Abstract

Using the reflection of linearly polarized light from electrooptic material with an interdigital arrangement of electrodes, an electrically controllable diffraction (ECD) grating has been constructed for a He–Ne 3.39-μm laser. An intracavity modulation of 30% was obtained for a He–Ne 3.39-μm laser by setting the ECD grating inside the resonator with an applied voltage of 50 V.

© 1977 Optical Society of America

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References

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  1. J. F. St. Ledger, E. A. Ash, Electron. Lett. 4, 99 (1968).
    [CrossRef]
  2. J. M. Hammer, Appl. Phys. Lett. 18, 147 (1971).
    [CrossRef]
  3. M. A. R. P. De Barros, M. G. F. Wilson, Electron. Lett. 7, 267 (1971).
    [CrossRef]
  4. R. A. Meyer, Appl. Opt. 11, 613 (1972).
    [CrossRef] [PubMed]
  5. T. Motoki, Appl. Opt. 12, 1472 (1973).
    [CrossRef] [PubMed]
  6. M. T. V. Scibor-Rylski, Electron. Lett. 9, 310 (1973).
    [CrossRef]
  7. V. Ramachandran, A. W. Palmer, M. T. V. Scibor-Rylski, J. Phys. D 8, 1923 (1975).
    [CrossRef]
  8. S. Ramo, J. R. Whinnery, T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1965), p. 150.
  9. T. Hasegawa, H. Sato, IEEE Trans. Sonics Ultrason. SU-19, 183 (1972).
    [CrossRef]
  10. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 401.
  11. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 482.
  12. At an anomalous dispersion region in wavelength, the loss coefficient of EO material is considered to be approximately independent of the external electric field for dielectrics.
  13. For example, A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1971), p. 222.
  14. W. W. Rigrod, J. Appl. Phys. 34, 2602 (1963).
    [CrossRef]
  15. D. C. Sinclair, W. E. Bell, Gas Laser Technology (Holt, Rinehart and Winston, New York, 1969), p. 113.
  16. For an inhomogeneously broadened gain medium, the parameter y becomes zero; thus, the ratio of ψ(0,y) to ψ(0,ξ) is equal to unity.
  17. G. H. Haertling, C. E. Land, J. Am. Ceram. Soc. 54, 1 (1971).
    [CrossRef]
  18. H. Sato, K. Toda, J. Appl. Phys. 47, 4031 (1976).
    [CrossRef]
  19. H. Sato, T. Hasegawa, Digests of Q.E. Group Meeting, I.E.C.E. of Japan, QE 71-41 (1971).

1976 (1)

H. Sato, K. Toda, J. Appl. Phys. 47, 4031 (1976).
[CrossRef]

1975 (1)

V. Ramachandran, A. W. Palmer, M. T. V. Scibor-Rylski, J. Phys. D 8, 1923 (1975).
[CrossRef]

1973 (2)

T. Motoki, Appl. Opt. 12, 1472 (1973).
[CrossRef] [PubMed]

M. T. V. Scibor-Rylski, Electron. Lett. 9, 310 (1973).
[CrossRef]

1972 (2)

T. Hasegawa, H. Sato, IEEE Trans. Sonics Ultrason. SU-19, 183 (1972).
[CrossRef]

R. A. Meyer, Appl. Opt. 11, 613 (1972).
[CrossRef] [PubMed]

1971 (3)

J. M. Hammer, Appl. Phys. Lett. 18, 147 (1971).
[CrossRef]

M. A. R. P. De Barros, M. G. F. Wilson, Electron. Lett. 7, 267 (1971).
[CrossRef]

G. H. Haertling, C. E. Land, J. Am. Ceram. Soc. 54, 1 (1971).
[CrossRef]

1968 (1)

J. F. St. Ledger, E. A. Ash, Electron. Lett. 4, 99 (1968).
[CrossRef]

1963 (1)

W. W. Rigrod, J. Appl. Phys. 34, 2602 (1963).
[CrossRef]

Ash, E. A.

J. F. St. Ledger, E. A. Ash, Electron. Lett. 4, 99 (1968).
[CrossRef]

Bell, W. E.

D. C. Sinclair, W. E. Bell, Gas Laser Technology (Holt, Rinehart and Winston, New York, 1969), p. 113.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 401.

De Barros, M. A. R. P.

M. A. R. P. De Barros, M. G. F. Wilson, Electron. Lett. 7, 267 (1971).
[CrossRef]

Haertling, G. H.

G. H. Haertling, C. E. Land, J. Am. Ceram. Soc. 54, 1 (1971).
[CrossRef]

Hammer, J. M.

J. M. Hammer, Appl. Phys. Lett. 18, 147 (1971).
[CrossRef]

Hasegawa, T.

T. Hasegawa, H. Sato, IEEE Trans. Sonics Ultrason. SU-19, 183 (1972).
[CrossRef]

H. Sato, T. Hasegawa, Digests of Q.E. Group Meeting, I.E.C.E. of Japan, QE 71-41 (1971).

Land, C. E.

G. H. Haertling, C. E. Land, J. Am. Ceram. Soc. 54, 1 (1971).
[CrossRef]

Ledger, J. F. St.

J. F. St. Ledger, E. A. Ash, Electron. Lett. 4, 99 (1968).
[CrossRef]

Meyer, R. A.

Motoki, T.

Palmer, A. W.

V. Ramachandran, A. W. Palmer, M. T. V. Scibor-Rylski, J. Phys. D 8, 1923 (1975).
[CrossRef]

Ramachandran, V.

V. Ramachandran, A. W. Palmer, M. T. V. Scibor-Rylski, J. Phys. D 8, 1923 (1975).
[CrossRef]

Ramo, S.

S. Ramo, J. R. Whinnery, T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1965), p. 150.

Rigrod, W. W.

W. W. Rigrod, J. Appl. Phys. 34, 2602 (1963).
[CrossRef]

Sato, H.

H. Sato, K. Toda, J. Appl. Phys. 47, 4031 (1976).
[CrossRef]

T. Hasegawa, H. Sato, IEEE Trans. Sonics Ultrason. SU-19, 183 (1972).
[CrossRef]

H. Sato, T. Hasegawa, Digests of Q.E. Group Meeting, I.E.C.E. of Japan, QE 71-41 (1971).

Scibor-Rylski, M. T. V.

V. Ramachandran, A. W. Palmer, M. T. V. Scibor-Rylski, J. Phys. D 8, 1923 (1975).
[CrossRef]

M. T. V. Scibor-Rylski, Electron. Lett. 9, 310 (1973).
[CrossRef]

Sinclair, D. C.

D. C. Sinclair, W. E. Bell, Gas Laser Technology (Holt, Rinehart and Winston, New York, 1969), p. 113.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 482.

Toda, K.

H. Sato, K. Toda, J. Appl. Phys. 47, 4031 (1976).
[CrossRef]

Van Duzer, T.

S. Ramo, J. R. Whinnery, T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1965), p. 150.

Whinnery, J. R.

S. Ramo, J. R. Whinnery, T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1965), p. 150.

Wilson, M. G. F.

M. A. R. P. De Barros, M. G. F. Wilson, Electron. Lett. 7, 267 (1971).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 401.

Yariv, A.

For example, A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1971), p. 222.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. M. Hammer, Appl. Phys. Lett. 18, 147 (1971).
[CrossRef]

Electron. Lett. (3)

M. A. R. P. De Barros, M. G. F. Wilson, Electron. Lett. 7, 267 (1971).
[CrossRef]

J. F. St. Ledger, E. A. Ash, Electron. Lett. 4, 99 (1968).
[CrossRef]

M. T. V. Scibor-Rylski, Electron. Lett. 9, 310 (1973).
[CrossRef]

IEEE Trans. Sonics Ultrason. (1)

T. Hasegawa, H. Sato, IEEE Trans. Sonics Ultrason. SU-19, 183 (1972).
[CrossRef]

J. Am. Ceram. Soc. (1)

G. H. Haertling, C. E. Land, J. Am. Ceram. Soc. 54, 1 (1971).
[CrossRef]

J. Appl. Phys. (2)

H. Sato, K. Toda, J. Appl. Phys. 47, 4031 (1976).
[CrossRef]

W. W. Rigrod, J. Appl. Phys. 34, 2602 (1963).
[CrossRef]

J. Phys. D (1)

V. Ramachandran, A. W. Palmer, M. T. V. Scibor-Rylski, J. Phys. D 8, 1923 (1975).
[CrossRef]

Other (8)

S. Ramo, J. R. Whinnery, T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1965), p. 150.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 401.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 482.

At an anomalous dispersion region in wavelength, the loss coefficient of EO material is considered to be approximately independent of the external electric field for dielectrics.

For example, A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1971), p. 222.

D. C. Sinclair, W. E. Bell, Gas Laser Technology (Holt, Rinehart and Winston, New York, 1969), p. 113.

For an inhomogeneously broadened gain medium, the parameter y becomes zero; thus, the ratio of ψ(0,y) to ψ(0,ξ) is equal to unity.

H. Sato, T. Hasegawa, Digests of Q.E. Group Meeting, I.E.C.E. of Japan, QE 71-41 (1971).

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Figures (11)

Fig. 1
Fig. 1

Model of electrically controllable diffraction (ECD) grating with related coordinates.

Fig. 2
Fig. 2

Equivalent reflectance pattern of an ECD grating; (a) pattern at static condition, (b) pattern at dynamic condition, with applied voltage and (c)–(e) equivalently separated components of dynamic pattern (b), where the vertical scale is reflectance and D = (a′ + d′)/2.

Fig. 3
Fig. 3

Calculated static diffraction pattern as a function of diffraction angle θ for various incident angles θi.

Fig. 4
Fig. 4

Intensity deviations in terms of external modulation degree Mex vs applied voltage V for the setting angles of 55–70°. The inset shows external modulation degree Mex vs setting angle θs for various applied voltages of 20–100 V.

Fig. 5
Fig. 5

Schematic experimental diagrams: (a) electrode configuration of the ECD grating used, (b) setup for measuring diffraction patterns, and (c) setup for optical intracavity modulation.

Fig. 6
Fig. 6

Measured diffraction pattern at θi = 60°, in comparison with numerically calculated results.

Fig. 7
Fig. 7

Normalized intensities of zeroth-order peak as a function of incident angle θi for intracavity and extracavity settings of the ECD grating compared with the reflectance of PLZT ceramic itself.

Fig. 8
Fig. 8

External modulation degree Mex vs applied peak voltage Vp for various setting angles θs. The calculated curve of the inset is calibrated at the linear region (based on Fig. 4).

Fig. 9
Fig. 9

Intracavity modulation degree Min vs applied peak voltage Vp for various setting angles θs.

Fig. 10
Fig. 10

Examples of experimental waveforms; (a) in-phase modulation, (b) 180° out-of-phase modulation, and (c) double-frequency modulation without optical biasing effect due to polarization.

Fig. 11
Fig. 11

Equivalently separated reflection patterns of that shown in Fig. 2(e).

Equations (47)

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R + ( θ i ) = R 0 ( θ i ) + Δ R ( θ i ; V )
R - ( θ i ) = R 0 ( θ i ) + Δ R ( θ i ; - V ) ,
a = a cos θ i , d = d cos θ i .
f ( x ) = f 1 ( x ) + f 2 ( x ) + f 3 ( x ) ,
f 3 ( x ) = f 3 ( x ) + f 3 ( x ) .
F ( k ) = F [ f ( x ) ] = F [ f 1 ( x ) ] + F [ f 2 ( x ) ] + F [ f 3 ( x ) ] = F 1 ( k ) + F 2 ( k ) + F 3 ( k ) ,
k = ( 2 π / λ ) sin θ ,
F 1 ( k ) = F 0 ( k ) · sin [ ( N + 1 ) k ( a + d ) ] sin [ k ( a + d ) / 2 ] ,
F 2 ( k ) = F 0 ( k ) · sin [ 2 ( N + 1 ) k ( a + d ) ] sin [ k ( a + d ) ] ,
F 3 ( k ) = F 0 ( k ) · sin [ ( 2 N + 1 ) k ( a + d ) ] sin [ k ( a + d ) ] ,
F 3 ( k ) = F 0 ( k ) · sin [ 2 ( N + 1 ) k ( a + d ) ] sin [ k ( a + d ) ] ,
F 0 ( k ) = R e - ( R - ) 1 / 2 a exp ( - i δ ) · sin ( k a / 2 ) ( k a / 2 ) ,
F 0 ( k ) = ( R + ) - ( R - ) 1 / 2 d exp ( - i δ + ) · sin ( k d / 2 ) ( k d / 2 ) ,
F 0 ( k ) = ( R - ) 1 / 2 d exp ( - i δ - ) · sin ( k d / 2 ) ( k d / 2 ) ,
F 0 ( k ) = ( R - ) 1 / 2 ( 2 a + d ) · sin [ k ( 2 a + d ) / 2 ] [ k ( 2 a + d ) / 2 ] .
I ( k ) = F ( k ) F ( k ) * = F 1 ( k ) + F 2 ( k ) + F 3 ( k ) 2 ,
R ( θ i ) = ( q - cos θ i ) 2 + p 2 ( q + cos θ i ) 2 + p 2 · ( q - sin θ i tan θ i ) 2 + p 2 ( q + sin θ i tan θ i ) 2 + p 2 ,
p 2 = 1 2 { - ( n 2 - κ 2 - sin 2 θ i ) + 4 n 2 κ 2 + [ ( n 2 - κ 2 - sin 2 θ i ) 2 ] 1 / 2 } ,
q 2 = 1 2 { ( n 2 - κ 2 - sin 2 θ i ) + 4 n 2 κ 2 + [ ( n 2 - κ 2 - sin 2 θ i ) 2 ] 1 / 2 } .
n = n 0 + Δ n = n 0 + 1 2 n 0 3 r ( V / d ) ,
R = R ( θ i ; V ) = R ( θ i ; 0 ) + Δ R ( θ i ; V ) .
R + ( θ i ) = R ( θ i ; V ) , R - ( θ i ) = R ( θ i ; - V ) ,
R + ( θ i ) - R - ( θ i ) = R ( θ i ; V ) - R ( θ i ; - V ) 2 Δ R .
I ( k ) = I ( θ i ; θ , V ) = I 0 ( k , θ i ; 0 ) + Δ I ( k , θ i ; V ) ,
M ex = Δ I ( k , θ i ; V ) I 0 ( k , θ i ; 0 ) .
I = I s ( X 2 - 1 ) = I s { [ G / ( 1 - R T ) ] 2 - 1 } ,
G = ( L / c ) G 0 π 1 / 2 ψ ( 0 , ξ ) ,
R T = R TO + Δ R ( V ) ,
I I s { [ G 2 ( 1 - R TO ) 2 - 1 ] + 2 G 2 ( 1 - R TO ) 3 Δ R } ,
I out = I T = I s T { [ G 2 ( 1 - R TO ) 2 - 1 ] + 2 G 2 ( 1 - R TO ) 3 Δ R ( V ) } ,
I out = I s T [ G 2 ( 1 - R TO ) 2 - 1 ] ( 1 + M in ) ,
M in = 2 G 2 ( 1 - R TO ) 3 · 1 [ G 2 / ( 1 - R TO ) 2 - 1 ] Δ R ( V ) .
F 0 ( k ) = [ R e - ( R - ) 1 / 2 a exp ( - i δ ) · sin ( k a / 2 ) ( k a / 2 ) ,
F 1 ( k ) = F 0 ( k ) { exp ( i k D ) + exp ( - i k D ) + exp ( i 3 k D ) + exp ( - i 3 k D ) + + exp [ i ( 2 N + 1 ) k D ] + exp [ - i ( 2 N + 1 ) k D ] } = 2 F 0 ( k ) [ cos k D + cos 3 k D + + cos ( 2 N + 1 ) k D ] = 2 F 0 ( k ) R e [ exp ( i l k D ) + exp ( i 3 k D ) + + exp [ i ( 2 N + 1 ) k D ] } ,
D = ( a + d ) / 2.
Re { exp ( i k D ) + exp ( i 3 k D ) + + exp [ i ( 2 N + 1 ) k D ] } = 1 2 sin [ 2 ( N + 1 ) k D ] sin ( k D ) .
F 1 ( k ) = R e - ( R - ) 1 / 2 a exp ( - i δ ) · { sin ( k a / 2 ) ( k a / 2 ) } × { sin [ ( N + 1 ) k ( a + d ) ] sin [ k ( a + d ) / 2 ] } ,
F 2 ( k ) = ( R + ) - ( R - ) 1 / 2 d exp ( - i δ + ) · { sin ( k d / 2 ) ( k d / 2 ) } × { sin [ 2 ( N + 1 ) k ( a + d ) ] sin [ k ( a + d ) ] } .
F 3 ( k ) = ( R - ) 1 / 2 d exp ( - i δ - ) · { sin ( k d / 2 ) ( k d / 2 ) } × { sin [ ( 2 N + 1 ) k ( a + d ) ] sin [ k ( a + d ) ] } ,
F 3 ( k ) = ( R - ) 1 / 2 ( 2 a + d ) { sin [ k ( 2 a + d ) / 2 ] [ k ( 2 a + d ) / 2 ] } × { sin [ 2 ( N + 1 ) k ( a + d ) ] sin [ k ( a + d ) ] } .
α t = G 0 ( π ) 1 / 2 [ 1 + ( I / I s ) ] 1 / 2 ψ ( 0 , ξ ) ,
ξ = y [ 1 + ( I / I s ) ] 1 / 2 ,
y = ( ln 2 ) 1 / 2 ( Δ ν L / Δ ν D ) ,
G 0 = G 0 ( π ) 1 / 2 ψ ( 0 , ξ ) ,
X = G 0 / α t = [ 1 + ( I / I s ) ] 1 / 2 ψ ( 0 , y ) ψ ( 0 , ξ ) .
X = G / ( 1 - R T ) ,
G = ( L / c ) G 0 .

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