Abstract

The high frequency operation of a low-voltage electrooptic modulator based on a strip-loaded BaTiO3 thin film waveguide structure has been demonstrated. The epitaxial BaTiO3 thin film on an MgO substrate forms a composite structure with a low effective dielectric constant of 20.8 at 40 GHz. A 3.9 V half-wave voltage with a 3.7 GHz 3-dB bandwidth and a 150 pm/V effective electrooptic coefficient is obtained for the 3.2mm-long modulator at 1.55 µm. Broadband modulation up to 40 GHz is measured with a calibrated detection system. Numerical simulations indicate that the BaTiO3 thin film modulator has the potential for a 3-dB operational bandwidth in excess of 40 GHz through optimized design.

© 2004 Optical Society of America

1. Introduction

Electrooptic waveguide modulators are essential for high-speed and wide bandwidth optical communication systems and ultrafast information processing applications. BaTiO3 is an attractive ferroelectric material for electrooptic modulators due to its large electrooptic coefficients [1]. However, bulk BaTiO3 has a large dielectric constant that limits its high-speed and wide bandwidth operation. The bandwidth is primarily limited by the velocity mismatch between the optical and microwave signals. For high-speed and wideband applications, BaTiO3 thin film modulators are being developed [24]. By using a composite structure of BaTiO3/MgO, a lower effective dielectric constant is obtained. This improves velocity matching between the microwave and optical waves [5]. In this report we describe our development of a traveling wave modulator based on a strip-loaded BaTiO3 thin film waveguide structure for high-speed and wideband operation. The thin film waveguide modulator has a low half-wave voltage of 3.9 V for a 3.2mm-long electrode. Optical modulation up to 40 GHz was directly measured with a calibrated detection system.

2. Fabrication

A schematic cross-section of the thin film electrooptic waveguide modulator is shown in Fig. 1(a).

 

Fig. 1. (a) Schematic cross-section of the electrooptic waveguide modulator. (b) Low frequency electrooptic modulator performance at 1561 nm wavelength. Applied 1 kHz triangle-driving voltages with 2 V DC bias on 3.2 mm long electrode (bottom trace, 4 V/div) and modulation output signal (top trace, 0.2 V/div).

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The waveguide has a strip-loaded structure for low-loss (<1dB/cm) and single-mode operation [6]. The modulator was fabricated from a 570 nm thick epitaxial BaTiO3 thin film grown on a (100) oriented MgO substrate by a two-step low-pressure metalorganic chemical vapor deposition (MOCVD) process [7]. The Si3N4 strip-loaded layer was 4 µm wide and 125 nm thick, fabricated by standard plasma enhanced chemical vapor deposition and reactive ion etching processes [6]. The waveguide was aligned to the <110> crystallographic direction of the MgO substrate. The waveguide pattern was transferred by reactive ion etching the Si3N4 layer using a CF4-based chemistry. A lithographic liftoff process with subsequent deposition of 15 nm Cr and 350 nm Au by E-beam evaporation was used to obtain the coplanar electrodes. The electrode length and gap were 3.2 mm and 8 µm, respectively.

3. Modulation characterization and results

The electrooptic response of the phase modulator was first characterized at a low driving frequency. Linearly polarized light (λ=1561 nm) was coupled into the waveguide through a single-mode lensed-fiber with a 2-µm beam spot (Nanonics Imaging Ltd.). The linearly polarized input light was oriented at+45° with respect to the MgO<001> direction and the output polarizer was rotated 90° relative to the input polarization. The waveguide output was collected by a 40X microscope objective and focused on a photoreceiver (New Focus, Model: 2033). The half-wave voltage Vπ was measured by applying a 1 kHz triangular waveform with DC bias to the electrodes. The applied electric signal and output modulated signal are shown in Fig. 1(b). The maximum and minimum output intensities were observed when DC bias voltages were 0.05 V and 3.95 V, respectively. The half-wave voltage of the modulator was 3.9 V with 2 V DC bias at 1561 nm, corresponding to an effective electrooptic coefficient of 150 pm/V with an overlap factor of 0.59 [8].

 

Fig. 2. Schematic diagram of the modulator characterization setup.

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The high-frequency response was characterized by a calibrated direct detection system, shown in Fig. 2. The output of a 15-mW CW DFB laser diode at 1561 nm was coupled into the thin film waveguide through the same single-mode lensed-fiber. The output light from the waveguide was coupled into a single mode fiber-optic polarizer. The fiber-optic polarizer oriented at -45° relative to the MgO<001> direction was utilized as the analyzer to convert the phase modulator into an intensity modulator. A pigtailed photoreceiver module with a 39 GHz bandwidth (U2t Photonics AG, Model: XPRV2021) was connected to the output of the fiber-optic polarizer. A 65 GHz broadband microwave amplifier with 27 dB maximum gain and 23 dBm saturated output power (Centellax Inc., Model: OA4MVM) was used to drive the modulator through a wide bandwidth probe on the electrode. The output of the electrode was connected to a 50Ω termination load. A 45 GHz bandwidth bias-tee was used to combine DC bias voltages with microwave signals. Microwave signals from 50 MHz to 40.05 GHz were generated by one port of a vector network analyzer (Agilent-8722ES). The demodulated microwave signals from the wide bandwidth photoreceiver were then measured with the vector network analyzer (VNA).

The characteristic impedance (Zm) of the coplanar waveguide electrode was about 30Ω at 40 GHz. The reflected microwave power loss, S11, was -6 dB to -8 dB over the 50 MHz to 40.05 GHz ranges, as shown in Fig. 3(a). The total microwave power loss through the 3.2mm-long electrode as a function of frequency is shown in Fig. 3(b). The ripple of the transmitted power is due to multiple reflections caused by the impedance mismatch.

 

Fig.3. Microwave power loss characterization of the electrodes. (a) Reflected loss (S11); (b) transmitted loss (S21); (c) fitted loss assuming a linear and square root frequency dependence; (d) dielectric and radiation losses assuming a linear frequency dependence; (e) conductor loss assuming a square root frequency dependence.

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The total frequency dependent transmitted power loss, α(f), in Fig. 3(c) is described by the function [9]:

α(f)=αc·L·f+αd·L·f

where α c is the metallic conductor loss coefficient, α d is the dielectric and radiation loss coefficient, L is the electrode length, and f is the frequency. The dielectric and radiation loss coefficient was 0.3±0.1 dB·cm -1·GHz -1 in Fig. 3(d). The conductor loss coefficient was measured to be 1.0±0.1 dB·cm -1·GHz -0.5 in Fig. 3(e). The high conductor loss coefficient is attributed to the thin coplanar gold electrodes. A thicker gold layer can significantly improve the conductor loss performance [10].

The effective microwave index of the modulator was evaluated from VNA time-domain measurements of the transmission response from the coplanar electrodes [11]. Transmission response in the time-domain is converted from frequency domain information over the 50 MHz to 40.05 GHz frequency range using an inverse Fourier transform in near real-time. A microwave impulse was coupled into one side of the coplanar electrode from a transmitter port of the VNA, and the transmitted impulse was collected from the opposite end of the electrode by a receiver port of the VNA. Through the measured microwave impulse transmission time, the effective microwave index, Nm, can be directly obtained as,

Nm=c·τL

where c is the speed of light in vacuum, L is the electrode length, and τ is the transmission time of the microwave impulse along the electrode. Fig. 4(a) shows a 35 ps microwave transmission time for an impulse along the 3.2mm-long electrode. From Eq. (2), the effective microwave index, Nm, is 3.3. The effective composite BaTiO3/MgO dielectric constant is given by [12],

εBaTiO3/mgO=2·Nm21

From Eq. (3), the effective composite BaTiO3/MgO dielectric constant is calculated as 20.8. The value of the effective composite BaTiO3/MgO dielectric constant is smaller than that of z-cut LiNbO3 (εr=εx·εz=35.1) [14], and much smaller than that of BaTiO3r~500 at 40 GHz) [5]. The lower composite εr of BaTiO3/MgO and the high effective electrooptic coefficients of the BaTiO3 thin film are promising for high-speed modulation operation.

 

Fig. 4. (a) Measured 35 ps time delay for a 3.2 mm long electrodes. (b) Calculated effective microwave index as a function of frequency through measured electrical S-parameters.

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Because the tens of picoseconds impulse width is dominated by high frequency components, the measured index reflects the electrode’s effective microwave index in the high frequency range. This is verified by the calculated effective microwave index dispersion curve from the measured electrical S-parameters [14]. As shown in Fig. 4(b), as the frequency increases, the effective microwave refractive index decreases. At high frequency (>10 GHz), its value is close to that determined by the transmission response measurement.

The optical response of the modulator at high frequency was measured with the calibrated direct detection system, shown in Fig. 2. The modulator was DC biased at 2.0 V and operated at the linear transfer portion of the modulator to maximize the modulation signal. The measured optical response from 50 MHz to 40.05 GHz is shown in Fig. 5(a). Broadband modulation was observed out to 40 GHz, primarily limited by velocity mismatch (Nm=3.3 at 40 GHz, effective optical refractive index neff=2.16 at 1.55 µm), impedance mismatch (Zm=30Ω) and the high microwave loss of the electrode (α c=1.0±0.1 dB·cm -1·GHz -0.5 and α d=0.3±0.1 dB·cm -1·GHz -1). Due to impedance mismatch, the optical response falls off rapidly at a frequency less than 3 GHz. The -3 dB bandwidth of the modulator was 3.7 GHz. Fig. 5(b) shows the result of theoretical simulation [13] based on the measured effective microwave index dispersion curve, electrode loss and impedance mismatch. The theoretical simulation and measured data are in good agreement. Fig. 5(c) is the theoretical simulation result, assuming the same velocity mismatch characteristics, but a better impedance matching (Zm=45 Ω) and a typical conductor loss, α c=0.5 1 0.5 dB·cm -1·GHz -0.5 [9] through optimized design of the electrodes and a thick gold layer. The simulation results indicate that significant improvement of the high frequency response is possible through optimized design using a thick SiO2 buffer layer and thick electrodes to achieve velocity matching, impedance matching, and low electrode loss.

 

Fig. 5. Frequency response of the modulator. (a) Measured response from the calibrated detection system; (b) predicted response for Zm=30 Ω, Nm=3.3 at 40 GHz, αc=1.0 1 dB·cm -1·GHz -0.5 and αd=0.3 dB·cm -1·GHz -1 ; (c) calculated response for Zm=45 Ω, Nm=3.3 at 40 GHz, αc=0.5 dB·cm -1·GHz -0.5 and αd=0.3 dB·cm -1·GHz -1.

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To compare the BaTiO3 thin film modulators with LiNbO3 modulators, we utilize the following figure of merit F [16]:

F=(1.484neff3reffΓαcλG)

where Γ is the microwave-optical overlap factor, λ is the optical wavelength, and G is the electrode gap. For comparison, we use αc=0.45 dB·cm -1·GHz -0.5, λ=1.55 µm, and G=15 µm, as in reference [16]. The neff, reff and Γ are 2.16, 150 pm/V and 0.59, respectively. The figure of merit F for BaTiO3 thin film modulators is then ~30 GHz/V2, much larger than that for LiNbO3 modulators, 1 GHz/V2 [16].

4. Conclusions

In summary, we have fabricated and tested a BaTiO3 thin film traveling wave electrooptic modulator. The 3.2mm-long modulator exhibits a low half-wave voltage of 3.9 V at a 2.0 V DC bias. The -3dB electrical bandwidth is 3.7 GHz. The calculated effective electrooptic coefficient is as high as 150 pm/V at 1561 nm wavelength. An effective microwave index as low as 3.3 at 40 GHz was measured for the thin film modulator. Broadband modulation out to 40 GHz was observed. Numerical simulation indicates that compact, low power electro-optic waveguide modulators with a 40 GHz 3-dB bandwidth might be possible using the high EO coefficient of BaTiO3 thin films.

Acknowledgments

The authors acknowledge financial support from the US Air Force under contract AFRL-33615-02-C-5053, and the NSF under contracts ECS-0123469 and MRSEC DMR-0076977.

References and Links

1. M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electrooptic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B 50, 5941–5949 (1994). [CrossRef]  

2. D.M. Gill, C.W. Conrad, G. Ford, B.W. Wessels, and S.T. Ho, “Thin-film channel waveguide electro-optic modulator in epitaxial BaTiO3,” Appl. Phys. Lett. 71, 1783–1785 (1997). [CrossRef]  

3. A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin film optical waveguide modulators,” Appl. Phys. Lett. 81, 1375–1377 (2002). [CrossRef]  

4. P. Tang, D.J. Towner, A. L. Meier, and B. W. Wessels, “Low-voltage, polarization-insensitive, electro-optic modulator based on a polydomain barium titanate thin film,” Appl. Phys. Lett. 85, 4615–4617 (2004). [CrossRef]  

5. T. Hamano, D. J. Towner, and B. W. Wessels, “Relative dielectric constant of epitaxial BaTiO3 thin films in the GHz frequency range,” Appl. Phys. Lett. 83, 5274–5276 (2003). [CrossRef]  

6. P. Tang, D.J. Towner, A. L. Meier, and B.W. Wessels, “Polarisation-insensitive Si3N4 strip-loaded BaTiO3 thin-film waveguide with low propagation losses,” Electron. Lett. 39,1651–1652 (2003). [CrossRef]  

7. D. J. Towner, J. Ni, T.J. Marks, and B.W. Wessels, “Effects of two-stage deposition on the structure and properties of heteroepitaxial BaTiO3 thin films,” J. Cryst. Growth 255, 107–113 (2003). [CrossRef]  

8. P. Tang, D. J. Towner, A. L. Meier, and B. W. Wessels, “Low-loss electrooptic BaTiO3 thin film waveguide modulator,” IEEE Photon. Technol. Lett. 16, 1837–1839 (2004). [CrossRef]  

9. G. K. Gopalakrishnan, W. K. Burns, R. W. McElhanon, C. G. Bulmer, and A. S. Greenblatt, “Performance and modeling of broadband LiNbO3 traveling wave optical intensity modulators,” J. Lightwave Technol. 12, 1807–1818 (1994). [CrossRef]  

10. D. M. Gill and A. Chowdhury, “Electro-optic polymer-based modulator design and perormance for 40 Gb/s system applications,” J. Lightwave Technol. 20, 2145–2153 (2002). [CrossRef]  

11. P. Tang, A. L. Meier, D. J. Towner, T. Hamano, and B. W. Wessels, “BaTiO3 waveguide modulators with 360 pm/V effective electro-optic coefficient at 1.55 µm, ” in Optical Amplifiers and Their Applications/Integrated Photonics Research Topical Meetings (The Optical Society of America, Washington, DC, 2004), PD3-1.

12. N. Dagli, “Wide-bandwidth lasers and modulators for RF photonics,” IEEE Trans. Microwave Theory Tech. 47, 1151–1171 (1999). [CrossRef]  

13. K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, (Norwood, MA: Artech House, 1996).

14. K. Kubota, J. Noda, and O. Mikami, “Traveling wave optical modulator using a directional coupler LiNbO3 waveguide,” IEEE J. Quantum Electron. 16, 754–760 (1980). [CrossRef]  

15. G. Gonzales, Microwave Transition Amplifiers, (Englewood Cliffs, NJ: Prentice, 1984).

16. A. Chowdhury and L. McCaughan, “Figure of merit for near-velocity-matched traveling-wave modulators,” Opt. Lett. 26, 1317–1319 (2001). [CrossRef]  

References

  • View by:
  • |

  1. M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, �??Dielectric, elastic, piezoelectric, electrooptic, and elasto-optic tensors of BaTiO3 crystals,�?? Phys. Rev. B 50, 5941-5949 (1994).
    [CrossRef]
  2. D.M. Gill, C.W. Conrad, G. Ford, B.W. Wessels, and S.T. Ho, �??Thin-film channel waveguide electro-optic modulator in epitaxial BaTiO3,�?? Appl. Phys. Lett. 71, 1783-1785 (1997).
    [CrossRef]
  3. A. Petraru, J. Schubert, M. Schmid, and C. Buchal, �??Ferroelectric BaTiO3 thin film optical waveguide modulators,�?? Appl. Phys. Lett. 81, 1375-1377 (2002).
    [CrossRef]
  4. P. Tang, D.J. Towner, A. L. Meier, and B. W. Wessels, �??Low-voltage, polarization-insensitive, electro-optic modulator based on a polydomain barium titanate thin film,�?? Appl. Phys. Lett. 85, 4615-4617 (2004).
    [CrossRef]
  5. T. Hamano, D. J. Towner, and B. W. Wessels, �??Relative dielectric constant of epitaxial BaTiO3 thin films in the GHz frequency range,�?? Appl. Phys. Lett. 83, 5274-5276 (2003).
    [CrossRef]
  6. P. Tang, D.J. Towner, A. L. Meier, and B.W. Wessels, �??Polarisation-insensitive Si3N4 strip-loaded BaTiO3 thin-film waveguide with low propagation losses,�?? Electron. Lett. 39, 1651-1652 (2003).
    [CrossRef]
  7. D. J. Towner, J. Ni, T.J. Marks, and B.W. Wessels, �??Effects of two-stage deposition on the structure and properties of heteroepitaxial BaTiO3 thin films,�?? J. Cryst. Growth 255, 107-113 (2003).
    [CrossRef]
  8. P. Tang, D. J. Towner, A. L. Meier, and B. W. Wessels, �??Low-loss electrooptic BaTiO3 thin film waveguide modulator,�?? IEEE Photon. Technol. Lett. 16, 1837-1839 (2004).
    [CrossRef]
  9. G. K. Gopalakrishnan, W. K. Burns, R. W. McElhanon, C. G. Bulmer, and A. S. Greenblatt, �??Performance and modeling of broadband LiNbO3 traveling wave optical intensity modulators,�?? J. Lightwave Technol. 12, 1807-1818 (1994).
    [CrossRef]
  10. D. M. Gill, and A. Chowdhury, �??Electro-optic polymer-based modulator design and perormance for 40 Gb/s system applications,�?? J. Lightwave Technol. 20, 2145-2153 (2002).
    [CrossRef]
  11. P. Tang, A. L. Meier, D. J. Towner, T. Hamano, and B. W. Wessels, �??BaTiO3 waveguide modulators with 360 pm/V effective electro-optic coefficient at 1.55 �?�m, �?? in Optical Amplifiers and TheirApplications/Integrated Photonics Research Topical Meetings (The Optical Society of America, Washington, DC, 2004), PD3-1.
  12. N. Dagli, �??Wide-bandwidth lasers and modulators for RF photonics,�?? IEEE Trans. Microwave Theory Tech. 47, 1151-1171 (1999).
    [CrossRef]
  13. K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, (Norwood, MA: Artech House, 1996).
  14. K. Kubota, J. Noda, and O. Mikami, �??Traveling wave optical modulator using a directional coupler LiNbO3 waveguide,�?? IEEE J. Quantum Electron. 16, 754-760 (1980).
    [CrossRef]
  15. G. Gonzales, Microwave Transition Amplifiers, (Englewood Cliffs, NJ: Prentice, 1984).
  16. A. Chowdhury, and L. McCaughan, �??Figure of merit for near-velocity-matched traveling-wave modulators,�?? Opt. Lett. 26, 1317-1319 (2001).
    [CrossRef]

Appl. Phys. Lett. (4)

D.M. Gill, C.W. Conrad, G. Ford, B.W. Wessels, and S.T. Ho, �??Thin-film channel waveguide electro-optic modulator in epitaxial BaTiO3,�?? Appl. Phys. Lett. 71, 1783-1785 (1997).
[CrossRef]

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, �??Ferroelectric BaTiO3 thin film optical waveguide modulators,�?? Appl. Phys. Lett. 81, 1375-1377 (2002).
[CrossRef]

P. Tang, D.J. Towner, A. L. Meier, and B. W. Wessels, �??Low-voltage, polarization-insensitive, electro-optic modulator based on a polydomain barium titanate thin film,�?? Appl. Phys. Lett. 85, 4615-4617 (2004).
[CrossRef]

T. Hamano, D. J. Towner, and B. W. Wessels, �??Relative dielectric constant of epitaxial BaTiO3 thin films in the GHz frequency range,�?? Appl. Phys. Lett. 83, 5274-5276 (2003).
[CrossRef]

Electron. Lett. (1)

P. Tang, D.J. Towner, A. L. Meier, and B.W. Wessels, �??Polarisation-insensitive Si3N4 strip-loaded BaTiO3 thin-film waveguide with low propagation losses,�?? Electron. Lett. 39, 1651-1652 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Kubota, J. Noda, and O. Mikami, �??Traveling wave optical modulator using a directional coupler LiNbO3 waveguide,�?? IEEE J. Quantum Electron. 16, 754-760 (1980).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. Tang, D. J. Towner, A. L. Meier, and B. W. Wessels, �??Low-loss electrooptic BaTiO3 thin film waveguide modulator,�?? IEEE Photon. Technol. Lett. 16, 1837-1839 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

N. Dagli, �??Wide-bandwidth lasers and modulators for RF photonics,�?? IEEE Trans. Microwave Theory Tech. 47, 1151-1171 (1999).
[CrossRef]

J. Cryst. Growth (1)

D. J. Towner, J. Ni, T.J. Marks, and B.W. Wessels, �??Effects of two-stage deposition on the structure and properties of heteroepitaxial BaTiO3 thin films,�?? J. Cryst. Growth 255, 107-113 (2003).
[CrossRef]

J. Lightwave Technol. (2)

G. K. Gopalakrishnan, W. K. Burns, R. W. McElhanon, C. G. Bulmer, and A. S. Greenblatt, �??Performance and modeling of broadband LiNbO3 traveling wave optical intensity modulators,�?? J. Lightwave Technol. 12, 1807-1818 (1994).
[CrossRef]

D. M. Gill, and A. Chowdhury, �??Electro-optic polymer-based modulator design and perormance for 40 Gb/s system applications,�?? J. Lightwave Technol. 20, 2145-2153 (2002).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, �??Dielectric, elastic, piezoelectric, electrooptic, and elasto-optic tensors of BaTiO3 crystals,�?? Phys. Rev. B 50, 5941-5949 (1994).
[CrossRef]

Other (3)

K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, (Norwood, MA: Artech House, 1996).

G. Gonzales, Microwave Transition Amplifiers, (Englewood Cliffs, NJ: Prentice, 1984).

P. Tang, A. L. Meier, D. J. Towner, T. Hamano, and B. W. Wessels, �??BaTiO3 waveguide modulators with 360 pm/V effective electro-optic coefficient at 1.55 �?�m, �?? in Optical Amplifiers and TheirApplications/Integrated Photonics Research Topical Meetings (The Optical Society of America, Washington, DC, 2004), PD3-1.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic cross-section of the electrooptic waveguide modulator. (b) Low frequency electrooptic modulator performance at 1561 nm wavelength. Applied 1 kHz triangle-driving voltages with 2 V DC bias on 3.2 mm long electrode (bottom trace, 4 V/div) and modulation output signal (top trace, 0.2 V/div).

Fig. 2.
Fig. 2.

Schematic diagram of the modulator characterization setup.

Fig.3.
Fig.3.

Microwave power loss characterization of the electrodes. (a) Reflected loss (S11); (b) transmitted loss (S21); (c) fitted loss assuming a linear and square root frequency dependence; (d) dielectric and radiation losses assuming a linear frequency dependence; (e) conductor loss assuming a square root frequency dependence.

Fig. 4.
Fig. 4.

(a) Measured 35 ps time delay for a 3.2 mm long electrodes. (b) Calculated effective microwave index as a function of frequency through measured electrical S-parameters.

Fig. 5.
Fig. 5.

Frequency response of the modulator. (a) Measured response from the calibrated detection system; (b) predicted response for Zm=30 Ω, Nm=3.3 at 40 GHz, αc=1.0 1 dB·cm -1·GHz -0.5 and αd=0.3 dB·cm -1·GHz -1 ; (c) calculated response for Zm=45 Ω, Nm=3.3 at 40 GHz, αc=0.5 dB·cm -1·GHz -0.5 and αd=0.3 dB·cm -1·GHz -1.

Equations (4)

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α ( f ) = α c · L · f + α d · L · f
N m = c · τ L
ε B a T i O 3 / m g O = 2 · N m 2 1
F = ( 1 . 484 n eff 3 r eff Γ α c λ G )

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