Abstract

We propose and analyze a new type of optical amplifier that is formed by addition of gain in the periodic cladding of a transverse Bragg resonance waveguide [Opt. Lett. 27, 936 (2002)]. Using the coupled-wave formalism, we calculate the mode profiles, the exponential gain constant, and, for comparison, the gain enhancement compared with those of conventional semiconductor optical amplifiers. In contrast with coupled-mode theory, in one-dimensional structures (e.g., the distributed-feedback laser) the exponential gain constant in the longitudinal direction is involved in both longitudinal and transverse confinement, and its solution has to be achieved self-consistently, together with the quantized guiding channel width.

© 2003 Optical Society of America

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References

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  1. H. Stoll and A. Yariv, Opt. Commun. 8, 5 (1973).
    [CrossRef]
  2. P. Yeh and A. Yariv, Opt. Commun. 19, 427 (1976).
    [CrossRef]
  3. M. Nakamura, A. Yariv, H. W. Yen, and S. Somekh, Appl. Phys. Lett. 22, 515 (1973).
    [CrossRef]
  4. A. Yariv and H. W. Yen, Opt. Commun. 10, 120 (1974).
    [CrossRef]
  5. A. Yariv, Opt. Lett. 27, 936 (2002).
    [CrossRef]
  6. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, Oxford, 1997).
  7. R. J. Lang, K. Dzurko, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
    [CrossRef]

2002

1998

R. J. Lang, K. Dzurko, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

1976

P. Yeh and A. Yariv, Opt. Commun. 19, 427 (1976).
[CrossRef]

1974

A. Yariv and H. W. Yen, Opt. Commun. 10, 120 (1974).
[CrossRef]

1973

H. Stoll and A. Yariv, Opt. Commun. 8, 5 (1973).
[CrossRef]

M. Nakamura, A. Yariv, H. W. Yen, and S. Somekh, Appl. Phys. Lett. 22, 515 (1973).
[CrossRef]

Demars, S.

R. J. Lang, K. Dzurko, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Dzurko, K.

R. J. Lang, K. Dzurko, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Hardy, A. A.

R. J. Lang, K. Dzurko, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Lang, R. J.

R. J. Lang, K. Dzurko, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Nakamura, M.

M. Nakamura, A. Yariv, H. W. Yen, and S. Somekh, Appl. Phys. Lett. 22, 515 (1973).
[CrossRef]

Schoenfelder, A.

R. J. Lang, K. Dzurko, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Somekh, S.

M. Nakamura, A. Yariv, H. W. Yen, and S. Somekh, Appl. Phys. Lett. 22, 515 (1973).
[CrossRef]

Stoll, H.

H. Stoll and A. Yariv, Opt. Commun. 8, 5 (1973).
[CrossRef]

Welch, D. F.

R. J. Lang, K. Dzurko, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Yariv, A.

A. Yariv, Opt. Lett. 27, 936 (2002).
[CrossRef]

P. Yeh and A. Yariv, Opt. Commun. 19, 427 (1976).
[CrossRef]

A. Yariv and H. W. Yen, Opt. Commun. 10, 120 (1974).
[CrossRef]

M. Nakamura, A. Yariv, H. W. Yen, and S. Somekh, Appl. Phys. Lett. 22, 515 (1973).
[CrossRef]

H. Stoll and A. Yariv, Opt. Commun. 8, 5 (1973).
[CrossRef]

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, Oxford, 1997).

Yeh, P.

P. Yeh and A. Yariv, Opt. Commun. 19, 427 (1976).
[CrossRef]

Yen, H. W.

A. Yariv and H. W. Yen, Opt. Commun. 10, 120 (1974).
[CrossRef]

M. Nakamura, A. Yariv, H. W. Yen, and S. Somekh, Appl. Phys. Lett. 22, 515 (1973).
[CrossRef]

Appl. Phys. Lett.

M. Nakamura, A. Yariv, H. W. Yen, and S. Somekh, Appl. Phys. Lett. 22, 515 (1973).
[CrossRef]

IEEE J. Quantum Electron.

R. J. Lang, K. Dzurko, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Opt. Commun.

A. Yariv and H. W. Yen, Opt. Commun. 10, 120 (1974).
[CrossRef]

H. Stoll and A. Yariv, Opt. Commun. 8, 5 (1973).
[CrossRef]

P. Yeh and A. Yariv, Opt. Commun. 19, 427 (1976).
[CrossRef]

Opt. Lett.

Other

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, Oxford, 1997).

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Figures (2)

Fig. 1
Fig. 1

Top view of a two-dimensional periodic waveguiding structure: a guiding channel of width W (core) between two semi-infinite arrays of air holes in a periodic pattern, e.g., a triangular lattice (cladding). Also shown, in the core, are the two in-plane k-vectors of plane waves Ei and Er that compose the waveguide mode.

Fig. 2
Fig. 2

Transverse (x) modal profile, with the shaded region indicating the core width, for L=5 µm and Icore=Iclad. Two structures are considered: for the figure at the left there is no gain in the core region [Icore=0], and, for the figure at the right, gain is present in the core [Icore=Iclad].

Tables (1)

Tables Icon

Table 1 Calculated Parameters, with and without Core Gain

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

2Er,t-μr2Er,tt2=0.
d2Edx2+ω2μR-βR2E+iω2μI-2βRβIE=0,
Rr=m,nRmn expiKmn·r,
Kmn=m2π/bxˆ+n2π/azˆ.
Rx=R0-21 cos2πbx,
101=1abu.c.rexp-i2πbxdxdz
d2Edx2+k02E-2ω2μ1 cos2πbxE+ iω2μI-2βRβIE=0,  
Ez,x,t=Ax exp-ik0x+Bx expik0x×expiωt-βzExexpiωt-βz;
dAdx=γA+κ*B expi2k0-π/bx,  dBdx=-γB+κA exp-i2k0-π/bx
γ=ω2μIclad2k0-βRβIk0,  κ=-iω2μ12k0.
Ecladx=Fexp-iπx/b×γ-iΔk sinhSL-x-S coshSL-xγ-iΔk sinhSL-S coshSL+exp+iπx/bκ sinhSL-xγ-iΔk sinhSL-S coshSL,
Sκ2+γ-iΔk21/2,  Δkk0-π/b,
Ecorex=exp-ikx+W/2±expikx+W/2,
kk01+i2k02ω2μIcore-2βRβI.
exp-ikW2=F,  expikW2=±κFγ-iΔk-S cothSL.
expikW=±κγ-iΔk-S cothSL,
Sκ2+γ-iΔk21/2,  γ=ω2μIclad2k0-βRβIk0,  κ=-iω2μ12k0,  k02ω2μR0-βR2,  kk01+i2k02ω2μIcore-2βRβI.
expβRβIk0-ω2μIcore2k0W= κγ-iΔk-S cothSL,  
2k0W=Phase±κγ-iΔk-S cothSL.
Ex=Ecladx0<xLEcorex-Wx0Eclad-x+W-L+Wx<-W.

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