Abstract

An efficient, 10.4-GHz bulk phase modulator is demonstrated that produces frequency-modulated optical bandwidths in excess of 300 GHz in a double-pass configuration with modest microwave drive power. The waveguide resonator design employs velocity matching to maximize phase-modulation efficiency and a modified form of cutoff waveguide coupling to achieve a high microwave cavity Q factor that reduces power requirements. The measured microwave performance of the modulator agrees well with performance predicted from fully anisotropic, three-dimensional numerical simulations.

© 2004 Optical Society of America

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References

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  1. S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
    [CrossRef]
  2. S. Skupsky, R. S. Craxton, “Irradiation uniformity for high-compression laser-fusion experiments,” Phys. Plasmas 6, 2157–2163 (1999).
    [CrossRef]
  3. T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
    [CrossRef]
  4. “Two-dimensional SSD on OMEGA,” Laboratory for Laser Energetics LLE Rev. 69, 1–10, NTIS document No. DOE/SF/19460-152 (1996). Copies can be obtained from the National Technical Information Service, Springfield, Va. 22161.
  5. “Results of imploding-target burnthrough experiments using SSD smoothing,” Laboratory for Laser Energetics LLE Rev.48, 169–178, NTIS document No. DOE/DP40200-175 (1991). Copies can be obtained from the National Technical Information Service, Springfield, Va. 22161.
  6. G. Carter, “Tunable high-efficiency microwave frequency shifting of infrared lasers,” Appl. Phys. Lett. 32, 810–812 (1978).
    [CrossRef]
  7. N. H. Tran, T. F. Gallagher, J. P. Watjen, G. R. Janik, C. B. Carlisle, “High efficiency resonant cavity microwave optical modulator,” Appl. Opt. 24, 4282–4284 (1985).
    [CrossRef] [PubMed]
  8. T. F. Gallagher, N. H. Tran, J. P. Watjen, “Principles of a resonant cavity optical modulator,” Appl. Opt. 25, 510–514 (1986).
    [CrossRef] [PubMed]
  9. A. A. Godil, “Partially loaded microwave waveguide resonant standing wave electro-optic modulator,” U.S. Patent5,414,552 (9May1995). This modulator is available from New Focus, Inc., San Jose, Calif. 95134; see also http://www.newfocus.com .
  10. F.-Z. Guo, C.-T. Yu, L. Chen, T. Kobayashi, Y. Chen, “Quasi-velocity-matched electrooptic phase modulator for the synthesis of ultrashort optical pulses,” IEEE J. Quantum Electron. 33, 879–882 (1997).
    [CrossRef]
  11. A. A. Godil, A. S. Hou, B. A. Auld, D. M. Bloom, “Harmonic mode locking of a Nd:BEL laser using a 20-GHz dielectric resonator/optical modulator,” Opt. Lett. 16, 1765–1767 (1991).
    [CrossRef] [PubMed]
  12. E. Bonek, M. Knecht, G. Magerl, K. Preis, K. R. Richter, “Coupling and tuning of trapped-mode microwave resonators,” Arch. Elektr. Uebertrag. 32, 209–214 (1978).
  13. I. P. Kaminow, J. Liu, “Propagation characteristics of partially loaded two-conductor transmission line for broadband light modulators,” Proc. IEEE 51, 132–136 (1963).
    [CrossRef]
  14. R. S. Weis, T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
    [CrossRef]
  15. Y. Ohmachi, K. Sawamoto, H. Toyoda, “Dielectric properties of LiNbO3 single crystal up to 9 Gc,” Jpn. J. Appl. Phys. 6, 1467–1468 (1967).
    [CrossRef]
  16. D. M. Pozar, Microwave Engineering, 2nd ed. (Wiley, New York, 1998).
  17. Micro-Stripes, available from Flomerics, Inc., Southborough, Mass. 01772; see also http://www.flomerics.com .
  18. D. Kajfez, Q Factor (Vector Fields, Oxford, Miss., 1994).

1999 (1)

S. Skupsky, R. S. Craxton, “Irradiation uniformity for high-compression laser-fusion experiments,” Phys. Plasmas 6, 2157–2163 (1999).
[CrossRef]

1997 (2)

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

F.-Z. Guo, C.-T. Yu, L. Chen, T. Kobayashi, Y. Chen, “Quasi-velocity-matched electrooptic phase modulator for the synthesis of ultrashort optical pulses,” IEEE J. Quantum Electron. 33, 879–882 (1997).
[CrossRef]

1996 (1)

“Two-dimensional SSD on OMEGA,” Laboratory for Laser Energetics LLE Rev. 69, 1–10, NTIS document No. DOE/SF/19460-152 (1996). Copies can be obtained from the National Technical Information Service, Springfield, Va. 22161.

1991 (1)

1989 (1)

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

1986 (1)

1985 (2)

N. H. Tran, T. F. Gallagher, J. P. Watjen, G. R. Janik, C. B. Carlisle, “High efficiency resonant cavity microwave optical modulator,” Appl. Opt. 24, 4282–4284 (1985).
[CrossRef] [PubMed]

R. S. Weis, T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

1978 (2)

G. Carter, “Tunable high-efficiency microwave frequency shifting of infrared lasers,” Appl. Phys. Lett. 32, 810–812 (1978).
[CrossRef]

E. Bonek, M. Knecht, G. Magerl, K. Preis, K. R. Richter, “Coupling and tuning of trapped-mode microwave resonators,” Arch. Elektr. Uebertrag. 32, 209–214 (1978).

1967 (1)

Y. Ohmachi, K. Sawamoto, H. Toyoda, “Dielectric properties of LiNbO3 single crystal up to 9 Gc,” Jpn. J. Appl. Phys. 6, 1467–1468 (1967).
[CrossRef]

1963 (1)

I. P. Kaminow, J. Liu, “Propagation characteristics of partially loaded two-conductor transmission line for broadband light modulators,” Proc. IEEE 51, 132–136 (1963).
[CrossRef]

Auld, B. A.

Bloom, D. M.

Boehly, T. R.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Bonek, E.

E. Bonek, M. Knecht, G. Magerl, K. Preis, K. R. Richter, “Coupling and tuning of trapped-mode microwave resonators,” Arch. Elektr. Uebertrag. 32, 209–214 (1978).

Brown, D. L.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Carlisle, C. B.

Carter, G.

G. Carter, “Tunable high-efficiency microwave frequency shifting of infrared lasers,” Appl. Phys. Lett. 32, 810–812 (1978).
[CrossRef]

Chen, L.

F.-Z. Guo, C.-T. Yu, L. Chen, T. Kobayashi, Y. Chen, “Quasi-velocity-matched electrooptic phase modulator for the synthesis of ultrashort optical pulses,” IEEE J. Quantum Electron. 33, 879–882 (1997).
[CrossRef]

Chen, Y.

F.-Z. Guo, C.-T. Yu, L. Chen, T. Kobayashi, Y. Chen, “Quasi-velocity-matched electrooptic phase modulator for the synthesis of ultrashort optical pulses,” IEEE J. Quantum Electron. 33, 879–882 (1997).
[CrossRef]

Craxton, R. S.

S. Skupsky, R. S. Craxton, “Irradiation uniformity for high-compression laser-fusion experiments,” Phys. Plasmas 6, 2157–2163 (1999).
[CrossRef]

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Gallagher, T. F.

Gaylord, T. K.

R. S. Weis, T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

Godil, A. A.

A. A. Godil, A. S. Hou, B. A. Auld, D. M. Bloom, “Harmonic mode locking of a Nd:BEL laser using a 20-GHz dielectric resonator/optical modulator,” Opt. Lett. 16, 1765–1767 (1991).
[CrossRef] [PubMed]

A. A. Godil, “Partially loaded microwave waveguide resonant standing wave electro-optic modulator,” U.S. Patent5,414,552 (9May1995). This modulator is available from New Focus, Inc., San Jose, Calif. 95134; see also http://www.newfocus.com .

Guo, F.-Z.

F.-Z. Guo, C.-T. Yu, L. Chen, T. Kobayashi, Y. Chen, “Quasi-velocity-matched electrooptic phase modulator for the synthesis of ultrashort optical pulses,” IEEE J. Quantum Electron. 33, 879–882 (1997).
[CrossRef]

Hou, A. S.

Janik, G. R.

Kajfez, D.

D. Kajfez, Q Factor (Vector Fields, Oxford, Miss., 1994).

Kaminow, I. P.

I. P. Kaminow, J. Liu, “Propagation characteristics of partially loaded two-conductor transmission line for broadband light modulators,” Proc. IEEE 51, 132–136 (1963).
[CrossRef]

Keck, R. L.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Kelly, J. H.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Kessler, T.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Kessler, T. J.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Knauer, J. P.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Knecht, M.

E. Bonek, M. Knecht, G. Magerl, K. Preis, K. R. Richter, “Coupling and tuning of trapped-mode microwave resonators,” Arch. Elektr. Uebertrag. 32, 209–214 (1978).

Kobayashi, T.

F.-Z. Guo, C.-T. Yu, L. Chen, T. Kobayashi, Y. Chen, “Quasi-velocity-matched electrooptic phase modulator for the synthesis of ultrashort optical pulses,” IEEE J. Quantum Electron. 33, 879–882 (1997).
[CrossRef]

Kumpan, S. A.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Letzring, S.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Letzring, S. A.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Liu, J.

I. P. Kaminow, J. Liu, “Propagation characteristics of partially loaded two-conductor transmission line for broadband light modulators,” Proc. IEEE 51, 132–136 (1963).
[CrossRef]

Loucks, S. J.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Magerl, G.

E. Bonek, M. Knecht, G. Magerl, K. Preis, K. R. Richter, “Coupling and tuning of trapped-mode microwave resonators,” Arch. Elektr. Uebertrag. 32, 209–214 (1978).

Marshall, F. J.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

McCrory, R. L.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Morse, S. F. B.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Ohmachi, Y.

Y. Ohmachi, K. Sawamoto, H. Toyoda, “Dielectric properties of LiNbO3 single crystal up to 9 Gc,” Jpn. J. Appl. Phys. 6, 1467–1468 (1967).
[CrossRef]

Pozar, D. M.

D. M. Pozar, Microwave Engineering, 2nd ed. (Wiley, New York, 1998).

Preis, K.

E. Bonek, M. Knecht, G. Magerl, K. Preis, K. R. Richter, “Coupling and tuning of trapped-mode microwave resonators,” Arch. Elektr. Uebertrag. 32, 209–214 (1978).

Richter, K. R.

E. Bonek, M. Knecht, G. Magerl, K. Preis, K. R. Richter, “Coupling and tuning of trapped-mode microwave resonators,” Arch. Elektr. Uebertrag. 32, 209–214 (1978).

Sawamoto, K.

Y. Ohmachi, K. Sawamoto, H. Toyoda, “Dielectric properties of LiNbO3 single crystal up to 9 Gc,” Jpn. J. Appl. Phys. 6, 1467–1468 (1967).
[CrossRef]

Seka, W.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Short, R. W.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Skupsky, S.

S. Skupsky, R. S. Craxton, “Irradiation uniformity for high-compression laser-fusion experiments,” Phys. Plasmas 6, 2157–2163 (1999).
[CrossRef]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Soures, J. M.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Toyoda, H.

Y. Ohmachi, K. Sawamoto, H. Toyoda, “Dielectric properties of LiNbO3 single crystal up to 9 Gc,” Jpn. J. Appl. Phys. 6, 1467–1468 (1967).
[CrossRef]

Tran, N. H.

Verdon, C. P.

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Watjen, J. P.

Weis, R. S.

R. S. Weis, T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

Yu, C.-T.

F.-Z. Guo, C.-T. Yu, L. Chen, T. Kobayashi, Y. Chen, “Quasi-velocity-matched electrooptic phase modulator for the synthesis of ultrashort optical pulses,” IEEE J. Quantum Electron. 33, 879–882 (1997).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. A (1)

R. S. Weis, T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

Appl. Phys. Lett. (1)

G. Carter, “Tunable high-efficiency microwave frequency shifting of infrared lasers,” Appl. Phys. Lett. 32, 810–812 (1978).
[CrossRef]

Arch. Elektr. Uebertrag. (1)

E. Bonek, M. Knecht, G. Magerl, K. Preis, K. R. Richter, “Coupling and tuning of trapped-mode microwave resonators,” Arch. Elektr. Uebertrag. 32, 209–214 (1978).

IEEE J. Quantum Electron. (1)

F.-Z. Guo, C.-T. Yu, L. Chen, T. Kobayashi, Y. Chen, “Quasi-velocity-matched electrooptic phase modulator for the synthesis of ultrashort optical pulses,” IEEE J. Quantum Electron. 33, 879–882 (1997).
[CrossRef]

J. Appl. Phys. (1)

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Jpn. J. Appl. Phys. (1)

Y. Ohmachi, K. Sawamoto, H. Toyoda, “Dielectric properties of LiNbO3 single crystal up to 9 Gc,” Jpn. J. Appl. Phys. 6, 1467–1468 (1967).
[CrossRef]

Laboratory for Laser Energetics LLE Rev. (1)

“Two-dimensional SSD on OMEGA,” Laboratory for Laser Energetics LLE Rev. 69, 1–10, NTIS document No. DOE/SF/19460-152 (1996). Copies can be obtained from the National Technical Information Service, Springfield, Va. 22161.

Opt. Commun. (1)

T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, C. P. Verdon, “Initial performance results of the OMEGA laser system,” Opt. Commun. 133, 495–506 (1997).
[CrossRef]

Opt. Lett. (1)

Phys. Plasmas (1)

S. Skupsky, R. S. Craxton, “Irradiation uniformity for high-compression laser-fusion experiments,” Phys. Plasmas 6, 2157–2163 (1999).
[CrossRef]

Proc. IEEE (1)

I. P. Kaminow, J. Liu, “Propagation characteristics of partially loaded two-conductor transmission line for broadband light modulators,” Proc. IEEE 51, 132–136 (1963).
[CrossRef]

Other (5)

“Results of imploding-target burnthrough experiments using SSD smoothing,” Laboratory for Laser Energetics LLE Rev.48, 169–178, NTIS document No. DOE/DP40200-175 (1991). Copies can be obtained from the National Technical Information Service, Springfield, Va. 22161.

D. M. Pozar, Microwave Engineering, 2nd ed. (Wiley, New York, 1998).

Micro-Stripes, available from Flomerics, Inc., Southborough, Mass. 01772; see also http://www.flomerics.com .

D. Kajfez, Q Factor (Vector Fields, Oxford, Miss., 1994).

A. A. Godil, “Partially loaded microwave waveguide resonant standing wave electro-optic modulator,” U.S. Patent5,414,552 (9May1995). This modulator is available from New Focus, Inc., San Jose, Calif. 95134; see also http://www.newfocus.com .

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic representation of a cutoff waveguide-coupled resonator showing an electro-optic crystal of length L positioned in an air-filled, rectangular waveguide of width a and height b. The waveguide width sets the modulator operating frequency below the cutoff frequency in the air-filled sections, but above cutoff in the crystal. The cutoff waveguide sections act as high reflectors for the standing waves inside the electro-optic crystal resonator. The input waveguide width a′ supports traveling waves at the operating frequency that evanescently couple to the input waveguide through the coupling distance d coupling. (b) The microwave and optical electric fields, E micro and E opt, are oriented along the crystalline c axis to take advantage of the large electro-optic tensor element r 33 in LiNbO3. (c) A tapered input waveguide provides a transition from standard waveguide dimensions to dimensions required for critical coupling into the modulator crystal. A small beam port in the input waveguide bend provides optical access to the crystal but does not disturb the microwave input since it is significantly smaller than the microwave wavelength.

Fig. 2
Fig. 2

Effective interaction length with velocity matching in LiNbO3 modulators plotted versus crystal length for several different velocity-matching conditions, including a bulk modulator with no velocity matching (light solid curve), perfect velocity matching (heavy solid curve), and variations of velocity mismatch in 10% graduations (dashed curves). The case of perfect matching is essentially linear with respect to interaction length, with modulation due to interaction with counterpropagating microwave fields.

Fig. 3
Fig. 3

(a) Coupling coefficient βcoupling plotted versus coupling distance for a waveguide-coupled LiNbO3 modulator. The analytic values calculated from Eq. (2) are plotted (dashed curve) for only positive coupling distances, assuming the input waveguide and crystal heights are equal. Values from Micro-Stripes simulation modeling LiNbO3 as an isotropic dielectric, as well as using the tensor values for the dielectric constant, are plotted as dotted and solid curves, respectively. Critical coupling was experimentally observed for d coupling = 1.07 mm and plotted. (b) The modulator TE104 mode resonance frequency and (c) Q factor for a cutoff-coupled, LiNbO3 waveguide modulator are plotted versus crystal position. The resonance frequency shows how the effective crystal length varies with the coupling distance, whereas the Q factor is essentially unchanged for the same range of values.

Fig. 4
Fig. 4

Magnitude of the simulated complex reflectivity plotted versus excitation frequency illustrates the TE10n mode structure of the waveguide resonator formed by the LiNbO3 crystal. The modulator can be optimally coupled for any of these resonances, although a velocity-mismatch penalty would be incurred for any resonance other than the TE104 mode.

Fig. 5
Fig. 5

Double-pass phase-modulation performance was measured with a grating spectrometer. (a) The FM bandwidth produced by the modulator is estimated by finding the simulated spectrum (dashed curve), including the instrumental response, that best fits the measured spectrum (solid curve). Resolved FM sidebands self-calibrate the spectrometer images since the modulation frequency is measured with high accuracy. (b) SSD bandwidth dependence on microwave power shows the P 1/2 dependence predicted by Eq. (3).

Tables (1)

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Table 1 LiNbO3 Properties

Equations (3)

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νphase=cε31-fc/f02, fc=c2aε3,
βcoupling=16π3Q0Leffaacos2π2aa1-aa22εr-λ02a2εrεr-1×λ01-λ02a2×exp-2πdcouplinga1-2aλ02,
δmod=βLλopt4πfmodabLn36r332ε33Q0Pin1/2;

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