Abstract

This paper presents a detailed investigation of the physical mechanisms underlying the disruption of a lithium niobate electrooptic modulator by RF pulses. It is shown that short-term modulator disruption is a direct consequence of resistive heating within the metal conductor of the coplanar waveguide electrode, which leads to a thermo-optic optical phase shift in the waveguides of the modulator. Resistive heating is also shown to contribute to permanent modulator damage at higher RF power. These results indicate that short-term RF disruption, and possibly RF damage, can be mitigated through improved thermal management. They also predict that short-term photonic link disruption can be reduced, if not eliminated, by use of a phase modulated photonic link.

© 2009 OSA

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2009 (1)

F. Bucholtz, C. A. Villarruel, P. F. Knapp, J. Shue, T. D. Andreadis, R. T. Schermer, J. Gil Gil, and K. J. Williams, “Susceptibility of a Lithium Niobate Modulator to High-Power Microwave Pulses,” Electron. Lett. 45(5), 272–273 (2009).
[CrossRef]

2007 (1)

V. Gopalan, V. Dierolf, and D. A. Scrymgeour, “Defect-Domain Wall Interactions in Trigonal Ferroelectrics,” Annu. Rev. Mater. Res. 37(1), 449–489 (2007).
[CrossRef]

2006 (1)

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the Performance of RF-Over-Fiber Links and Their Impact on Device Design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[CrossRef]

2005 (1)

L. Moretti, M. Iodice, F. G. Della Corte, and I. Rendina, “Temperature Dependence of the Thermo-Optic Coefficient of Lithium Niobate, from 300 to 515 K in the Visible and Infrared Regions,” J. Appl. Phys. 98(3), 036101 (2005).
[CrossRef]

2003 (1)

2000 (1)

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

1997 (1)

M. J. LaGasse and S. Thaniyavarn, “Bias-Free High-Dynamic-Range Phase-Modulated Fiber-Optic Link,” IEEE Photon. Technol. Lett. 9(5), 681–683 (1997).
[CrossRef]

1996 (1)

F. Zhao and ., “Temperature Dependence of Light-Induced Scattering in a Ce:Fe:LiNbO3 Photorefractive Crystal,” Opt. Eng. 35(7), 1985–1992 (1996).
[CrossRef]

1995 (1)

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51(2), 1520–1531 (1995).
[CrossRef] [PubMed]

1992 (1)

G. Cocorullo and I. Rendina, “Thermo-Optical Modulation at 1.5 μm in Silicon Etalon,” Electron. Lett. 28(1), 83–84 (1992).
[CrossRef]

1982 (2)

R. C. Alferness, “Waveguide Electrooptic Modulators,” IEEE Trans. Microw. Theory Tech. 30(8), 1121–1137 (1982).
[CrossRef]

S. K. Korotky, W. Minford, L. Buhl, M. Divino, and R. Alferness, “Mode Size and Method for Estimating the Propagation Constant of a Single-Mode Ti:LiNbO3 Strip Waveguides,” IEEE J. Quantum Electron. 18(10), 1796–1801 (1982).
[CrossRef]

Ackerman, E. I.

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the Performance of RF-Over-Fiber Links and Their Impact on Device Design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[CrossRef]

Alferness, R.

S. K. Korotky, W. Minford, L. Buhl, M. Divino, and R. Alferness, “Mode Size and Method for Estimating the Propagation Constant of a Single-Mode Ti:LiNbO3 Strip Waveguides,” IEEE J. Quantum Electron. 18(10), 1796–1801 (1982).
[CrossRef]

Alferness, R. C.

R. C. Alferness, “Waveguide Electrooptic Modulators,” IEEE Trans. Microw. Theory Tech. 30(8), 1121–1137 (1982).
[CrossRef]

Anderson, D. Z.

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51(2), 1520–1531 (1995).
[CrossRef] [PubMed]

Andreadis, T. D.

F. Bucholtz, C. A. Villarruel, P. F. Knapp, J. Shue, T. D. Andreadis, R. T. Schermer, J. Gil Gil, and K. J. Williams, “Susceptibility of a Lithium Niobate Modulator to High-Power Microwave Pulses,” Electron. Lett. 45(5), 272–273 (2009).
[CrossRef]

Attanasio, D. V.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

Betts, G. E.

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the Performance of RF-Over-Fiber Links and Their Impact on Device Design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[CrossRef]

Bossi, D. E.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

Bucholtz, F.

F. Bucholtz, C. A. Villarruel, P. F. Knapp, J. Shue, T. D. Andreadis, R. T. Schermer, J. Gil Gil, and K. J. Williams, “Susceptibility of a Lithium Niobate Modulator to High-Power Microwave Pulses,” Electron. Lett. 45(5), 272–273 (2009).
[CrossRef]

Buhl, L.

S. K. Korotky, W. Minford, L. Buhl, M. Divino, and R. Alferness, “Mode Size and Method for Estimating the Propagation Constant of a Single-Mode Ti:LiNbO3 Strip Waveguides,” IEEE J. Quantum Electron. 18(10), 1796–1801 (1982).
[CrossRef]

Cocorullo, G.

G. Cocorullo and I. Rendina, “Thermo-Optical Modulation at 1.5 μm in Silicon Etalon,” Electron. Lett. 28(1), 83–84 (1992).
[CrossRef]

Cox, C. H.

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the Performance of RF-Over-Fiber Links and Their Impact on Device Design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[CrossRef]

Della Corte, F. G.

L. Moretti, M. Iodice, F. G. Della Corte, and I. Rendina, “Temperature Dependence of the Thermo-Optic Coefficient of Lithium Niobate, from 300 to 515 K in the Visible and Infrared Regions,” J. Appl. Phys. 98(3), 036101 (2005).
[CrossRef]

Dierolf, V.

V. Gopalan, V. Dierolf, and D. A. Scrymgeour, “Defect-Domain Wall Interactions in Trigonal Ferroelectrics,” Annu. Rev. Mater. Res. 37(1), 449–489 (2007).
[CrossRef]

Divino, M.

S. K. Korotky, W. Minford, L. Buhl, M. Divino, and R. Alferness, “Mode Size and Method for Estimating the Propagation Constant of a Single-Mode Ti:LiNbO3 Strip Waveguides,” IEEE J. Quantum Electron. 18(10), 1796–1801 (1982).
[CrossRef]

Fritz, D. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

Gil Gil, J.

F. Bucholtz, C. A. Villarruel, P. F. Knapp, J. Shue, T. D. Andreadis, R. T. Schermer, J. Gil Gil, and K. J. Williams, “Susceptibility of a Lithium Niobate Modulator to High-Power Microwave Pulses,” Electron. Lett. 45(5), 272–273 (2009).
[CrossRef]

Gopalan, V.

V. Gopalan, V. Dierolf, and D. A. Scrymgeour, “Defect-Domain Wall Interactions in Trigonal Ferroelectrics,” Annu. Rev. Mater. Res. 37(1), 449–489 (2007).
[CrossRef]

Hallemeier, P. F.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

Iodice, M.

L. Moretti, M. Iodice, F. G. Della Corte, and I. Rendina, “Temperature Dependence of the Thermo-Optic Coefficient of Lithium Niobate, from 300 to 515 K in the Visible and Infrared Regions,” J. Appl. Phys. 98(3), 036101 (2005).
[CrossRef]

Kissa, K. M.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

Knapp, P. F.

F. Bucholtz, C. A. Villarruel, P. F. Knapp, J. Shue, T. D. Andreadis, R. T. Schermer, J. Gil Gil, and K. J. Williams, “Susceptibility of a Lithium Niobate Modulator to High-Power Microwave Pulses,” Electron. Lett. 45(5), 272–273 (2009).
[CrossRef]

Korotky, S. K.

S. K. Korotky, W. Minford, L. Buhl, M. Divino, and R. Alferness, “Mode Size and Method for Estimating the Propagation Constant of a Single-Mode Ti:LiNbO3 Strip Waveguides,” IEEE J. Quantum Electron. 18(10), 1796–1801 (1982).
[CrossRef]

Lafaw, D. A.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

LaGasse, M. J.

M. J. LaGasse and S. Thaniyavarn, “Bias-Free High-Dynamic-Range Phase-Modulated Fiber-Optic Link,” IEEE Photon. Technol. Lett. 9(5), 681–683 (1997).
[CrossRef]

Li, G. L.

Maack, D.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

McBrien, G. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

Minford, W.

S. K. Korotky, W. Minford, L. Buhl, M. Divino, and R. Alferness, “Mode Size and Method for Estimating the Propagation Constant of a Single-Mode Ti:LiNbO3 Strip Waveguides,” IEEE J. Quantum Electron. 18(10), 1796–1801 (1982).
[CrossRef]

Moretti, L.

L. Moretti, M. Iodice, F. G. Della Corte, and I. Rendina, “Temperature Dependence of the Thermo-Optic Coefficient of Lithium Niobate, from 300 to 515 K in the Visible and Infrared Regions,” J. Appl. Phys. 98(3), 036101 (2005).
[CrossRef]

Murphy, E. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

Prince, J. L.

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the Performance of RF-Over-Fiber Links and Their Impact on Device Design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[CrossRef]

Rendina, I.

L. Moretti, M. Iodice, F. G. Della Corte, and I. Rendina, “Temperature Dependence of the Thermo-Optic Coefficient of Lithium Niobate, from 300 to 515 K in the Visible and Infrared Regions,” J. Appl. Phys. 98(3), 036101 (2005).
[CrossRef]

G. Cocorullo and I. Rendina, “Thermo-Optical Modulation at 1.5 μm in Silicon Etalon,” Electron. Lett. 28(1), 83–84 (1992).
[CrossRef]

Schermer, R. T.

F. Bucholtz, C. A. Villarruel, P. F. Knapp, J. Shue, T. D. Andreadis, R. T. Schermer, J. Gil Gil, and K. J. Williams, “Susceptibility of a Lithium Niobate Modulator to High-Power Microwave Pulses,” Electron. Lett. 45(5), 272–273 (2009).
[CrossRef]

Scrymgeour, D. A.

V. Gopalan, V. Dierolf, and D. A. Scrymgeour, “Defect-Domain Wall Interactions in Trigonal Ferroelectrics,” Annu. Rev. Mater. Res. 37(1), 449–489 (2007).
[CrossRef]

Shue, J.

F. Bucholtz, C. A. Villarruel, P. F. Knapp, J. Shue, T. D. Andreadis, R. T. Schermer, J. Gil Gil, and K. J. Williams, “Susceptibility of a Lithium Niobate Modulator to High-Power Microwave Pulses,” Electron. Lett. 45(5), 272–273 (2009).
[CrossRef]

Thaniyavarn, S.

M. J. LaGasse and S. Thaniyavarn, “Bias-Free High-Dynamic-Range Phase-Modulated Fiber-Optic Link,” IEEE Photon. Technol. Lett. 9(5), 681–683 (1997).
[CrossRef]

Villarruel, C. A.

F. Bucholtz, C. A. Villarruel, P. F. Knapp, J. Shue, T. D. Andreadis, R. T. Schermer, J. Gil Gil, and K. J. Williams, “Susceptibility of a Lithium Niobate Modulator to High-Power Microwave Pulses,” Electron. Lett. 45(5), 272–273 (2009).
[CrossRef]

Williams, K. J.

F. Bucholtz, C. A. Villarruel, P. F. Knapp, J. Shue, T. D. Andreadis, R. T. Schermer, J. Gil Gil, and K. J. Williams, “Susceptibility of a Lithium Niobate Modulator to High-Power Microwave Pulses,” Electron. Lett. 45(5), 272–273 (2009).
[CrossRef]

Wooten, E. L.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

Yi-Yan, A.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

Yu, P. K. L.

Zhao, F.

F. Zhao and ., “Temperature Dependence of Light-Induced Scattering in a Ce:Fe:LiNbO3 Photorefractive Crystal,” Opt. Eng. 35(7), 1985–1992 (1996).
[CrossRef]

Zozulya, A. A.

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51(2), 1520–1531 (1995).
[CrossRef] [PubMed]

Annu. Rev. Mater. Res. (1)

V. Gopalan, V. Dierolf, and D. A. Scrymgeour, “Defect-Domain Wall Interactions in Trigonal Ferroelectrics,” Annu. Rev. Mater. Res. 37(1), 449–489 (2007).
[CrossRef]

Electron. Lett. (2)

G. Cocorullo and I. Rendina, “Thermo-Optical Modulation at 1.5 μm in Silicon Etalon,” Electron. Lett. 28(1), 83–84 (1992).
[CrossRef]

F. Bucholtz, C. A. Villarruel, P. F. Knapp, J. Shue, T. D. Andreadis, R. T. Schermer, J. Gil Gil, and K. J. Williams, “Susceptibility of a Lithium Niobate Modulator to High-Power Microwave Pulses,” Electron. Lett. 45(5), 272–273 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. K. Korotky, W. Minford, L. Buhl, M. Divino, and R. Alferness, “Mode Size and Method for Estimating the Propagation Constant of a Single-Mode Ti:LiNbO3 Strip Waveguides,” IEEE J. Quantum Electron. 18(10), 1796–1801 (1982).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A Review of Lithium Niobate Modulators for Fiber-Optic Communications Systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. J. LaGasse and S. Thaniyavarn, “Bias-Free High-Dynamic-Range Phase-Modulated Fiber-Optic Link,” IEEE Photon. Technol. Lett. 9(5), 681–683 (1997).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (2)

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the Performance of RF-Over-Fiber Links and Their Impact on Device Design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[CrossRef]

R. C. Alferness, “Waveguide Electrooptic Modulators,” IEEE Trans. Microw. Theory Tech. 30(8), 1121–1137 (1982).
[CrossRef]

J. Appl. Phys. (1)

L. Moretti, M. Iodice, F. G. Della Corte, and I. Rendina, “Temperature Dependence of the Thermo-Optic Coefficient of Lithium Niobate, from 300 to 515 K in the Visible and Infrared Regions,” J. Appl. Phys. 98(3), 036101 (2005).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Eng. (1)

F. Zhao and ., “Temperature Dependence of Light-Induced Scattering in a Ce:Fe:LiNbO3 Photorefractive Crystal,” Opt. Eng. 35(7), 1985–1992 (1996).
[CrossRef]

Phys. Rev. A (1)

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51(2), 1520–1531 (1995).
[CrossRef] [PubMed]

Other (18)

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Figures (13)

Fig. 1
Fig. 1

Schematic of an antenna-fed photonic link. Electromagnetic shielding and nonconductive fiber-optic cables isolate the laser and receiver electronics from high-power pickup at the antenna. Only the modulator is exposed to external electromagnetic sources.

Fig. 2
Fig. 2

Schematic diagram of the integrated-optic, Mach-Zehnder EO modulator used in this study. Light launched into the input optical waveguide of the LN crystal is split equally into two paths at the first y-branch, and then interfered at the second y-branch. Separate RF and bias electrodes apply an electric field to the LN crystal, which in turn modulates the optical phase of the two waveguides via the EO effect.

Fig. 3
Fig. 3

Schematic diagram of the experimental setup. The circuit element after the photodiode represents a low-pass filter.

Fig. 4
Fig. 4

Linear voltage ramp applied to the bias electrode (a), and resulting slowly-varying modulator transmission (b). The red curve in (b) plots the modulator response prior to RF pulsing, while the blue plots the response during an applied RF pulse burst. Each narrow spike on the blue curve coincides with a RF pulse, while the broader after-pulse following each spike is indicative of a lingering, non-instantaneous response.

Fig. 5
Fig. 5

Modulator transmission following the application of a single RF pulse (a), and the corresponding change in MZ relative phase, normalized to its maximum value (b). The curves overlap in (b), which indicates that the shape of each after-pulse was independent of the RF pulse power. The change in relative phase Δϕ0 was not plotted during the RF pulse (0≤t≤1μs) due to measurement uncertainty.

Fig. 6
Fig. 6

Relationship between after-pulse amplitude and (a) peak pulse power, and (b) pulse width, following the application of a single RF pulse. Solid lines correspond to linear fits to the data, and demonstrate that 0|max was linearly proportional to both pulse power and pulse width in the ranges shown.

Fig. 7
Fig. 7

Change in MZ relative phase induced by a single pair of pulses (a), and the resulting increase in after-pulse amplitude following the second pulse (b). The different curves in (a) correspond different pulse spacing, incremented from 100 to 500 μs. Time t = 0 coincides with the start of the second pulse. In (a) data is not plotted during each RF pulse. The solid line in (b) corresponds to an exponential fit, with time constant 270 μs.

Fig. 8
Fig. 8

Change in MZ relative phase induced by a pulse train of 20 identical RF pulses. The exponential decay of the relative phase envelope during pulsing indicates that the modulator approached a steady state. The time constant of the steady-state buildup, 270 μs, closely matched that of the subsequent relaxation. Data is not plotted during each pulse, leading to discontinuity in the curve.

Fig. 9
Fig. 9

Schematic diagram of the modulator cross-section. The axes coincide with the principal axes of the LN crystal.

Fig. 10
Fig. 10

Measured and simulated temporal evolution of the RF-induced relative phase change. Simulated results correspond to the case in which both optical waveguides were shifted off center with respect to the CPW electrodes by 0.24 μm in the –z direction.

Fig. 11
Fig. 11

Simulated dependence of the RF-induced steady-state (left axis) and transient (right axis) relative phase change on the waveguide-electrode center-to-center offset, Δzoffset .

Fig. 12
Fig. 12

Phase modulated version of the photonic link in Fig. 1, which utilizes a LN EO phase modulator, asymmetric MZ phase demodulator, and balanced photodiode detection. This link is irresponsive to slow variations in optical phase.

Fig. 13
Fig. 13

Simulated fraction of thermal conduction that occurs along the y-direction, within the center CPW conductor, as a function of distance along the electrode. Times indicated refer to the time elapsed from the start of the 1 μs pulse.

Tables (1)

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Table 1 Physical Properties Used in Thermal Model

Equations (35)

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T M Z = T a v g 2 ( 1 + η cos φ ) ,
φ = φ R F + φ S V
φ R F = π V i n V π , R F
φ S V = π V b i a s V π , b i a s + φ 0
V o u t ( t ) = ( P l a s e r T f i b e r Z o u t 1 + Z T / Z o u t ) T M Z ( t ) ,
T M Z = T a v g 2 [ 1 + η ( cos φ R F cos φ S V sin φ R F sin φ S V ) ] .
V i n ( t ) = V 0 ( t ) sin ω R F t ,
cos φ R F = J 0 ( π V 0 V π , R F ) + 2 m = 1 J 2 m ( π V 0 V π , R F ) cos 2 m ω R F t
sin φ R F = 2 m = 0 J 2 m + 1 ( π V 0 V π , R F ) sin ( 2 m + 1 ) ω R F t ,
T M Z ( S V ) = T a v g 2 [ 1 + η cos φ S V J 0 ( π V 0 V π ) ] .
T M Z ( S V ) T a v g 2 ( V 0 > > V π )
T M Z ( S V ) = T a v g 2 ( 1 + η cos φ S V ) ( V 0 = 0 ) .
T M Z ( S V ) T a v g 1 2 ( 1 + cos φ 0 )
Δ φ 0 ( t ) φ 0 ( t ) φ 0 ( 0 )
| Δ φ 0 | max max ( | Δ φ 0 ( t ) | ) ,
Δ φ ( t ) = Δ φ ( n ) ( t ) + Δ φ ( S ) ( t )
Δ φ ( n ) ( t ) = 2 π λ 0 y 0 L o y 0 [ Δ n e f f , 1 ( y , t ) Δ n e f f , 2 ( y , t ) ] d y
Δ φ ( S ) ( t ) = 2 π n λ 0 y 0 L o y 0 [ Δ S y , e f f , 1 ( y , t ) Δ S y , e f f , 2 ( y , t ) ] d y
Δ n e f f , i ( y , t ) = | ψ i ( x , z ) | 2 Δ n ( x , y , z , t ) d x d z ,
Δ S y , e f f , i ( y , t ) = | ψ i ( x , z ) | 2 Δ S y ( x , y , z , t ) d x d z ,
| ψ i ( x , z ) | 2 d x d z = 1 .
ρ C p T t ( κ T ) = Q
P R F ( y , t ) = P i n , R F ( t ) e 2 α y
d P R F ( y , t ) d y = 2 α P i n , R F ( t ) e 2 α y ,
Q c ( y , t ) = 2 α F c P i n , R F ( t ) e 2 α y w c h e
Q o ( y , t ) = α ( 1 F c ) P i n , R F ( t ) e 2 α y w o h e
Q ( y , t ) Q ( 0 , t ) e 2 α y ,
Δ n ( x , y , z , t ) A Δ T ( x , y , z , t ) ,
Δ φ ( t ) π α λ 0 ( 1 e 2 α L e ) [ Δ n e f f , 1 ( 0 , t ) Δ n e f f , 2 ( 0 , t ) ] ,
| ψ i | 2 = ( 64 2 x 2 π w m h m 3 ) exp [ 8 ( z z i w m ) 2 4 ( x h m ) 2 ]
Δ T c ( y ) U p u l s e Q c ( y , 0 ) ρ C p P i n , R F ( 0 ) = 2 α F c e 2 α y w c h e ρ C p .
( κ T ) = x z ( κ x z T ) + κ 2 T y 2
ρ e C p , e T y z t κ e 2 T y z y 2 = Q c
ρ e C p , e T x z t x z ( κ x z T x z ) = Q c
κ e 2 T y z / y 2 ( κ T ) = ( 1 + T x z / t T y z / t ) 1 for (Q c = 0),

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