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Abstract
The doubly periodic Si photonic crystal waveguide radiates the guided slow light into free space as an optical beam. The waveguide also functions as a beam steering device, in which the steering angle is changed substantially by a slight variation in the wavelength generated due to the large angular dispersion of the slow light. A similar function is obtained when the wavelength is fixed and the refractive index of the waveguide is changed. In this study, we tested two kinds of integrated heater structures and observed the beam steering using the thermo-optic effect. For a p–i–p doped waveguide, the heating current was made to flow directly across the waveguide and a beam steering range of 21° was obtained with a relatively low heating power and high-speed response of the order of 100 kHz, maintaining a narrow beam divergence of 0.1−0.3° and a 120 resolution points. We also performed a preliminary life test of the device but did not observe any severe degradation in the temperature variation of 80–430 K for the duration up to 20‒40 h. For a TiN heater device, we obtained the comparable beam steering characteristics, but the required heating power increased, and the response speed decreased drastically.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical beam steering devices that orient an optical beam toward a target are crucial components in the manufacturing of devices such as printers, copiers, laser displays, laser processors, security sensors, and light detection and ranging (LiDAR) systems, among others. Recently, LiDARs have become a global topic owing to their applications in advanced driver assistance systems and automatic vehicles. However, the current LiDARs work with a spinning sensor or moving mirror for beam steering; therefore, they are large, expensive, and unreliable to vibration of vehicles, among others. A nonmechanical solid-state LiDAR is expected to overcome these problems. Recently, LiDARs incorporating a micro-electro-mechanical system mirror have been developed as semi-nonmechanical devices [1] that are suitable for low-cost mass production using the complementary metal-oxide semiconductor (CMOS) process. However, it is difficult to simultaneously achieve a high speed and sharp optical beam, which can be obtained by a reasonably large mirror, such as, a mirror with a diameter of several millimeters. These days, optical phased arrays (OPAs) and waveguide diffraction gratings fabricated by the Si photonics CMOS process are being studied extensively as such nonmechanical devices. OPAs [2–7] consisting of a large number of optical micro-antennas synthesize an arbitrary beam by controlling the optical phase of each antenna. However, it is not easy to obtain the diffraction-limit beam with a very narrow beam divergence (δθ << 1.0°) because it requires extremely fine control; this makes it difficult to achieve a large number of resolution points and simple beam scanning. In waveguide diffraction gratings, on the other hand, the diffraction-limit beam is obtained more easily while its steering range is narrower [8].
We have proposed a slow-light beam steering device that uses photonic crystal waveguide (PCW) with a surface diffraction grating [9]. It provides a large steering angle for a small wavelength variation without degrading the beam quality because PCW produces slow light that shows large angular dispersion similar to that reported for multilayer stacked Bragg waveguides [10]. We obtained a steering range (∆θ) of 23° for a wavelength sweep of 29 nm in that device. We also achieved ∆θ = 23° for a wavelength sweep range (Δλ) of 20 nm by using a similar device, but this device had a doubly periodic photonic crystal pattern instead of the surface grating [11]. In both devices, we used a bench top tunable laser source in the wavelength sweep. For practical LiDARs, we need to prepare a compact module of the swept laser source, but it still remains a challenge.
In this study, we demonstrate a beam steering device driven by the thermo-optic effect, instead of the wavelength sweep. We tested two heater structures: p–i–p doped Si PCW and TiN adjacent to the PCW. In the p–i–p device, the PCW is directly used as a heater so that the heating is concentrated around the waveguide core. For the TiN device, the PCW is indirectly heated so that the response speed is slower. In Sections 2 and 3, we describe the optical part and heater part of these devices, respectively, along with their theoretical characteristics. In Section 4, we present the experimental beam steering and evaluation of the response speed as well as the preliminary life test of the device.
2. Device and optical characteristics
The devices with different heater structures are schematically shown in Fig. 1. We formed a Si PCW having doubly periodic hole diameters in a triangular lattice and a line defect core in the silicon-on-insulator (210 nm Si layer and 2 μm SiO2 BOX layer), which was cladded by 2 μm SiO2. For the fundamental lattice constant of the PCW (a), the double period was 2a along the waveguide. The hole diameter was modulated as 2r ± ∆r in a V-shaped pattern. In such a structure, the guided slow-light mode in the photonic band is folded into the air light cone and radiated into free space by the double periodicity. The radiation can be controlled by increasing or decreasing ∆r; we evaluated in the photonic band calculation and experiment that the radiation coefficient is 100−150 dB/cm when ∆r is 10 nm [11]. The aperture length of the radiation along the waveguide (longitudinal direction) becomes longer when the radiation is moderately suppressed. In the direction orthogonal to the waveguide (lateral direction), the aperture length almost corresponds to the waveguide width (more precisely, the effective modal width). The far-field pattern (FFP) of the beam reflects this aperture distribution and becomes narrow and wide in the longitudinal and lateral directions, respectively; this produces a fan beam [9‒11].
Fig. 1 Schematic of beam steering device with (a) p–i–p doped Si PCW or (b) TiN heaters buried inside upper SiO2 cladding adjacent to the PCW.
In this paper, we discuss the beam steering only in the longitudinal direction, which is controlled by the thermo-optic effect. (The beam steering in the lateral direction and two-dimensional steering have been demonstrated in [11]). The radiation angle in the longitudinal direction θ taken from the direction normal to the Si slab is determined by the equivalent modal index of the folded photonic band, neq, as follows [9,11]:
where k0 and β are the wavenumber in the vacuum and the propagation constant of the slow-light mode, respectively; these values depend on the material index of the PCW, n. The index sensitivity of θ is given as follows [9]:where ng is the group index of the slow light. In this study, ng is greater than 20 and neq is always less than 1 on the condition of light radiation; therefore, the sensitivity is almost proportional to ng, and a large ng gives a wide steering range for a small variation of n. In Fig. 2(a), the line at ∆T = 0 K (meaning no heating) is an example of the calculated photonic band. Here, we used a software, Lumerical Solutions Inc., FDTD Solutions, assuming that a = 400 nm and 2r = 210 nm; the number of hole rows on each side of the waveguide core was 10, and transverse electric (TE) polarization was excited. We changed n of the Si layer of the PCW based on the temperature shift ∆T, and shifted the band to the low frequency side using a linear approximation. The temperature dependence of the Si index nSi is expressed as follows [12]:In the SiO2 cladding, we fixed nSiO2 = 1.44 because the temperature dependence of SiO2 is 180 times less than that of Si [13]. When we assumed the wavelength λ = 1580 nm as the band edge for ∆T = 0 K, θ was obtained for ΔT as shown in Fig. 2(b). The angle increases with the increase in the temperature. The slight nonlinearity arises from the band bending near the band edge. For example, when ∆T is 300 K, ∆θ is 24° and when ∆T is 400 K, ∆θ is 29° although θ > 30° does not satisfy the pure guided mode condition of the PCW and cannot be used for low-loss beam steering.Fig. 2 Calculation of (a) the photonic band of PCW with ∆r = 0 and (b) the radiation angle of light with heating. The gray zone in (a) depicts the SiO2 light cone showing the radiation condition.
3. Heaters and thermal characteristics
Figures 3(a) and 3(b) show the detail of the two heater structures that we studied. Figure 3(a) shows the first structure in which a p-type dopant is implanted into the Si slab except around the core of the PCW to form a p–i–p junction. The current is made to flow across the waveguide to directly heat around the core. This structure achieves a higher heating efficiency and higher speed than those of the second structure shown in Fig. 3(b). However, the free carrier absorption due to the doping increases the propagation loss when the i region is narrowed to reduce the series resistance of the current flow. To suppress the optical absorption loss to approximately 10 dB/cm (which is smaller than the measured passive loss due to the scattering for the fabricated PCWs), we set the i region as 1.6 μm wide and the spacing between the p+ regions outside the p regions for the metal contact to be 6 μm. We assume the doping concentrations of the p and p+ regions to be NA = 1.05 × 1018 cm−3 and NA+ = 1.9 × 1020 cm−3, respectively, the sheet resistance of the p region to be 2.1 kΩ/□, and the corresponding resistivity to be 0.044 Ω·cm; the latter two are experimentally evaluated values.
Fig. 3 Temperature simulation by FEM. (a) Total view of the simulation model (left) and magnified top view around the PCW (right) for the p–i–p device. (b) Those for the TiN device. (c) Temperature distribution of model (a) for heating power density P/L = 0.22 W/cm. (d) That of model (b) for P/L = 0.46 W/cm.
Figure 3(b) shows the second structure in which the two TiN heaters are arranged on both sides of the PCW, and the current is made to flow in the longitudinal direction. We assume the resistivity of TiN to be 1.2 × 10−4 Ω·cm and its width and thickness to be 15 μm and 120 nm, respectively. Two TiN layers separated by a space of 12 μm are buried inside the upper SiO2 cladding with a >1.2-μm spacing from the Si slab; this arrangement ensures that the absorption of the guided slow light by TiN is negligible and the radiated beam is not blocked. However, the heating efficiency and heat capacity may become poor and large, respectively, resulting in a slow response speed.
We calculated the temperature distribution using a software of the finite element method (FEM), Murata Software Co. Ltd., Femtet, with three-dimensional models, as shown in the same figures, and material constants in Table 1 [14]. We set the model size to be 12 μm in the longitudinal direction and sufficiently large in the cross-sectional directions, i.e., 90 μm in width and 70 μm in height. The Si substrate was thicker than 700 μm in the experiment but set in the model to be 50 μm. Between the substrate and the bottom of the model fixed at a reference temperature, we also assumed a thermal semi-insulator to simulate the imperfect attachment of the substrate to a Peltier cooler used in the experiment. Its thickness and thermal conductivity were assumed to be 5 μm and 0.01 W/K·cm, respectively, so that the simulated temperature roughly fit to the experimental results, as shown later. Other boundaries of the model were terminated by thermally insulating walls. The results are shown in Figs. 3(c) and 3(d). In the p–i–p device, for which a power density P/L = 0.22 W/cm was injected, the waveguide core was intensively heated and ∆T reached a temperature greater than 300 K. In the TiN device, for which P/L = 0.46 W/cm was injected, the heat was widespread into the substrate. The ∆T inside TiN was raised up to 420−460 K range for a comparable ∆T at the waveguide core because of the indirect heating.
Table 1. Material constants used for calculating the thermal characteristics.
4. Experiment
We fabricated the devices on a 200-mm silicon-on-insulator (the detail was the same as that mentioned in Sections 2 and 3) using CMOS process with KrF excimer laser exposure and a phase-shift mask. The two types of structures fabricated are shown in Fig. 4. We coupled the TE-polarized laser light from a tunable laser source into a spot-size converter integrated at the end of the chip and connected to the PCW via the Si wire waveguide. The FFP of the radiated beam was observed by using an optical setup with the InGaAs camera, as shown in Fig. 5(a). As mentioned in Section 2, the FFP of the fan beam was sharp and wide in the θ and ϕ directions, respectively. For the p–i–p device, θ changed from 10° to 33° (the steering range ∆θ was 23°) for the wavelength sweep between 1546 and 1577 nm (∆λ = 28 nm), which is similar to that in [11].
Fig. 4 Fabricated devices. (a) p–i–p device with L = 800 μm, a = 400 nm, 2r = 200 nm, and ∆r = 10 nm. (b) TiN device with L = 1000 μm, 2r = 220 nm, and ∆r = 4 nm.
Fig. 5 FFP of radiated beam (a) p–i–p device at λ = 1563 nm with no heating. (b) p–i–p device with heating. (c) TiN device with heating.
Then, we applied the DC voltage to the p–i–p junction at a fixed wavelength slightly shorter than the band edge of the guided mode under the no-heating condition (i.e., λ = 1576 nm), as mentioned in Section 2. We observed a super-linear increase of the injection current for the applied voltage with a threshold voltage of ~10 V. We calculated the electronic potential distribution on such condition using a software, Lumerical Solutions Inc., DEVICE. We realized that such threshold characteristics arose from the partial reverse bias condition in the p–i–p junction similar to that in a p–n–p bipolar transistor. Figure 5(b) shows the shift of the FFP for the heating power P. We obtained the wide steering range with maintaining the sharp profile in the θ direction. At θ = 10°–25°, the central intensity of the beam disappeared and the FFP looked to be double-peaked. This was caused by the interference between upward radiation and downward one reflected back by the bottom surface of the Si substrate; we observed actually that the profile became single-peaked when the reflection was suppressed. Figure 6 summarizes θ and δθ (full-width at half-maximum in the θ direction at the maximum intensity in the ϕ direction) measured for P. For the p–i–p device, we obtained ∆θ = 21°, which was comparable to that for the wavelength sweep, with P = 1.3 W (P/L = 0.16 W/cm). ∆θ was slightly smaller than that of the wavelength sweep because the guided mode condition became narrower due to the setting the wavelength shorter than the band edge. Comparing the θ range between Fig. 2(b) and Fig. 6(a), we can estimate ∆T to be 340 K. We also observed δθ ranging from 0.1°‒0.3° and the average value of δθ to be 0.18°. The number of resolution points, N, given by ∆θ/δθ was 120. If the waveguide length is extended to longer than 1 mm and ∆r is moderately reduced to suppress the radiation, the effective aperture length is elongated, δθ is reduced to less than 0.1°, and therefore, N > 200 will be obtainable. One may anxious about the limitation of Δθ, but it can be expanded arbitrarily by adding an image-magnifying lens system with maintaining the value of N.
Fig. 6 Measured beam steering characteristics with heating power. (a) Radiation angle θ. (b) Beam divergence δθ. The abrupt increase and decrease in δθ arise from the change of sidelobe level; when the sidelobe level exceeds the half intensity of the main lobe, the total width from the main lobe to the sidelobe was counted as δθ.
Figure 5(c) shows the FFPs for the TiN device. In this case, we set the initial λ just at the band edge showing a particularly large ng, and therefore, the FFP was expanded and disordered due to the increased loss, shortened aperture length and nonuniform radiation angle, among others. For higher heating powers, we observed the beam steering and the suppression of the expansion and disordering because of the decrease in ng, resulting in a small δθ up to 0.2°. We obtained Δθ = 26°, for which the above-mentioned comparison of the θ range gives ΔT ≈350 K. However, we had to use a large power P = 4.8 W (P/L = 0.48 W/cm) to obtain this Δθ value, which reflects the low heating efficiency. The simulated power density shown in Section 3 agreed with this value almost precisely because we optimized the parameters of the thermal semi-insulator in the simulation to obtain this fitting. The precise agreement was not obtained for the p–i–p device, which might be due to slight disagreement between the simulated and experimental condition. Anyway, we could confirm that the heating efficiency of the p–i–p device is several times higher than the TiN device’s.
We also evaluated the response speed of these devices by applying an AC voltage at the frequency f and measuring Δθ from time-averaged FFP. The results are shown in Fig. 7. For the p–i–p device, we obtained ∆θ ≈25° at f ≤ 10 kHz, which is comparable with the wavelength sweep and DC measurements. As f was increased further, ∆θ decreased gradually, but still, ∆θ = 20° was maintained at f = 100 kHz and –3 dB cutoff frequency was higher than 600 kHz. This was considered to be attributed to the heating concentrated around the waveguide core, which accelerated the heat diffusion. In the TiN device, on the other hand, ∆θ was reduced to 10° at f = 1 Hz. This slow response is considered to be due to the poor heating efficiency. However, these different responses might be originating from more complicated reasons. We performed the time varying simulation for these devices and estimated the cutoff frequencies to be 10 kHz and 250 Hz, respectively. This difference should reflect the different heating efficiencies and heat capacities, but these values also differ from the experimental ones by 2‒3 orders. To explain the experimental results fully, we may have to consider the heat conduction through Al electrodes and the heat capacity including the Peltier cooler and heat sink, which should be investigated further in future studies.
Fig. 7 Measurement of response speed. The inset shows the time-averaged FFP when the AC voltage was applied at f = 1 kHz.
Finally we present a preliminary life test of the p–i–p device to check if the rapid heat cycle induces some severe damages into the structure. To operate the device continuously, we fabricated a simple fiber module, as shown in Fig. 8(a), where the chip and lensed fibers were fixed on AlN substrate using an ultraviolet curing resin. Significant degradation of the optical coupling was not observed even with the heating. The observation of Δθ at f = 1 kHz was observed continuously at different temperatures estimated from Δθ, as shown in Fig. 8(b). Severe damages were not observed in the range of ΔT ≈80‒430 K for the duration up to 20‒40 h; the slight decrease in Δθ at longer than 10 h was not due to the device itself but due to destabilization of the used voltage source and electrical amplifier.
Fig. 8 Evaluation of stability. (a) Simple fiber module. (b) Long time measurement of the steering range at different temperature for the AC current injection at f = 1 kHz.
5. Conclusion
In this study, we proposed compact optical beam steering devices, which are based on Si doubly periodic PCW and driven by two kinds of heaters. We succeeded in demonstrating the beam steering electrically. In the p–i–p device, with a relatively low heating power P = 1.3 W and high-speed response of 100 kHz, we observed a beam steering range ∆θ = 21° (estimated temperature of 340 K), maintaining a narrow beam divergence δθ = 0.1−0.3° (0.18° in an average). The number of resolution points N for the averaged δθ was 120, which will be enhanced further by elongating the device with moderately suppressing the radiation. In the preliminary life test of this device, we did not observe any severe damages for the continuous operation up to 20‒40 h. In the TiN device, we also obtained the comparable beam steering characteristics. However, the required heating power was as large as 4.8 W and the response speed was much slower, which might reflect the low heating efficiency and insufficient heat sink.
Funding
Accelerated Innovation Research Initiative Turning Top Science and Ideas into High-Impact Values (ACCEL); Japan Science and Technology Agency (JST) (JPMJAC1603).
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