Abstract

A four-arm grazing-incidence cavity (GIC) is demonstrated. It ensures stable single-mode operation in a pulsed laser system by interferometrically enhancing mode selection; the corresponding standard GIC operates on five modes. We show that the four-arm GIC gives the best overall performance in terms of mode selectivity and threshold when compared with the standard GIC or with three-arm GIC’s. In addition, an analysis of the interference effect is detailed that allows the four-arm GIC to be optimized for mode selection. Threshold gain and cavity losses are calculated, and the predicted mode spacing and complex reflectance are experimentally verified.

© 1998 Optical Society of America

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References

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  1. I. Shoshan, N. N. Danon, and U. P. Oppenheim, “Narrowband operation of a pulsed dye laser without intracavity beam expansion,” J. Appl. Phys. 48, 4495–4497 (1977).
    [CrossRef]
  2. M. Littman and H. Metcalf, “Spectrally narrow pulsed dye laser without beam expander,” Appl. Opt. 17, 2224–2227 (1978).
    [CrossRef] [PubMed]
  3. M. Littman, “Single-mode pulsed tunable dye laser,” Appl. Opt. 23, 4465–4468 (1984).
    [CrossRef] [PubMed]
  4. K. W. Kangas, D. D. Lowenthal, and C. H. Muller III, “Single-longitudinal-mode, tunable, pulsed Ti:sapphire laser oscillator,” Opt. Lett. 14, 21–23 (1989).
    [CrossRef] [PubMed]
  5. M. G. Littman, “Single-mode operation of a grazing incidence pulsed dye laser,” Opt. Lett. 3, 138–140 (1978).
    [CrossRef] [PubMed]
  6. S. Saikan, “Nitrogen-laser-pumped single-mode dye laser,” Appl. Phys. 17, 41–44 (1978).
    [CrossRef]
  7. S. G. Dinev, I. G. Koprinkov, K. V. Stamenov, and K. A. Stankov, “A-novel double grazing-incidence single-mode dye laser,” Appl. Phys. 22, 287–291 (1980).
    [CrossRef]
  8. N. D. Hung and P. Brechignac, “A single-mode single-grating grazing incidence pulsed dye laser,” Opt. Commun. 54, 151–154 (1985).
    [CrossRef]
  9. J. M. Boon-Engering, L. A. W. Gloster, W. F. van der Veer, I. T. McKinnie, W. Hogervorst, and T. A. King, “Highly efficient single-longitudinal-mode β-BaB2O4 optical parametric oscillator with a new cavity design,” Opt. Lett. 20, 2087–2089 (1995).
    [CrossRef] [PubMed]
  10. Do-Kyeong Ko, Gwon Lim, Sung-Ho Kim, Byung Heon Cha, and Jongmin Lee, “Self-seeding in a dual-cavity-type pulsed Ti:sapphire laser oscillator,” Opt. Lett. 20, 710–712 (1995).
    [CrossRef] [PubMed]
  11. D. J. Binks, L. A. W. Gloster, I. T. McKinnie, and T. A. King, “Frequency locking of a pulsed single longitudinal mode laser in a coupled cavity resonator,” Appl. Opt. 36, 9371–9377 (1997).
    [CrossRef]
  12. D. J. Binks, D. K. Ko, L. A. W. Gloster, and T. A. King, “Pulsed single mode laser oscillation in a new coupled cavity design,” Opt. Commun. 146, 173–176 (1998).
    [CrossRef]
  13. G. Z. Zhang and D. W. Tokaryk, “Lasing threshold reduction in grating tuned-cavities,” Appl. Opt. 36, 5855–5858 (1997).
    [CrossRef] [PubMed]
  14. P. W. Smith, “Stabilized, single-frequency output from a long laser cavity,” IEEE J. Quantum Electron. QE-1, 343–348 (1965).
    [CrossRef]
  15. P. W. Smith, “On the stabilization of a high-power single frequency laser,” IEEE J. Quantum Electron. QE-2, 666–668 (1966).
    [CrossRef]
  16. J. R. Fontana, “Mixed-polarization modes of Michelson-type optical resonators,” IEEE J. Quantum Electron. QE-4, 678–685 (1968).
    [CrossRef]
  17. J. R. Fontana, “Modes in coupled optical resonators with active media,” IEEE Trans. Microwave Theory Tech. MTT-12, 400–405 (1964).
    [CrossRef]
  18. W. W. Rigrod, “Selectivity of open-ended interferometric resonators,” IEEE J. Quantum Electron. QE-6, 9–14 (1970).
    [CrossRef]

1998 (1)

D. J. Binks, D. K. Ko, L. A. W. Gloster, and T. A. King, “Pulsed single mode laser oscillation in a new coupled cavity design,” Opt. Commun. 146, 173–176 (1998).
[CrossRef]

1997 (2)

1995 (2)

1989 (1)

1985 (1)

N. D. Hung and P. Brechignac, “A single-mode single-grating grazing incidence pulsed dye laser,” Opt. Commun. 54, 151–154 (1985).
[CrossRef]

1984 (1)

1980 (1)

S. G. Dinev, I. G. Koprinkov, K. V. Stamenov, and K. A. Stankov, “A-novel double grazing-incidence single-mode dye laser,” Appl. Phys. 22, 287–291 (1980).
[CrossRef]

1978 (3)

1977 (1)

I. Shoshan, N. N. Danon, and U. P. Oppenheim, “Narrowband operation of a pulsed dye laser without intracavity beam expansion,” J. Appl. Phys. 48, 4495–4497 (1977).
[CrossRef]

1970 (1)

W. W. Rigrod, “Selectivity of open-ended interferometric resonators,” IEEE J. Quantum Electron. QE-6, 9–14 (1970).
[CrossRef]

1968 (1)

J. R. Fontana, “Mixed-polarization modes of Michelson-type optical resonators,” IEEE J. Quantum Electron. QE-4, 678–685 (1968).
[CrossRef]

1966 (1)

P. W. Smith, “On the stabilization of a high-power single frequency laser,” IEEE J. Quantum Electron. QE-2, 666–668 (1966).
[CrossRef]

1965 (1)

P. W. Smith, “Stabilized, single-frequency output from a long laser cavity,” IEEE J. Quantum Electron. QE-1, 343–348 (1965).
[CrossRef]

1964 (1)

J. R. Fontana, “Modes in coupled optical resonators with active media,” IEEE Trans. Microwave Theory Tech. MTT-12, 400–405 (1964).
[CrossRef]

Binks, D. J.

D. J. Binks, D. K. Ko, L. A. W. Gloster, and T. A. King, “Pulsed single mode laser oscillation in a new coupled cavity design,” Opt. Commun. 146, 173–176 (1998).
[CrossRef]

D. J. Binks, L. A. W. Gloster, I. T. McKinnie, and T. A. King, “Frequency locking of a pulsed single longitudinal mode laser in a coupled cavity resonator,” Appl. Opt. 36, 9371–9377 (1997).
[CrossRef]

Boon-Engering, J. M.

Brechignac, P.

N. D. Hung and P. Brechignac, “A single-mode single-grating grazing incidence pulsed dye laser,” Opt. Commun. 54, 151–154 (1985).
[CrossRef]

Danon, N. N.

I. Shoshan, N. N. Danon, and U. P. Oppenheim, “Narrowband operation of a pulsed dye laser without intracavity beam expansion,” J. Appl. Phys. 48, 4495–4497 (1977).
[CrossRef]

Dinev, S. G.

S. G. Dinev, I. G. Koprinkov, K. V. Stamenov, and K. A. Stankov, “A-novel double grazing-incidence single-mode dye laser,” Appl. Phys. 22, 287–291 (1980).
[CrossRef]

Fontana, J. R.

J. R. Fontana, “Mixed-polarization modes of Michelson-type optical resonators,” IEEE J. Quantum Electron. QE-4, 678–685 (1968).
[CrossRef]

J. R. Fontana, “Modes in coupled optical resonators with active media,” IEEE Trans. Microwave Theory Tech. MTT-12, 400–405 (1964).
[CrossRef]

Gloster, L. A. W.

Heon Cha, Byung

Hogervorst, W.

Hung, N. D.

N. D. Hung and P. Brechignac, “A single-mode single-grating grazing incidence pulsed dye laser,” Opt. Commun. 54, 151–154 (1985).
[CrossRef]

Kangas, K. W.

Kim, Sung-Ho

King, T. A.

Ko, D. K.

D. J. Binks, D. K. Ko, L. A. W. Gloster, and T. A. King, “Pulsed single mode laser oscillation in a new coupled cavity design,” Opt. Commun. 146, 173–176 (1998).
[CrossRef]

Ko, Do-Kyeong

Koprinkov, I. G.

S. G. Dinev, I. G. Koprinkov, K. V. Stamenov, and K. A. Stankov, “A-novel double grazing-incidence single-mode dye laser,” Appl. Phys. 22, 287–291 (1980).
[CrossRef]

Lee, Jongmin

Lim, Gwon

Littman, M.

Littman, M. G.

Lowenthal, D. D.

McKinnie, I. T.

Metcalf, H.

Muller III, C. H.

Oppenheim, U. P.

I. Shoshan, N. N. Danon, and U. P. Oppenheim, “Narrowband operation of a pulsed dye laser without intracavity beam expansion,” J. Appl. Phys. 48, 4495–4497 (1977).
[CrossRef]

Rigrod, W. W.

W. W. Rigrod, “Selectivity of open-ended interferometric resonators,” IEEE J. Quantum Electron. QE-6, 9–14 (1970).
[CrossRef]

Saikan, S.

S. Saikan, “Nitrogen-laser-pumped single-mode dye laser,” Appl. Phys. 17, 41–44 (1978).
[CrossRef]

Shoshan, I.

I. Shoshan, N. N. Danon, and U. P. Oppenheim, “Narrowband operation of a pulsed dye laser without intracavity beam expansion,” J. Appl. Phys. 48, 4495–4497 (1977).
[CrossRef]

Smith, P. W.

P. W. Smith, “On the stabilization of a high-power single frequency laser,” IEEE J. Quantum Electron. QE-2, 666–668 (1966).
[CrossRef]

P. W. Smith, “Stabilized, single-frequency output from a long laser cavity,” IEEE J. Quantum Electron. QE-1, 343–348 (1965).
[CrossRef]

Stamenov, K. V.

S. G. Dinev, I. G. Koprinkov, K. V. Stamenov, and K. A. Stankov, “A-novel double grazing-incidence single-mode dye laser,” Appl. Phys. 22, 287–291 (1980).
[CrossRef]

Stankov, K. A.

S. G. Dinev, I. G. Koprinkov, K. V. Stamenov, and K. A. Stankov, “A-novel double grazing-incidence single-mode dye laser,” Appl. Phys. 22, 287–291 (1980).
[CrossRef]

Tokaryk, D. W.

van der Veer, W. F.

Zhang, G. Z.

Appl. Opt. (4)

Appl. Phys. (2)

S. Saikan, “Nitrogen-laser-pumped single-mode dye laser,” Appl. Phys. 17, 41–44 (1978).
[CrossRef]

S. G. Dinev, I. G. Koprinkov, K. V. Stamenov, and K. A. Stankov, “A-novel double grazing-incidence single-mode dye laser,” Appl. Phys. 22, 287–291 (1980).
[CrossRef]

IEEE J. Quantum Electron. (4)

P. W. Smith, “Stabilized, single-frequency output from a long laser cavity,” IEEE J. Quantum Electron. QE-1, 343–348 (1965).
[CrossRef]

P. W. Smith, “On the stabilization of a high-power single frequency laser,” IEEE J. Quantum Electron. QE-2, 666–668 (1966).
[CrossRef]

J. R. Fontana, “Mixed-polarization modes of Michelson-type optical resonators,” IEEE J. Quantum Electron. QE-4, 678–685 (1968).
[CrossRef]

W. W. Rigrod, “Selectivity of open-ended interferometric resonators,” IEEE J. Quantum Electron. QE-6, 9–14 (1970).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. R. Fontana, “Modes in coupled optical resonators with active media,” IEEE Trans. Microwave Theory Tech. MTT-12, 400–405 (1964).
[CrossRef]

J. Appl. Phys. (1)

I. Shoshan, N. N. Danon, and U. P. Oppenheim, “Narrowband operation of a pulsed dye laser without intracavity beam expansion,” J. Appl. Phys. 48, 4495–4497 (1977).
[CrossRef]

Opt. Commun. (2)

N. D. Hung and P. Brechignac, “A single-mode single-grating grazing incidence pulsed dye laser,” Opt. Commun. 54, 151–154 (1985).
[CrossRef]

D. J. Binks, D. K. Ko, L. A. W. Gloster, and T. A. King, “Pulsed single mode laser oscillation in a new coupled cavity design,” Opt. Commun. 146, 173–176 (1998).
[CrossRef]

Opt. Lett. (4)

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Figures (10)

Fig. 1
Fig. 1

(a) Standard GIC, (b) Michelson GIC, (c) Fox–Smith GIC, (d) four-arm GIC.

Fig. 2
Fig. 2

General four-arm interferometer resonator including the initial field and the field after one round trip.

Fig. 3
Fig. 3

Real and imaginary components of threshold gain for the four-arm interferometer resonator (calculated with the values listed in Table 1).

Fig. 4
Fig. 4

Fractional interferometric loss for the four-arm interferometer resonator (calculated with the values listed in Table 1). The positions of the potential modes are marked with filled circles.

Fig. 5
Fig. 5

Experimental setup of the four-arm GIC.

Fig. 6
Fig. 6

Étalon transmissions showing the mode structure of pulses from (a) the standard GIC, (b) the Michelson GIC, (c) the Fox–Smith GIC, and (d) the four-arm GIC. Each cavity was operated at 1.2 times threshold. The threshold of the standard GIC and the Fox–Smith GIC was 18.5±0.5 mJ/pulse, and for the Michelson and four-arm GIC’s it was 14.5±0.5 mJ/pulse.

Fig. 7
Fig. 7

Étalon transmission showing dual-mode operation of the four-arm GIC.

Fig. 8
Fig. 8

Experimental setup for verifying the predicted complex reflectance profiles: M’s, mirrors; BS’s, beam splitters; PD, photodiode; SG, signal generator; SM’s, steering mirrors; Amp., amplifier.

Fig. 9
Fig. 9

Comparison of the theoretical reflectance profile of the complex output coupler formed by the beam splitter and mirrors M2M4 (calculated with the values listed in Table 2) and the experimental normalized intensity of the reflected light.

Fig. 10
Fig. 10

(a) Zero- and first-order diffraction from a grating of field, E. (b) Time reversal of (a). (c) Zero- and first-order diffraction from a grating of two fields, Er and Et (r and t are the zeroth- and first-order diffraction coefficients at large angle, respectively; r and t are the zeroth- and first-order diffraction coefficients at small angle, respectively).

Tables (2)

Tables Icon

Table 1 Cavity Parameters for the Four-Arm GIC

Tables Icon

Table 2 Cavity Parameters for the Complex Output Coupler

Equations (39)

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fj=rj exp(i2kLj),j=1, 2, 3, 4;
k=2πηλ,
rBS2+tBStBS=1,
rBS=-rBS.
α1=rBSf2rBSf1,
α2=tBSf4tBSf1.
β1=rBSf2tBSf3,
β2=tBSf4rBSf3.
γ1=tBSf2rBSf1g,
γ2=rBSf4tBSf1g.
δ1=tBSf2tBSf3,
δ2=rBSf4rBSf3.
nCp=n!p!(n-p)!.
nCpδ1pδ2n-p.
En=E0p=0nnCpδ1pδ2n-p.
Esub=E0n=0p=0nnCpδ1pδ2n-p.
Esub=E0n=0(δ1+δ2)n.
Esub=E01-(δ1+δ2).
Esub=E0[1-(δ1+δ2)n+1]1-(δ1+δ2).
=|(δ1+δ2)n+1| =(tBStBSr2r3+rBS2r3r4)n+1.
EFS=E01-δ1-δ2 (β1+β2)(γ1+γ2).
Ert=11-δ1-δ2 (β1+β2)(γ1+γ2)+α1+α2E0,
ErtE0=gf1[rBS2f2+tBStBSf4-f2f3f4(rBS2+tBStBS)2][1-f3(tBStBSf2+rBS2f4)].
ErtE0=gf1[RBSf2+TBSf4-f2f3f4(RBS+TBS)][1-f3(TBSf2+RBSf4)].
g=[1-f3(TBSf2+RBSf4)]f1[RBSf2+TBSf4-f2f3f4(RBS+TBS)].
(1-L)gg*=1.
rOC=[RBSf2+TBSf4-f2f3f4(RBS+TBS)][1-f3(TBSf2+RBSf4)],
g=1f1(RBSf2+TBSf4),
L=1-r12{r22RBS2+r42TBS2+2r2r4RBSTBS cos[2k(L2-L4)]},
ROC=r22RBS2+r42TBS2+2r2r4RBSTBS cos[2k(L2-L4)].
g=[1-f3f4RBS]TBSf1f4.
ROC=r42TBS21+r32r42R2-2r3r4RBS cos[2k(L3+L4)].
L=1-TBS2r12r42(1-RBSr3r4)2×1+4RBSr3r4(1-RBSr3r4)2 sin2[k(L3+L4)]-1.
RFP=1-TP2(1-RP)2 1+4RP(1-RP)2 sin2(klP)-1.
F=4RBSr3r4(1-RBSr3r4)2,
A(k)={1+F sin2[k(L3+L4)]}-1.
r2+tt=1,
r=-r.
r2+tt=1-A,

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