Abstract

A simple result of scalar diffraction theory is used to derive the round trip phase accrual of a plane wave in dye laser oscillators containing gratings. This is used to determine configurations where the standing wave condition is satisfied at the feedback wavelength throughout an angle scan. We find that at least one such exactly synchronous configuration always exists regardless of oscillator type.

© 1985 Optical Society of America

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References

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  1. K. Liu, M. G. Littman, “Novel Geometry for Single-Mode Scanning of Tunable Lasers,” Opt. Lett. 6, 117 (1981).
    [CrossRef] [PubMed]
  2. M. G. Littman, “Single-Mode Pulsed Tunable Dye Laser,” Appl. Opt. 23, 4465 (1984).
    [CrossRef] [PubMed]
  3. M. G. Littman, “Single-Mode Operation of Grazing-Incidence Pulsed Dye Laser,” Opt. Lett. 3, 138 (1978).
    [CrossRef] [PubMed]
  4. T. W. Hansch, “Repetitively Pulsed Tunable Dye Laser for High Resolution Spectroscopy,” Appl. Opt. 11, 895 (1972).
    [CrossRef] [PubMed]
  5. M. G. Littman, H. J. Metcalf, “Spectrally Narrow Pulsed Dye Laser without Beam Expander,” Appl. Opt. 17, 2224 (1978).
    [CrossRef] [PubMed]
  6. I. Shoshan, N. Danon, U. Oppenheim, “Narrowband Operation of a Pulsed Dye Laser Without Intracavity Beam Expansion,” J. Appl. Phys. 48, 4495 (1977).
    [CrossRef]

1984

1981

1978

1977

I. Shoshan, N. Danon, U. Oppenheim, “Narrowband Operation of a Pulsed Dye Laser Without Intracavity Beam Expansion,” J. Appl. Phys. 48, 4495 (1977).
[CrossRef]

1972

Danon, N.

I. Shoshan, N. Danon, U. Oppenheim, “Narrowband Operation of a Pulsed Dye Laser Without Intracavity Beam Expansion,” J. Appl. Phys. 48, 4495 (1977).
[CrossRef]

Hansch, T. W.

Littman, M. G.

Liu, K.

Metcalf, H. J.

Oppenheim, U.

I. Shoshan, N. Danon, U. Oppenheim, “Narrowband Operation of a Pulsed Dye Laser Without Intracavity Beam Expansion,” J. Appl. Phys. 48, 4495 (1977).
[CrossRef]

Shoshan, I.

I. Shoshan, N. Danon, U. Oppenheim, “Narrowband Operation of a Pulsed Dye Laser Without Intracavity Beam Expansion,” J. Appl. Phys. 48, 4495 (1977).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Geometry for discussing relative phase of diffracted wave.

Fig. 2
Fig. 2

General configuration for a Littrow oscillator. A denotes the axis of rotation for the grating.

Fig. 3
Fig. 3

Generalized oscillator with N internal elements (j = 1,… N).

Fig. 4
Fig. 4

General configuration for GIM oscillator with A as the rotation axis for the tuning mirror.

Fig. 5
Fig. 5

Synchronous displaced configuration for a GIM oscillator.

Fig. 6
Fig. 6

General configuration for a GIL oscillator with A as the rotation axis for the tuning (Littrow) grating.

Equations (16)

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sin θ + sin i = m λ / d = m g / k ,
E d m = E i G m ( P ) .
G ( u ) = m G m ( P ) exp ( i g u m ) ( m = 1 , 0 , 1 , 2 ) ,
2 sin Φ = m g / k .
G m ( P ) exp [ 2 i k ( x 0 + x 1 cos Φ ) ]
ψ = 2 k ( x 0 + x 1 cos Φ ) .
ψ = 2 k [ x 0 cos θ 0 + j = 1 N x j ( cos θ j + cos i j ) + x N + 1 cos i N + 1 ] .
sin i + sin Φ = m g / k .
ψ = 2 k [ x 0 + x 2 + x 1 ( cos i + cos Φ ) ] .
sin θ + sin i = m g / k ,
2 sin ϕ = m g / k ,
ψ = 2 k [ x 0 + x 1 ( cos i + cos θ ) + x 2 cos ϕ ] .
Δ ψ = 4 π Δ x Δ ν ¯ 2 π x 1 ( d 2 ν ¯ 0 cos 3 Φ 0 ) 1 ( Δ ν ¯ / ν ¯ 0 ) 2 ,
Δ x = x 0 + x 2 + x 1 [ 1 + cos ( Φ 0 i ) ] / cos Φ 0 ,
| Δ x | ( 2 Δ v ¯ ) 1 ,
| x 1 | ( d 2 ν ¯ 0 3 cos 3 Φ 0 ) / ( Δ ν ¯ ) 2 .

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