Abstract

The light amplification properties of fractal and asymmetric multilayer resonator structures which contain a light amplifying medium in the middle layer are studied theoretically. The amplitude gain of transmitted light is analyzed by use of two-dimensional plots which we denote gain maps. The gain map, which is plotted against two different structural parameters, illustrates some regularities in the location of gain peaks and bandgaps. Cantor structures exhibit gain peaks at the edges of multiple bandgaps, and those peaks are higher and sharper than those of periodic structures. Asymmetric resonator structures are found to provide more gain than symmetric ones when the gain length is short. A comparison between the gain and the group velocity of light is also presented, together with the electromagnetic energy distributions in the multilayers.

©2005 Optical Society of America

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References

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    [Crossref]
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    [Crossref]

2002 (3)

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[Crossref]

E. Cojocaru, “Characteristics of the temporal pulse response from the forbidden gap of a quasiperiodic Cantor multilayer,” J. Appl. Phys. 91, 4000–4004 (2002).
[Crossref]

J. Gerardin and A. Lakhtakia, “Spectral response of Cantor multilayers made of materials with negative refractive index,” Phys. Lett. A 301, 377–381 (2002).
[Crossref]

2000 (1)

1999 (2)

M. Lehman and M. Garavaglia, “Beam reflection from multilayers with periodic and fractal distributions,” J. Mod. Opt. 46, 1579–1593 (1999).

T. Okamoto, “Light amplification by multilayers with fractal gain structures,” Proc. SPIE 3749, 122–123 (1999).
[Crossref]

1998 (2)

C. Sibilia, I. S. Nefedov, M. Scalora, and M. Bertolotti, “Electromagnetic mode density for finite quasi-periodic structures,” J. Opt. Soc. Am. B 15, 1947–1952 (1998).
[Crossref]

F. Garzia, P. Masciulli, C. Sibilia, and M. Bertolotti, “Temporal pulse response of a Cantor filter,” Opt. Commun. 147, 333–340 (1998).
[Crossref]

1996 (3)

1994 (1)

1991 (1)

X. Sun and D. L. Jaggard, “Wave interactions with generalized Cantor bar fractal multilayers,” J. Appl. Phys. 70, 2500–2507 (1991).
[Crossref]

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

Bertolotti, M.

Cojocaru, E.

E. Cojocaru, “Characteristics of the temporal pulse response from the forbidden gap of a quasiperiodic Cantor multilayer,” J. Appl. Phys. 91, 4000–4004 (2002).
[Crossref]

Dowling, J. P.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

Gaponenko, S. V.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[Crossref]

Garavaglia, M.

M. Lehman and M. Garavaglia, “Beam reflection from multilayers with periodic and fractal distributions,” J. Mod. Opt. 46, 1579–1593 (1999).

Garzia, F.

F. Garzia, P. Masciulli, C. Sibilia, and M. Bertolotti, “Temporal pulse response of a Cantor filter,” Opt. Commun. 147, 333–340 (1998).
[Crossref]

Gerardin, J.

J. Gerardin and A. Lakhtakia, “Spectral response of Cantor multilayers made of materials with negative refractive index,” Phys. Lett. A 301, 377–381 (2002).
[Crossref]

Hattori, H. T.

Hoekstra, H.

Jaggard, D. L.

X. Sun and D. L. Jaggard, “Wave interactions with generalized Cantor bar fractal multilayers,” J. Appl. Phys. 70, 2500–2507 (1991).
[Crossref]

Lakhtakia, A.

J. Gerardin and A. Lakhtakia, “Spectral response of Cantor multilayers made of materials with negative refractive index,” Phys. Lett. A 301, 377–381 (2002).
[Crossref]

Lavrinenko, A. V.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[Crossref]

Lehman, M.

M. Lehman and M. Garavaglia, “Beam reflection from multilayers with periodic and fractal distributions,” J. Mod. Opt. 46, 1579–1593 (1999).

Lisboa, O.

Masciulli, P.

Nefedov, I. S.

Okamoto, T.

T. Okamoto, “Light amplification by multilayers with fractal gain structures,” Proc. SPIE 3749, 122–123 (1999).
[Crossref]

Ranieri, P.

Sandomirski, K. S.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[Crossref]

Scalora, M.

C. Sibilia, I. S. Nefedov, M. Scalora, and M. Bertolotti, “Electromagnetic mode density for finite quasi-periodic structures,” J. Opt. Soc. Am. B 15, 1947–1952 (1998).
[Crossref]

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

Schneider, V. M.

Sibilia, C.

Sun, X.

X. Sun and D. L. Jaggard, “Wave interactions with generalized Cantor bar fractal multilayers,” J. Appl. Phys. 70, 2500–2507 (1991).
[Crossref]

Wijnands, F.

Zhukovsky, S. V.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[Crossref]

J. Appl. Phys. (2)

X. Sun and D. L. Jaggard, “Wave interactions with generalized Cantor bar fractal multilayers,” J. Appl. Phys. 70, 2500–2507 (1991).
[Crossref]

E. Cojocaru, “Characteristics of the temporal pulse response from the forbidden gap of a quasiperiodic Cantor multilayer,” J. Appl. Phys. 91, 4000–4004 (2002).
[Crossref]

J. Mod. Opt. (1)

M. Lehman and M. Garavaglia, “Beam reflection from multilayers with periodic and fractal distributions,” J. Mod. Opt. 46, 1579–1593 (1999).

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

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

Opt. Commun. (1)

F. Garzia, P. Masciulli, C. Sibilia, and M. Bertolotti, “Temporal pulse response of a Cantor filter,” Opt. Commun. 147, 333–340 (1998).
[Crossref]

Opt. Lett. (1)

Phys. Lett. A (1)

J. Gerardin and A. Lakhtakia, “Spectral response of Cantor multilayers made of materials with negative refractive index,” Phys. Lett. A 301, 377–381 (2002).
[Crossref]

Phys. Rev. E (2)

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[Crossref]

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

SPIE (1)

T. Okamoto, “Light amplification by multilayers with fractal gain structures,” Proc. SPIE 3749, 122–123 (1999).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1.

Multilayer structures used for the analysis. Refractive indices n 1, n 2, and n 3 used for the analysis are 2.30, 1.45, and 1.45(1-0.0001i), respectively.

Fig. 2.
Fig. 2.

Amplitude gain distributions for (a) Cantor and (b) periodic structures, both of which are symmetric about the central gain layer. (c) and (d) are partially magnified versions of (a) and (b), respectively, showing high gain spots.

Fig. 3.
Fig. 3.

(a) Cross-section A (c =5) and (b) Cross-section B (c/l =9) in Fig. 2(a).

Fig. 4.
Fig. 4.

Amplitude gain distributions for (a) Cantor and (b) periodic structures with the gain length of 1. (c) and (d) are partially magnified versions of (a) and (b), respectively. Circles in (c) and (d) denote the position of high gain spots.

Fig. 5.
Fig. 5.

Amplitude gain (blue curve) and mode density (red curve) plotted against input frequency normalized by the midgap (Bragg) frequency for a Cantor structure of level 4. (a) is partially magnified in (b).

Fig. 6.
Fig. 6.

Energy density distributions inside a Cantor multilayer structure. (a) ω/ω 0 = 2.6352. (b) ω/ω 0 = 2.9008.

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