Abstract

Closed-form analytical expressions are presented for predicting the harmonic and intermodulation performance of electro-optic modulators synthesized from Mach–Zehnder, directional coupler, and y-fed coupler modulators. The special case of an electro-optic modulator excited by a two-tone signal is considered in detail, and the results are compared with previously reported results obtained by using a fast Fourier transform.

© 1993 Optical Society of America

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References

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  1. T. R. Halemane, S. K. Korotky, “Distortion characteristics of optical directional coupler modulators,” IEEE Trans. Microwave Theory Tech. 38, 669–673 (1990).
    [CrossRef]
  2. K. T. Koai, P. L. Liu, “Digital and quasi-linear electrooptic modulators synthesized from directional couplers,” IEEE J. Quantum Electron. QE-22, 2191–2194 (1986).
    [CrossRef]
  3. P. L. Liu, B. J. Li, Y. S. Trinso, “In search of linear electrooptic amplitude modulators,” IEEE Photon. Tech. Lett. 3, 144–146 (1991).
    [CrossRef]
  4. B. H. Kolner, D. W. Dolfi, “Intermodulation distortion and compression in an integrated electrooptic modulator,” Appl. Opt. 26, 3676–3680 (1987).
    [CrossRef] [PubMed]
  5. M. T. Abuelma'atti, “Large signal analysis of optical directional coupler modulators,” IEEE Trans. Microwave Theory Tech. 40, 1722–1725 (1992).
    [CrossRef]
  6. IMSLReference Manual, 9th ed. (International Mathematical and Statistical Libraries, Houston, Tex., 1982) Vol. 2, Chap. I.
  7. G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961).

1992 (1)

M. T. Abuelma'atti, “Large signal analysis of optical directional coupler modulators,” IEEE Trans. Microwave Theory Tech. 40, 1722–1725 (1992).
[CrossRef]

1991 (1)

P. L. Liu, B. J. Li, Y. S. Trinso, “In search of linear electrooptic amplitude modulators,” IEEE Photon. Tech. Lett. 3, 144–146 (1991).
[CrossRef]

1990 (1)

T. R. Halemane, S. K. Korotky, “Distortion characteristics of optical directional coupler modulators,” IEEE Trans. Microwave Theory Tech. 38, 669–673 (1990).
[CrossRef]

1987 (1)

1986 (1)

K. T. Koai, P. L. Liu, “Digital and quasi-linear electrooptic modulators synthesized from directional couplers,” IEEE J. Quantum Electron. QE-22, 2191–2194 (1986).
[CrossRef]

Abuelma'atti, M. T.

M. T. Abuelma'atti, “Large signal analysis of optical directional coupler modulators,” IEEE Trans. Microwave Theory Tech. 40, 1722–1725 (1992).
[CrossRef]

Dolfi, D. W.

Halemane, T. R.

T. R. Halemane, S. K. Korotky, “Distortion characteristics of optical directional coupler modulators,” IEEE Trans. Microwave Theory Tech. 38, 669–673 (1990).
[CrossRef]

Koai, K. T.

K. T. Koai, P. L. Liu, “Digital and quasi-linear electrooptic modulators synthesized from directional couplers,” IEEE J. Quantum Electron. QE-22, 2191–2194 (1986).
[CrossRef]

Kolner, B. H.

Korn, G. A.

G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961).

Korn, T. M.

G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961).

Korotky, S. K.

T. R. Halemane, S. K. Korotky, “Distortion characteristics of optical directional coupler modulators,” IEEE Trans. Microwave Theory Tech. 38, 669–673 (1990).
[CrossRef]

Li, B. J.

P. L. Liu, B. J. Li, Y. S. Trinso, “In search of linear electrooptic amplitude modulators,” IEEE Photon. Tech. Lett. 3, 144–146 (1991).
[CrossRef]

Liu, P. L.

P. L. Liu, B. J. Li, Y. S. Trinso, “In search of linear electrooptic amplitude modulators,” IEEE Photon. Tech. Lett. 3, 144–146 (1991).
[CrossRef]

K. T. Koai, P. L. Liu, “Digital and quasi-linear electrooptic modulators synthesized from directional couplers,” IEEE J. Quantum Electron. QE-22, 2191–2194 (1986).
[CrossRef]

Trinso, Y. S.

P. L. Liu, B. J. Li, Y. S. Trinso, “In search of linear electrooptic amplitude modulators,” IEEE Photon. Tech. Lett. 3, 144–146 (1991).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

K. T. Koai, P. L. Liu, “Digital and quasi-linear electrooptic modulators synthesized from directional couplers,” IEEE J. Quantum Electron. QE-22, 2191–2194 (1986).
[CrossRef]

IEEE Photon. Tech. Lett. (1)

P. L. Liu, B. J. Li, Y. S. Trinso, “In search of linear electrooptic amplitude modulators,” IEEE Photon. Tech. Lett. 3, 144–146 (1991).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

T. R. Halemane, S. K. Korotky, “Distortion characteristics of optical directional coupler modulators,” IEEE Trans. Microwave Theory Tech. 38, 669–673 (1990).
[CrossRef]

M. T. Abuelma'atti, “Large signal analysis of optical directional coupler modulators,” IEEE Trans. Microwave Theory Tech. 40, 1722–1725 (1992).
[CrossRef]

Other (2)

IMSLReference Manual, 9th ed. (International Mathematical and Statistical Libraries, Houston, Tex., 1982) Vol. 2, Chap. I.

G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961).

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Figures (5)

Fig. 1
Fig. 1

Interferometric modulator based on the Mach–Zehnder structure.

Fig. 2
Fig. 2

Directional coupler intensity modulator.

Fig. 3
Fig. 3

y-fed or 1 × 2 directional coupler modulator.

Fig. 4
Fig. 4

Normalized coefficient F3/F1 versus normalized bias voltage for an electro-optic modulator synthesized from Mach– Zehnder and directional coupler modulators: a, η = 0.7, kL = 0.25π; b, η = 0.7, kL = 0.2π; c, η = 0.4, kL = 0.988π.

Fig. 5
Fig. 5

Normalized coefficient F3/F1 versus normalized bias voltage for an electro-optic modulator synthesized from Mach– Zehnder and y-fed directional coupler modulators: a, η = 0.883, kL = 0.25π; b, η = 1.24, kL = 0.2π; c, η = 0.57, kL = 0.988π.

Tables (2)

Tables Icon

Table 1 Parameters of Directional Coupler Modulators

Tables Icon

Table 2 Parameters of y-Fed Coupler Modulators a

Equations (17)

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I / I 0 = f ( V / V s ) ,
f ( V V s ) = 1 2 ( 1 + cos π V V s )
f ( V V s ) = sin 2 { k L [ 1 + 3 ( V / V s ) 2 ] 1 / 2 } 1 + 3 ( V / V s ) 2
f ( V / V s ) = a 2 cos 2 [ π ( r / 2 ) ] + [ ( a x b y ) / r ] 2 sin 2 [ ( π / 2 ) r ]
f ( V V s ) = A 0 + n = 1 6 A n cos [ n π ( V V s + C ) ] ,
I I 0 = f A ( V a V s ) f B ( V b V s )
V a V s = β b + k = 1 K β k sin w k t ,
I I 0 = 1 2 [ 1 + cos π ( β b + k = 1 K β k sin w k t ) ] × { A 0 + n = 1 6 A n cos [ η n π ( β b + k = 1 K β k sin w k t ) ] } .
I α 1 , α 2 , , α K = A 0 T ( π β b ) Π k = 1 K J | α k | ( π β k ) + n = 1 6 1 2 A n { 2 T ( n π η β b 1 ) Π k = 1 K J | α k | ( n π η β k ) + T [ ( 1 + n η ) π β b 2 ] Π k = 1 K J | α k | [ ( 1 + n η ) π β k ] + T [ ( 1 n η ) π β b 3 ] Π k = 1 K J | α k | [ ( 1 n η ) π β k ] } ,
V m / V s = β ( sin w 1 t + sin w 2 t ) .
J r ( X ) ( X / 2 ) r r ! ,
I 1 , 0 = ½ β π F 1 ;
I 2 , 1 = 1 / 16 β 3 π 3 F 3 ;
I 3 , 0 = 1 / 48 β 3 π 3 F 3 ;
I 1 , 1 = ¼ β 2 π 2 F 2 ;
I 2 , 0 = β 2 π 2 F 2 ,
F m = A 0 T ( π β b ) + n = 1 6 A n 2 { 2 ( n η ) m T ( n π η β b 1 ) + ( 1 + n η ) m T [ ( 1 + n η ) π β b 2 ] + ( 1 n η ) m T [ ( 1 n η ) π β b 3 ] } ,

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