Abstract

Based on the geometrical modeling of the unified gain coefficient and the reported amplified spontaneous emission (ASE) output energy measurement εASE versus amplifying excitation length, lAMP in a KrF laser oscillator, we managed, as an example, to explain the ASE output energy behavior both numerically and analytically. In this approach, introducing the ASE gain-coefficient profile for the KrF laser, g0,KrFASE, was not avoidable. It was found that while the g0,KrFASE profile follows the introduced gain-modeling formulation, it is, however, slightly lower than the KrF laser gain profile, g0,KrFexp, deduced from the measurements reported by different researchers. The present approach, up to the present time, is able to explain all of the existing ambiguities on understanding the ASE behavior.

© 2012 Optical Society of America

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References

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  1. D. A. Leonard, Appl. Phys. Lett. 7, 4 (1965).
    [CrossRef]
  2. O. Svelto, Principles of Lasers, 5th ed. (Springer, 2010).
  3. A. M. Hunter and R. O. Hunter, IEEE J. Quantum Electron. 17, 1879 (1981).
    [CrossRef]
  4. G. Haag, M. Munz, and G. Marowsky, IEEE J. Quantum Electron. 19, 1149 (1983).
    [CrossRef]
  5. D. D. Lowenthal and J. M. Eggleston, IEEE J. Quantum Electron. 22, 1165 (1986).
    [CrossRef]
  6. R. H. Lehmberg and J. L. Giuliani, J. Appl. Phys. 94, 31 (2003).
    [CrossRef]
  7. E. C. Harvey, C. J. Hooker, M. H. Key, A. K. Kidd, J. M. D. Lister, M. J. Shaw, and W. T. Leland, J. Appl. Phys. 70, 5238 (1991).
    [CrossRef]
  8. A. Sasaki, K. I. Ueda, H. Takuma, and K. Kasuya, J. Appl. Phys. 65, 231 (1989).
    [CrossRef]
  9. S. Sarikhani and A. Hariri, Opt. Commun. 283, 118 (2010).
    [CrossRef]
  10. A. Hariri and S. Sarikhani, Opt. Commun. 284, 2153 (2011).
    [CrossRef]
  11. G. Kühnle, U. Teubner, and S. Szatmári, Appl. Phys. B 51, 71 (1990).
    [CrossRef]
  12. A. Hariri, Optical Amplifiers, G. Nemova, ed. (Nova, 2011), Chap. 7.
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    [CrossRef]
  15. J. E. Andrew and P. E. Dyer, Opt. Commun. 54, 117 (1985).
    [CrossRef]
  16. J. K. Rice, G. C. Tisone, and E. L. Patterson, IEEE J. Quantum Electron. 16, 1315 (1980).
    [CrossRef]
  17. J. Banic, T. Efthimiopoulos, and B. P. Stoicheff, Appl. Phys. Lett. 37, 686 (1980).
    [CrossRef]
  18. S. Watanabe, S. Shiratori, T. Sato, and H. Kashiwagi, Appl. Phys. Lett. 33, 141 (1978).
    [CrossRef]
  19. S. Watanabe, T. Sato, and H. Kashiwagi, Opt. Commun. 22, 143 (1977).
    [CrossRef]
  20. G. J. Hirst and M. J. Shaw, Appl. Phys. B 52, 331 (1991).
    [CrossRef]
  21. A. M. Hawryluk, J. A. Mangano, and J. H. Jacob, Appl. Phys. Lett. 31, 164 (1977).
    [CrossRef]

2011 (1)

A. Hariri and S. Sarikhani, Opt. Commun. 284, 2153 (2011).
[CrossRef]

2010 (1)

S. Sarikhani and A. Hariri, Opt. Commun. 283, 118 (2010).
[CrossRef]

2008 (1)

A. Hariri, M. Jaberi, and S. Ghoreyshi, Opt. Commun. 281, 3841 (2008).
[CrossRef]

2003 (1)

R. H. Lehmberg and J. L. Giuliani, J. Appl. Phys. 94, 31 (2003).
[CrossRef]

1991 (2)

E. C. Harvey, C. J. Hooker, M. H. Key, A. K. Kidd, J. M. D. Lister, M. J. Shaw, and W. T. Leland, J. Appl. Phys. 70, 5238 (1991).
[CrossRef]

G. J. Hirst and M. J. Shaw, Appl. Phys. B 52, 331 (1991).
[CrossRef]

1990 (1)

G. Kühnle, U. Teubner, and S. Szatmári, Appl. Phys. B 51, 71 (1990).
[CrossRef]

1989 (1)

A. Sasaki, K. I. Ueda, H. Takuma, and K. Kasuya, J. Appl. Phys. 65, 231 (1989).
[CrossRef]

1986 (1)

D. D. Lowenthal and J. M. Eggleston, IEEE J. Quantum Electron. 22, 1165 (1986).
[CrossRef]

1985 (1)

J. E. Andrew and P. E. Dyer, Opt. Commun. 54, 117 (1985).
[CrossRef]

1983 (1)

G. Haag, M. Munz, and G. Marowsky, IEEE J. Quantum Electron. 19, 1149 (1983).
[CrossRef]

1981 (1)

A. M. Hunter and R. O. Hunter, IEEE J. Quantum Electron. 17, 1879 (1981).
[CrossRef]

1980 (2)

J. K. Rice, G. C. Tisone, and E. L. Patterson, IEEE J. Quantum Electron. 16, 1315 (1980).
[CrossRef]

J. Banic, T. Efthimiopoulos, and B. P. Stoicheff, Appl. Phys. Lett. 37, 686 (1980).
[CrossRef]

1979 (1)

S. Watanabe, T. Sato, and H. Kashiwagi, IEEE J. Quantum Electron. 15, 322 (1979).
[CrossRef]

1978 (1)

S. Watanabe, S. Shiratori, T. Sato, and H. Kashiwagi, Appl. Phys. Lett. 33, 141 (1978).
[CrossRef]

1977 (2)

S. Watanabe, T. Sato, and H. Kashiwagi, Opt. Commun. 22, 143 (1977).
[CrossRef]

A. M. Hawryluk, J. A. Mangano, and J. H. Jacob, Appl. Phys. Lett. 31, 164 (1977).
[CrossRef]

1965 (1)

D. A. Leonard, Appl. Phys. Lett. 7, 4 (1965).
[CrossRef]

Andrew, J. E.

J. E. Andrew and P. E. Dyer, Opt. Commun. 54, 117 (1985).
[CrossRef]

Banic, J.

J. Banic, T. Efthimiopoulos, and B. P. Stoicheff, Appl. Phys. Lett. 37, 686 (1980).
[CrossRef]

Dyer, P. E.

J. E. Andrew and P. E. Dyer, Opt. Commun. 54, 117 (1985).
[CrossRef]

Efthimiopoulos, T.

J. Banic, T. Efthimiopoulos, and B. P. Stoicheff, Appl. Phys. Lett. 37, 686 (1980).
[CrossRef]

Eggleston, J. M.

D. D. Lowenthal and J. M. Eggleston, IEEE J. Quantum Electron. 22, 1165 (1986).
[CrossRef]

Ghoreyshi, S.

A. Hariri, M. Jaberi, and S. Ghoreyshi, Opt. Commun. 281, 3841 (2008).
[CrossRef]

Giuliani, J. L.

R. H. Lehmberg and J. L. Giuliani, J. Appl. Phys. 94, 31 (2003).
[CrossRef]

Haag, G.

G. Haag, M. Munz, and G. Marowsky, IEEE J. Quantum Electron. 19, 1149 (1983).
[CrossRef]

Hariri, A.

A. Hariri and S. Sarikhani, Opt. Commun. 284, 2153 (2011).
[CrossRef]

S. Sarikhani and A. Hariri, Opt. Commun. 283, 118 (2010).
[CrossRef]

A. Hariri, M. Jaberi, and S. Ghoreyshi, Opt. Commun. 281, 3841 (2008).
[CrossRef]

A. Hariri, Optical Amplifiers, G. Nemova, ed. (Nova, 2011), Chap. 7.

Harvey, E. C.

E. C. Harvey, C. J. Hooker, M. H. Key, A. K. Kidd, J. M. D. Lister, M. J. Shaw, and W. T. Leland, J. Appl. Phys. 70, 5238 (1991).
[CrossRef]

Hawryluk, A. M.

A. M. Hawryluk, J. A. Mangano, and J. H. Jacob, Appl. Phys. Lett. 31, 164 (1977).
[CrossRef]

Hirst, G. J.

G. J. Hirst and M. J. Shaw, Appl. Phys. B 52, 331 (1991).
[CrossRef]

Hooker, C. J.

E. C. Harvey, C. J. Hooker, M. H. Key, A. K. Kidd, J. M. D. Lister, M. J. Shaw, and W. T. Leland, J. Appl. Phys. 70, 5238 (1991).
[CrossRef]

Hunter, A. M.

A. M. Hunter and R. O. Hunter, IEEE J. Quantum Electron. 17, 1879 (1981).
[CrossRef]

Hunter, R. O.

A. M. Hunter and R. O. Hunter, IEEE J. Quantum Electron. 17, 1879 (1981).
[CrossRef]

Jaberi, M.

A. Hariri, M. Jaberi, and S. Ghoreyshi, Opt. Commun. 281, 3841 (2008).
[CrossRef]

Jacob, J. H.

A. M. Hawryluk, J. A. Mangano, and J. H. Jacob, Appl. Phys. Lett. 31, 164 (1977).
[CrossRef]

Kashiwagi, H.

S. Watanabe, T. Sato, and H. Kashiwagi, IEEE J. Quantum Electron. 15, 322 (1979).
[CrossRef]

S. Watanabe, S. Shiratori, T. Sato, and H. Kashiwagi, Appl. Phys. Lett. 33, 141 (1978).
[CrossRef]

S. Watanabe, T. Sato, and H. Kashiwagi, Opt. Commun. 22, 143 (1977).
[CrossRef]

Kasuya, K.

A. Sasaki, K. I. Ueda, H. Takuma, and K. Kasuya, J. Appl. Phys. 65, 231 (1989).
[CrossRef]

Key, M. H.

E. C. Harvey, C. J. Hooker, M. H. Key, A. K. Kidd, J. M. D. Lister, M. J. Shaw, and W. T. Leland, J. Appl. Phys. 70, 5238 (1991).
[CrossRef]

Kidd, A. K.

E. C. Harvey, C. J. Hooker, M. H. Key, A. K. Kidd, J. M. D. Lister, M. J. Shaw, and W. T. Leland, J. Appl. Phys. 70, 5238 (1991).
[CrossRef]

Kühnle, G.

G. Kühnle, U. Teubner, and S. Szatmári, Appl. Phys. B 51, 71 (1990).
[CrossRef]

Lehmberg, R. H.

R. H. Lehmberg and J. L. Giuliani, J. Appl. Phys. 94, 31 (2003).
[CrossRef]

Leland, W. T.

E. C. Harvey, C. J. Hooker, M. H. Key, A. K. Kidd, J. M. D. Lister, M. J. Shaw, and W. T. Leland, J. Appl. Phys. 70, 5238 (1991).
[CrossRef]

Leonard, D. A.

D. A. Leonard, Appl. Phys. Lett. 7, 4 (1965).
[CrossRef]

Lister, J. M. D.

E. C. Harvey, C. J. Hooker, M. H. Key, A. K. Kidd, J. M. D. Lister, M. J. Shaw, and W. T. Leland, J. Appl. Phys. 70, 5238 (1991).
[CrossRef]

Lowenthal, D. D.

D. D. Lowenthal and J. M. Eggleston, IEEE J. Quantum Electron. 22, 1165 (1986).
[CrossRef]

Mangano, J. A.

A. M. Hawryluk, J. A. Mangano, and J. H. Jacob, Appl. Phys. Lett. 31, 164 (1977).
[CrossRef]

Marowsky, G.

G. Haag, M. Munz, and G. Marowsky, IEEE J. Quantum Electron. 19, 1149 (1983).
[CrossRef]

Munz, M.

G. Haag, M. Munz, and G. Marowsky, IEEE J. Quantum Electron. 19, 1149 (1983).
[CrossRef]

Patterson, E. L.

J. K. Rice, G. C. Tisone, and E. L. Patterson, IEEE J. Quantum Electron. 16, 1315 (1980).
[CrossRef]

Rice, J. K.

J. K. Rice, G. C. Tisone, and E. L. Patterson, IEEE J. Quantum Electron. 16, 1315 (1980).
[CrossRef]

Sarikhani, S.

A. Hariri and S. Sarikhani, Opt. Commun. 284, 2153 (2011).
[CrossRef]

S. Sarikhani and A. Hariri, Opt. Commun. 283, 118 (2010).
[CrossRef]

Sasaki, A.

A. Sasaki, K. I. Ueda, H. Takuma, and K. Kasuya, J. Appl. Phys. 65, 231 (1989).
[CrossRef]

Sato, T.

S. Watanabe, T. Sato, and H. Kashiwagi, IEEE J. Quantum Electron. 15, 322 (1979).
[CrossRef]

S. Watanabe, S. Shiratori, T. Sato, and H. Kashiwagi, Appl. Phys. Lett. 33, 141 (1978).
[CrossRef]

S. Watanabe, T. Sato, and H. Kashiwagi, Opt. Commun. 22, 143 (1977).
[CrossRef]

Shaw, M. J.

G. J. Hirst and M. J. Shaw, Appl. Phys. B 52, 331 (1991).
[CrossRef]

E. C. Harvey, C. J. Hooker, M. H. Key, A. K. Kidd, J. M. D. Lister, M. J. Shaw, and W. T. Leland, J. Appl. Phys. 70, 5238 (1991).
[CrossRef]

Shiratori, S.

S. Watanabe, S. Shiratori, T. Sato, and H. Kashiwagi, Appl. Phys. Lett. 33, 141 (1978).
[CrossRef]

Stoicheff, B. P.

J. Banic, T. Efthimiopoulos, and B. P. Stoicheff, Appl. Phys. Lett. 37, 686 (1980).
[CrossRef]

Svelto, O.

O. Svelto, Principles of Lasers, 5th ed. (Springer, 2010).

Szatmári, S.

G. Kühnle, U. Teubner, and S. Szatmári, Appl. Phys. B 51, 71 (1990).
[CrossRef]

Takuma, H.

A. Sasaki, K. I. Ueda, H. Takuma, and K. Kasuya, J. Appl. Phys. 65, 231 (1989).
[CrossRef]

Teubner, U.

G. Kühnle, U. Teubner, and S. Szatmári, Appl. Phys. B 51, 71 (1990).
[CrossRef]

Tisone, G. C.

J. K. Rice, G. C. Tisone, and E. L. Patterson, IEEE J. Quantum Electron. 16, 1315 (1980).
[CrossRef]

Ueda, K. I.

A. Sasaki, K. I. Ueda, H. Takuma, and K. Kasuya, J. Appl. Phys. 65, 231 (1989).
[CrossRef]

Watanabe, S.

S. Watanabe, T. Sato, and H. Kashiwagi, IEEE J. Quantum Electron. 15, 322 (1979).
[CrossRef]

S. Watanabe, S. Shiratori, T. Sato, and H. Kashiwagi, Appl. Phys. Lett. 33, 141 (1978).
[CrossRef]

S. Watanabe, T. Sato, and H. Kashiwagi, Opt. Commun. 22, 143 (1977).
[CrossRef]

Appl. Phys. B (2)

G. Kühnle, U. Teubner, and S. Szatmári, Appl. Phys. B 51, 71 (1990).
[CrossRef]

G. J. Hirst and M. J. Shaw, Appl. Phys. B 52, 331 (1991).
[CrossRef]

Appl. Phys. Lett. (4)

A. M. Hawryluk, J. A. Mangano, and J. H. Jacob, Appl. Phys. Lett. 31, 164 (1977).
[CrossRef]

J. Banic, T. Efthimiopoulos, and B. P. Stoicheff, Appl. Phys. Lett. 37, 686 (1980).
[CrossRef]

S. Watanabe, S. Shiratori, T. Sato, and H. Kashiwagi, Appl. Phys. Lett. 33, 141 (1978).
[CrossRef]

D. A. Leonard, Appl. Phys. Lett. 7, 4 (1965).
[CrossRef]

IEEE J. Quantum Electron. (5)

S. Watanabe, T. Sato, and H. Kashiwagi, IEEE J. Quantum Electron. 15, 322 (1979).
[CrossRef]

J. K. Rice, G. C. Tisone, and E. L. Patterson, IEEE J. Quantum Electron. 16, 1315 (1980).
[CrossRef]

A. M. Hunter and R. O. Hunter, IEEE J. Quantum Electron. 17, 1879 (1981).
[CrossRef]

G. Haag, M. Munz, and G. Marowsky, IEEE J. Quantum Electron. 19, 1149 (1983).
[CrossRef]

D. D. Lowenthal and J. M. Eggleston, IEEE J. Quantum Electron. 22, 1165 (1986).
[CrossRef]

J. Appl. Phys. (3)

R. H. Lehmberg and J. L. Giuliani, J. Appl. Phys. 94, 31 (2003).
[CrossRef]

E. C. Harvey, C. J. Hooker, M. H. Key, A. K. Kidd, J. M. D. Lister, M. J. Shaw, and W. T. Leland, J. Appl. Phys. 70, 5238 (1991).
[CrossRef]

A. Sasaki, K. I. Ueda, H. Takuma, and K. Kasuya, J. Appl. Phys. 65, 231 (1989).
[CrossRef]

Opt. Commun. (5)

S. Sarikhani and A. Hariri, Opt. Commun. 283, 118 (2010).
[CrossRef]

A. Hariri and S. Sarikhani, Opt. Commun. 284, 2153 (2011).
[CrossRef]

A. Hariri, M. Jaberi, and S. Ghoreyshi, Opt. Commun. 281, 3841 (2008).
[CrossRef]

J. E. Andrew and P. E. Dyer, Opt. Commun. 54, 117 (1985).
[CrossRef]

S. Watanabe, T. Sato, and H. Kashiwagi, Opt. Commun. 22, 143 (1977).
[CrossRef]

Other (2)

O. Svelto, Principles of Lasers, 5th ed. (Springer, 2010).

A. Hariri, Optical Amplifiers, G. Nemova, ed. (Nova, 2011), Chap. 7.

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Figures (2)

Fig. 1.
Fig. 1.

The numerical calculation of the ASE output energy εASE versus KrF excitation length, lAMP. CASE and Cexp refer to cases when g0,KrFASE and g0,KrFexp parameters (according to Table 1) were used. (○) refers to measurements as given in [11]. g0,KrFASE, g0,KrFexp, and g0,KrFASE/g0,KrFexp versus lAMP shown in the inset of the figure. (▴) refers to experimental gain measurements for KrF lasers and appeared in [7,1420].

Fig. 2.
Fig. 2.

Analytical calculation of the ASE output energy. The dotted line shows the case when b=0 in Eq. (8); dashed lines refer to the cases when i=1, 2, 3 … are used in Eq. (8). The solid line corresponds to the case when all terms are used.

Tables (1)

Tables Icon

Table 1. Gain Parameters, m, b, and γLmax, Used for the Numerical and Analytical Calculation

Equations (11)

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

nph(z)z=g0(z)nph(z)+(Ω(z)4π)N2cτsp,
Ω(z)4π=12(1z/z2+d2/4),
g0exact=m+1+γLmaxz+bγLmaxi=1i(i+1)!(bz)i,
g0approx=m+1+γLmaxz.
nph(z)z=g0(nph(z)+(Ω(z)/4π)cσstimτsp).
G0G0(z;m,b,γLmax)=mz+lnz1+γLmaxγLmaxi=1i(i+1)(bz)i+1(i+1)!,
nph(z)=(Ω/4π)cσstimτsp(eG0(z)G0(zth)1)
εASE(z)=(Ω/4π)hνScσstimτspz{(zzth)1+γLmaxem(zzth)exp[γLmaxi=1i(i+1)(bz)i+1(bzth)i+1(i+1)!]1}.
IASE(z,b=0)=(Ω/4π)Isϕ[(z/zth)1+γLmaxem(zzth)1]
εASE(z,b=0)=π2(Ω4π)ΔN(ν)VhνSz[(zzth)1+γLmaxem(zzth)1]
εASE(z,y)=(Ω/4π)hνscσstimτspzy{(zzth)1+γLz,max(yyth)γLy,max×emz(zzth)emy(yyth)exp[γLz,maxi=1i(i+1)(bz)i+1(bzth)i+1(i+1)!γLy,maxi=1i(i+1)(ay)i+1(ayth)i+1(i+1)!]1}

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