Abstract

An athermal design for the KTP electro-optical modulator is presented. By using the wave coupling theory of linear electro-optic effect and taking account of thermal expansion, the more accurate athermal static phase retardation (ASPR) directions in potassium titanyl phosphate (KTP) are found, and the optimized design for a transverse amplitude modulator at ASPR orientation is obtained. The numerical results show that the modulator with an athermal Soleil–Babinet compensator is of excellent thermal stability, and the acceptable error of the ASPR direction is less than 0.1°.

© 2007 Optical Society of America

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References

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  1. F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, "KxRb1−xTiOPO4: a new nonlinear optical material," J. Appl. Phys. 47, 4980-4985 (1976).
    [CrossRef]
  2. J. D. Bierlein and C. B. Arweiler, "Electro-optic and dielectric properties of KTiOPO4," Appl. Phys. Lett. 49, 917-919 (1986).
    [CrossRef]
  3. X. D. Wang, P. Basséras, and R. J. Dwayne Miller, "Investigation of KTiOPO4 as an electro-optic amplitude modulator," Appl. Phys. Lett. 59, 519-521 (1991).
    [CrossRef]
  4. C. A. Ebbers, "Thermally insensitive, single-crystal, biaxial electro-optic modulators," J. Opt. Soc. Am. B 12, 1012-1020 (1995).
    [CrossRef]
  5. X. Q. Lu and S. H. Chen, "Single-crystal KNbO3, KTP electro-optic switches without thermal-induced static phase retardation," Chin. J. Laser A26, 502-506 (1999).
  6. D. D. Wu and W. L. She, "Optimal design of electro-optic modulator of biaxial crystal," Acta Phys. Sin. 54, 134-138 (2005).
  7. W. L. She and W. K. Lee, "Wave coupling theory of linear electrooptic effect," Opt. Commun. 195, 303-311 (2001).
    [CrossRef]
  8. Y. I. Sirotin and M. P. Shaskolskaya, "Optical properties of crystals," in Fundamentals of Crystal Physics (Mir, 1982), Chap. 4, pp. 216-239.
  9. W. Wiechmann, S. Kubota, T. Fukui, and H. Masuda, "Refractive-index temperature derivatives of potassium titanyl phosphate," Opt. Lett. 18, 1208-1210 (1993).
    [CrossRef] [PubMed]
  10. D. K. T. Chu, "Piezoelectric and acoustic properties of KTP and its isomorphs," Master's thesis (University of Delaware, 1991).
  11. J. D. Bierlein and H. Vanberzeele, "Potassium titanyl phosphate: properties and new applications," J. Opt. Soc. Am. B 6, 622-633 (1989).
    [CrossRef]
  12. J. D. Bierlein and C. B. Arweiler, "Electro-optic and dielectric properties of KTiOPO4," Appl. Phys. Lett. 49, 917-919 (1986).
    [CrossRef]

2005 (1)

D. D. Wu and W. L. She, "Optimal design of electro-optic modulator of biaxial crystal," Acta Phys. Sin. 54, 134-138 (2005).

2001 (1)

W. L. She and W. K. Lee, "Wave coupling theory of linear electrooptic effect," Opt. Commun. 195, 303-311 (2001).
[CrossRef]

1999 (1)

X. Q. Lu and S. H. Chen, "Single-crystal KNbO3, KTP electro-optic switches without thermal-induced static phase retardation," Chin. J. Laser A26, 502-506 (1999).

1995 (1)

1993 (1)

1991 (1)

X. D. Wang, P. Basséras, and R. J. Dwayne Miller, "Investigation of KTiOPO4 as an electro-optic amplitude modulator," Appl. Phys. Lett. 59, 519-521 (1991).
[CrossRef]

1989 (1)

1986 (2)

J. D. Bierlein and C. B. Arweiler, "Electro-optic and dielectric properties of KTiOPO4," Appl. Phys. Lett. 49, 917-919 (1986).
[CrossRef]

J. D. Bierlein and C. B. Arweiler, "Electro-optic and dielectric properties of KTiOPO4," Appl. Phys. Lett. 49, 917-919 (1986).
[CrossRef]

1976 (1)

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, "KxRb1−xTiOPO4: a new nonlinear optical material," J. Appl. Phys. 47, 4980-4985 (1976).
[CrossRef]

Acta Phys. Sin. (1)

D. D. Wu and W. L. She, "Optimal design of electro-optic modulator of biaxial crystal," Acta Phys. Sin. 54, 134-138 (2005).

Appl. Phys. Lett. (3)

J. D. Bierlein and C. B. Arweiler, "Electro-optic and dielectric properties of KTiOPO4," Appl. Phys. Lett. 49, 917-919 (1986).
[CrossRef]

X. D. Wang, P. Basséras, and R. J. Dwayne Miller, "Investigation of KTiOPO4 as an electro-optic amplitude modulator," Appl. Phys. Lett. 59, 519-521 (1991).
[CrossRef]

J. D. Bierlein and C. B. Arweiler, "Electro-optic and dielectric properties of KTiOPO4," Appl. Phys. Lett. 49, 917-919 (1986).
[CrossRef]

Chin. J. Laser (1)

X. Q. Lu and S. H. Chen, "Single-crystal KNbO3, KTP electro-optic switches without thermal-induced static phase retardation," Chin. J. Laser A26, 502-506 (1999).

J. Appl. Phys. (1)

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, "KxRb1−xTiOPO4: a new nonlinear optical material," J. Appl. Phys. 47, 4980-4985 (1976).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

W. L. She and W. K. Lee, "Wave coupling theory of linear electrooptic effect," Opt. Commun. 195, 303-311 (2001).
[CrossRef]

Opt. Lett. (1)

Other (2)

Y. I. Sirotin and M. P. Shaskolskaya, "Optical properties of crystals," in Fundamentals of Crystal Physics (Mir, 1982), Chap. 4, pp. 216-239.

D. K. T. Chu, "Piezoelectric and acoustic properties of KTP and its isomorphs," Master's thesis (University of Delaware, 1991).

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Figures (4)

Fig. 1
Fig. 1

(Color online) (a) Schematic of transverse amplitude modulator, and (b) relation between the laboratory coordinate system ( X , Y , Z ) and crystal coordinate system ( x , y , z ) .

Fig. 2
Fig. 2

Temperature dependence of zero-field leakage.

Fig. 3
Fig. 3

(a) Output intensity at 25 ° C (solid curve) and 75 ° C (dashed curve) and (b) difference between them ( Δ I ) as a function of external electric field when the light propagates along one of the ASPR directions ( θ = 32.5 ° , φ = 0 ).

Fig. 4
Fig. 4

Output intensity at 25 ° C (solid curve) and 75 ° C (dashed curve) as functions of the external electric field when the propagation directions are along (a) θ = 32.4 ° , φ = 0 and (b) θ = 32.6 ° , φ = 0 .

Equations (26)

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E ( t ) = E ( 0 ) + [ 1 2 E ( ω ) exp ( i ω t ) + c. c. ] ,
E ( ω ) = E 1 ( ω ) + E 2 ( ω ) = E 1 ( r ) exp ( i k 1 r ) + E 2 ( r ) exp ( i k 2 r ) ,
E ( ω ) = E 1 ( ω ) + E 2 ( ω ) = E 1 ( r ) exp ( i k 1 r ) + E 2 ( r ) exp ( i k 2 r ) .
E 1 ( r ) = E 1 ( r ) a , E 2 ( r ) = E 2 ( r ) b , E ( 0 ) = E 0 c ,
d E 1 ( r ) d r = i d 1 E 2 ( r ) e i Δ k r i d 2 E 1 ( r ) ,
d E 2 ( r ) d r = i d 3 E 1 ( r ) e i Δ k r i d 4 E 2 ( r ) ,
d 1 = k 0 2 n 1 r e f f 1 E 0 , d 2 = k 0 2 n 1 r e f f 2 E 0 ,
d 3 = k 0 2 n 2 r e f f 1 E 0 , d 4 = k 0 2 n 2 r e f f 3 E 0 ,
a = ( cos θ cos φ cos δ sin φ sin δ , cos θ sin φ cos δ + cos φ sin δ , −sin θ cos δ ) ,
b = ( cos θ cos φ sin δ sin φ cos δ , −cos θ sin φ sin δ + cos φ cos δ , sin θ sin δ ) ,
cot δ = cot 2 Ω sin 2 θ cos 2 θ cos 2 φ + sin 2 φ cos θ sin ( 2 φ ) ,
cot 2 Ω = n x 2 ( n z 2 n y 2 ) n z 2 ( n y 2 n x 2 ) ,
1 n 1 2 = 1 2 ( 1 sin 2 θ cos 2 φ n x 2 + 1 sin 2 θ sin 2 φ n y 2 + sin 2 θ n z 2 ) + 1 2 [ ( 1 sin 2 θ cos 2 φ n x 2 + 1 sin 2 θ sin 2 φ n y 2 + sin 2 θ n z 2 ) 2 4 ( sin 2 θ cos 2 φ n y 2 n z 2 + sin 2 θ sin 2 φ n z 2 n x 2 + cos 2 θ n x 2 n y 2 ) ] 0.5 ,
1 n 2 2 = 1 2 ( 1 sin 2 θ cos 2 φ n x 2 + 1 sin 2 θ sin 2 φ n y 2 + sin 2 θ n z 2 ) 1 2 [ ( 1 sin 2 θ cos 2 φ n x 2 + 1 sin 2 θ sin 2 φ n y 2 + sin 2 θ n z 2 ) 4 ( sin 2 θ cos 2 φ n y 2 n z 2 + sin 2 θ sin 2 φ n z 2 n x 2 + cos 2 θ n x 2 n y 2 ) ] 0.5 .
Γ static = 2 π λ l ( n 2 n 1 ) ,
l = l 0 ( 1 + a Δ T ) ,
n 2 T n 1 T + a ( n 2 n 1 ) = 0 .
d E 1 ( r ) d r i d 2 E 1 ( r ) ,
d E 2 ( r ) d r i d 4 E 2 ( r ) ,
d 2 = k 0 sin θ cos 2 θ cos ξ 2 n 1 E 0 ( n x 4 r 13 + 2 n x 2 n z 2 r 51 + n x 4 r 33 tan 2 θ ) ,
d 4 = k 0 n y 4 r 23 2 n 2 E 0 sin θ cos ξ .
E 1 ( ω ) E 1 ( 0 ) e i ( k 1 d 2 ) r ,
E 2 ( ω ) E 2 ( 0 ) e i ( k 2 d 4 ) r .
I o u t = I i n sin 2 ( Γ 2 ) ,
Γ = ( d 2 d 4 ) l + Γ 0 ,
Γ 0 = k 0 ( n 1 n 2 ) ( l + l ) .

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