. Guglielmi, “Optical limiting of fullerene derivatives embedded in sol-gel materials,” in Photoactive Organic Materials Science and Applications, F. Kajzer, ed., NATO ASI Ser. B 572, 159–174 (1996).
[CrossRef]

Cada, M.

J. He and M. Cada, “Combined distributed feedback and Fabry–Perot structures with a phase-matching layer for bistable devices,” Appl. Phys. Lett. 61, 2150–2152 (1992).
[CrossRef]

Caleo, L.

Campillo, A. J.

Chang, P. S.

Z. X. Zhang, W. Qiu, E. Y. B. Pun, P. S. Chang, and Y. Q. Shen, “Doped polymer films with high nonlinear refractive indices,” Electron. Lett. 32, 129–130 (1996).
[CrossRef]

Chapple, P. B.

J. A. Hermann, P. B. Chapple, J. Staromlynska, and P. J. Wilson, “Design criteria for optical power limiters,” in Nonlinear Optical Materials for Switching and Limiting, M. J. Soileau, ed., Proc. SPIE 2229, 167–178 (1994).
[CrossRef]

Clark III, W. W.

G. L. Wood, W. W. Clark III, M. J. Miller, G. J. Salamo, and E. J. Sharp, “Evaluation of passive optical limiters and switches,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE 1105, 154–181 (1989).
[CrossRef]

Cooperman, G. D.

H. G. Winful and G. D. Cooperman, “Self-pulsing and chaos in distributed feedback bistable optical devices,” Appl. Phys. Lett. 40, 298–300 (1982).
[CrossRef]

Costa, M. M.

C. R. Mendoca, M. M. Costa, J. A. Giacometti, F. D. Nunes, and S. C. Zilio, “Nonlinear refractive indices of polyesterene films doped with azobenzene dye Disperse Red 1,” Electron. Lett. 34, 116–117 (1998).
[CrossRef]

Dogariu, A.

Dowling, J. P.

M. Scolara, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic bandgap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef]

Dubovitsky, S.

S. Dubovitsky and W. H. Steier, “Analysis of optical bistability in a nonlinear coupled resonator,” IEEE J. Quantum Electron. 28, 585–589 (1992).
[CrossRef]

Garmire, E.

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structure,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Giacometti, J. A.

C. R. Mendoca, M. M. Costa, J. A. Giacometti, F. D. Nunes, and S. C. Zilio, “Nonlinear refractive indices of polyesterene films doped with azobenzene dye Disperse Red 1,” Electron. Lett. 34, 116–117 (1998).
[CrossRef]

Guglielmi, M.

R. Bozio, M. Meneghetti, R. Signorini, M. Maggini, G. Scorrano, M. Prato, G. Brusatin, M. Guglielmi, “Optical limiting of fullerene derivatives embedded in sol-gel materials,” in Photoactive Organic Materials Science and Applications, F. Kajzer, ed., NATO ASI Ser. B 572, 159–174 (1996).
[CrossRef]

Hagan, D. J.

Hall, L.

N. S. Pate, L. Hall, L. Katherine, and K. A. Raushenbach, “Interferometric all-optical switches for ultrafast signal processing,” Appl. Opt. 27, 2831–2842 (1998).
[CrossRef]

He, J.

J. He and M. Cada, “Combined distributed feedback and Fabry–Perot structures with a phase-matching layer for bistable devices,” Appl. Phys. Lett. 61, 2150–2152 (1992).
[CrossRef]

Hermann, J. A.

J. A. Hermann, P. B. Chapple, J. Staromlynska, and P. J. Wilson, “Design criteria for optical power limiters,” in Nonlinear Optical Materials for Switching and Limiting, M. J. Soileau, ed., Proc. SPIE 2229, 167–178 (1994).
[CrossRef]

Hollins, R. C.

R. C. Hollins, “Overview of research on nonlinear optical limiters at DERA (Defence Evaluation & Research Agency),” in Photosensitive Optical Materials and Devices II, M. P. Andrews, ed., Proc. SPIE 3282, 2–8 (1988).
[CrossRef]

Ichimure, A.

K. Ishizu, T. Ikemoto, and A. Ichimure, “Architecture of polymeric superstructures formed by locking cubic lattices of core-shell polymer microspheres,” Polymer 39, 449–454 (1998).
[CrossRef]

Ikemoto, T.

K. Ishizu, T. Ikemoto, and A. Ichimure, “Architecture of polymeric superstructures formed by locking cubic lattices of core-shell polymer microspheres,” Polymer 39, 449–454 (1998).
[CrossRef]

Ishizu, K.

K. Ishizu, T. Ikemoto, and A. Ichimure, “Architecture of polymeric superstructures formed by locking cubic lattices of core-shell polymer microspheres,” Polymer 39, 449–454 (1998).
[CrossRef]

K. Ishizu, F. Naruse, and R. Saito, “The aggregation behavior of core-shell type polymer microspheres,” Polymer 35, 2329–2334 (1994).
[CrossRef]

Katherine, L.

N. S. Pate, L. Hall, L. Katherine, and K. A. Raushenbach, “Interferometric all-optical switches for ultrafast signal processing,” Appl. Opt. 27, 2831–2842 (1998).
[CrossRef]

Lin, H. B.

Luria, S. M.

S. M. Luria, “Preferred density of sunglasses,” Am. J. Optom. Physiol. Opt. 61, 397–402 (1984).
[CrossRef] [PubMed]

Maggini, M.

R. Bozio, M. Meneghetti, R. Signorini, M. Maggini, G. Scorrano, M. Prato, G. Brusatin, M. Guglielmi, “Optical limiting of fullerene derivatives embedded in sol-gel materials,” in Photoactive Organic Materials Science and Applications, F. Kajzer, ed., NATO ASI Ser. B 572, 159–174 (1996).
[CrossRef]

Marburger, J. H.

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structure,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Masciulli, P.

Matsuda, S.

R. Rangel-Rojo, S. Yamada, S. Matsuda, and H. D. Yankelevich, “Large near-resonance third-order nonlinearity in an azobenzene-functionalized polymer film,” Appl. Phys. Lett. 72, 1021–1023 (1998).
[CrossRef]

Mendoca, C. R.

C. R. Mendoca, M. M. Costa, J. A. Giacometti, F. D. Nunes, and S. C. Zilio, “Nonlinear refractive indices of polyesterene films doped with azobenzene dye Disperse Red 1,” Electron. Lett. 34, 116–117 (1998).
[CrossRef]

Meneghetti, M.

R. Bozio, M. Meneghetti, R. Signorini, M. Maggini, G. Scorrano, M. Prato, G. Brusatin, M. Guglielmi, “Optical limiting of fullerene derivatives embedded in sol-gel materials,” in Photoactive Organic Materials Science and Applications, F. Kajzer, ed., NATO ASI Ser. B 572, 159–174 (1996).
[CrossRef]

Miles, P.

Miller, M. J.

G. L. Wood, W. W. Clark III, M. J. Miller, G. J. Salamo, and E. J. Sharp, “Evaluation of passive optical limiters and switches,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE 1105, 154–181 (1989).
[CrossRef]

Naruse, F.

K. Ishizu, F. Naruse, and R. Saito, “The aggregation behavior of core-shell type polymer microspheres,” Polymer 35, 2329–2334 (1994).
[CrossRef]

Nunes, F. D.

C. R. Mendoca, M. M. Costa, J. A. Giacometti, F. D. Nunes, and S. C. Zilio, “Nonlinear refractive indices of polyesterene films doped with azobenzene dye Disperse Red 1,” Electron. Lett. 34, 116–117 (1998).
[CrossRef]

Pate, N. S.

N. S. Pate, L. Hall, L. Katherine, and K. A. Raushenbach, “Interferometric all-optical switches for ultrafast signal processing,” Appl. Opt. 27, 2831–2842 (1998).
[CrossRef]

Prato, M.

R. Bozio, M. Meneghetti, R. Signorini, M. Maggini, G. Scorrano, M. Prato, G. Brusatin, M. Guglielmi, “Optical limiting of fullerene derivatives embedded in sol-gel materials,” in Photoactive Organic Materials Science and Applications, F. Kajzer, ed., NATO ASI Ser. B 572, 159–174 (1996).
[CrossRef]

Pun, E. Y. B.

Z. X. Zhang, W. Qiu, E. Y. B. Pun, P. S. Chang, and Y. Q. Shen, “Doped polymer films with high nonlinear refractive indices,” Electron. Lett. 32, 129–130 (1996).
[CrossRef]

Qiu, W.

Z. X. Zhang, W. Qiu, E. Y. B. Pun, P. S. Chang, and Y. Q. Shen, “Doped polymer films with high nonlinear refractive indices,” Electron. Lett. 32, 129–130 (1996).
[CrossRef]

Rangel-Rojo, R.

R. Rangel-Rojo, S. Yamada, S. Matsuda, and H. D. Yankelevich, “Large near-resonance third-order nonlinearity in an azobenzene-functionalized polymer film,” Appl. Phys. Lett. 72, 1021–1023 (1998).
[CrossRef]

Ranieri, P.

Raushenbach, K. A.

N. S. Pate, L. Hall, L. Katherine, and K. A. Raushenbach, “Interferometric all-optical switches for ultrafast signal processing,” Appl. Opt. 27, 2831–2842 (1998).
[CrossRef]

Said, A. A.

Saito, R.

K. Ishizu, F. Naruse, and R. Saito, “The aggregation behavior of core-shell type polymer microspheres,” Polymer 35, 2329–2334 (1994).
[CrossRef]

Salamo, G. J.

G. L. Wood, W. W. Clark III, M. J. Miller, G. J. Salamo, and E. J. Sharp, “Evaluation of passive optical limiters and switches,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE 1105, 154–181 (1989).
[CrossRef]

Scolara, M.

M. Scolara, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic bandgap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef]

Scorrano, G.

R. Bozio, M. Meneghetti, R. Signorini, M. Maggini, G. Scorrano, M. Prato, G. Brusatin, M. Guglielmi, “Optical limiting of fullerene derivatives embedded in sol-gel materials,” in Photoactive Organic Materials Science and Applications, F. Kajzer, ed., NATO ASI Ser. B 572, 159–174 (1996).
[CrossRef]

Sharp, E. J.

G. L. Wood, W. W. Clark III, M. J. Miller, G. J. Salamo, and E. J. Sharp, “Evaluation of passive optical limiters and switches,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE 1105, 154–181 (1989).
[CrossRef]

Shen, Y. Q.

Z. X. Zhang, W. Qiu, E. Y. B. Pun, P. S. Chang, and Y. Q. Shen, “Doped polymer films with high nonlinear refractive indices,” Electron. Lett. 32, 129–130 (1996).
[CrossRef]

Shi, C.-X.

C.-X. Shi, “Optical bistability in reflective fiber grating,” IEEE J. Quantum Electron. 31, 2037–2043 (1995).
[CrossRef]

Sibilia, C.

Signorini, R.

R. Bozio, M. Meneghetti, R. Signorini, M. Maggini, G. Scorrano, M. Prato, G. Brusatin, M. Guglielmi, “Optical limiting of fullerene derivatives embedded in sol-gel materials,” in Photoactive Organic Materials Science and Applications, F. Kajzer, ed., NATO ASI Ser. B 572, 159–174 (1996).
[CrossRef]

Staromlynska, J.

J. A. Hermann, P. B. Chapple, J. Staromlynska, and P. J. Wilson, “Design criteria for optical power limiters,” in Nonlinear Optical Materials for Switching and Limiting, M. J. Soileau, ed., Proc. SPIE 2229, 167–178 (1994).
[CrossRef]

Steier, W. H.

S. Dubovitsky and W. H. Steier, “Analysis of optical bistability in a nonlinear coupled resonator,” IEEE J. Quantum Electron. 28, 585–589 (1992).
[CrossRef]

Tonucci, R. J.

Tran, P.

Van Stryland, E. W.

Werner, J. S.

J. S. Werner, “Children’s sunglasses: caveat emptor,” Optom. Vision Sci. 68, 318–320 (1991).
[CrossRef]

Wilson, P. J.

J. A. Hermann, P. B. Chapple, J. Staromlynska, and P. J. Wilson, “Design criteria for optical power limiters,” in Nonlinear Optical Materials for Switching and Limiting, M. J. Soileau, ed., Proc. SPIE 2229, 167–178 (1994).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

C. R. Mendoca, M. M. Costa, J. A. Giacometti, F. D. Nunes, and S. C. Zilio, “Nonlinear refractive indices of polyesterene films doped with azobenzene dye Disperse Red 1,” Electron. Lett. 34, 116–117 (1998).
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Figures (6)

Fig. 1
Fig. 1

Transmitted intensity as a function of incident intensity for structure with |nnl|=0.01 for various numbers of layers. All of the limiters clamp the transmitted intensity to a limiting value.

Fig. 2
Fig. 2

Transmitted intensity is plotted as a function of incident intensity on a semi-log scale for structures with |nnl|=0.01 for different numbers of layers. This plot illustrates the transition section between low and high incident intensities and the saturation to a limiting value.

Fig. 3
Fig. 3

Indices of refraction are plotted across the structure of 300 layers with |nnl|=0.01. The decay of the intensity across the structure is thus demonstrated.

Fig. 4
Fig. 4

Evolution of transmittance spectra for structures with |nnl|=0.01 with increasing number of layers is shown. The nonlinear behavior of the limiter is responsible for the formation of a stopband at the desired frequency.

Fig. 5
Fig. 5

Plot demonstrates the evolution of the transmittance spectra made of 300 layers with |nnl|=0.01 as a function of increased incident intensity. As the incident intensity is increased, the stopband becomes deeper and wider.

Fig. 6
Fig. 6

Values of limiting intensities are plotted as a function of the number of layers for nnl values of ±0.005, ±0.01, and ±0.02. The values obtained from numerical calculations, shown on the plot as squares, triangles, and diamonds, follow exactly the curves predicted by the analytical model.

Equations (12)

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n=n0+nnlI,
ajbj=12 exp(ikj+1tj+1)1+kj+1kjexp(-ikj+1tj+1)1-kj+1kjexp(ikj+1tj+1)1-kj+1kjexp(-ikj+1tj+1)1+kj+1kjaj+1bj+1,
a0b0=M1×M2××MN×aN0,
i dA1(z)dz=ωc [(n01-n02)+(nnl1-nnl2)I(z)]×exp-i πd2Λ sin πd2Λπ×A2(z)expi2ωn0c-2πΛz-ωc[n¯nlI(z)×A1(z)],
i dA2(z)dz=-ωc [(n01-n02)+(nnl1-nnl2)I(z)]expi πd2Λsin πd2Λπ×A1(z)expi2ωn0c-2πΛz+ωc[n¯nlI(z)×A2(z)],
n0=n01d1+n02d2Λ,n¯nl=nnl1d1+nnl2d2Λ,
dA1(z)dz=-ωc 2nnlπ[|A1(z)|2+|A2(z)|2]A2(z)expi2ωn0c-2πΛz,
dA2(z)dz=-ωc 2nnlπ[|A1(z)|2+|A2(z)|2]A1(z)exp-i2ωn0c-2πΛz.
A1(z)=1+2 exp-4iIoutnnl(L-z)Λn0+exp-8iIoutnnl(L-z)Λn02+2 exp-8iIoutnnl(L-z)Λn01/2A1out.
i(z)=1+cos4Ioutnnl(L-z)Λn02 cos4Ioutnnl(L-z)Λn0Iout.
Iin=12 1cos4Iouta+1Iout,
ILimiting=π4 n0Nnnl.

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