Abstract

In an active waveguide in which the refractive index of the inner part is smaller than that of the outer part, there is modal gain if the field-medium gain is higher than a threshold value that is a function of the refractive-index step. The threshold current density is shown to decrease as the refractive-index step increases. This behavior can be explained by considering the interplay between the creation of energy in the medium gain and lateral loss.

© 1990 Optical Society of America

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References

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  1. L. M. Dolguinov, L. V. Drtizhinina, P. G. Eliseev, A. N. Lapshin, M. G. Mil’vidskii, B. N. Sverdlov, “Injection heterolaser based on GaInAsSb four component solid solution,” Sov. J. Quantum Electron. 8, 416 (1978).
    [CrossRef]
  2. C. Caneau, A. K. Srivastava, A. G. Dentai, J. L. Zyskind, C. A. Burrus, M. A. Pollack, “Reduction of threshold current density of 2.2 μm GaInAsSb/AlGaASSb injection lasers,” Electron. Lett. 22, 992–993 (1986).
    [CrossRef]
  3. A. Joullié, C. Alibert, J. Bhan, H. Mani, F. Pitard, E. Tour-nié, “Sources adaptées au domaine de longueur d’onde 2–3 μm,” in Materials and Technologies for Optical Communications, A. P. Brenac, ed., Proc. Soc. Photo-Opt. Instrum. Eng.866, 126–134 (1987).
  4. A. Joullié, F. Jia Hua, F. Karouta, H. Mani, C. Alibert, “III–V alloys based on GaSb for optical communications at 2.0–4.5 μm,” in Optical Fibers and Detectors, T. Pearsall, J. P. Noblanc, eds., Proc. Soc. Photo-Opt. Instrum. Eng.587, 46–57 (1987).
    [CrossRef]
  5. J. Arnaud, “Quantum mechanical explanation of spontaneous emission K-factor. A comment,” Electron. Lett. 19, 688–689 (1983).
    [CrossRef]
  6. A. Joullié, “Préparation d’hétérostructures GalnAsSb/GaSb émettant à 2.5 μm,” rapport final de contrat (Ministère de l’Industrie et de la Recherche, Paris, 1987).
  7. J. Fesquet, “Gain of twin antiguiding active slabs,” J. Opt. Soc. A 3, 369–372 (1986).
    [CrossRef]
  8. J. Fesquet, “Decrease of current density for the antiguiding slab structure GaSb/GalnAsSb/GaSb with a metallic coating,” Ann. Telecommun. 43, 112–116 (1988)
  9. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).
  10. M. A. Afromowitz, “Refractive index of GaAlAs,” Solid State Commun. 15, 59–63 (1974).
    [CrossRef]

1988

J. Fesquet, “Decrease of current density for the antiguiding slab structure GaSb/GalnAsSb/GaSb with a metallic coating,” Ann. Telecommun. 43, 112–116 (1988)

1986

C. Caneau, A. K. Srivastava, A. G. Dentai, J. L. Zyskind, C. A. Burrus, M. A. Pollack, “Reduction of threshold current density of 2.2 μm GaInAsSb/AlGaASSb injection lasers,” Electron. Lett. 22, 992–993 (1986).
[CrossRef]

J. Fesquet, “Gain of twin antiguiding active slabs,” J. Opt. Soc. A 3, 369–372 (1986).
[CrossRef]

1983

J. Arnaud, “Quantum mechanical explanation of spontaneous emission K-factor. A comment,” Electron. Lett. 19, 688–689 (1983).
[CrossRef]

1978

L. M. Dolguinov, L. V. Drtizhinina, P. G. Eliseev, A. N. Lapshin, M. G. Mil’vidskii, B. N. Sverdlov, “Injection heterolaser based on GaInAsSb four component solid solution,” Sov. J. Quantum Electron. 8, 416 (1978).
[CrossRef]

1974

M. A. Afromowitz, “Refractive index of GaAlAs,” Solid State Commun. 15, 59–63 (1974).
[CrossRef]

Afromowitz, M. A.

M. A. Afromowitz, “Refractive index of GaAlAs,” Solid State Commun. 15, 59–63 (1974).
[CrossRef]

Alibert, C.

A. Joullié, C. Alibert, J. Bhan, H. Mani, F. Pitard, E. Tour-nié, “Sources adaptées au domaine de longueur d’onde 2–3 μm,” in Materials and Technologies for Optical Communications, A. P. Brenac, ed., Proc. Soc. Photo-Opt. Instrum. Eng.866, 126–134 (1987).

A. Joullié, F. Jia Hua, F. Karouta, H. Mani, C. Alibert, “III–V alloys based on GaSb for optical communications at 2.0–4.5 μm,” in Optical Fibers and Detectors, T. Pearsall, J. P. Noblanc, eds., Proc. Soc. Photo-Opt. Instrum. Eng.587, 46–57 (1987).
[CrossRef]

Arnaud, J.

J. Arnaud, “Quantum mechanical explanation of spontaneous emission K-factor. A comment,” Electron. Lett. 19, 688–689 (1983).
[CrossRef]

Bhan, J.

A. Joullié, C. Alibert, J. Bhan, H. Mani, F. Pitard, E. Tour-nié, “Sources adaptées au domaine de longueur d’onde 2–3 μm,” in Materials and Technologies for Optical Communications, A. P. Brenac, ed., Proc. Soc. Photo-Opt. Instrum. Eng.866, 126–134 (1987).

Burrus, C. A.

C. Caneau, A. K. Srivastava, A. G. Dentai, J. L. Zyskind, C. A. Burrus, M. A. Pollack, “Reduction of threshold current density of 2.2 μm GaInAsSb/AlGaASSb injection lasers,” Electron. Lett. 22, 992–993 (1986).
[CrossRef]

Caneau, C.

C. Caneau, A. K. Srivastava, A. G. Dentai, J. L. Zyskind, C. A. Burrus, M. A. Pollack, “Reduction of threshold current density of 2.2 μm GaInAsSb/AlGaASSb injection lasers,” Electron. Lett. 22, 992–993 (1986).
[CrossRef]

Dentai, A. G.

C. Caneau, A. K. Srivastava, A. G. Dentai, J. L. Zyskind, C. A. Burrus, M. A. Pollack, “Reduction of threshold current density of 2.2 μm GaInAsSb/AlGaASSb injection lasers,” Electron. Lett. 22, 992–993 (1986).
[CrossRef]

Dolguinov, L. M.

L. M. Dolguinov, L. V. Drtizhinina, P. G. Eliseev, A. N. Lapshin, M. G. Mil’vidskii, B. N. Sverdlov, “Injection heterolaser based on GaInAsSb four component solid solution,” Sov. J. Quantum Electron. 8, 416 (1978).
[CrossRef]

Drtizhinina, L. V.

L. M. Dolguinov, L. V. Drtizhinina, P. G. Eliseev, A. N. Lapshin, M. G. Mil’vidskii, B. N. Sverdlov, “Injection heterolaser based on GaInAsSb four component solid solution,” Sov. J. Quantum Electron. 8, 416 (1978).
[CrossRef]

Eliseev, P. G.

L. M. Dolguinov, L. V. Drtizhinina, P. G. Eliseev, A. N. Lapshin, M. G. Mil’vidskii, B. N. Sverdlov, “Injection heterolaser based on GaInAsSb four component solid solution,” Sov. J. Quantum Electron. 8, 416 (1978).
[CrossRef]

Fesquet, J.

J. Fesquet, “Decrease of current density for the antiguiding slab structure GaSb/GalnAsSb/GaSb with a metallic coating,” Ann. Telecommun. 43, 112–116 (1988)

J. Fesquet, “Gain of twin antiguiding active slabs,” J. Opt. Soc. A 3, 369–372 (1986).
[CrossRef]

Jia Hua, F.

A. Joullié, F. Jia Hua, F. Karouta, H. Mani, C. Alibert, “III–V alloys based on GaSb for optical communications at 2.0–4.5 μm,” in Optical Fibers and Detectors, T. Pearsall, J. P. Noblanc, eds., Proc. Soc. Photo-Opt. Instrum. Eng.587, 46–57 (1987).
[CrossRef]

Joullié, A.

A. Joullié, C. Alibert, J. Bhan, H. Mani, F. Pitard, E. Tour-nié, “Sources adaptées au domaine de longueur d’onde 2–3 μm,” in Materials and Technologies for Optical Communications, A. P. Brenac, ed., Proc. Soc. Photo-Opt. Instrum. Eng.866, 126–134 (1987).

A. Joullié, F. Jia Hua, F. Karouta, H. Mani, C. Alibert, “III–V alloys based on GaSb for optical communications at 2.0–4.5 μm,” in Optical Fibers and Detectors, T. Pearsall, J. P. Noblanc, eds., Proc. Soc. Photo-Opt. Instrum. Eng.587, 46–57 (1987).
[CrossRef]

A. Joullié, “Préparation d’hétérostructures GalnAsSb/GaSb émettant à 2.5 μm,” rapport final de contrat (Ministère de l’Industrie et de la Recherche, Paris, 1987).

Karouta, F.

A. Joullié, F. Jia Hua, F. Karouta, H. Mani, C. Alibert, “III–V alloys based on GaSb for optical communications at 2.0–4.5 μm,” in Optical Fibers and Detectors, T. Pearsall, J. P. Noblanc, eds., Proc. Soc. Photo-Opt. Instrum. Eng.587, 46–57 (1987).
[CrossRef]

Lapshin, A. N.

L. M. Dolguinov, L. V. Drtizhinina, P. G. Eliseev, A. N. Lapshin, M. G. Mil’vidskii, B. N. Sverdlov, “Injection heterolaser based on GaInAsSb four component solid solution,” Sov. J. Quantum Electron. 8, 416 (1978).
[CrossRef]

Mani, H.

A. Joullié, F. Jia Hua, F. Karouta, H. Mani, C. Alibert, “III–V alloys based on GaSb for optical communications at 2.0–4.5 μm,” in Optical Fibers and Detectors, T. Pearsall, J. P. Noblanc, eds., Proc. Soc. Photo-Opt. Instrum. Eng.587, 46–57 (1987).
[CrossRef]

A. Joullié, C. Alibert, J. Bhan, H. Mani, F. Pitard, E. Tour-nié, “Sources adaptées au domaine de longueur d’onde 2–3 μm,” in Materials and Technologies for Optical Communications, A. P. Brenac, ed., Proc. Soc. Photo-Opt. Instrum. Eng.866, 126–134 (1987).

Mil’vidskii, M. G.

L. M. Dolguinov, L. V. Drtizhinina, P. G. Eliseev, A. N. Lapshin, M. G. Mil’vidskii, B. N. Sverdlov, “Injection heterolaser based on GaInAsSb four component solid solution,” Sov. J. Quantum Electron. 8, 416 (1978).
[CrossRef]

Pitard, F.

A. Joullié, C. Alibert, J. Bhan, H. Mani, F. Pitard, E. Tour-nié, “Sources adaptées au domaine de longueur d’onde 2–3 μm,” in Materials and Technologies for Optical Communications, A. P. Brenac, ed., Proc. Soc. Photo-Opt. Instrum. Eng.866, 126–134 (1987).

Pollack, M. A.

C. Caneau, A. K. Srivastava, A. G. Dentai, J. L. Zyskind, C. A. Burrus, M. A. Pollack, “Reduction of threshold current density of 2.2 μm GaInAsSb/AlGaASSb injection lasers,” Electron. Lett. 22, 992–993 (1986).
[CrossRef]

Srivastava, A. K.

C. Caneau, A. K. Srivastava, A. G. Dentai, J. L. Zyskind, C. A. Burrus, M. A. Pollack, “Reduction of threshold current density of 2.2 μm GaInAsSb/AlGaASSb injection lasers,” Electron. Lett. 22, 992–993 (1986).
[CrossRef]

Sverdlov, B. N.

L. M. Dolguinov, L. V. Drtizhinina, P. G. Eliseev, A. N. Lapshin, M. G. Mil’vidskii, B. N. Sverdlov, “Injection heterolaser based on GaInAsSb four component solid solution,” Sov. J. Quantum Electron. 8, 416 (1978).
[CrossRef]

Tour-nié, E.

A. Joullié, C. Alibert, J. Bhan, H. Mani, F. Pitard, E. Tour-nié, “Sources adaptées au domaine de longueur d’onde 2–3 μm,” in Materials and Technologies for Optical Communications, A. P. Brenac, ed., Proc. Soc. Photo-Opt. Instrum. Eng.866, 126–134 (1987).

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

Zyskind, J. L.

C. Caneau, A. K. Srivastava, A. G. Dentai, J. L. Zyskind, C. A. Burrus, M. A. Pollack, “Reduction of threshold current density of 2.2 μm GaInAsSb/AlGaASSb injection lasers,” Electron. Lett. 22, 992–993 (1986).
[CrossRef]

Ann. Telecommun.

J. Fesquet, “Decrease of current density for the antiguiding slab structure GaSb/GalnAsSb/GaSb with a metallic coating,” Ann. Telecommun. 43, 112–116 (1988)

Electron. Lett.

C. Caneau, A. K. Srivastava, A. G. Dentai, J. L. Zyskind, C. A. Burrus, M. A. Pollack, “Reduction of threshold current density of 2.2 μm GaInAsSb/AlGaASSb injection lasers,” Electron. Lett. 22, 992–993 (1986).
[CrossRef]

J. Arnaud, “Quantum mechanical explanation of spontaneous emission K-factor. A comment,” Electron. Lett. 19, 688–689 (1983).
[CrossRef]

J. Opt. Soc. A

J. Fesquet, “Gain of twin antiguiding active slabs,” J. Opt. Soc. A 3, 369–372 (1986).
[CrossRef]

Solid State Commun.

M. A. Afromowitz, “Refractive index of GaAlAs,” Solid State Commun. 15, 59–63 (1974).
[CrossRef]

Sov. J. Quantum Electron.

L. M. Dolguinov, L. V. Drtizhinina, P. G. Eliseev, A. N. Lapshin, M. G. Mil’vidskii, B. N. Sverdlov, “Injection heterolaser based on GaInAsSb four component solid solution,” Sov. J. Quantum Electron. 8, 416 (1978).
[CrossRef]

Other

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

A. Joullié, “Préparation d’hétérostructures GalnAsSb/GaSb émettant à 2.5 μm,” rapport final de contrat (Ministère de l’Industrie et de la Recherche, Paris, 1987).

A. Joullié, C. Alibert, J. Bhan, H. Mani, F. Pitard, E. Tour-nié, “Sources adaptées au domaine de longueur d’onde 2–3 μm,” in Materials and Technologies for Optical Communications, A. P. Brenac, ed., Proc. Soc. Photo-Opt. Instrum. Eng.866, 126–134 (1987).

A. Joullié, F. Jia Hua, F. Karouta, H. Mani, C. Alibert, “III–V alloys based on GaSb for optical communications at 2.0–4.5 μm,” in Optical Fibers and Detectors, T. Pearsall, J. P. Noblanc, eds., Proc. Soc. Photo-Opt. Instrum. Eng.587, 46–57 (1987).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Uniform antiguiding slab waveguide. The refractive index of the inner part is smaller than that of the outer medium.

Fig. 2
Fig. 2

Modal gain variations [in decibels per millimeter (dB/mm)] of the antiguiding active slab as a function of the half thickness d (in micrometers) for several field-medium gain values (dB/mm). There is amplification for d values higher than a half-thickness threshold value that depends on the field-medium gain g. The free-space wavelength, the refractive index of the active medium, and that of the surrounding medium are λ = 2.2 μm, nr = 3.71, and n′ = 3.77, respectively.

Fig. 3
Fig. 3

Threshold pumping rate parameter Pth [(dB/mm)μm] variations of an antiguiding active slab as a function of the refractive-index step. The dashed curve corresponds to the asymptotic expression relating the Pth parameter to Δn when Δn ≈ 0.

Fig. 4
Fig. 4

Pumping rate parameter P = 2gd [(dB/mm)μm] variations versus the active medium half-thickness d (μm) corresponding to a modal gain of 30 dB/mm. λ = 2.2 μm, nr = 3.71, and n′ = 3.77.

Fig. 5
Fig. 5

Minimum pumping rate parameter Pm [(dB/mm)μm] as a function of the refractive-index step Δn = nrn′r for both the guiding (Δn > 0) and antiguiding (Δn < 0) cases. Pm is the minimum value of the pump parameter as the distance d varies.

Equations (14)

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k = k 0 ( n r + i n i ) = k r i g ,
E ( x , z , t ) = E ( x ) exp [ i ( β z ω t ) ] ,
β β r i β i ,
E ( x ) = A exp ( i k x x ) ( x > d ) , E ( x ) = cos ( k x x ) ( d > x > d ) , E ( x ) = A exp ( i k x x ) ( x < d ) .
k x 2 + β 2 = k 2 , k x 2 + β 2 = k 2 .
k x = k x r i k x i , k x = k x r + i k x i .
( 1 k x / k x ) / ( 1 + k x / k x ) = exp ( 2 i k x d ) .
B = sin 2 [ V ( 1 B ) 1 / 2 ] ,
V d ( 2 k r Δ k g t h 2 2 i k r g th ) 1 / 2 ,
B V 2 ,
k x 2 k r g th d i d ( 2 k r Δ k g th 2 ) .
2 k r Δ k g th 2 ( 1 4 k r 2 d 2 ) + k x r 2 k x i 2 .
P th ( 2 | Δ n | / n r ) 1 / 2 ,
R = [ ( n r n r ) / ( n r + n r ) ] 2 1 .

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