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Abstract
The phase error imposed in optical phased arrays (OPAs) for beam scanning LiDAR is unavoidable due to minute dimensional fluctuations that occur during the waveguide manufacturing process. To compensate for the phase error, in this study, a fast-running beamforming algorithm is developed based on the rotating element vector method. The proposed algorithm is highly suitable for OPA devices comprised of polymer waveguides, where thermal crosstalk between phase modulators is suppressed effectively, allowing for each phase modulator to be controlled independently. The beamforming speed is determined by the number of phase adjustments. Hence, by using the least square approximation for a 32-channel polymer waveguide OPA device the number of phase adjustments needed to complete beamforming was reduced and the beamforming time was shortened to 16 seconds.
© 2022 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical phased array (OPA) is useful for scanning the angle of radiated output light by controlling the phase distribution of the light passing through the optical waveguide array. Using the photonic integrated circuit technology, OPA beam scanners are manufactured in the form of small chip which can perform beam scanning without any moving parts, such as rotating mirrors used in conventional mechanical beam scanners. OPA beam scanners, thus, ensure high operational stability, can be miniaturized, and are advantageous for mass production. The OPA beam scanners have been actively studied to implement compact LiDAR required for autonomous vehicles and unmanned devices [1–4]. The compact OPA beam scanner technology is also important for image projection [5] and free-space communications [6].
The phase distribution of light passing through a waveguide array is determined in proportion to the waveguide lengths, but the output light has a phase shift due to slight difference in waveguide width which originates from the fabrication errors. Therefore, a beamforming procedure becomes necessary to equalize the phase difference between waveguide channels. Gradient descent algorithm [7–9] and genetic algorithm [10] have been used as conventional beamforming algorithms in which feedback control of the phase modulator is performed by monitoring the far-field beam profile. The gradient descent algorithm calculates partial differential values from output intensity as a function of phase change, and then adjusts the phase distribution to achieve maximum main lobe intensity. However, it tends to stall with steps orthogonal to each other near the maximum, which would increase the number of phase adjustments. The genetic algorithm selects better individuals than the existing ones through survival of the fittest in the population and creates an improved new population. Because of the repeating process of creation and evaluation of many individuals, significant amount of memory and computing resources are consumed.
The reduction in beam divergence angle and the increase in scanning resolution are important for high performance OPAs. In this regard, it is necessary to increase the number of OPA waveguide channels [11], which leads to longer beamforming time. Thus, a high-efficiency fast-running beamforming algorithm is required. In the present study, we have implemented an effective beamforming algorithm based on the rotating element vector (REV) method [12] and achieved faster beamforming speed than the previous methods. The REV method has been applied for radio-frequency phased array constructing smart antennas, synthetic aperture radars, and aerospace communications [13–15].
Polymer waveguide device has the merits of large thermo-optic (TO) effect, which is attractive for demonstrating OPA devices with large number of phase modulators that should be controlled independently with low electrical power. The polymeric OPA devices has been recently demonstrated by our group, in which independent control of phase modulators with a negligible thermal crosstalk and a low driving power of 2 mW was demonstrated [16,17]. The REV method was previously applied to a silicon waveguide OPA device; however, due to severe thermal crosstalk between adjacent phase modulators, the beamforming condition was not maintained during beam scanning, and it was necessary to perform beamforming with respect to many points of radiation angles [18]. In this work, we apply the REV method to polymer waveguide OPAs and demonstrate fast and stable phase distribution control required for efficient beamforming and scanning. The beamforming speed was determined by the number of phase adjustments required for completing the beamforming. Thus, the least square approximation (LSA) was implemented to improve the beamforming speed by minimizing the number of phase adjustments.
2. Implementation of the REV method for beamforming of OPA
A schematic of an OPA beam scanner is shown in Fig. 1(a). Light from a laser diode is incident on a polymer waveguide and split into N channels via the Y-branches. It is then passed through a phase modulator array and beam concentrator to reduce the waveguide array pitch, and finally, radiates into free space. The electric field of the output light of each waveguide is represented as Gaussian profile, then the electric field distribution $f(x)$ at the OPA output facet is given by a summation of the output lights from each waveguide located at ${x_n}$ for a channel number n,
Fig. 1. (a) Schematic of an OPA beam scanner where incident light on the polymer waveguide from the laser diode is split through a 1×N beam splitter, then passed through a phase modulator array and a beam concentrator with reduced waveguide pitch. (b) At the end of OPA, the electric field distribution is given as $f(x)$ which forms the far-field pattern $g({k_x})$ after propagating beyond the Fresnel region. θ is the propagating angle, x is a position on the near-field plane, ${k_x}$ is angular spatial frequency on the far-field plane, and z is the propagation direction.
One can find a point P on the plane of far-field, at z = z0, where the output electric field of OPA produces a bright spot through constructive interference. The electric field reaching the point P is defined as follows,
where, ${E_P}$ and ${\Theta _P}$ are the resultant amplitude and phase from the summation of all the electric fields arriving at P. In the beamforming process using the REV method, it is necessary to measure the dependence of ${g_P}$ only on the phase variation of the nth channel output light. To consider this effect, ${\hat{g}_P}$ is formulated excluding the field of nth channel from the amount of ${g_P}$, followed by addition of the same magnitude of electric field with a modified phase ${\delta _n}$ as follows,Here, the total field at P excluding the nth channel field is defined as ${E_{ex}}\exp (j{\Theta _{ex}})$, which are drawn on the complex plane in Fig. 2. The phase modulation of nth channel produces the vector rotating over the circle. The intensity of ${\hat{g}_P}$ is given by the absolute square of Eq. (6) as follows (see Supplement 1 for detailed derivation),
It becomes a sinusoidal function with respect to the modulated phase of the nth channel ${\delta _n}$, and becomes maximum when ${\delta _n} = {\Theta _{ex}} - {\theta _n}$, i.e., when the phase is properly corrected. To find the amount of phase correction, it is necessary to measure ${|{{{\hat{g}}_P}} |^2}$ depending on the phase change of each channel. Using the least square approximation (LSA) for the sine curve fitting, the amount of phase correction could be found by measuring the ${|{{{\hat{g}}_P}} |^2}$ for a few numbers of the variable ${\delta _n}$.
Fig. 2. Representation of electric field vectors on complex plane, where ${g_P}$ is the electric field that has reached an arbitrary point P on the far-field plane. ${E_n}\exp ({j{\theta_n}} )$ is the electric field that has passed through the nth channel. ${E_{ex}}\exp ({j{\Theta _{ex}}} )$ is defined as the value excluding ${E_n}\exp ({j{\theta_n}} )$ from ${g_P}$. On modulating the phase of the nth channel and adding it to the ${E_{ex}}\exp ({j{\Theta _{ex}}} )$, ${\hat{g}_P}$ is obtained. Beamforming can be performed by finding the amount of phase correction ${\delta _n}$, which makes ${\hat{g}_P}$ maximum. ${\hat{g}_P}$ become maximum when ${\delta _n} = {\Theta _{ex}} - {\theta _n}$.
3. Comparison of the beamforming algorithms
To prove the merits of the proposed REV method for the beamforming of the OPA with a large number of channels, numerical simulation was performed for 1024-channels OPA in comparison to the genetic and gradient descent algorithms. The wavelength was 1550 nm, the beam waist of Gaussian beam on each channel was 0.5 μm, and the channel pitch was 2 μm. The electric field of light passed through OPA was expressed as the sum of Gaussian profiles as in Eq. (1), and the far-field intensity distribution was calculated using fast Fourier transform (FFT). The initial phase distribution was set to random values between 0 and 2π on each channel, as shown in Fig. 3(a), and the far-field intensity distribution appeared as a scattered light along the horizon direction (see Fig. 3(b)). In the actual beamforming procedure, the CPU calculation time was negligible and most of the time was spent for capturing the far-field image and controlling the phase distribution. Therefore, the speed of the algorithm can be compared with the number of phase adjustments.
Fig. 3. In the initial state, (a) the phase distribution of the 1024-channel OPA output and (b) the corresponding far-field intensity profile. After beamforming, (c) and (d) show the phase distribution and the far-field intensity profile achieved by the genetic algorithm, respectively; (e) and (f) show the phase distribution and the far-field intensity profile achieved by the gradient descent algorithm, respectively; (g) and (h) show the results obtained by the REV method.
In the Genetic algorithm, an individual consisted of a set of 1024 phase values, and a generation comprised of 500 individuals. Depending on the main beam power (or concentrated beam power at the brightest spot) achieved by each individual, a probability of selection was assigned to the individual. Initially, there was no significant difference of the selection probability or the main beam intensity between individuals. As the steps were repeated, the individuals with high selection probability were predominantly collected and the collection criteria were adaptively increased. A new individual was generated by transferring the phase information between two randomly selected individuals. At this time, the phase of the random channel was changed to a random value using a mutation with a probability of 5%. The phase distribution and far-field intensity distribution after repeating 500 generations are shown in Fig. 3(c) and (d), respectively. However, the intensity of the main beam was 67% of the ideal value because of the low probability of finding the optimal phase distribution on 1024 channels.
In case of the gradient descent algorithm, the gradient of the far-field intensity at a point was calculated with respect to phase distribution change, then the phase distribution was adjusted in the direction of intensity increase. The phase distribution and far-field intensity distribution after beamforming by gradient decent method are shown in Fig. 3(e) and (f), respectively. In comparison to the genetic algorithm, the phase distribution was equalized better, and the main beam intensity was higher. However, to achieve this beamforming quality, phase distribution adjustment over 10,000 times were required.
In the REV method proposed in this study, a bright spot in the far-field produced by the constructive interference was selected for power monitoring, then the intensity variations of the spot depending upon 4 different phases in each channel were measured. The amount of phase correction in Eq. (7) for each channel was obtained next by using the LSA. After finding the amount of phase correction for all the channels, they were simultaneously updated for all the channels to achieve the beamforming at once. The phase distribution and far-field intensity distribution after beamforming are shown in Fig. 3(g) and (h), respectively. Phase equalization was achieved with high efficiency, and the main beam intensity reached to 99.9% of the ideal value.
For each algorithm, the main beam intensity evolution was calculated for the number of phase adjustments, as shown in Fig. 4. While the intensity increased gradually for genetic and gradient decent algorithms, in the REV method, the intensity changed abruptly when the phase correction values were applied to all the channels at once after 4,000 times of phase adjustments. Table 1 summarizes the number of phase adjustments required for the final beamforming, final main beam intensity, normalized main lobe power fraction, and side mode suppression ratio (SMSR). It is clearly shown that the REV method is superior to the other algorithms.
Fig. 4. The evolution of main beam intensity with respect to the number of phase adjustments to achieve the beamforming for REV method, gradient descent (GD) algorithm, and genetic algorithm.
Table 1. Comparison between the beamforming algorithms
4. Design and fabrication of the polymer waveguide OPA
To fabricate the OPA device, fluorinated acrylate polymers produced by ChemOptics Co. (LFR series) were used. The polymer exhibited low absorption loss for 1550 nm band and a small birefringence and was used for demonstrating tunable wavelength filters and various optical devices [19,20]. LFR polymers with refractive indices of 1.372 and 1.397 were adopted for cladding and core layers, and it was confirmed that an optical waveguide with a core of 4.0 × 3.0 μm2 satisfied the single-mode waveguide condition exhibiting a mode field diameter of 4.8 × 4.1 μm2.
As shown in Fig. 5, the OPA device consists of 1×32 splitter, 32-channel TO phase modulator array, and S-bend beam concentrators to reduce the spacing of the output waveguides to 10 μm. The TO phase modulator array has thin metal film heaters on the top of waveguides [21]. For the smaller pitch of output waveguide array, the larger beam scanning angle is obtainable by increasing the side lobe diffraction angle. However, the waveguide spacing is limited because of the directional coupling between the adjacent waveguides. According to the beam propagation method simulation, when light was incident on one of the two parallel waveguides with a spacing of 10 μm, crosstalk was less than -25 dB after propagating 1 mm. For waveguide pitch of 10 μm, the side lobe was located at ±8.9° and the intensity over the main lobe was -3.5 dB.
Fig. 5. Polymer waveguide OPA device consisting of 1×32 beam splitter, 32-channel phase modulator array, and S-bend beam concentrator to reduce the pitch of the output waveguides. A cylindrical lens was placed at the output end for vertical collimation of the output beam, and a 45° mirror was aligned to direct the output beam vertically. Distributed feedback (DFB) laser was connected to the input of the OPA device.
The applied power to bring π phase change in the TO phase modulator, Pπ was calculated via thermal analysis of the polymer waveguide cross section. A polymer film of 18 μm thickness was coated on a silicon wafer, and the width of the metal film heater was 10 μm. For a given heating power applied on the metal heater, the temperature distribution over the waveguide cross section and the effective index change of the waveguide mode were both calculated. In the finite element simulation, the thermal conductivity of the polymer material was set to 0.2 W/mK, the TO coefficient was -1.8 × 10−4/°C, and the silicon substrate acted as heat sink. As a result, Pπ of 2.1 mW was obtained [22,23].
As the first step of fabricating polymer waveguide OPA device, lower cladding LFR polymer was spin coated on a silicon substrate and cured by UV exposure. A core pattern was formed on the lower cladding polymer by photolithography process using AZ-5214 photoresist, followed by oxygen plasma etching to form a groove pattern of 4 μm wide and 3 μm deep. The groove was filled up by coating the core polymer. The polymer waveguide fabrication was completed by coating an upper cladding polymer. After depositing Cr-Au of 10−100 nm, an electrode pattern was formed via photolithography, and the metal was wet-etched to complete the phase modulator electrode. The wafer was diced to separate the OPA chips, the input and output facets were polished, and V-groove fiber block was connected. The chip was placed on a thermo-electric cooler (TEC) attached to an aluminum package, and the electrode of the chip was wired to a PCB board. Packaging was completed by aligning a cylindrical lens to the device output end for vertical collimation of output beam, and a 45° mirror was placed to direct the output beam vertically [24].
5. Beamforming and scanning experiments
An ultra-high numerical aperture (UHNA) fiber was used to connect a 1550 nm DFB laser to the polymer waveguide of OPA device, and the electrodes of phase modulator array was connected to a control board. To observe the far-field profile from the output beam of the polymer waveguide OPA device, CCD camera was placed as shown in Fig. 6(a). Before the beamforming, the output light was appeared as shown in Fig. 6(b), scattered horizontally because of initial random phase distribution. A relatively brighter spot among the scattered beam was selected as a reference to execute the REV method, and the phase of each channel was changed to 4 different values to obtain the phase dependent intensity graph, as shown in Fig. 7. From the 5 values of intensities as a function of phases, the LSA was used to find the amount of phase correction δn for each channel. The standard deviation between the fitted values and the measured values was less than 10−4. The amount of phase correction for all the channels were obtained through 128 times of phase control and power monitoring process, and then applied to all the phase modulators to complete the beamforming and converge the beam at one point (see Fig. 6(c)). The total time for beamforming took 16 seconds, which was mostly limited by time of power monitoring step, which could be improved by using a photodetector aligned to the reference point instead of the CCD camera.
Fig. 6. (a) Measurement setup with the OPA package connected to the control board and IC. A CCD camera was used to measure the output beam during the beamforming and the beam steering. (b) Far-field pattern captured by the CCD camera before the beamforming. (c) Far-field pattern was converged at one point after the beamforming.
Fig. 7. (a) Intensity variation at one point of far-field image depending upon the phase of each channel for 5 different phase values. The 5 different phase values are chosen as -120°, -60°, 0°, 60°, and 120°. The amount of phase correction, δn are obtained by using LSA for only 6 of 32 channels which are drawn for convenience. (b) The phase correction values for the entire channel.
After the beamforming, beam steering was performed by applying incremental slope phase distribution to the phase modulator array. The phase distribution applied to the modulator array and the far-field image during beam steering are shown in Fig. 8. The initial beamforming conditions were not disturbed during the entire beam steering process, and no additional scattered light other than the side lobe appeared. The intensity variation occurred during the beam scanning was precisely corresponds to the diffraction profile of single channel polymer waveguide. The whole process of beamforming and beam steering can be found in Visualization 1.
Fig. 8. After completing the beamforming, the phase control signal was adjusted to produce an incremental slope phase distribution for scanning the beam. The phase control signal is shown on the left column and the corresponding scanning beam is shown in the right column.
The speed of beam scanning was reported in our previous publication [21], where the scanning speed was rather slow. However, by optimizing the waveguide structure to reduce the TO response time, the scanning speed can be greatly improved, and the rise time can be reduced to less than 100 μs [25,26]. Moreover, for increasing the scanning angle, we are currently working on a hybrid type OPA device that can reduce the output waveguide array pitch by using a silicon nitride waveguide with high refractive index contrast, which has been presented in our recent publication [4].
6. Conclusions
A fast-running beamforming algorithm suitable for an OPA with a large number of channels was proposed based on REV method. To reduce the sampling points for fast calculation, LSA was also adopted. In terms of numerical analysis, we demonstrated that the REV method has excellent converging efficiency and fast beamforming speed compared to the other methods. The proposed REV method was applied to the beamforming of polymer waveguide OPA, which provided highly efficient phase control by virtue of the large TO effect. By applying the REV method on a 32-channel polymer waveguide OPA device, fast and high-quality beamforming was achieved. The thermal power applied on one heater caused no thermal crosstalk to the adjacent phase modulator, and it ensured completely independent phase distribution control. Therefore, the condition of phase correction was not perturbed during the entire beam scanning process. The number of waveguide channel will be increased to 1024 in our next step of OPA beam scanner research. When the number of channels increases, the main beam intensity change depending on the single channel phase modulation becomes weak. Hence, we are currently working on a method using a photodetector array with sufficient sensitivity.
Funding
National Research Foundation of Korea (2020R1A2C2101562); Agency for Defense Development (UD200034RD).
Acknowledgments
This research was supported by the Defense Challengeable Future Technology Program of Agency for Defense Development (ADD), Republic of Korea and National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. C. V. Poulton, A. Yaacobi, D. B. Cole, M. J. Byrd, M. Raval, D. Vermeulen, and M. R. Watts, “Coherent solid-state LIDAR with silicon photonic optical phased arrays,” Opt. Lett. 42(20), 4091 (2017). [CrossRef]
2. C.-S. Im, B. Bhandari, K.-P. Lee, S.-M. Kim, M.-C. Oh, and S.-S. Lee, “Silicon nitride optical phased array based on a grating antenna enabling wavelength-tuned beam steering,” Opt. Express 28(3), 3270 (2020). [CrossRef]
3. C.-S. Im, B. Bhandari, S.-M. Kim, M.-C. Oh, K.-P. Lee, T. Kim, and S.-S. Lee, “Backward-Emitting Silicon Nitride Optical Phased Array Enabling Efficient Wavelength-Tuned Beam Steering,” IEEE Photonics J. 12(5), 1–10 (2020). [CrossRef]
4. C.-S. Im, S.-M. Kim, K.-P. Lee, S.-H. Ju, J.-H. Hong, S. W. Yoon, T. Kim, E.-S. Lee, B. Bhandari, C. Zhou, S.-Y. Ko, Y.-H. Kim, M.-C. Oh, and S.-S. Lee, “Hybrid Integrated Silicon Nitride Polymer Optical Phased Array for Efficient Light Detection and Ranging,” J. Lightwave Technol. 8724, 4402–4409 (2021). [CrossRef]
5. M. Raval, A. Yaacobi, and M. R. Watts, “Integrated visible light phased array system for autostereoscopic image projection,” Opt. Lett. 43(15), 3678 (2018). [CrossRef]
6. C. V. Poulton, M. J. Byrd, P. Russo, E. Timurdogan, M. Khandaker, Di. Vermeulen, and M. R. Watts, “Long-Range LiDAR and Free-Space Data Communication with High-Performance Optical Phased Arrays,” IEEE J. Sel. Top. Quantum Electron. 25(5), 1 (2019). [CrossRef]
7. W. Xie, T. Komljenovic, J. Huang, M. Tran, M. Davenport, A. Torres, P. Pintus, and J. Bowers, “Heterogeneous silicon photonics sensing for autonomous cars [Invited],” Opt. Express 27(3), 3642 (2019). [CrossRef]
8. J. K. Doylend, M. J. R. Heck, J. T. Bovington, J. D. Peters, L. A. Coldren, and J. E. Bowers, “Two-dimensional free-space beam steering with an optical phased array on silicon-on-insulator,” Opt. Express 19(22), 21595–21604 (2011). [CrossRef]
9. P. Wang, G. Luo, Y. Xu, Y. Li, Y. Su, J. Ma, R. Wang, Z. Yang, X. Zhou, Y. Zhang, and J. Pan, “Design and fabrication of a SiN-Si dual-layer optical phased array chip,” Photon. Res. 8(6), 912–919 (2020). [CrossRef]
10. M. C. Shin, A. Mohanty, K. Watson, G. R. Bhatt, C. T. Phare, S. A. Miller, M. Zadka, B. S. Lee, X. Ji, I. Datta, and M. Lipson, “Chip-scale blue light phased array,” Opt. Lett. 45(7), 1934 (2020). [CrossRef]
11. S. Chung, H. Abediasl, and H. Hashemi, “A Monolithically Integrated Large-Scale Optical Phased Array in Silicon-on-Insulator CMOS,” IEEE J. Solid-State Circuits 53(1), 275–296 (2018). [CrossRef]
12. S. Mano and T. Katagi, “A method for measuring amplitude and phase of each radiating element of a phased array antenna,” Electron. commun. Jpn. 65(5), 58–64 (1982). [CrossRef]
13. K. Nishimori, K. Cho, Y. Takatori, and T. Hori, “Automatic calibration method using transmitting signals of an adaptive array for TDD systems,” IEEE Trans. Veh. Technol. 50(6), 1636–1640 (2001). [CrossRef]
14. M. Shimada, S. Member, O. Isoguchi, T. Tadono, and K. Isono, “PALSAR Radiometric and Geometric Calibration,” IEEE Trans. Geosci. Remote Sens. 47(1), 3915–3932 (2009). [CrossRef]
15. T. Takahashi, S. Member, N. Nakamoto, and M. Ohtsuka, “On-Board Calibration Methods for Mechanical Distortions of Satellite Phased Array Antennas,” IEEE Trans. Antennas Propag. 60(3), 1362–1372 (2012). [CrossRef]
16. Z. Zhang and N. Keil, “Thermo-optic devices on polymer platform,” Opt. Commun. 362, 101–114 (2016). [CrossRef]
17. M.-C. Oh, W.-S. Chu, J.-S. Shin, J.-W. Kim, K.-J. Kim, J.-K. Seo, H.-K. Lee, Y.-O. Noh, and H.-J. Lee, “Polymeric optical waveguide devices exploiting special properties of polymer materials,” Opt. Commun. 362, 3–12 (2016). [CrossRef]
18. Q. Zhang, L. Zhang, Z. Li, W. Wu, G. Wang, X. Sun, W. Zhao, and W. Zhang, “Antenna Array Initial Condition Calibration Method for Integrated Optical Phased Array,” Acta Photonica Sinica 49(7), 726001 (2020). [CrossRef]
19. T.-H. Park, S.-M. Kim, S.-H. Park, J.-K. Seo, H.-G. Lee, and M.-C. Oh, “Polymer waveguide WDM channel selector operating over the entire C and L bands,” Opt. Express 26(13), 16323 (2018). [CrossRef]
20. S.-H. Park, J.-K. Seo, J. Park, H.-K. Lee, J.-S. Shin, and M.-C. Oh, “Transmission type tunable wavelength filters based on polymer waveguide Bragg reflectors,” Opt. Commun. 362, 96–100 (2016). [CrossRef]
21. S.-M. Kim, T.-H. Park, C.-S. Im, S.-S. Lee, T. Kim, and M.-C. Oh, “Temporal response of polymer waveguide beam scanner with thermo-optic phase-modulator array,” Opt. Express 28(3), 3768 (2020). [CrossRef]
22. X. Xie, D. Li, T.-H. Tsai, J. Liu, P. V Braun, and D. G. Cahill, “Thermal conductivity, heat capacity, and elastic constants of water-soluble polymers and polymer blends,” Macromolecules 49(3), 972–978 (2016). [CrossRef]
23. Y.-O. Noh, H.-J. Lee, J. J. Ju, M. Kim, S. H. Oh, and M.-C. Oh, “Continuously tunable compact lasers based on thermo-optic polymer waveguides with Bragg gratings,” Opt. Express 16(22), 18194 (2008). [CrossRef]
24. S.-M. Kim, E.-S. Lee, K.-W. Chun, J. Jin, and M.-C. Oh, “Compact solid-state optical phased array beam scanners based on polymeric photonic integrated circuits,” Sci. Rep. 11(1), 1–9 (2021). [CrossRef]
25. C. Wang, D. Zhang, X. Zhang, S. Ding, J. Wang, R. Cheng, F. Wang, Z. Cui, and C. Chen, “Bottom-metal-printed thermo-optic waveguide switches based on low-loss fluorinated polycarbonate materials,” Opt. Express 28(14), 20773–20784 (2020). [CrossRef]
26. Q. Xu, M. Jiang, D. Niu, X. Wang, L. Wang, K. S. Chiang, and D. Zhang, “Fast and low-power thermo-optic switch based on organic–inorganic hybrid strip-loaded waveguides,” Opt. Lett. 43(20), 5102–5105 (2018). [CrossRef]
