Abstract

We describe the principles of a resonant cavity optical modulator capable of modulation frequencies in the 10-GHz range. The dispersive properties of waveguides are used to achieve phase matching of the optical and rf waves, which differ in velocity by a factor of 3 in bulk electrooptic materials. The difference in propagation velocities also allows us to form a rectangular cavity with two opposite sides open through which the optical beam may be easily passed. A modulator employing this design is thus both efficient in its use of rf power and is easily optically aligned.

© 1986 Optical Society of America

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References

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  1. I. P. Kaminow, E. H. Turner, “Electrooptic Light Modulators,” Proc. IEEE 54, 1374 (1966).
    [CrossRef]
  2. G. C. Bjorklund, “Frequency-Modulation Spectroscopy: A New Method for Measuring Weak Absorption and Dispersions,” Opt. Lett. 5, 15 (1980).
    [CrossRef] [PubMed]
  3. A. Yariv, Quantum Electronics (Wiley, New York, 1975).
  4. I. P. Kaminow, J. Liu, “Propagation Characteristics of Partially Loaded Two-Conductor Transmission Line for Broadband Light Modulators,” Proc. IEEE 51, 132 (1963).
    [CrossRef]
  5. M. E. El-Shandwily, S.M. El-Dinary, “Travelling-Wave Coherent Light-Phase Modulator,” IEEE Trans. Microwave Theory Tech. MTT-20, 132 (1972).
    [CrossRef]
  6. G. M. Carter, “Tunable High Efficiency Microwave Frequency Shifting of Infrared Lasers,” Appl. Phys. Lett. 32, 810 (1978).
    [CrossRef]
  7. W. W. Rigrod, I. P. Kaminow, “Wide Band Microwave Light Modulation,” Proc. IEEE 51, 137 (1963).
    [CrossRef]
  8. N. H. Tran, T. F. Gallagher, J. P. Watjen, G. Janik, C. Carlisle, “High Efficiency Resonant Cavity Microwave Optical Modulator,” Appl. Opt. 24, 4282 (1985).
    [CrossRef] [PubMed]
  9. S. Ramo, J. R. Whinnery, Field and Waves in Modern Radio (Wiley, New York, 1953).
  10. P. V. Lenzo, E. H. Turner, E. G. Spencer, A. A. Ballman, “Electrooptic Coefficients and Elastic Wave Propagation in Single Domain Ferroelectric Lithium Tantalate,” Appl. Phys. Lett. 8, 81 (1966).
    [CrossRef]

1985 (1)

1980 (1)

1978 (1)

G. M. Carter, “Tunable High Efficiency Microwave Frequency Shifting of Infrared Lasers,” Appl. Phys. Lett. 32, 810 (1978).
[CrossRef]

1972 (1)

M. E. El-Shandwily, S.M. El-Dinary, “Travelling-Wave Coherent Light-Phase Modulator,” IEEE Trans. Microwave Theory Tech. MTT-20, 132 (1972).
[CrossRef]

1966 (2)

I. P. Kaminow, E. H. Turner, “Electrooptic Light Modulators,” Proc. IEEE 54, 1374 (1966).
[CrossRef]

P. V. Lenzo, E. H. Turner, E. G. Spencer, A. A. Ballman, “Electrooptic Coefficients and Elastic Wave Propagation in Single Domain Ferroelectric Lithium Tantalate,” Appl. Phys. Lett. 8, 81 (1966).
[CrossRef]

1963 (2)

W. W. Rigrod, I. P. Kaminow, “Wide Band Microwave Light Modulation,” Proc. IEEE 51, 137 (1963).
[CrossRef]

I. P. Kaminow, J. Liu, “Propagation Characteristics of Partially Loaded Two-Conductor Transmission Line for Broadband Light Modulators,” Proc. IEEE 51, 132 (1963).
[CrossRef]

Ballman, A. A.

P. V. Lenzo, E. H. Turner, E. G. Spencer, A. A. Ballman, “Electrooptic Coefficients and Elastic Wave Propagation in Single Domain Ferroelectric Lithium Tantalate,” Appl. Phys. Lett. 8, 81 (1966).
[CrossRef]

Bjorklund, G. C.

Carlisle, C.

Carter, G. M.

G. M. Carter, “Tunable High Efficiency Microwave Frequency Shifting of Infrared Lasers,” Appl. Phys. Lett. 32, 810 (1978).
[CrossRef]

El-Dinary, S.M.

M. E. El-Shandwily, S.M. El-Dinary, “Travelling-Wave Coherent Light-Phase Modulator,” IEEE Trans. Microwave Theory Tech. MTT-20, 132 (1972).
[CrossRef]

El-Shandwily, M. E.

M. E. El-Shandwily, S.M. El-Dinary, “Travelling-Wave Coherent Light-Phase Modulator,” IEEE Trans. Microwave Theory Tech. MTT-20, 132 (1972).
[CrossRef]

Gallagher, T. F.

Janik, G.

Kaminow, I. P.

I. P. Kaminow, E. H. Turner, “Electrooptic Light Modulators,” Proc. IEEE 54, 1374 (1966).
[CrossRef]

I. P. Kaminow, J. Liu, “Propagation Characteristics of Partially Loaded Two-Conductor Transmission Line for Broadband Light Modulators,” Proc. IEEE 51, 132 (1963).
[CrossRef]

W. W. Rigrod, I. P. Kaminow, “Wide Band Microwave Light Modulation,” Proc. IEEE 51, 137 (1963).
[CrossRef]

Lenzo, P. V.

P. V. Lenzo, E. H. Turner, E. G. Spencer, A. A. Ballman, “Electrooptic Coefficients and Elastic Wave Propagation in Single Domain Ferroelectric Lithium Tantalate,” Appl. Phys. Lett. 8, 81 (1966).
[CrossRef]

Liu, J.

I. P. Kaminow, J. Liu, “Propagation Characteristics of Partially Loaded Two-Conductor Transmission Line for Broadband Light Modulators,” Proc. IEEE 51, 132 (1963).
[CrossRef]

Ramo, S.

S. Ramo, J. R. Whinnery, Field and Waves in Modern Radio (Wiley, New York, 1953).

Rigrod, W. W.

W. W. Rigrod, I. P. Kaminow, “Wide Band Microwave Light Modulation,” Proc. IEEE 51, 137 (1963).
[CrossRef]

Spencer, E. G.

P. V. Lenzo, E. H. Turner, E. G. Spencer, A. A. Ballman, “Electrooptic Coefficients and Elastic Wave Propagation in Single Domain Ferroelectric Lithium Tantalate,” Appl. Phys. Lett. 8, 81 (1966).
[CrossRef]

Tran, N. H.

Turner, E. H.

I. P. Kaminow, E. H. Turner, “Electrooptic Light Modulators,” Proc. IEEE 54, 1374 (1966).
[CrossRef]

P. V. Lenzo, E. H. Turner, E. G. Spencer, A. A. Ballman, “Electrooptic Coefficients and Elastic Wave Propagation in Single Domain Ferroelectric Lithium Tantalate,” Appl. Phys. Lett. 8, 81 (1966).
[CrossRef]

Watjen, J. P.

Whinnery, J. R.

S. Ramo, J. R. Whinnery, Field and Waves in Modern Radio (Wiley, New York, 1953).

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

G. M. Carter, “Tunable High Efficiency Microwave Frequency Shifting of Infrared Lasers,” Appl. Phys. Lett. 32, 810 (1978).
[CrossRef]

P. V. Lenzo, E. H. Turner, E. G. Spencer, A. A. Ballman, “Electrooptic Coefficients and Elastic Wave Propagation in Single Domain Ferroelectric Lithium Tantalate,” Appl. Phys. Lett. 8, 81 (1966).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

M. E. El-Shandwily, S.M. El-Dinary, “Travelling-Wave Coherent Light-Phase Modulator,” IEEE Trans. Microwave Theory Tech. MTT-20, 132 (1972).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (3)

I. P. Kaminow, E. H. Turner, “Electrooptic Light Modulators,” Proc. IEEE 54, 1374 (1966).
[CrossRef]

I. P. Kaminow, J. Liu, “Propagation Characteristics of Partially Loaded Two-Conductor Transmission Line for Broadband Light Modulators,” Proc. IEEE 51, 132 (1963).
[CrossRef]

W. W. Rigrod, I. P. Kaminow, “Wide Band Microwave Light Modulation,” Proc. IEEE 51, 137 (1963).
[CrossRef]

Other (2)

S. Ramo, J. R. Whinnery, Field and Waves in Modern Radio (Wiley, New York, 1953).

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a modulator showing the propagating optical beam and the polarizations of the optical and rf electric fields.

Fig. 2
Fig. 2

Cross section of the waveguide.

Fig. 3
Fig. 3

Perspective view of the resonant cavity optical modulator showing the LiTaO3 filling one section of the waveguide to form the resonant cavity and the two air filled sections at the ends which are cut off.

Fig. 4
Fig. 4

(a) Side view of the modulator showing the location of the LiTaO3. (b) The electric field variation along the center line of the modulator showing the evanescent fields in the air filled pieces of waveguide at the end.

Fig. 5
Fig. 5

Geometry for a multiple-pass arrangement to use the microwave power more efficiently. A LiTaO3 crystal of length l is d/2 from each of two end mirrors.

Tables (2)

Tables Icon

Table I Relevant Properties of LiTaO3a

Tables Icon

Table II Operating Parameters of Modulators

Equations (32)

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n = n e n e 3 r 33 E 2 ,
δ 0 = ( π n e 3 r 33 E l ) / λ ,
δ = δ 0 sin ( χ / 2 ) χ / 2 ,
χ = l ω { 1 υ o 1 υ p } .
E opt = cos ( ω 0 t + δ sin ω t ) .
E opt = m J m ( δ ) cos ( ω 0 + m ω ) t .
I m ( δ ) = J m 2 ( δ ) .
f c = c / ( 2 b ) .
k p = [ 2 π f 1 ( f c / f ) 2 ] / c .
k a = [ 2 π f c 1 ( f / f c ) 2 ] / c .
H z = A sin π x b exp [ i ( ω t k z ) ] + c c ,
E y = A i ω k c π b cos π x b exp [ i ( ω t k z ) ] + c c ,
H x = k 2 i ω k c 2 π b A cos π x b exp [ i ( ω t k z ) ] + c c ,
υ p = c / [ 1 ( f c / f ) 2 ] .
f f c = { 1 n 2 } 1 / 2 .
tan Φ = k a k p ,
exp ( 4 i Φ ) = exp ( 2 i k p l )
k p l = 2 Φ + m π ,
Q = 1 / Δ .
U = 0 2 crystal E 2 dxdydz + 0 2 air E 2 dxdydz ,
for m even E = E 0 cos π x b cos k p z ,
for m odd E = E 0 cos π x b sin k p z .
m even E = E 0 cos π x b cos k p l 2 exp [ ( z l / 2 ) k a ] ,
for m odd E = E 0 cos π x b sin k p l 2 exp [ ( z l / 2 ) k a ] .
| E | = E 0 cos π x b cos Φ exp [ ( z l / 2 ) k a ] .
U = E 0 2 abl 8 { 0 ( sin Φ cos Φ ϴ + 1 ) + 0 cos 2 Φ ϴ tan Φ = a b l 8 0 E 0 2 K ,
K = 1 + sin Φ cos Φ ϴ + cos 2 Φ ϴ tan ϴ ,
U = Q W L / ω .
E 0 = { 8 Q W L ω 0 abl K } 1 / 2 .
E ± = { 2 Q W L ω 0 abl K } 1 / 2 .
δ = π n e 3 r 33 λ { Q W L 2 l ω 0 a b K } 1 / 2 .
( l n 2 c + d 2 c ) = m f .

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