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 [2–4]. 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 V_π 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 (Z_m) 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]:

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, N_m, can be directly obtained as,

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, N_m, is 3.3. The effective composite BaTiO₃/MgO dielectric constant is given by [12],

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 (${\epsilon }_r=\sqrt{{\epsilon }_x·{\epsilon }_z}=35.1$) [14], and much smaller than that of BaTiO₃ (ε_r~500 at 40 GHz) [5]. The lower composite ε_r 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 (N_m=3.3 at 40 GHz, effective optical refractive index n_eff=2.16 at 1.55 µm), impedance mismatch (Z_m=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 (Z_m=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 Z_m=30 Ω, N_m=3.3 at 40 GHz, α_c=1.0 1 dB·cm ^-1·GHz ^-0.5 and α_d=0.3 dB·cm ^-1·GHz ^-1 ; (c) calculated response for Z_m=45 Ω, N_m=3.3 at 40 GHz, α_c=0.5 dB·cm ^-1·GHz ^-0.5 and α_d=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]:

where Γ is the microwave-optical overlap factor, λ is the optical wavelength, and G is the electrode gap. For comparison, we use α_c=0.45 dB·cm ^-1·GHz ^-0.5, λ=1.55 µm, and G=15 µm, as in reference [16]. The n_eff, r_eff 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.