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

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References

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  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)

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]

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]

1988 (3)

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]

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

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.

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]

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]

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)

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

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]

Opt. Commun. (4)

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

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

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.

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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)

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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 .

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