Abstract

Group velocity dispersion is calculated in weakly guiding slab guides having depressed index layer(s) next to the guiding region. Negative guide dispersion is easily obtained in the single mode regime. The amount of negative dispersion increases with index depth and physical width of the depressed index region.

© 1990 Optical Society of America

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References

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  1. R. L. Fork, C. H. Brito-Cruz, P. C. Becker, C. V. Shank, “Compression of Optical Pulses to Six Femtoseconds by Using Cubic Phase Compensation,” Opt. Lett. 12, 483–486 (1987).
    [CrossRef] [PubMed]
  2. J. E. Bowers, P. A. Morton, S. W. Sorzine, “Activity Mode-Locked Semiconductor Lasers,” IEEE J. Quantum Electron. QE-25, 1426–1433 (1989).
    [CrossRef]
  3. A. Dienes, Y. Peng, A. Knoesen, “Group Velocity Dispersion in Asymmetric Slab Guides,” Appl. Opt. 28, 12–14 (1989).
    [CrossRef] [PubMed]
  4. H. Kogelnik, V. Ramaswamy, “Scaling Rules for Thin-Film Optical Waveguides,” Appl. Opt. 13, 1857–1862 (1974).
    [CrossRef] [PubMed]
  5. D. W. Hewak, J. W. Y. Lit, “Generalized Dispersion Properties of a Four-Layer Thin-Film Waveguide,” Appl. Opt. 26, 833–841 (1987).
    [CrossRef] [PubMed]
  6. S. Kawakami, S. Nishida, “Characteristics of Doubly-Clad Optical Fiber with a Low Index Inner Cladding,” IEEE J. Quantum Electron. QE-10, 879–887 (1974).
    [CrossRef]
  7. Y. Ohtaka, S. Kawakami, S. Nishida, “Transmission Characteristics of a Multilayer Dielectric Slab Optical Waveguide with Strongly Evanescent Wave Layers,” Trans. IECE Japn. 57-C, 187–191 (1974).
  8. Y. Peng, “Group Velocity Dispersion in Multilayer Planar Optical Waveguides,” M.Sc. Thesis, U. California, Davis (1990), unpublished.
  9. M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

1989 (2)

J. E. Bowers, P. A. Morton, S. W. Sorzine, “Activity Mode-Locked Semiconductor Lasers,” IEEE J. Quantum Electron. QE-25, 1426–1433 (1989).
[CrossRef]

A. Dienes, Y. Peng, A. Knoesen, “Group Velocity Dispersion in Asymmetric Slab Guides,” Appl. Opt. 28, 12–14 (1989).
[CrossRef] [PubMed]

1987 (2)

1974 (3)

S. Kawakami, S. Nishida, “Characteristics of Doubly-Clad Optical Fiber with a Low Index Inner Cladding,” IEEE J. Quantum Electron. QE-10, 879–887 (1974).
[CrossRef]

Y. Ohtaka, S. Kawakami, S. Nishida, “Transmission Characteristics of a Multilayer Dielectric Slab Optical Waveguide with Strongly Evanescent Wave Layers,” Trans. IECE Japn. 57-C, 187–191 (1974).

H. Kogelnik, V. Ramaswamy, “Scaling Rules for Thin-Film Optical Waveguides,” Appl. Opt. 13, 1857–1862 (1974).
[CrossRef] [PubMed]

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

Becker, P. C.

Bowers, J. E.

J. E. Bowers, P. A. Morton, S. W. Sorzine, “Activity Mode-Locked Semiconductor Lasers,” IEEE J. Quantum Electron. QE-25, 1426–1433 (1989).
[CrossRef]

Brito-Cruz, C. H.

Dienes, A.

Fork, R. L.

Hewak, D. W.

Kawakami, S.

S. Kawakami, S. Nishida, “Characteristics of Doubly-Clad Optical Fiber with a Low Index Inner Cladding,” IEEE J. Quantum Electron. QE-10, 879–887 (1974).
[CrossRef]

Y. Ohtaka, S. Kawakami, S. Nishida, “Transmission Characteristics of a Multilayer Dielectric Slab Optical Waveguide with Strongly Evanescent Wave Layers,” Trans. IECE Japn. 57-C, 187–191 (1974).

Knoesen, A.

Kogelnik, H.

Lit, J. W. Y.

Morton, P. A.

J. E. Bowers, P. A. Morton, S. W. Sorzine, “Activity Mode-Locked Semiconductor Lasers,” IEEE J. Quantum Electron. QE-25, 1426–1433 (1989).
[CrossRef]

Nishida, S.

Y. Ohtaka, S. Kawakami, S. Nishida, “Transmission Characteristics of a Multilayer Dielectric Slab Optical Waveguide with Strongly Evanescent Wave Layers,” Trans. IECE Japn. 57-C, 187–191 (1974).

S. Kawakami, S. Nishida, “Characteristics of Doubly-Clad Optical Fiber with a Low Index Inner Cladding,” IEEE J. Quantum Electron. QE-10, 879–887 (1974).
[CrossRef]

Ohtaka, Y.

Y. Ohtaka, S. Kawakami, S. Nishida, “Transmission Characteristics of a Multilayer Dielectric Slab Optical Waveguide with Strongly Evanescent Wave Layers,” Trans. IECE Japn. 57-C, 187–191 (1974).

Peng, Y.

A. Dienes, Y. Peng, A. Knoesen, “Group Velocity Dispersion in Asymmetric Slab Guides,” Appl. Opt. 28, 12–14 (1989).
[CrossRef] [PubMed]

Y. Peng, “Group Velocity Dispersion in Multilayer Planar Optical Waveguides,” M.Sc. Thesis, U. California, Davis (1990), unpublished.

Ramaswamy, V.

Shank, C. V.

Sorzine, S. W.

J. E. Bowers, P. A. Morton, S. W. Sorzine, “Activity Mode-Locked Semiconductor Lasers,” IEEE J. Quantum Electron. QE-25, 1426–1433 (1989).
[CrossRef]

Appl. Opt. (3)

IEEE J. Quantum Electron. (2)

S. Kawakami, S. Nishida, “Characteristics of Doubly-Clad Optical Fiber with a Low Index Inner Cladding,” IEEE J. Quantum Electron. QE-10, 879–887 (1974).
[CrossRef]

J. E. Bowers, P. A. Morton, S. W. Sorzine, “Activity Mode-Locked Semiconductor Lasers,” IEEE J. Quantum Electron. QE-25, 1426–1433 (1989).
[CrossRef]

Opt. Lett. (1)

Trans. IECE Japn. (1)

Y. Ohtaka, S. Kawakami, S. Nishida, “Transmission Characteristics of a Multilayer Dielectric Slab Optical Waveguide with Strongly Evanescent Wave Layers,” Trans. IECE Japn. 57-C, 187–191 (1974).

Other (2)

Y. Peng, “Group Velocity Dispersion in Multilayer Planar Optical Waveguides,” M.Sc. Thesis, U. California, Davis (1990), unpublished.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

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Figures (4)

Fig. 1
Fig. 1

Index profiles of the depressed index planar guides.

Fig. 2
Fig. 2

Group velocity dispersion D / Δ n = V 0 d 2 ( V 0 b ) / d V 0 2 for the asymmetric four-layer guide [Fig. 1(b)] for various values of notch depth. The dot on each curve indicates single-mode limit: a = 32, d1/d0 = 1/7; 1, asymmetric three layer (g = 0); 2, g = −5; 3, g = −8.4; g = −16.6.

Fig. 3
Fig. 3

Group velocity dispersion Dn for asymmetric four-layer guides with varying notch layer width: a = 32; g = −12; 1, d1/d0 = 0.075; 2, d1/d0 = 0.1; 3, d1/d0 = 1/7.

Fig. 4
Fig. 4

Group velocity dispersion Dn for symmetric five-layer guides [Fig. 1(a)]: d1/d0 = 1/7; 1, g = −12; 2, g = −16.6.

Equations (13)

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b = N 2 - n 2 2 n 0 2 - n 2 2
g = n 1 2 - n 2 2 n 0 2 - n 2 2
a = n 2 2 - n - 1 2 n 0 2 - n 2 2
V j = ω c d j ( n 0 2 - n 2 2 ) 1 / 2 .
V 0 ( 1 - b ) 1 / 2 = m π + φ - 1 , 0 2 + φ 1 , 0 2 ,
φ 1 , 0 = 2 tan - 1 { ( b - g 1 - b ) 1 / 2 tanh [ tanh - 1 ( b b - g ) 1 / 2 + V 1 ( b - g ) 1 / 2 ] } ,
φ - 1 , 0 = { φ 1 , 0 symmetric [ Fig .1 ( a ) ] , 2 tan - 1 ( a + b 1 - b ) 1 / 2 asymmetric [ Fig .1 ( b ) ] .
Δ τ g g = L c Δ λ λ Δ n V 0 d 2 ( V 0 b ) d V 0 2 = L c Δ λ λ D .
- g V 1 < ˜ 2
V 0 d 2 ( V 0 b ) d V 0 2 = D Δ n = f ( V 0 , b , V 1 , g , a ) .
a TM = n 0 4 n - 1 4 n 2 2 - n - 1 2 n 0 2 - n 2 2 ,
g TM = n 0 4 n 1 4 n 1 2 - n 2 2 n 0 2 - n 2 2 ,
V 1 TM = n 1 2 n 0 2 V 1 TM .

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