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Abstract
Solid-state light detection and ranging, capable of performing beam scanning without using any mechanical moving parts, requires a phase-modulator array. Polymers facilitate the fabrication of efficient phase modulators with low drive power, owing to their high thermo-optic (TO) effect and low thermal conductivity. We designed and fabricated a polymeric phase-modulator array and analyzed the temporal response of the TO phase modulator. The frequency response of the phase modulator was measured for a Mach–Zehnder interferometer (MZI), and the transfer function was modeled in terms of multiple poles and zeros. The frequency response of a fabricated beam-scanning device incorporating the TO phase modulator was also measured. The temporal response of the beam scanner was confirmed to coincide well with that of the MZI modulator. The device exhibited a fast rise time of 12 ms, accompanied by slight power variations appearing for a long period (over hundreds of seconds), which originated from the inherent viscoelastic effect of the polymer materials.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical phased-array (OPA) devices are useful for scanning an output beam in free space by controlling the relative phase distribution of the guided light, and they do not involve any mechanical moving parts [1–4]. To steer the beam, the phase of light passing through each waveguide of OPA has to be controlled independently. For this purpose, a thermo-optic phase modulator (TOPM) array with micro heaters formed on the waveguide is required.
Several groups have been working on OPA devices with TOPMs based on Si optical waveguides [3–8]. As Si photonic devices have tightly confined guided modes, they exhibit small volume and high density, and can be fabricated through the standard CMOS fabrication processes. However, thermal crosstalk due to the high thermal conductivity of the Si material hinders independent control of the thermal phase [6,7]. In addition, the strong mode confinement of Si waveguides induces a nonlinear phase change when the power of the input light is increased, which limits the maximum output power of the OPA [8]. They can also produce significant phase errors between the arrayed waveguides, if small fabrication defects are present on the waveguide sidewalls. A silicon nitride waveguide is an alternative for implementing the OPA. It has much lower optical nonlinearity than Si owing to the lower Kerr effect and the larger waveguide core [9]. However, the thermo-optic (TO) coefficient of SiN is less than one-tenth of that of Si, which increases the driving power of the TOPM [10,11]. Compared to other materials, polymers feature high TO coefficients and low thermal conductivity, facilitating low-power driving of the phase-modulator array and low thermal crosstalk. Moreover, the low index contrast of polymer waveguides enables larger waveguide dimension to reduce the optical power density, which is desirable for the prevention of nonlinear phase changes [12,13].
In polymeric OPA devices, the scanning speed, which is dependent on the temporal response of the polymer-based TOPM, is of prime concern. Hence, it should be analyzed properly to optimize the operation speed and ensure stable long-term operation. In the mechanical stress–strain relationship of polymers, the temporal response is subject to the viscoelastic property, which includes a fast elastic response as well as a slow response due to molecular rearrangement [14,15]. Similar phenomena are observed in the temporal response of a TO variable optical attenuator made of polymers [16]. The response time for the TO effect in the polymer waveguide can be improved significantly by optimizing the heat flow and reducing the heat mass in a strip-loaded surface plasmon waveguide [17,18].
In this study, we designed and fabricated a polymer-based OPA device and investigated the temporal response of the TOPM. An 8-channel Mach–Zehnder interferometer (MZI) device was fabricated alongside the OPA device, on the same wafer, by combining each of the two output waveguides of a 16-channel TOPM array. When a step-function input signal was applied to the TOPM, a rise time of 12 ms was measured. However, after rapid rise, a slight power change was observed over a long period of time, which could be ascribed to the viscous molecular rearrangement of polymer. Both fast and slow temporal responses were modeled in terms of poles and zeros pertaining to the frequency response. Then, a step response, reconstructed from the transfer function corresponding to seven poles, was found to mimic the experimental results closely. We also examined the temporal response of the OPA by monitoring the far-field profile during beam scanning, which coincided with the results observed from the MZI temporal response.
2. Design and fabrication of the polymeric OPA device
The polymer waveguide for the proposed OPA device was designed with the core and cladding polymers with refractive indices of 1.397 and 1.372, respectively. The channel waveguide for satisfying the single-mode condition resulted in a core dimension of 4.0 × 3.0 µm2, giving rise to a mode field diameter (MFD) of 4.8 × 4.1 µm2. The proposed OPA consisted of a 1 × 16 power splitter, 16-channel TOPM array, and S-bend for diminishing the output waveguide pitch to 12 µm, as shown in Fig. 1(a). For the smaller waveguide pitch, the side lobe appears at the wider angle from the main lobe in the far field pattern, which widens the output beam scanning range. If the pitch become too close, however, mode coupling between adjacent waveguides arise. Beam propagation method simulations showed that the corresponding crosstalk was less than −25 dB for 12 µm pitch after 1 mm propagation. In this case, the side lobe in the far field became 3.5 dB smaller than the main lobe, appearing at angles of ± 7.2°.
Fig. 1. (a) 16-channel optical phased array (OPA) device structure consisting of 1 × 16 power splitter, phase modulator array, and s-bends, and cross-section of thermo-optic phase modulator., (b) Far-field beam patterns according to the phase distribution imposed on the phase-modulator array.
The initial phase distribution of the 16-channel waveguide was adjusted with the TOPM to obtain a focused light beam at the center. Then, by applying additional thermal power to produce an inclined phase distribution, the beam was diffracted to a certain angle proportional to the inclination, as illustrated in Fig. 1(b). The efficiency of the TOPM was evaluated by Pπ, the power required to induce a phase shift of π, and it was estimated using thermal analysis, as shown in Fig. 2. The waveguide cross-section is defined to have a 18 µm thick polymer film over a Si substrate and a 10 µm wide heater on top of the polymer film. The finite-element method was exploited to inspect the refractive-index profile resulting from the heat distribution. The effective index was then derived from the heat distribution. A typical polymer, exhibiting a thermal conductivity of 0.2 W/mK and TO coefficient of −2.5 × 10−4/°C yielded a Pπ of 2.1 mW [19,20].
Fig. 2. Temperature distribution produced by the heat on the micro-heater placed on top of the polymer waveguide.
For the fabrication of the polymeric OPA device, low-loss polymers from ChemOptics Co., with refractive indices of 1.372 and 1.397 were incorporated as the core and cladding layers, respectively. They are composed of UV-curable acrylate polymers with large fluorine content, leading to low absorption loss at 1550 nm. The birefringence of the polymer was as low as 1.0 × 10−4, which helped suppress the polarization dependence in various optical devices [21,22].
The cladding polymer was spin-coated on a silicon substrate and then cured by UV under N2 atmosphere. The amount of energy for polymerization was over 3,600 mJ/cm2 under a UV-A lamp. Waveguide patterns were inscribed on the cladding through photolithography and O2 plasma dry etching, with width 4 µm and depth 3 µm. The core polymer was subsequently coated to fill up the grooves, and the entire surface was etched once again until only the core structure was left. The cladding polymer was coated in a similar manner, to complete the optical waveguide After Cr–Au was deposited to a thickness of 10–100 nm, an electrode pattern was formed through a photolithography process. The metal was finally wet-etched to form the microheaters by using Au etchant (potassium monoiodide solution from Sigma-Aldrich) and Cr etchant (CR-7 from Cyantek), sequentially. Each chip available on the wafer was diced and polished for fiber pigtailing. The device was mounted on a metallic case including a thermoelectric cooler, and the heaters were wire bonded to the pins of the case.
3. Temporal and frequency response of the polymer-waveguide TOPM
The device was characterized using a 1550 nm distributed feedback laser. A high-index-contrast small-core fiber with an MFD of 4 µm, from Nufern Co. (UHNA3), was aligned with the polymer waveguide. A fiber-optic polarization controller was used to adjust the input polarization as TE. The insertion loss of an 11 mm long straight waveguide was measured to be 0.9 dB, which comprised a propagation loss of 0.3 dB/cm and coupling loss of 0.3 dB/facet. The electrodes, which were formed atop the straight waveguide to drive the TOPM, were 10 µm wide and 2 mm long and their resistance was 45 Ω. Pads and connecting electrode are much wider than the heating electrode so that their power consumption was negligible.
By combining the two output waveguides of a 16-channel TOPM array, an 8-channel MZI device was prepared for obtaining an intensity-modulated output signal, as shown in Fig. 3(a). The device was fabricated along with the OPA. A setup for observing the output signals from the 8-channel MZI is depicted in Fig. 3(b). The MZI output signal shown in Fig. 3(c) exhibited Pπ of 2.5 mW. The amplitude difference is caused by the output fiber alignment error during the rough measurement to measure the Pπ and initial phases. In this result, the randomness of initial phase differences between the 8 channel MZIs were observed.
Fig. 3. (a) 8-channel Mach–Zehnder interferometer (MZI) device constructed by connecting each of the two channels of the 16 phase modulators to obtain an intensity-modulated signal, (b) temporal response measurement setup, and (c) output intensity-modulated signals from the 8-channel MZI for an applied power signal with period 0.2 s.
To perform the OPA scanning, the TOPM was operated by a step control signal, and therefore, it was important to examine the step response of the TOPM. To measure the step response over a long period, an input square-wave signal with period 1,000 seconds was applied to produce an output power change, as shown in Fig. 4(a). The output signal exhibited spiking peaks due to the fast change of phase in step response. For the phase change exceeding π rad, the step response of the MZI went through a minimum and maximum value to reach the final value, as shown in Fig. 4(b). The corresponding phase change was calculated, to discover the temporal response for the entire large phase change, as shown in Fig. 5. According to the enlarged graph, it was found that the 10% to 90% rise time and the corresponding fall time were 12.7 ms and 13.4 ms, respectively. In this step response, one can also find the output step response was slightly increasing at long times, potentially deteriorating the performance of OPA.
Fig. 4. (a) Step response output of Mach–Zehnder interferometer (MZI) device for input phase-modulation amplitude over π, (b) transfer function of MZI corresponding to the phase-modulated (PM) input signal producing the phase change over π, explaining how the rapidly changing signal shape has appeared.
Fig. 5. Phase change of Mach–Zehnder interferometer (MZI) modulator converted from the modulated output intensity, in which one can find the quick response at the beginning as well as the slight increase in phase appearing at over 500 s. In the two enlarged graphs for the time spans of 5 and 0.05 s, it is shown that the TOPM responds very quickly, with a rising time of 12 ms.
To further validate the temporal response of the TOPM, the frequency response was measured. For frequencies ranging from 1 mHz to 1 kHz, when a small-amplitude sinusoidal signal producing a phase modulation of λ/20 was applied under a bias of π/2, the output signal was measured as shown in Fig. 6(a). The phase change was extracted from the output intensity signal. On increasing the frequency, the output signal amplitude was observed to decline along with the phase delay. To find the dependence of signal amplitude, a large-amplitude signal was applied to produce a phase modulation over 5λ, as shown in Fig. 6(b). Owing to the large phase change, the modulated light intensity produced a multiple-period sinusoidal signal. However, the converted phase change graph showed the same period as the applied voltage. The ratio of the output phase change to the input power of the TOPM was defined as the phase modulation efficiency (rad/W), and the phase delay was calculated to draw a Bode plot as shown in Fig. 7. By comparing the two results for different input signal amplitudes, it was confirmed that the frequency response was not susceptible to the thermal power amplitude. To verify if the frequency response has any temperature dependence, the substrate temperature was elevated to 50 °C, and we confirmed the frequency response has no temperature dependence.
Fig. 6. Intensity-modulated signal of the thermo-optic phase modulator (TOPM) Mach–Zehnder interferometer (MZI) measured for various input frequencies. Optical output signals are converted to the corresponding phase changes, and the time scale is normalized with the period of the input signal. To compare the response, depending on the input heating power, (a) small-signal modulation response was measured by applying a voltage to impose λ/20 phase change, and (b) large-signal response was measured by imposing a phase change over 5λ.
Fig. 7. (a) Bode plot of phase-modulation efficiency and (b) phase change; the primary single pole is located near 116 Hz.
The frequency response of the TOPM could be modeled as a simple single-pole system by drawing an asymptotic line on the Bode plot. The 3-dB bandwidth was 37.9 Hz for a time constant of 4.2 ms. It was found that, in the low-frequency band below 10 Hz, the efficiency decreased gradually with increase in the frequency, implying that the frequency response may not be adequately modeled by a single pole. Hence, to explain the temporal response of the polymer material, a generalized Maxwell model engaging multiple poles and zeros was adopted [23]. The positions of the poles and zeros were estimated using a MATLAB software function named “tfest”, to derive the Bode plots corresponding to the experimental results. The resulting Bode plots are shown in Fig. 8. The transfer functions, represented by number of poles and zeros, are summarized in Table 1. As compared with the actual measured step response, when the number of poles was seven, instead of three, as shown in Fig. 9, the reconstructed step response was closer to the actual measurement result. When the number of poles increased further, the transfer function became unstable with a diverging step response.
Fig. 8. Bode plot reproduced by generalized Maxwell model incorporating (a) three poles and (b) seven poles, which is quite close to the experimental results as the number of poles increases, as shown in (c) overlapped Bode plot
Fig. 9. Step response reconstructed from the transfer functions described in Table 1, which is comparable to the measurement results.
Table 1. Transfer functions obtained from the generalized Maxwell model to represent the experimental results depending on the number of poles incorporated.
4. Temporal response of the OPA beam scanner
The polymeric OPA chip was packaged with a cylindrical lens for collimation in the vertical direction and a mirror for directing the beam upward, as shown in Fig. 10. An IR CCD camera was placed to observe the output far-field pattern of the OPA. Prior to initializing the phase, the far-field pattern of the OPA output was distributed along a horizontal line, as shown in Fig. 11(a). A gradient-decent hill-climbing algorithm was adopted to adjust the phase of the TOPM while observing the far field. The algorithm finds the optimum direction of the phase change of each channel, which causes far field to converge at a point [24]. When the phase initialization was fulfilled, as shown in Fig. 11(b), the far field was focused at the center, resulting in a diffraction pattern with two side lobes. As shown in Figs. 11(c) and (d), the beam was scanned laterally by imposing an inclined phase distribution upon the TOPM. When the input laser power was 12 dBm, the output main beam power was measured as 6.8 dBm. The difference in intensity between the main lobe and side lobe, from the CCD image data, was 4.8 dB, which was slightly higher than the designed value of 3.5 dB. This discrepancy could be attributed to the slightly larger waveguide mode compared to the design, which provided smaller divergence angle. The side lobe was located at 7.0°, compared to the design result of 7.2°.
Fig. 10. Photograph of the polymer-waveguide optical phased array (OPA) package including a cylindrical lens for vertical collimation and a 45° mirror for upward emission.
Fig. 11. CCD camera images taken during optical phased array (OPA) beam scanning operation. (a) Scattered pattern observed before the phase equalization, (b) far-field diffraction pattern obtained after the phase initialization, in which the main lobe and two side lobes can be observed, and (c) and (d) beam scanned to the left and right directions, respectively.
To measure the optical power change of the main beam during the beam scanning, a photodetector (PD) was aligned to monitor the power of the main beam, as shown in Fig. 12(a). The beam was scanned out of the PD by controlling the OPA to produce a step response of optical power, as shown in Fig. 12(b). As in the case of the step response of MZI, the power change measured in the beam scanning exhibited a fast rise time followed by slow power increase over a long period. The OPA step response was drawn over the MZI step response, as shown in Fig. 12(c), where the two graphs overlap closely. The difference observed during the falling step of the signal could have occurred because the beam was moved beyond the detector.
Fig. 12. (a) Setup to measure the temporal response of the optical phased array (OPA) beam scanner, (b) step response of the OPA beam scanner during horizontal beam scanning, (c) comparison of the step response functions obtained from the beam-scanning experiment with the OPA device and the phase-modulation experiment with the Mach–Zehnder interferometer (MZI) device.
5. Conclusion
We proposed an OPA beam-scanning device based on a polymer-waveguide phase modulator and explored the temporal response characteristics of the TOPM. Polymeric phase modulator array fabricated in this work exhibited Pπ of 2.5 mW, which was significantly lower than that of Si photonic devices. When the OPA device was controlled by a step function, it was found that the polymeric TOPM had a fast elastic response followed by a slow phase change over hundreds of seconds due to the viscoelastic effect of the polymer. The frequency response of an MZI device was investigated to scrutinize its unique temporal response. By incorporating multiple poles and zeros into the Bode plot, we derived a transfer function to describe the unique temporal response of the polymeric phase modulator. Then the transfer function was effective to reconstruct the step response obtained from the experiment. Finally, the step response of the OPA beam scanner was measured, and the result was coincided with the MZI’s step response. In the design of OPA beam scanners made of polymeric phase modulators, the transfer function proposed in this work will be useful for developing a control algorithm that can overcome the unique phase changes resulting from the viscoelastic effect.
Funding
National Research Foundation of Korea (2017R1A2A1A17069702); Agency for Defense Development (UE171060RD).
Acknowledgments
The authors express their gratitude to Dr. Chang-Joon Chae from the Agency for Defense Development, Dr. Young-Ho Kim, Dr. Sung-Yong Ko, and Kyeong-Pyo Lee from the i3 System, Inc., for their helpful discussions.
Disclosures
The authors declare no conflicts of interest.
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