Abstract

The modes of a laser cavity with a tilted corner cube reflector are simulated by the imaging method; the separate effects for both rotations of the corner cube and the mirror of the cavity are then studied.

© 1984 Optical Society of America

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References

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  1. G. Zhou, A. J. Alfey, L. W. Casperson, Appl. Opt. 21, 1670 (1982).
    [CrossRef] [PubMed]
  2. For example, H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
    [CrossRef]
  3. D. C. Hanna, IEEE J. Quantum Electron. QE-5, 483 (1969).
    [CrossRef]
  4. G. D. Boyd, J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).
  5. C. Flammer, Spheroidal Wave Functions (Stanford U. P., Palo Alto, Calif., 1957).
  6. E. R. Peck, J. Opt. Soc. Am. 52, 253 (1962).
    [CrossRef]
  7. R. Hauck, H. P. Kortz, H. Weber, Appl. Opt. 19, 598 (1980).
    [CrossRef] [PubMed]

1982 (1)

1980 (1)

1969 (1)

D. C. Hanna, IEEE J. Quantum Electron. QE-5, 483 (1969).
[CrossRef]

1966 (1)

For example, H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

1962 (1)

1961 (1)

G. D. Boyd, J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).

Alfey, A. J.

Boyd, G. D.

G. D. Boyd, J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).

Casperson, L. W.

Flammer, C.

C. Flammer, Spheroidal Wave Functions (Stanford U. P., Palo Alto, Calif., 1957).

Gordon, J. P.

G. D. Boyd, J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).

Hanna, D. C.

D. C. Hanna, IEEE J. Quantum Electron. QE-5, 483 (1969).
[CrossRef]

Hauck, R.

Kogelnik, H.

For example, H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Kortz, H. P.

Li, T.

For example, H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Peck, E. R.

Weber, H.

Zhou, G.

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

G. D. Boyd, J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).

IEEE J. Quantum Electron. (1)

D. C. Hanna, IEEE J. Quantum Electron. QE-5, 483 (1969).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. IEEE (1)

For example, H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Other (1)

C. Flammer, Spheroidal Wave Functions (Stanford U. P., Palo Alto, Calif., 1957).

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of the imaginary mirror M′ for a retroreflecting corner cube mirror resonator.

Fig. 2
Fig. 2

Projected geometry (on the X-Z plane) of an equivalent scheme for a corner cube and spherical mirror ( P 0 P 1 ¯ + μ P i Q ¯ = P 0 P i ¯ + μ P i Q ¯).

Fig. 3
Fig. 3

Resonant cavity with tilted mirror.

Fig. 4
Fig. 4

Curves of small β vs α and with related measurement data.

Fig. 5
Fig. 5

Experimental setup for a Nd:YAG corner cube laser pulse oscillator.

Fig. 6
Fig. 6

Output energy measurement vs rotation angle of the corner cube.

Fig. 7
Fig. 7

Beam astigmatism of the cavity with tilted corner cube retroreflector: (a) without beam expander; (b) with beam expander.

Equations (20)

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f ( X ) = f ( - X ) and g ( Y ) = g ( - Y ) .
γ x γ y f ( X ) g ( Y ) = surface , M i k 2 π ρ exp ( - i k ρ ) f ( X ) g ( Y ) d X d Y = surface , M i k 2 π ρ × exp ( - i k ρ ) f ( - X ) g ( - Y ) d X d Y ,
γ X γ Y f ( X ) g ( Y ) = i exp ( - i k 2 L ) λ 2 L - a a - a a × K ( X , X ) K ( Y , Y ) f ( - X ) g ( - Y ) d X d Y
K ( X , X ) = exp [ - i k 4 L ( - 2 X X + g 0 X 2 + g 0 X 2 ) ] , K ( Y , Y ) = exp [ - i k 4 L ( - 2 Y Y + g 0 Y 2 + g 0 Y 2 ) ] ,
γ X γ Y f ( X ) g ( X ) = i exp [ - i k ( L - L X ) ] exp [ - i k ( L - L Y ) ] [ 2 λ ( L - L X ) ] 1 / 2 [ 2 λ ( L - L Y ) ] 1 / 2 × - a a - a a K X ( X , X ) K Y ( Y , Y ) × f ( - X ) g ( - Y ) d X d Y ,
K X ( X , X ) = exp [ - i k 4 ( L - L X ) ( - 2 X X + g X X 2 + g X X 2 ) ] , K Y ( Y , Y ) = exp [ - i k 4 ( L - L Y ) ( - 2 Y Y + g Y Y 2 + g Y Y 2 ) ] ,
g X = 1 - 2 ( L - L X ) R             g Y = 1 - 2 ( L - L Y ) R ,
L X = l - t μ 2 ( 1 - sin 2 θ ) ( μ 2 - sin 2 θ ) 3 / 2             L Y = l - t ( μ 2 - sin 2 θ ) 1 / 2 ,
l = t ( 1 - sin 2 θ ) 1 / 2 + t sin 2 θ ( μ 2 - sin 2 θ ) 1 / 2 .
f ( X ) = F m ( - C X a X ) = ( - 1 ) m F m ( C X a X ) Γ ( m 2 + 1 ) Γ ( m + 1 ) × ( - 1 ) m H m ( C X a X ) exp ( - C X X 2 2 a 2 ) ,
g ( Y ) = G m ( - C Y a Y ) = ( - 1 ) n G n ( C Y a Y ) Γ ( n 2 + 1 ) Γ ( n + 1 ) × ( - 1 ) n H n ( C Y a Y ) exp ( - C Y Y 2 2 a 2 ) ,
γ X γ Y = σ m σ n exp [ i k ( L X + L Y ) ] = X m X n i exp [ - i k ( 2 L - L X - L Y ) ] ,
X m ( C X ) = 2 C X π i m R 0 m ( 1 ) ( C X , 1 ) ;             X n ( C Y ) = 2 C Y π i n R 0 n ( 1 ) ( C Y , 1 ) , C X = 2 π [ a 2 2 ( L - L X ) λ ] ;             C Y = 2 π [ a 2 2 ( L - L Y ) ] , F m ( C X , X / a ) S o m ( C X , X / a ) ;             G n ( C Y , Y / a ) S o n ( C Y , Y / a ) .
2 π ( q + 1 ) = | π 2 - k ( 2 L - L X - L Y ) + ( m + n ) π 2 | ,
ν ν 0 = ( q + 1 ) + ¼ ( m + n + 1 ) ,
1 ν 0 = 2 L - L X - L Y C = 1 ν 0 - 1 C L X + L Y
α D = 1 - X m X n 2 .
tan β = R sin α R cos α - L ,
L α = L cos β = L ( cos α - L R ) 1 - 2 L R cos α + L 2 R 2 ,
X α = L sin β = L sin α 1 - 2 L R cos α + L 2 R 2 .

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