Abstract

We propose a novel device that exhibits nonreciprocity in optical reflection or transmission. The device is formed by two frequency-doubling crystals and a suitable dichroic mirror or a filter. The nonreciprocity may exceed 100 and be accompanied by nonlinear reflection or transmission. Applications in unidirectional and mode-locked lasers are discussed.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Koechner, Solid-State Laser Engineering, 2nd ed. (Springer-Verlag, Berlin, 1988), pp. 223 and 449.
  2. H.-J. Cirkel, F. P. Schäfer, “Passive non-reciprocal element for travelling wave ring-lasers,” Opt. Commun. 5, 183–186 (1972).
    [CrossRef]
  3. F. W. Kowalski, P. D. Hale, S. J. Shattil, “Broadband continuous laser,” Opt. Lett. 13, 622–624 (1988).
    [CrossRef] [PubMed]
  4. O. E. Nani, A. B. Selunskii, “Acousto-optic interferometric non-reciprocal element,” Sov. J. Quantum Electron. 20, 1006–1008 (1990).
  5. K. A. Stankov, “A mirror with an intensity-dependent reflection coefficient,” Appl. Phys. B 45, 191–195 (1988).
    [CrossRef]
  6. K. A. Stankov, J. Jethwa, “A new mode-locking technique using a nonlinear mirror,” Opt. Commun. 66, 41–46 (1988).
    [CrossRef]
  7. K. A. Stankov, “Mode-locking by a frequency-doubling crystal: generation of transform-limited ultrashort light pulses,” Opt. Lett. 14, 359–361 (1989).
    [CrossRef] [PubMed]
  8. J. R. M. Barr, D. M. Hughes, “Coupled cavity modelocking of a Nd:YAG laser using second-harmonic generation,” Appl. Phys. B 49, 323–325 (1989).
    [CrossRef]
  9. K. A. Stankov, “Negative feedback using a nonlinear mirror for the generation of a long train of short light pulses,” Appl. Phys. B 52, 158–162 (1991).
    [CrossRef]
  10. I. Ch. Buchvarov, S. M. Saltiel, K. A. Stankov, D. Georgiev, “Extremely long train of ultrashort pulses from an actively mode-locked pulsed Nd:YAG laser,” Opt. Commun. 83, 65–70 (1991).
    [CrossRef]
  11. J. A. Armstrong, N. Blombergen, J. Ducuing, P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
  12. V. P. Tzolov, M. G. Mirkov, K. A. Stankov, “Analysis of a frequency-doubling nonlinear mirror with enhanced nonlinearity,” Opt. Commun. 84, 95–98 (1991).
    [CrossRef]

1991 (3)

K. A. Stankov, “Negative feedback using a nonlinear mirror for the generation of a long train of short light pulses,” Appl. Phys. B 52, 158–162 (1991).
[CrossRef]

I. Ch. Buchvarov, S. M. Saltiel, K. A. Stankov, D. Georgiev, “Extremely long train of ultrashort pulses from an actively mode-locked pulsed Nd:YAG laser,” Opt. Commun. 83, 65–70 (1991).
[CrossRef]

V. P. Tzolov, M. G. Mirkov, K. A. Stankov, “Analysis of a frequency-doubling nonlinear mirror with enhanced nonlinearity,” Opt. Commun. 84, 95–98 (1991).
[CrossRef]

1990 (1)

O. E. Nani, A. B. Selunskii, “Acousto-optic interferometric non-reciprocal element,” Sov. J. Quantum Electron. 20, 1006–1008 (1990).

1989 (2)

J. R. M. Barr, D. M. Hughes, “Coupled cavity modelocking of a Nd:YAG laser using second-harmonic generation,” Appl. Phys. B 49, 323–325 (1989).
[CrossRef]

K. A. Stankov, “Mode-locking by a frequency-doubling crystal: generation of transform-limited ultrashort light pulses,” Opt. Lett. 14, 359–361 (1989).
[CrossRef] [PubMed]

1988 (3)

F. W. Kowalski, P. D. Hale, S. J. Shattil, “Broadband continuous laser,” Opt. Lett. 13, 622–624 (1988).
[CrossRef] [PubMed]

K. A. Stankov, “A mirror with an intensity-dependent reflection coefficient,” Appl. Phys. B 45, 191–195 (1988).
[CrossRef]

K. A. Stankov, J. Jethwa, “A new mode-locking technique using a nonlinear mirror,” Opt. Commun. 66, 41–46 (1988).
[CrossRef]

1972 (1)

H.-J. Cirkel, F. P. Schäfer, “Passive non-reciprocal element for travelling wave ring-lasers,” Opt. Commun. 5, 183–186 (1972).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Blombergen, J. Ducuing, P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Blombergen, J. Ducuing, P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Barr, J. R. M.

J. R. M. Barr, D. M. Hughes, “Coupled cavity modelocking of a Nd:YAG laser using second-harmonic generation,” Appl. Phys. B 49, 323–325 (1989).
[CrossRef]

Blombergen, N.

J. A. Armstrong, N. Blombergen, J. Ducuing, P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Buchvarov, I. Ch.

I. Ch. Buchvarov, S. M. Saltiel, K. A. Stankov, D. Georgiev, “Extremely long train of ultrashort pulses from an actively mode-locked pulsed Nd:YAG laser,” Opt. Commun. 83, 65–70 (1991).
[CrossRef]

Cirkel, H.-J.

H.-J. Cirkel, F. P. Schäfer, “Passive non-reciprocal element for travelling wave ring-lasers,” Opt. Commun. 5, 183–186 (1972).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Blombergen, J. Ducuing, P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Georgiev, D.

I. Ch. Buchvarov, S. M. Saltiel, K. A. Stankov, D. Georgiev, “Extremely long train of ultrashort pulses from an actively mode-locked pulsed Nd:YAG laser,” Opt. Commun. 83, 65–70 (1991).
[CrossRef]

Hale, P. D.

Hughes, D. M.

J. R. M. Barr, D. M. Hughes, “Coupled cavity modelocking of a Nd:YAG laser using second-harmonic generation,” Appl. Phys. B 49, 323–325 (1989).
[CrossRef]

Jethwa, J.

K. A. Stankov, J. Jethwa, “A new mode-locking technique using a nonlinear mirror,” Opt. Commun. 66, 41–46 (1988).
[CrossRef]

Koechner, W.

W. Koechner, Solid-State Laser Engineering, 2nd ed. (Springer-Verlag, Berlin, 1988), pp. 223 and 449.

Kowalski, F. W.

Mirkov, M. G.

V. P. Tzolov, M. G. Mirkov, K. A. Stankov, “Analysis of a frequency-doubling nonlinear mirror with enhanced nonlinearity,” Opt. Commun. 84, 95–98 (1991).
[CrossRef]

Nani, O. E.

O. E. Nani, A. B. Selunskii, “Acousto-optic interferometric non-reciprocal element,” Sov. J. Quantum Electron. 20, 1006–1008 (1990).

Pershan, P. S.

J. A. Armstrong, N. Blombergen, J. Ducuing, P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Saltiel, S. M.

I. Ch. Buchvarov, S. M. Saltiel, K. A. Stankov, D. Georgiev, “Extremely long train of ultrashort pulses from an actively mode-locked pulsed Nd:YAG laser,” Opt. Commun. 83, 65–70 (1991).
[CrossRef]

Schäfer, F. P.

H.-J. Cirkel, F. P. Schäfer, “Passive non-reciprocal element for travelling wave ring-lasers,” Opt. Commun. 5, 183–186 (1972).
[CrossRef]

Selunskii, A. B.

O. E. Nani, A. B. Selunskii, “Acousto-optic interferometric non-reciprocal element,” Sov. J. Quantum Electron. 20, 1006–1008 (1990).

Shattil, S. J.

Stankov, K. A.

V. P. Tzolov, M. G. Mirkov, K. A. Stankov, “Analysis of a frequency-doubling nonlinear mirror with enhanced nonlinearity,” Opt. Commun. 84, 95–98 (1991).
[CrossRef]

I. Ch. Buchvarov, S. M. Saltiel, K. A. Stankov, D. Georgiev, “Extremely long train of ultrashort pulses from an actively mode-locked pulsed Nd:YAG laser,” Opt. Commun. 83, 65–70 (1991).
[CrossRef]

K. A. Stankov, “Negative feedback using a nonlinear mirror for the generation of a long train of short light pulses,” Appl. Phys. B 52, 158–162 (1991).
[CrossRef]

K. A. Stankov, “Mode-locking by a frequency-doubling crystal: generation of transform-limited ultrashort light pulses,” Opt. Lett. 14, 359–361 (1989).
[CrossRef] [PubMed]

K. A. Stankov, “A mirror with an intensity-dependent reflection coefficient,” Appl. Phys. B 45, 191–195 (1988).
[CrossRef]

K. A. Stankov, J. Jethwa, “A new mode-locking technique using a nonlinear mirror,” Opt. Commun. 66, 41–46 (1988).
[CrossRef]

Tzolov, V. P.

V. P. Tzolov, M. G. Mirkov, K. A. Stankov, “Analysis of a frequency-doubling nonlinear mirror with enhanced nonlinearity,” Opt. Commun. 84, 95–98 (1991).
[CrossRef]

Appl. Phys. B (3)

J. R. M. Barr, D. M. Hughes, “Coupled cavity modelocking of a Nd:YAG laser using second-harmonic generation,” Appl. Phys. B 49, 323–325 (1989).
[CrossRef]

K. A. Stankov, “Negative feedback using a nonlinear mirror for the generation of a long train of short light pulses,” Appl. Phys. B 52, 158–162 (1991).
[CrossRef]

K. A. Stankov, “A mirror with an intensity-dependent reflection coefficient,” Appl. Phys. B 45, 191–195 (1988).
[CrossRef]

Opt. Commun. (4)

K. A. Stankov, J. Jethwa, “A new mode-locking technique using a nonlinear mirror,” Opt. Commun. 66, 41–46 (1988).
[CrossRef]

V. P. Tzolov, M. G. Mirkov, K. A. Stankov, “Analysis of a frequency-doubling nonlinear mirror with enhanced nonlinearity,” Opt. Commun. 84, 95–98 (1991).
[CrossRef]

I. Ch. Buchvarov, S. M. Saltiel, K. A. Stankov, D. Georgiev, “Extremely long train of ultrashort pulses from an actively mode-locked pulsed Nd:YAG laser,” Opt. Commun. 83, 65–70 (1991).
[CrossRef]

H.-J. Cirkel, F. P. Schäfer, “Passive non-reciprocal element for travelling wave ring-lasers,” Opt. Commun. 5, 183–186 (1972).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

J. A. Armstrong, N. Blombergen, J. Ducuing, P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Sov. J. Quantum Electron. (1)

O. E. Nani, A. B. Selunskii, “Acousto-optic interferometric non-reciprocal element,” Sov. J. Quantum Electron. 20, 1006–1008 (1990).

Other (1)

W. Koechner, Solid-State Laser Engineering, 2nd ed. (Springer-Verlag, Berlin, 1988), pp. 223 and 449.

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 (5)

Fig. 1
Fig. 1

Nonreciprocal optical device (inside the dashed box) incorporated into a ring laser: SHORT-SHG, short second-harmonic crystal; LONG-SHG, long second-harmonic crystal; DM, dichroic mirror; HS, harmonic splitter for extraction of the second harmonic; M, total reflector at the fundamental; GAIN, active medium. The laser generation will circulate clockwise since reflectivity in this direction is higher.

Fig. 2
Fig. 2

Dependence of the nonreciprocity in reflection Rcw/Rccw on the crystal length ratio a for several values of the reflectivity R1: (a) second-harmonic conversion efficiency in the short crystal, η′ = 0.1; (b) η′ = 0.5; (c) η′ = 0.9.

Fig. 3
Fig. 3

Nonreciprocity as a function of the dichroic mirror reflectivity R1 for three values of the conversion efficiency: (a) η′ = 0.1, (b)η′ = 0.5,(c) η′ = 0.9.

Fig. 4
Fig. 4

Variation of the nonreciprocity with the second-harmonic conversion efficiency: (a) R1 = 0.1, (b) R1 = 0.5, (c) R1 = 0.9.

Fig. 5
Fig. 5

Nonreciprocity as a function of the conversion efficiency for the phase condition Δϕ = π/2 + 2mπ (negative feedback mode): (a) R1 = 0.1, (b) R1 = 0.5, (c) R1 = 0.9.

Equations (7)

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

u = sech ( δ + δ 0 ) , v = tanh ( δ + δ 0 ) .
δ = σ ( ρ 1 2 + ρ 2 2 ) 1 / 2 z 1 = arctanh η .
δ = σ ( ρ 1 2 + ρ 2 2 ) 1 / 2 z 2 = a δ ( ρ 1 2 + ρ 2 2 ) 1 / 2 .
R cw = B { 1 - tanh 2 [ a ( B ) 1 / 2 arctanh ( η ) - arctanh ( η / B ) 1 / 2 ] } ,
R ccw = B { 1 - tanh 2 [ ( 1 / a ) ( B ) 1 / 2 arctanh ( n ) 1 / 2 - arctanh ( η / B ) 1 / 2 ] } ,
Δ ϕ = π / 2 ± ( 2 m + 1 ) π ,             m = 0 , 1 , 2 , 3 ,
Δ ϕ = π / 2 ± 2 m π .

Metrics