Abstract

Field confinement in a microchip laser with transversely varying gain and plane–plane cavity mirrors is theoretically discussed with a semiclassical treatment. We show that the common notion of a transverse cavity mode becomes closely linked to that of a longitudinal cavity mode owing to the key role that detuning of the longitudinal cavity frequency from the atomic resonance plays in the formation of the transverse field profile. In particular, we show that as the pump size decreases the laser emission is pulled toward the atomic resonance frequency on the negative detuning side. Strong mode pulling is interpreted as being due to the index-antiguiding effect induced by the pump and manifests itself as a ring pattern in the far-field spatial intensity.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974).
  2. H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
    [Crossref] [PubMed]
  3. L. W. Casperson and A. Yariv, Appl. Phys. Lett. 12, 355 (1968); G. J. Ernst and W. J. Witteman, IEEE J. Quantum Electron. QE-9, 911 (1973); IEEE J. Quantum Electron. QE-10, 757 (1974); L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974); U. Ganiel and Y. Silberberg, Appl. Opt. 14, 306 (1975); F. Salin and J. Squier, Opt. Lett. 17, 1352 (1992).
    [Crossref] [PubMed]
  4. L. W. Casperson and A. Yariv, Appl. Opt. 11, 462 (1972); C. Freed and H. A. Haus, IEEE J. Quantum Electron. QE-9, 219 (1973); G. J. Ernst and W. J. Witteman, IEEE J. Quantum Electron. QE-10, 37 (1974); H. Maeda and K. Shimoda, J. Appl. Phys. 46, 1235 (1975).
    [Crossref] [PubMed]
  5. L. Casperson and A. Yariv, Appl. Phys. Lett. 17, 259 (1970); P. A. Wolff, N. B. Abraham, and S. R. Smith, IEEE J. Quantum Electron. QE-13, 400 (1977); M. Maeda and N. B. Abraham, Phys. Rev. A 26, 3395 (1982).
    [Crossref]
  6. P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8194 (1992); P. K. Jakobsen, J. Lega, Q. Feng, M. Staley, J. V. Moloney, and A. C. Newell, Phys. Rev. A 49, 4189 (1994).
    [Crossref] [PubMed]
  7. J. J. Zayhowski and A. Mooradian, Opt. Lett. 14, 24, 618 (1989); F. Zhou and A. Ferguson, Electron. Lett. 26, 490 (1990); T. Taira, A. Mukai, Y. Nozawa, and T. Kobayashi, Opt. Lett. 16, 1955 (1991); P. Laporta, S. Taccheo, S. Longhi, O. Svelto, and G. Sacchi, Opt. Lett. 18, 1232 (1993).
    [Crossref] [PubMed]
  8. J. J. Zayhowski, Proc. Adv. Solid State Lasers 6, 9 (1991).
  9. N. MacKinnon and B. D. Sinclair, Opt. Commun. 94, 281 (1992).
    [Crossref]
  10. S. Longhi, G. Cerullo, V. Magni, S. Taccheo, and P. Laporta, Appl. Phys. Lett. 65, 3042 (1994).
    [Crossref]
  11. T. Y. Fan, Opt. Lett. 19, 554 (1994).
    [Crossref] [PubMed]
  12. G. K. Harkness and W. J. Firth, J. Mod. Opt. 39, 2023 (1992).
    [Crossref]
  13. S. Longhi, J. Opt. Soc. Am. B 11, 1098 (1994).
    [Crossref]
  14. K. Otsuka, D. Pieroux, and P. Mandel, Opt. Commun. 108, 265 (1994).
    [Crossref]
  15. L. A. Lugiato and L. M. Narducci, Z. Phys. B 71, 129 (1988).
    [Crossref]
  16. G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
    [Crossref] [PubMed]
  17. Q. Feng, J. V. Moloney, and A. C. Newell, Phys. Rev. A 50, R3601 (1994).
    [Crossref]
  18. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, London, 1980), p. 672.

1994 (6)

S. Longhi, G. Cerullo, V. Magni, S. Taccheo, and P. Laporta, Appl. Phys. Lett. 65, 3042 (1994).
[Crossref]

T. Y. Fan, Opt. Lett. 19, 554 (1994).
[Crossref] [PubMed]

S. Longhi, J. Opt. Soc. Am. B 11, 1098 (1994).
[Crossref]

K. Otsuka, D. Pieroux, and P. Mandel, Opt. Commun. 108, 265 (1994).
[Crossref]

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[Crossref] [PubMed]

Q. Feng, J. V. Moloney, and A. C. Newell, Phys. Rev. A 50, R3601 (1994).
[Crossref]

1992 (3)

G. K. Harkness and W. J. Firth, J. Mod. Opt. 39, 2023 (1992).
[Crossref]

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8194 (1992); P. K. Jakobsen, J. Lega, Q. Feng, M. Staley, J. V. Moloney, and A. C. Newell, Phys. Rev. A 49, 4189 (1994).
[Crossref] [PubMed]

N. MacKinnon and B. D. Sinclair, Opt. Commun. 94, 281 (1992).
[Crossref]

1991 (1)

J. J. Zayhowski, Proc. Adv. Solid State Lasers 6, 9 (1991).

1989 (1)

1988 (1)

L. A. Lugiato and L. M. Narducci, Z. Phys. B 71, 129 (1988).
[Crossref]

1972 (1)

1970 (1)

L. Casperson and A. Yariv, Appl. Phys. Lett. 17, 259 (1970); P. A. Wolff, N. B. Abraham, and S. R. Smith, IEEE J. Quantum Electron. QE-13, 400 (1977); M. Maeda and N. B. Abraham, Phys. Rev. A 26, 3395 (1982).
[Crossref]

1968 (1)

L. W. Casperson and A. Yariv, Appl. Phys. Lett. 12, 355 (1968); G. J. Ernst and W. J. Witteman, IEEE J. Quantum Electron. QE-9, 911 (1973); IEEE J. Quantum Electron. QE-10, 757 (1974); L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974); U. Ganiel and Y. Silberberg, Appl. Opt. 14, 306 (1975); F. Salin and J. Squier, Opt. Lett. 17, 1352 (1992).
[Crossref] [PubMed]

1966 (1)

Casperson, L.

L. Casperson and A. Yariv, Appl. Phys. Lett. 17, 259 (1970); P. A. Wolff, N. B. Abraham, and S. R. Smith, IEEE J. Quantum Electron. QE-13, 400 (1977); M. Maeda and N. B. Abraham, Phys. Rev. A 26, 3395 (1982).
[Crossref]

Casperson, L. W.

L. W. Casperson and A. Yariv, Appl. Opt. 11, 462 (1972); C. Freed and H. A. Haus, IEEE J. Quantum Electron. QE-9, 219 (1973); G. J. Ernst and W. J. Witteman, IEEE J. Quantum Electron. QE-10, 37 (1974); H. Maeda and K. Shimoda, J. Appl. Phys. 46, 1235 (1975).
[Crossref] [PubMed]

L. W. Casperson and A. Yariv, Appl. Phys. Lett. 12, 355 (1968); G. J. Ernst and W. J. Witteman, IEEE J. Quantum Electron. QE-9, 911 (1973); IEEE J. Quantum Electron. QE-10, 757 (1974); L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974); U. Ganiel and Y. Silberberg, Appl. Opt. 14, 306 (1975); F. Salin and J. Squier, Opt. Lett. 17, 1352 (1992).
[Crossref] [PubMed]

Cerullo, G.

S. Longhi, G. Cerullo, V. Magni, S. Taccheo, and P. Laporta, Appl. Phys. Lett. 65, 3042 (1994).
[Crossref]

Fan, T. Y.

Feng, Q.

Q. Feng, J. V. Moloney, and A. C. Newell, Phys. Rev. A 50, R3601 (1994).
[Crossref]

Firth, W. J.

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[Crossref] [PubMed]

G. K. Harkness and W. J. Firth, J. Mod. Opt. 39, 2023 (1992).
[Crossref]

Geddes, J. B.

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[Crossref] [PubMed]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, London, 1980), p. 672.

Harkness, G. K.

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[Crossref] [PubMed]

G. K. Harkness and W. J. Firth, J. Mod. Opt. 39, 2023 (1992).
[Crossref]

Indik, R.

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8194 (1992); P. K. Jakobsen, J. Lega, Q. Feng, M. Staley, J. V. Moloney, and A. C. Newell, Phys. Rev. A 49, 4189 (1994).
[Crossref] [PubMed]

Jakobsen, P. K.

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8194 (1992); P. K. Jakobsen, J. Lega, Q. Feng, M. Staley, J. V. Moloney, and A. C. Newell, Phys. Rev. A 49, 4189 (1994).
[Crossref] [PubMed]

Kogelnik, H.

Lamb, W. E.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974).

Laporta, P.

S. Longhi, G. Cerullo, V. Magni, S. Taccheo, and P. Laporta, Appl. Phys. Lett. 65, 3042 (1994).
[Crossref]

Li, T.

Longhi, S.

S. Longhi, J. Opt. Soc. Am. B 11, 1098 (1994).
[Crossref]

S. Longhi, G. Cerullo, V. Magni, S. Taccheo, and P. Laporta, Appl. Phys. Lett. 65, 3042 (1994).
[Crossref]

Lugiato, L. A.

L. A. Lugiato and L. M. Narducci, Z. Phys. B 71, 129 (1988).
[Crossref]

MacKinnon, N.

N. MacKinnon and B. D. Sinclair, Opt. Commun. 94, 281 (1992).
[Crossref]

Magni, V.

S. Longhi, G. Cerullo, V. Magni, S. Taccheo, and P. Laporta, Appl. Phys. Lett. 65, 3042 (1994).
[Crossref]

Mandel, P.

K. Otsuka, D. Pieroux, and P. Mandel, Opt. Commun. 108, 265 (1994).
[Crossref]

Moloney, J. V.

Q. Feng, J. V. Moloney, and A. C. Newell, Phys. Rev. A 50, R3601 (1994).
[Crossref]

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[Crossref] [PubMed]

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8194 (1992); P. K. Jakobsen, J. Lega, Q. Feng, M. Staley, J. V. Moloney, and A. C. Newell, Phys. Rev. A 49, 4189 (1994).
[Crossref] [PubMed]

Mooradian, A.

Narducci, L. M.

L. A. Lugiato and L. M. Narducci, Z. Phys. B 71, 129 (1988).
[Crossref]

Newell, A. C.

Q. Feng, J. V. Moloney, and A. C. Newell, Phys. Rev. A 50, R3601 (1994).
[Crossref]

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8194 (1992); P. K. Jakobsen, J. Lega, Q. Feng, M. Staley, J. V. Moloney, and A. C. Newell, Phys. Rev. A 49, 4189 (1994).
[Crossref] [PubMed]

Otsuka, K.

K. Otsuka, D. Pieroux, and P. Mandel, Opt. Commun. 108, 265 (1994).
[Crossref]

Pieroux, D.

K. Otsuka, D. Pieroux, and P. Mandel, Opt. Commun. 108, 265 (1994).
[Crossref]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, London, 1980), p. 672.

Sargent, M.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974).

Scully, M. O.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974).

Sinclair, B. D.

N. MacKinnon and B. D. Sinclair, Opt. Commun. 94, 281 (1992).
[Crossref]

Taccheo, S.

S. Longhi, G. Cerullo, V. Magni, S. Taccheo, and P. Laporta, Appl. Phys. Lett. 65, 3042 (1994).
[Crossref]

Wright, E. M.

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[Crossref] [PubMed]

Yariv, A.

L. W. Casperson and A. Yariv, Appl. Opt. 11, 462 (1972); C. Freed and H. A. Haus, IEEE J. Quantum Electron. QE-9, 219 (1973); G. J. Ernst and W. J. Witteman, IEEE J. Quantum Electron. QE-10, 37 (1974); H. Maeda and K. Shimoda, J. Appl. Phys. 46, 1235 (1975).
[Crossref] [PubMed]

L. Casperson and A. Yariv, Appl. Phys. Lett. 17, 259 (1970); P. A. Wolff, N. B. Abraham, and S. R. Smith, IEEE J. Quantum Electron. QE-13, 400 (1977); M. Maeda and N. B. Abraham, Phys. Rev. A 26, 3395 (1982).
[Crossref]

L. W. Casperson and A. Yariv, Appl. Phys. Lett. 12, 355 (1968); G. J. Ernst and W. J. Witteman, IEEE J. Quantum Electron. QE-9, 911 (1973); IEEE J. Quantum Electron. QE-10, 757 (1974); L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974); U. Ganiel and Y. Silberberg, Appl. Opt. 14, 306 (1975); F. Salin and J. Squier, Opt. Lett. 17, 1352 (1992).
[Crossref] [PubMed]

Zayhowski, J. J.

Appl. Opt. (2)

Appl. Phys. Lett. (3)

L. Casperson and A. Yariv, Appl. Phys. Lett. 17, 259 (1970); P. A. Wolff, N. B. Abraham, and S. R. Smith, IEEE J. Quantum Electron. QE-13, 400 (1977); M. Maeda and N. B. Abraham, Phys. Rev. A 26, 3395 (1982).
[Crossref]

L. W. Casperson and A. Yariv, Appl. Phys. Lett. 12, 355 (1968); G. J. Ernst and W. J. Witteman, IEEE J. Quantum Electron. QE-9, 911 (1973); IEEE J. Quantum Electron. QE-10, 757 (1974); L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974); U. Ganiel and Y. Silberberg, Appl. Opt. 14, 306 (1975); F. Salin and J. Squier, Opt. Lett. 17, 1352 (1992).
[Crossref] [PubMed]

S. Longhi, G. Cerullo, V. Magni, S. Taccheo, and P. Laporta, Appl. Phys. Lett. 65, 3042 (1994).
[Crossref]

J. Mod. Opt. (1)

G. K. Harkness and W. J. Firth, J. Mod. Opt. 39, 2023 (1992).
[Crossref]

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

Opt. Commun. (2)

K. Otsuka, D. Pieroux, and P. Mandel, Opt. Commun. 108, 265 (1994).
[Crossref]

N. MacKinnon and B. D. Sinclair, Opt. Commun. 94, 281 (1992).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (3)

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, Phys. Rev. A 50, 4310 (1994).
[Crossref] [PubMed]

Q. Feng, J. V. Moloney, and A. C. Newell, Phys. Rev. A 50, R3601 (1994).
[Crossref]

P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8194 (1992); P. K. Jakobsen, J. Lega, Q. Feng, M. Staley, J. V. Moloney, and A. C. Newell, Phys. Rev. A 49, 4189 (1994).
[Crossref] [PubMed]

Proc. Adv. Solid State Lasers (1)

J. J. Zayhowski, Proc. Adv. Solid State Lasers 6, 9 (1991).

Z. Phys. B (1)

L. A. Lugiato and L. M. Narducci, Z. Phys. B 71, 129 (1988).
[Crossref]

Other (2)

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, London, 1980), p. 672.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Normalized intensity profile of transverse modes TEM0, TEM2, and TEM4 for three different values of the cavity detuning δC: (A) δC = −2, (B) δC = 0, (C) δC = 2. The other parameters are T = 0.01, β = 1, and γ = 0.002. The dashed curves represent the transverse pump profiles.

Fig. 2
Fig. 2

(A) Mode width and (B) laser detuning of the fundamental transverse mode as functions of the cavity detuning for various pump widths. Curve 1, γ = 0.1; curve 2, γ = 0.5; curve 3, γ = 1; curve 4, γ = 2. The other parameters are T = 0.01 and β = 1. The dashed curve in (B) (partially obscured by the solid curves) represents the tuning curve predicted in the uniform pump case.

Fig. 3
Fig. 3

(A) Near-field and (B) far-field spatial patterns of the laser intensity for γ = 0.1 (solid curves) and for γ = 0.02 (dashed curves). The values of the various parameters are δC = −0.5, T = 0.01, β = 1, l = 500 μm, and λ0 = 1 μm.

Equations (14)

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

t 2 ϕ + ( δ L - δ C - i T 2 ) ϕ + α 0 l ( i + β δ L ) 1 + β 2 δ L 2 Δ e ϕ = 0 ,
ϕ ( r , k ) = exp ( i k · r ) ,
C = 1 + [ β ( δ C + k 2 ) 1 + β T / 2 ] 2 ,
δ L = δ C + k 2 1 + β T / 2 .
ϕ N ( x ) = sech 2 ν ( γ x ) H N [ tanh ( γ x ) ] .
( 1 - ξ 2 ) H - 2 ( 1 + 2 ν ) ξ H + λ H = 0 ,
w p < ( l λ 0 T ) 1 / 2 ,
I N ( θ ) = | - d x ϕ N ( x ) exp ( - i k 0 x θ ) | 2 ,
I 0 ( θ ) = | ( l k 0 ) 1 / 2 2 2 ( ν - 1 ) γ Γ ( ν + i k 0 l θ 2 γ ) Γ ( ν - i k 0 l θ 2 γ ) Γ ( 2 ν ) | 2 ,
l k 0 ( d 2 ϕ d r 2 + 1 r d ϕ d r ) + ( δ L - δ C - i T 2 ) ϕ + i + β δ L ( 1 + β 2 δ L 2 ) Δ e ϕ = 0 ,
ϕ ( r ) J 0 ( i σ r ) + i Y 0 ( i σ r ) ,
I ( θ ) = | 0 d r r ϕ ( r ) J 0 ( k 0 r θ ) | 2 ,
I ( θ ) = 1 ( θ 2 - θ d 2 ) + ( T / 2 l k 0 ) 2 ,
θ d ( δ L - δ C l k 0 ) 1 / 2 .

Metrics