Abstract

We show that thermally induced birefringence in an electro-optical crystal can play an important role in Q-switched Nd:YAG lasers with a high average power output. A compensation of the thermal effects in both active-element and electro-optical crystals is achieved by employing two identical Pockels cells instead of one, with a π/2 polarization rotator between them in the so-called ring modulator. Experiments that are carried out show that undesirable thermopolarization effects are essentially eliminated by using this new optical configuration. A detailed description in terms of Jones matrices of the properties of the proposed resonator is also included.

© 1993 Optical Society of America

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References

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  1. W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988), Chaps. 7 and 8.
  2. J. Richards, “Birefringence compensation in polarization coupled lasers,” Appl. Opt. 26, 2514–2517 (1987).
    [CrossRef] [PubMed]
  3. G. Michelangeli, E. Penco, G. Giuliani, E. Palange, “Q switching and cavity dumping of high-power Nd:YAG laser by means of a novel electro-optic configuration,” Opt. Lett. 11, 360–362 (1986).
    [CrossRef] [PubMed]
  4. I. P. Khristov, I. V. Tomov, S. M. Saltiel, “Self-heating effects in electro-optic light modulators,” Opt. Quantum Electron. 15, 289–295 (1983).
    [CrossRef]
  5. “Electro-optic properties of KH2PO4 and isomorphs,” information sheet (Cleveland Crystals, Inc., Cleveland, Ohio, 1984).
  6. R. C. Jones, “A new calculus for the treatment of optical systems VII: properties of the N-matrices,” J. Opt. Soc. Am. 38, 671–685 (1948).
    [CrossRef]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1968), Chap. 1.

1987 (1)

1986 (1)

1983 (1)

I. P. Khristov, I. V. Tomov, S. M. Saltiel, “Self-heating effects in electro-optic light modulators,” Opt. Quantum Electron. 15, 289–295 (1983).
[CrossRef]

1948 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1968), Chap. 1.

Giuliani, G.

Jones, R. C.

Khristov, I. P.

I. P. Khristov, I. V. Tomov, S. M. Saltiel, “Self-heating effects in electro-optic light modulators,” Opt. Quantum Electron. 15, 289–295 (1983).
[CrossRef]

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988), Chaps. 7 and 8.

Michelangeli, G.

Palange, E.

Penco, E.

Richards, J.

Saltiel, S. M.

I. P. Khristov, I. V. Tomov, S. M. Saltiel, “Self-heating effects in electro-optic light modulators,” Opt. Quantum Electron. 15, 289–295 (1983).
[CrossRef]

Tomov, I. V.

I. P. Khristov, I. V. Tomov, S. M. Saltiel, “Self-heating effects in electro-optic light modulators,” Opt. Quantum Electron. 15, 289–295 (1983).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1968), Chap. 1.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

I. P. Khristov, I. V. Tomov, S. M. Saltiel, “Self-heating effects in electro-optic light modulators,” Opt. Quantum Electron. 15, 289–295 (1983).
[CrossRef]

Other (3)

“Electro-optic properties of KH2PO4 and isomorphs,” information sheet (Cleveland Crystals, Inc., Cleveland, Ohio, 1984).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1968), Chap. 1.

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988), Chaps. 7 and 8.

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Figures (7)

Fig. 1
Fig. 1

Experiments with a conventional E-O Q-switched Nd:YAG laser: (a) optical scheme; M1, M2, mirrors; PC, Pockels cell; P, polarizer; Y, active element; 1, laser output; 2, 3, depolarized component outputs for the active medium and E-O crystal, respectively; (b) results; 1, total energy per pulse Eout1 from output 1; 2, depolarized pulse energy Eout2 due to the active medium; 3, depolarized pulse energy Eout3 due to the E-O crystal; 4, relative Q-switched pulse energy EQr1 measured by a photodiode as a function of average output power Pout.

Fig. 2
Fig. 2

Orientation of the indicatrix of the thermally stressed E-O crystal.

Fig. 3
Fig. 3

(a) Schematic of the ring modulator: M1–M3, mirrors; PC, Pockels cell; P, polarizer; Y, active element; (b) modified resonator for compensation of the thermal effects in both active element Y and E-O crystals PC1, PC2; R, optical rotator.

Fig. 4
Fig. 4

Dimensions of the resonator for thermal effect compensation employing an intracavity telescope (lenses L1 and L2) for beam divergence control. All dimensions are given in millimeters.

Fig. 5
Fig. 5

Ratio of the depolarization losses to the output pulse energy versus average laser power for the new scheme [Fig. 3(b)] measured in free-running generation: 1, without any PC’s; 2, with one cell, PC1, only; 3, with both cells, PC1 and PC2.

Fig. 6
Fig. 6

Ratio of the depolarization losses to the output pulse energy versus average laser power for the new compensation scheme with beam divergence control by an intracavity telescope (Fig. 4) measured in free-running generation: 1, with one cell, PC1, only; 2, with both cells, PC1 and PC2.

Fig. 7
Fig. 7

Experimental results in Q-switched mode with quarter-wave voltage applied: 1, giant-pulse energy Eout1; 2, relative depolarization losses Eout2/Eout1 versus average output power Pout.

Equations (27)

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g 0 g 0 n 0 n 0 - ln ( R ) - ln ( 0.02 ) 2 ln ( G 0 ) 0.73 ,
T ( r ) = T 0 + P 0 4 K ( r 0 2 - r 2 ) ,
n x = n 0 + ½ C E P 0 r 2 cos 2 θ , n y = n 0 - ½ C E P 0 r 2 cos 2 θ , n z = n e ,
Δ ϕ c = 2 π λ L C E P 0 r 2 cos 2 θ ,
Δ ϕ r = π λ r 63 n 0 3 U ( 3 n 0 T 1 n 0 + r 63 T 1 r 63 ) P 0 2 K ( r 0 2 - r 2 ) .
Δ ϕ r Δ ϕ c + Δ ϕ r 0.12.
ϕ = [ exp ( i Δ ϕ c / 2 ) 0 0 exp ( - i Δ ϕ c / 2 ) ] ,
ϕ ( π / 2 ) = α ( - π / 2 ) ϕ α ( π / 2 ) = ϕ ,
α ( θ ) = [ cos ( θ ) sin ( θ ) - sin ( θ ) cos ( θ ) ] .
δ = [ exp ( i δ / 2 ) 0 0 exp ( - i δ / 2 ) ] ,
δ = 2 π λ n 0 3 r 63 U ,
δ ( π / 2 ) = α ( - π / 2 ) δ α ( π / 2 ) = δ - 1 .
Σ = [ exp [ i ( Δ ϕ c + δ ) / 2 ] 0 0 exp [ - i ( Δ ϕ c + δ ) / 2 ] ] .
J S = P T M α ( - π / 4 ) ϕ R ( ± π / 2 ) ϕ α ( π / 4 ) M P R ,
J P = P R M α ( - π / 4 ) ϕ R ( π / 2 ) ϕ α ( π / 4 ) M P T .
M = [ 1 0 0 - 1 ] .
P R = [ 0 0 0 - R ] .
P T = [ T 0 0 0 ] ,
R ( ± π / 2 ) = ± [ 0 1 - 1 0 ] .
J = J S + J P = ± T R ( [ 0 1 0 0 ] + [ 0 0 1 0 ] ) = ± T R [ 0 1 1 0 ]
Σ R ( ± π / 2 ) ϕ = [ 0 ± exp ( i δ / 2 ) exp ( - i δ / 2 ) 0 ] , ϕ R ( ± π / 2 ) Σ = [ 0 ± exp ( - i δ / 2 ) exp ( i δ / 2 ) 0 ] .
J U = ± cos δ 2 J .
R ( U ) = ( T R ) 2 ( 1 + cos δ ) / 2.
Σ 2 = [ exp [ i ( Δ ϕ c - δ ) / 2 ] 0 0 exp [ - i ( Δ ϕ c - δ ) / 2 ] ] ,
Σ 1 R ( ± π / 2 ) Σ 2 = [ 0 ± exp ( i δ ) exp ( - i δ ) 0 ] , Σ 2 R ( ± π / 2 ) Σ 1 = [ 0 ± exp ( - i δ ) exp ( i δ ) o ] .
J U = ± cos ( δ ) J ,
R ( U ) = ( T R ) 2 ( 1 + cos 2 δ ) / 2.

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