Abstract

We theoretically investigate new coupling and indirect wave-mixing effects formed in a three-level atomic gain medium that is optically pumped by two mutually coherent beams that propagate in opposite directions. The interference of the pump beams and the saturation effects caused by the signal waves periodically modulate the gain along the amplifier that is due to spatial hole burning. In cases when the interference patterns of the pump and the signal waves are spatially synchronized, the signal gain becomes dependent on the frequencies and the optical phases of the pump and the signal waves. This dependence can be used for obtaining controllable narrow-band filters and for obtaining single-mode operation in lasers.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Abrams and R. Lind, “Degenerate four-wave mixing in absorbing media,” Opt. Lett. 2, 94–96 (1978).
    [CrossRef] [PubMed]
  2. G. J. Dunning and D. G. Steel, “Effects of unequal pump intensity in resonantly enhanced degenerate four wave mixing,” IEEE J. Quantum Electron. 18, 3–5 (1982).
    [CrossRef]
  3. P. J. Soan, A. D. Case, M. J. Damzen, and M. H. R. Hutchinson, “High-reflectivity four-wave mixing by saturable gain in Rhodamine 6G dye,” Opt. Lett. 17, 781–783 (1992).
    [CrossRef] [PubMed]
  4. M. Gruneisen, A. L. Gaeta, and R. W. Boyd, “Exact theory of pump-wave propagation and its effect on degenerate four-wave mixing in saturable-absorber media,” J. Opt. Soc. Am. B 2, 117–1121 (1985).
    [CrossRef]
  5. J. N. Nilsen and A. Yariv, “Non-degenerate four-wave mixing in a homogeneously broadened two level system with saturating pump waves,” IEEE J. Quantum Electron. 18, 1947–1952 (1982).
    [CrossRef]
  6. D. Timotijevic, M. Belic, and R. W. Boyd, “Two and four wave mixing with saturable absorption and gain,” IEEE J. Quantum Electron. 28, 1915–1921 (1992).
    [CrossRef]
  7. B. Fischer, J. L. Zyskind, J. W. Sulhoff, and D. J. DiGiovanni, “Nonlinear four-wave mixing in erbium-doped fibre amplifiers,” Electron. Lett. 29, 1858–1859 (1993); “Nonlinear wave mixing and induced gratings in erbium-doped fiber amplifiers,” Opt. Lett. 18, 2108–2110 (1993).
    [CrossRef] [PubMed]
  8. S. J. Frisken, “Transient Bragg reflection gratings in erbium-doped fiber amplifiers,” Opt. Lett. 17, 1776–1778 (1992).
    [CrossRef] [PubMed]
  9. P. Meystre and M. Sargent, Elements of Quantum Optics (Springer-Verlag, Berlin, 1991), p. 185.
  10. G. P. Agrawal and M. Lax, “Effects of interference on gain saturation in laser resonators,” J. Opt. Soc. Am. 69, 1717–1719 (1979); “Analytic evaluation of interference effects on laser output in a Fabry–Perot resonator,” J. Opt. Soc. Am. 71, 515–519 (1980).
    [CrossRef]
  11. M. Horowitz, R. Daisy, B. Fischer, and J. Zyskind, “Linewidth-narrowing mechanism in lasers by nonlinear wave mixing,” Opt. Lett. 19, 1404–1406 (1994); “Narrow linewidth, single mode erbium-doped fiber laser with intracavity wave-mixing in saturable absorber,” Electron. Lett. 30, 648–649 (1994).
    [CrossRef]
  12. M. Horowitz, R. Daisy, and B. Fischer, “Single-mode ring laser self-induced three-mirror cavity formed by intracavity wave mixing in a saturable absorber,” Opt. Lett. 21, 299–301 (1995).
    [CrossRef]
  13. Y. Cheng, J. T. Kringebotn, W. H. Loh, R. I. Lamming, and D. N. Payne, “Stable single-frequency traveling-wave fiber loop laser with an integral saturable-absorber-based tracking narrow-band filter,” Opt. Lett. 20, 875–877 (1995).
    [CrossRef] [PubMed]
  14. R. Paschota, J. Nilsson, L. Reekie, A. C. Trooper, and D. C. Hanna, “Single-frequency ytterbium-doped fiber laser stabilized by spatial hole burning,” Opt. Lett. 22, 40–42 (1997).
    [CrossRef]
  15. Y. Mitnick, M. Horowitz, and B. Fischer, “Bistability in cavities with erbium-doped fiber amplifier due to bidirectional pump-beam interference,” J. Opt. Soc. Am. B, 2079–2082 (1997).
    [CrossRef]
  16. C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991).
    [CrossRef]
  17. E. Desurvire, “Study of the complex atomic susceptibility of erbium-doped fiber amplifiers,” J. Lightwave Technol. 8, 1517–1527 (1990).
    [CrossRef]
  18. W. J. Miniscalo, “Erbium-doped glasses for fiber amplifiers at 1500 nm,” J. Lightwave Technol. 9, 234–249 (1991).
    [CrossRef]

1997 (1)

1995 (2)

1992 (3)

1991 (2)

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991).
[CrossRef]

W. J. Miniscalo, “Erbium-doped glasses for fiber amplifiers at 1500 nm,” J. Lightwave Technol. 9, 234–249 (1991).
[CrossRef]

1990 (1)

E. Desurvire, “Study of the complex atomic susceptibility of erbium-doped fiber amplifiers,” J. Lightwave Technol. 8, 1517–1527 (1990).
[CrossRef]

1985 (1)

M. Gruneisen, A. L. Gaeta, and R. W. Boyd, “Exact theory of pump-wave propagation and its effect on degenerate four-wave mixing in saturable-absorber media,” J. Opt. Soc. Am. B 2, 117–1121 (1985).
[CrossRef]

1982 (2)

J. N. Nilsen and A. Yariv, “Non-degenerate four-wave mixing in a homogeneously broadened two level system with saturating pump waves,” IEEE J. Quantum Electron. 18, 1947–1952 (1982).
[CrossRef]

G. J. Dunning and D. G. Steel, “Effects of unequal pump intensity in resonantly enhanced degenerate four wave mixing,” IEEE J. Quantum Electron. 18, 3–5 (1982).
[CrossRef]

1978 (1)

Abrams, R.

Belic, M.

D. Timotijevic, M. Belic, and R. W. Boyd, “Two and four wave mixing with saturable absorption and gain,” IEEE J. Quantum Electron. 28, 1915–1921 (1992).
[CrossRef]

Boyd, R. W.

D. Timotijevic, M. Belic, and R. W. Boyd, “Two and four wave mixing with saturable absorption and gain,” IEEE J. Quantum Electron. 28, 1915–1921 (1992).
[CrossRef]

M. Gruneisen, A. L. Gaeta, and R. W. Boyd, “Exact theory of pump-wave propagation and its effect on degenerate four-wave mixing in saturable-absorber media,” J. Opt. Soc. Am. B 2, 117–1121 (1985).
[CrossRef]

Case, A. D.

Cheng, Y.

Daisy, R.

Damzen, M. J.

Desurvire, E.

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991).
[CrossRef]

E. Desurvire, “Study of the complex atomic susceptibility of erbium-doped fiber amplifiers,” J. Lightwave Technol. 8, 1517–1527 (1990).
[CrossRef]

Dunning, G. J.

G. J. Dunning and D. G. Steel, “Effects of unequal pump intensity in resonantly enhanced degenerate four wave mixing,” IEEE J. Quantum Electron. 18, 3–5 (1982).
[CrossRef]

Fischer, B.

Frisken, S. J.

Gaeta, A. L.

M. Gruneisen, A. L. Gaeta, and R. W. Boyd, “Exact theory of pump-wave propagation and its effect on degenerate four-wave mixing in saturable-absorber media,” J. Opt. Soc. Am. B 2, 117–1121 (1985).
[CrossRef]

Giles, C. R.

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991).
[CrossRef]

Gruneisen, M.

M. Gruneisen, A. L. Gaeta, and R. W. Boyd, “Exact theory of pump-wave propagation and its effect on degenerate four-wave mixing in saturable-absorber media,” J. Opt. Soc. Am. B 2, 117–1121 (1985).
[CrossRef]

Hanna, D. C.

Horowitz, M.

Hutchinson, M. H. R.

Kringebotn, J. T.

Lamming, R. I.

Lind, R.

Loh, W. H.

Miniscalo, W. J.

W. J. Miniscalo, “Erbium-doped glasses for fiber amplifiers at 1500 nm,” J. Lightwave Technol. 9, 234–249 (1991).
[CrossRef]

Nilsen, J. N.

J. N. Nilsen and A. Yariv, “Non-degenerate four-wave mixing in a homogeneously broadened two level system with saturating pump waves,” IEEE J. Quantum Electron. 18, 1947–1952 (1982).
[CrossRef]

Nilsson, J.

Paschota, R.

Payne, D. N.

Reekie, L.

Soan, P. J.

Steel, D. G.

G. J. Dunning and D. G. Steel, “Effects of unequal pump intensity in resonantly enhanced degenerate four wave mixing,” IEEE J. Quantum Electron. 18, 3–5 (1982).
[CrossRef]

Timotijevic, D.

D. Timotijevic, M. Belic, and R. W. Boyd, “Two and four wave mixing with saturable absorption and gain,” IEEE J. Quantum Electron. 28, 1915–1921 (1992).
[CrossRef]

Trooper, A. C.

Yariv, A.

J. N. Nilsen and A. Yariv, “Non-degenerate four-wave mixing in a homogeneously broadened two level system with saturating pump waves,” IEEE J. Quantum Electron. 18, 1947–1952 (1982).
[CrossRef]

IEEE J. Quantum Electron. (3)

G. J. Dunning and D. G. Steel, “Effects of unequal pump intensity in resonantly enhanced degenerate four wave mixing,” IEEE J. Quantum Electron. 18, 3–5 (1982).
[CrossRef]

J. N. Nilsen and A. Yariv, “Non-degenerate four-wave mixing in a homogeneously broadened two level system with saturating pump waves,” IEEE J. Quantum Electron. 18, 1947–1952 (1982).
[CrossRef]

D. Timotijevic, M. Belic, and R. W. Boyd, “Two and four wave mixing with saturable absorption and gain,” IEEE J. Quantum Electron. 28, 1915–1921 (1992).
[CrossRef]

J. Lightwave Technol. (3)

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991).
[CrossRef]

E. Desurvire, “Study of the complex atomic susceptibility of erbium-doped fiber amplifiers,” J. Lightwave Technol. 8, 1517–1527 (1990).
[CrossRef]

W. J. Miniscalo, “Erbium-doped glasses for fiber amplifiers at 1500 nm,” J. Lightwave Technol. 9, 234–249 (1991).
[CrossRef]

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

M. Gruneisen, A. L. Gaeta, and R. W. Boyd, “Exact theory of pump-wave propagation and its effect on degenerate four-wave mixing in saturable-absorber media,” J. Opt. Soc. Am. B 2, 117–1121 (1985).
[CrossRef]

Opt. Lett. (6)

Other (5)

Y. Mitnick, M. Horowitz, and B. Fischer, “Bistability in cavities with erbium-doped fiber amplifier due to bidirectional pump-beam interference,” J. Opt. Soc. Am. B, 2079–2082 (1997).
[CrossRef]

B. Fischer, J. L. Zyskind, J. W. Sulhoff, and D. J. DiGiovanni, “Nonlinear four-wave mixing in erbium-doped fibre amplifiers,” Electron. Lett. 29, 1858–1859 (1993); “Nonlinear wave mixing and induced gratings in erbium-doped fiber amplifiers,” Opt. Lett. 18, 2108–2110 (1993).
[CrossRef] [PubMed]

P. Meystre and M. Sargent, Elements of Quantum Optics (Springer-Verlag, Berlin, 1991), p. 185.

G. P. Agrawal and M. Lax, “Effects of interference on gain saturation in laser resonators,” J. Opt. Soc. Am. 69, 1717–1719 (1979); “Analytic evaluation of interference effects on laser output in a Fabry–Perot resonator,” J. Opt. Soc. Am. 71, 515–519 (1980).
[CrossRef]

M. Horowitz, R. Daisy, B. Fischer, and J. Zyskind, “Linewidth-narrowing mechanism in lasers by nonlinear wave mixing,” Opt. Lett. 19, 1404–1406 (1994); “Narrow linewidth, single mode erbium-doped fiber laser with intracavity wave-mixing in saturable absorber,” Electron. Lett. 30, 648–649 (1994).
[CrossRef]

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 (7)

Fig. 1
Fig. 1

Schematic description of the three-level atomic system. The laser is pumped from a ground laser (level 1) to level 3. Optical amplification is obtained as a result of the transition from level 2 to level 1.

Fig. 2
Fig. 2

Wave intensities and spatial gain profiles along the amplifier with λs=2λp, where the maxima of the signal interference pattern coincide with minima of the pumping intensity. Ip and Is show the spatial distribution of the pump and the signal interference pattern; gun is the gain for the undepleted case in which the signal intensity is much smaller than the saturation intensity (Is=0.01), and g is the gain for a signal with a high intensity (Ist=10). Ipt=1.2, Ntσas=1, ηs=1.18.

Fig. 3
Fig. 3

Dependence of the average gain coefficient (gdc), the first Fourier coefficient (g1), and the total gain (gt=gdc+g1) for the cases shown in Fig. 2 (solid curves) and in Fig. 4 (dashed curves). For comparison the total gain dependence for the incoherent case in which the signal waves do not interfere is added (dashed–dotted curve). The intensities of the counterpropagating signals are assumed to be equal. Ntσas=1, ηs=1.18, Ipt=1.7.

Fig. 4
Fig. 4

Wave-mixing effect in a periodically pumped amplifier for λs=2λp, where the maxima of the signal interference pattern coincide with the maxima of the pumping intensity. Ip and Is show the spatial profile of the pump and the signal interference pattern; gun is the gain for the undepleted case in which the signal intensity is much smaller than the saturation intensity (Is=0.01), and g is the gain for a signal with high intensity (Ist=10). Ipt=1.2, Ntσas=1, ηs=1.18.

Fig. 5
Fig. 5

Schematic description of a nonlinear filter. l is the length of the amplifier (Am), M is an ideal mirror with reflectivity R=1, Iin and Iout are the intensities of the input and the output signal waves, and I+p and I-p are the intensities of the counterpropagating pump waves. One can adjust the wavelength for which the transmission of the filter is maximum by controlling the frequency and the optical phases of the pump waves.

Fig. 6
Fig. 6

Reflectivity of the filter shown in Fig. 5 versus the detuning between the signal and the pump [Δkl(2ks-kp)l]. Iin=0.6, Ntσasl=4.6, R=1, I+p=I-p=0.85, ηs=1.18.

Fig. 7
Fig. 7

Reflectivity of the filter shown in Fig. 5 versus the normalized signal intensity for the case when the two counterpropagating signals are mutually coherent and can interfere (uppermost curve) and for the case when the signal waves are mutually incoherent. Ntσasl=4.6, R=1, I+p=I-p=0.85, ηs=1.18.

Equations (7)

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

g=Ntσas ηsIp-11+Ip+Is,
a=Ntσap 1+Isηs/(1+ηs)1+Is+Ip,
g=Ntσas ηs(Ipt+cpUp+cp*Up-1)-11+Ipt+cpUp+cp*Up-1+Ist+csUs+cs*Us-1,
dA+s/dz=Ntσas(gdcA+s+g-1A-s),
dA-s/dz=-Ntσas(gdcA-s+g1A+s),
dA+p/dz=Ntσap(adcA+p+a-1A-p),
dA-p/dz=-Ntσap[adcA-p+a1A+p).

Metrics