Abstract

An analysis is made of the spectrum of a laser beam modulated by the electrooptic doppler shift for two important cases: where the applied electric field is a sawtooth function and where it is a triangular function. The spectra reduce to simple forms when the maximum frequency shift is an integral multiple of the modulation frequency.

© 1968 Optical Society of America

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References

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  1. M. A. Duguay, L. E. Hargrove, K. B. Jefferts, Appl. Phys. Lett. 9, 374 (1966).
    [Crossref]
  2. C. G. B. Garrett, M. A. Duguay, Appl. Phys. Lett. 9, 374 (1966).
    [Crossref]
  3. R. C. Cummings, Proc. IRE 45, 175 (1957).
    [Crossref]

1966 (2)

M. A. Duguay, L. E. Hargrove, K. B. Jefferts, Appl. Phys. Lett. 9, 374 (1966).
[Crossref]

C. G. B. Garrett, M. A. Duguay, Appl. Phys. Lett. 9, 374 (1966).
[Crossref]

1957 (1)

R. C. Cummings, Proc. IRE 45, 175 (1957).
[Crossref]

Cummings, R. C.

R. C. Cummings, Proc. IRE 45, 175 (1957).
[Crossref]

Duguay, M. A.

M. A. Duguay, L. E. Hargrove, K. B. Jefferts, Appl. Phys. Lett. 9, 374 (1966).
[Crossref]

C. G. B. Garrett, M. A. Duguay, Appl. Phys. Lett. 9, 374 (1966).
[Crossref]

Garrett, C. G. B.

C. G. B. Garrett, M. A. Duguay, Appl. Phys. Lett. 9, 374 (1966).
[Crossref]

Hargrove, L. E.

M. A. Duguay, L. E. Hargrove, K. B. Jefferts, Appl. Phys. Lett. 9, 374 (1966).
[Crossref]

Jefferts, K. B.

M. A. Duguay, L. E. Hargrove, K. B. Jefferts, Appl. Phys. Lett. 9, 374 (1966).
[Crossref]

Appl. Phys. Lett. (2)

M. A. Duguay, L. E. Hargrove, K. B. Jefferts, Appl. Phys. Lett. 9, 374 (1966).
[Crossref]

C. G. B. Garrett, M. A. Duguay, Appl. Phys. Lett. 9, 374 (1966).
[Crossref]

Proc. IRE (1)

R. C. Cummings, Proc. IRE 45, 175 (1957).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Sawtooth driving function and triangular driving function.

Fig. 2
Fig. 2

Spectra for sawtooth function for δ = 0.1, 0.25, and 0.5.

Fig. 3
Fig. 3

Spectra for triangular function for Ω = 10 and 100. Note: For both spectra shown here, there is an identical set of lines at −n. Lines marked (-) are 180° out of phase with those not marked.

Fig. 4
Fig. 4

Spectrum for triangular function for Ω = 2. Note: Lines marked (-) are 180° out of phase with those not marked.

Equations (17)

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Δ ω = ω 0 ( N / c ) V ,
V = d ( N L ) / d t = L d N / d t = L α d E / d t .
ω ( t ) = ω 0 + Δ ω max f ( t ) .
A n = ω s 2 π 0 2 π / ω s exp [ - i ( Ω ω s - n ω s ) t ] d t = + 1 2 π ( Ω - n ) { exp [ - i 2 π ( Ω - n ) ] - 1 } ,
Ω = ( ω 0 / c ) ( N L α E 0 / 2 π ) .
A n = Ω = 1 , A n Ω = 0 ,
e ( t ) = e 0 sin Ω π π e - j Ω π n = - + 1 Ω - n exp [ - i ( ω 0 + n ω s ) t ] .
A + n / A 0 = Ω ( Ω - n ) ,             A - n / A 0 = Ω ( Ω + n ) ,
I n / I m = δ 2 / ( m - n + δ ) 2 ,
A n = ω s 2 π { 0 π / ω s exp [ - i ( Ω ω s - n ω s ) t ] d t + e - 2 i Ω π π / ω s 2 π / ω s exp [ - i ( - Ω ω s - n ω s ) t ] d t } .
A n = - i e - i ( π / 2 ) Ω cos ( π / 2 ) Ω [ 1 / π ( Ω - n ) + 1 / π ( Ω + n ) ] , n odd ;
A n = e - i ( π / 2 ) Ω sin ( π / 2 ) Ω [ 1 / π ( Ω - n ) + 1 / π ( Ω + n ) ] , n even .
e ( t ) = e even ( t ) + e odd ( t ) ,
e odd ( t ) = e 0 - i cos ( π / 2 ) Ω π e - i ( π / 2 ) Ω × n = ± 1 , ± 3 , ( 1 Ω - n + 1 Ω + n ) exp [ - i ( ω 0 + n ω s ) t ] ,
e even ( t ) = e 0 sin ( π / 2 ) Ω π e - i ( π / 2 ) Ω × n = 0 , ± 2 , ± 4 , ( 1 Ω - n + 1 Ω + n ) exp [ - i ( ω 0 + n ω s ) t ] .
e odd ( t ) = - i 1 π n = ± 1 , ± 3 , ( 1 Ω - n + 1 Ω + n ) × exp [ - i ( ω 0 + n ω s ) t ] .
e odd ( t ) = - i 1 π n = 1 , 3 , 2 Ω Ω 2 - n 2 exp [ - i ( ω 0 + n ω s ) t ] ,

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