Abstract

Two-dimensional (2-D) integrated optical phased arrays (OPA) have many applications from optical imaging to LiDAR. Conventionally, 2-D beam-steering in an N × N OPA requires N2 phase shifters placed within the phased array aperture, resulting in a high per-element power consumption while limiting the minimum achievable element-to-element spacing. In this paper, we report an OPA architecture, where for 2-D beam-steering in an N × N OPA, only 2N phase shifters outside of the array aperture are used, which significantly reduces the total OPA power consumption and eliminates electrical routing within the aperture. As a proof of concept, an 8 × 8 OPA is implemented that uses 16 phase shifters to perform 2-D beam-steering without tuning the wavelength. Using the aperture size of 77 µm × 77 µm for the implemented OPA transmitter, far-field beam-steering over a range of about 7° is demonstrated.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

An optical phased array (OPA) is an array of optical emitting or receiving antennas (elements) that enables beam-forming and steering and is widely used in various applications including optical communications [1], LiDAR systems [24], projection systems [5], and 3-D imaging [6]. In such systems, the far-field beam is formed and steered by controlling the relative phases between optical elements within the array aperture. Benefiting from integrated photonic platforms, a number of OPAs have been demonstrated [215]. In the conventional implementation of a 2-D N × N element OPA, N2 phase shifters are used to perform per-element optical phase adjustment [25,7,8].

To form a narrow beam with a large side-lobe suppression ratio, which is steerable over a large field-of-view, a large number of closely placed elements (ideally with element spacing approaching half of the wavelength) within a large aperture is required. This results in a large power consumption in a conventional 2-D OPA with per-element phase shifters and makes the optical and electrical routing within the array aperture rather challenging.

In 2-D OPAs with grating based elements (e.g. grating couplers), this challenge can be addressed by steering the beam in one dimension through adjusting the relative phases between the elements, while using wavelength tuning for beam-steering in the other dimension [1215]. Despite excellent beam-steering results, this method requires a highly tunable laser (over a large wavelength range) and typically achieves a smaller steering range through wavelength tuning compared to the relative phases adjustment between the OPA elements.

In this paper, we introduce a novel OPA architecture, where for 2-D beam-steering in an N × N OPA, only 2N phase shifters outside of the array aperture are used to adjust the relative phases between elements and no laser wavelength tuning is performed. In the proposed scheme, the number of phase shifters for an N × N array is reduced from N2 (for a conventional 2-D OPA) to 2N, significantly reducing the power consumption of an OPA with a large number of elements. Furthermore, placing the phase shifters outside of the array aperture enables realization of OPAs with compact element spacing and eliminates the electrical routing within the aperture and the corresponding metallic-induced optical loss.

As a proof of concept, we have implemented an 8 × 8 OPA, which uses a single wavelength laser source and 16 phase shifters outside of the aperture to perform 2-D beam-steering. Using the aperture size of 77 µm × 77 µm (element spacing of 11 µm) for the implemented OPA transmitter, the far-field beam-steering range of approximately 7° is achieved.

2. Theory of operation

In an OPA, the beam forming and steering is performed by controlling the relative phases between the elements. Figure 1(a) shows the structure of the proposed N × N OPA, where N nanophotonic waveguides serving as rows cross N nanophotonic waveguides serving as columns. Consider the case that the electric field of optical wave entering the mth row is written as ${E_m} = {a_m}{e^{j{\phi _m}}}$, and the electric field of optical wave entering the nth column is written as ${E_n} = {b_n}{e^{j{\theta _n}}}$ where ${a_m}$,${b_n}$,${\phi _m}$, and ${\theta _n}$ are the amplitude of the optical field in the mth row, the amplitude of the optical field in the nth column, the phase of the optical signal in the mth row, and the phase of the optical signal in the nth column, respectively. Note that the term ${e^{j{\omega _0}t}}$, representing the optical frequency of the signal, is dropped for simplicity. Before the crossing point of the mth row and the nth column, two directional couplers with varying coupling ratio followed by a Y-junction are used to combine a fraction of the light from the mth row with a fraction of the light from the nth column. The Y-junction output is connected to a grating coupler, GCmn, acting as the OPA element. The length of each directional coupler as well as the etch level in the coupling region is adjusted to ensure all grating couplers receive the same power. The electric field at the input of GCmn is written as

$${E_{mn}} = \frac{1}{{\sqrt N }}\sqrt {\left({a_m^2 + b_n^2 + 2{a_m}{b_n}\cos ({\phi_m} - {\theta_n})} \right.)} \exp \left[ {j \,{{\tan }^{ - 1}}\left( {\frac{{{a_m}\sin {\phi_m} + {b_n}\sin {\theta_n}}}{{{a_m}\cos {\phi_m} + {b_n}\cos {\theta_n}}}} \right)} \right].$$

 figure: Fig. 1.

Fig. 1. Conceptual schematic of the proposed N × N OPA, where optical signals traveling in the row and column waveguides have (a) different phases and amplitudes and (b) different phases but the same amplitude.

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In this case, the relative phase between GCmn and GC(m+1)n can be written as

$$\Delta {\phi _{m + 1,m,n}} = {\tan ^{ - 1}}\left( {\frac{{{a_{m + 1}}\sin {\phi_{m + 1}} + {b_n}\sin {\theta_n}}}{{{a_{m + 1}}\cos {\phi_{m + 1}} + {b_n}\cos {\theta_n}}}} \right) - {\tan ^{ - 1}}\left( {\frac{{{a_m}\sin {\phi_m} + {b_n}\sin {\theta_n}}}{{{a_m}\cos {\phi_m} + {b_n}\cos {\theta_n}}}} \right).$$
Similarly, the relative phase between GCmn and GCm(n+1) can be written as
$$\Delta {\theta _{m,n + 1,n}} = {\tan ^{ - 1}}\left( {\frac{{{a_m}\sin {\phi_m} + {b_{n + 1}}\sin {\theta_{n + 1}}}}{{{a_m}\cos {\phi_m} + {b_{n + 1}}\cos {\theta_{n + 1}}}}} \right) - {\tan ^{ - 1}}\left( {\frac{{{a_m}\sin {\phi_m} + {b_n}\sin {\theta_n}}}{{{a_m}\cos {\phi_m} + {b_n}\cos {\theta_n}}}} \right).$$
Equations (2) and (3) indicate that the relative phase between adjacent elements can be set by adjusting the amplitude and phase of the optical waves in row and column waveguides outside the aperture. Note that the phase of the individual element cannot be independently set. However, the relative phase between the adjacent elements in the X and Y directions (in Fig. 1(a)) can be set to any value between 0 and 2π radians, enabling formation of a beam that can be steered in X and Y directions independently. For the case that ${a_m} = {b_n} = {a_0}$(Fig. 1(b)), Eq. (1) can be simplified as
$${E_{mn}} = \frac{2}{{\sqrt N }}{a_0}\left|{\cos \left( {\frac{{{\phi_m} - {\theta_n}}}{2}} \right)} \right|{e^{j\left( {\frac{{{\phi_m} + {\theta_n}}}{2}} \right)}}$$
In this case, the relative phase between the adjacent elements in rows and columns can be written as $\Delta {\phi _{m + 1,m,n}} = \frac{{{\phi _{m + 1}} - {\phi _m}}}{2}$ and $\Delta {\theta _{m,n + 1,n}} = \frac{{{\theta _{n + 1}} - {\theta _n}}}{2}$, respectively. In order to perform 2-D beam-steering, the relative phase between all adjacent elements in rows is set to the same value, i.e. $\Delta {\phi _{m + 1,m,n}} = \Delta \phi$ and, similarly, the relative phase between all adjacent elements in columns is set to $\Delta {\theta _{m,n + 1,n}} = \Delta \theta$. Therefore, 2N phase shifters can be used to perform 2-D beam-steering for an N × N OPA, which significantly reduces the power consumption for an OPA with a large number of elements, while eliminating the electrical routing within the aperture. Furthermore, moving the phase shifters outside of the aperture enables smaller element spacing for a 2-D phase array.

In Eq. (4), the amplitude of the electric field at GCmn is proportional to the term $|{\cos ({{{({\phi_m} - {\theta_n})} 2}} )} |$. Therefore, the light emission intensity from grating couplers may be lower than the conventional 2-D OPAs, where per-element phase shifters (with low phase dependent insertion loss) are used. To study the performance of the proposed 2-D OPA and also investigate the effect of the aforementioned phase dependent amplitude variation on the beam forming and steering, the Fraunhofer far-field approximation [16] is used to calculate the far-field interference pattern of an 8 × 8 OPA implemented based on the proposed architecture (with 16 off-aperture phase shifters), which is compared with that of a conventional 8 × 8 OPA with 64 per-element phase shifters in Fig. 2(a) for the case of diagonal beam-steering. The two OPAs have identical element structure with the same element spacing of 11 µm. The diagonal beam-steering is performed by setting the same relative phase of 0o, 30o, 60o, 120o, and 180o between the adjacent elements in both rows and columns. The normalized main lobe power for different steering angles for these two 8 × 8 OPAs is compared in Fig. 2(b). As predicted by Eq. (4), the intensity of the main lobe for the proposed OPA is generally lower than that of the conventional OPA. Note that in Fig. 2(a), for a relative phase of 180° between the adjacent elements in the proposed OPA, the intensity of every other element is zero (caused by the cosine term in Eq. (4)), effectively doubling the OPA element spacing, which results in a factor of 2 smaller lobe-spacing.

 figure: Fig. 2.

Fig. 2. (a) The far-field interference pattern of an 8 × 8 OPA with 64 per-element phase control (top row) and that of an 8 × 8 OPA with identical element structure and spacing but implemented based on the proposed architecture (bottom row). The diagonal beam-steering (with same relative phase between the elements in rows and columns) is performed. (b) The peak intensity of the main lobe in the far-field pattern for the conventional and proposed 8 × 8 OPAs.

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The side-lobe suppression ratio was calculated using the simulated far-field pattern in Fig. 2(a). In the conventional OPA with per-element phase control, the side-lobe suppression ratio of about 13 dB is calculated, which is reduced to about 9 dB for the proposed OPA with off-aperture phase adjustment due to the phase dependent amplitude effect described by Eq. (4). Note that the proposed architecture here can be used to form and steer a single beam and unlike 2D OPAs with per-element phase shifters, is not capable of multi-beam forming and steering.

3. System design

Figure 3(a) shows the structure of the implemented OPA transmitter. The input light is coupled into the chip using an on-chip grating coupler and is guided to a network of Y-junction splitters. The splitter network uniformly splits the coupled light into 16 branches. The phase of optical wave in the nanophotonic waveguide in each branch is adjusted through a thermal phase shifter. After phase adjustment, 8 nanophotonic waveguides serving as rows and 8 nanophotonic waveguides serving as columns are used to guide the optical waves to an array of 8 × 8 grating couplers serving as the OPA elements. Each grating coupler is placed near the crossing point of a row and a column waveguide and is fed by two directional couplers followed by a Y-junction combiner used to combine a fraction of the light from the corresponding row and column waveguides. The directional couplers have varying lengths to ensure that all grating couplers receive the same optical power. The spacing between the grating couplers within the array aperture is 11 µm and they are placed symmetrically with respect to the row and column waveguides as shown in Fig. 3(b). The microphotograph of the photonic chip is shown in Fig. 3(c). The chip has an area of 1000 µm × 950 µm, while the emitter aperture area is 77 µm × 77 µm. The chip is fabricated in the IME 180 nm silicon-on-insulator (SOI) photonic process.

 figure: Fig. 3.

Fig. 3. (a) The structure of the implemented 8 × 8 OPA with 16 phase shifters placed outside of the array aperture. (b) The structures of the grating couplers (as OPA elements) and directional couplers with varying lengths. (c) The microphotograph of the implemented 8 × 8 OPA chip fabricated in the IME 180 nm SOI process.

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Figures 4(a)–4(c) show the structure of different photonic devices used in the implementation of the proposed OPA. Figure 4(a) shows the 200 µm long thermal phase shifter, which consists of a metal heater on top of a silicon waveguide and two thermally isolating deep trenches on the sides to enhance the thermal efficiency. The phase shifter has a measured resistance of 350 Ω and Iπ of 4.5 mA.

 figure: Fig. 4.

Fig. 4. (a) The structure and the microphotograph of the implemented thermal phase shifter. (b) The structures of the nanophotonic waveguides, the waveguide crossing, directional couplers with varying length, the Y-junction [18], and the grating coupler serving as the OPA element. (c) Finite-Difference Time-Domain (FDTD) simulation results for the directional couplers with varying length and different silicon etch levels within the coupling region.

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Figure 4(b) shows the structure of a grating coupler (serving as the OPA element) along with the corresponding row and column waveguides and the feed network. The IME 180 nm SOI process offers three silicon etch levels that are used in the design of the compact directional couplers, grating couplers, and the compact waveguide crossings. Directional couplers with varying lengths are used in order to equally distribute the optical power in each row and column. To make the element spacing as small as possible, the coupling lengths should be minimized, which is achieved by partially etching the gap in the coupling region to increase the coupling coefficient for a given length. Considering the transmission and the coupling coefficients of the directional couplers, as well as the loss of the waveguide crossings, the required coupling lengths and the etch depth for the 7 directional couplers in each row/column are simulated, which are shown in Fig. 4(c). Note that the 500 nm wide 220 nm thick single-mode nanophotonic waveguides have a measured loss of under 2 dB/cm.

The design of the grating coupler serving as the OPA element follows the one presented in [17], however, the device dimensions and the number of gratings are modified to optimize the coupling efficiency for a compact footprint. The simulated efficiency of the grating coupler is about 30% at 1500 nm. To further reduce the element spacing, a compact waveguide crossing structure is designed that has a simulated insertion loss of under 0.3 dB with an isolation of more than 30 dB. To achieve symmetric routing, the grating couplers are placed at a 45 degree angle with respect to the column waveguides.

4. Characterization and measurement results

The measurement setup for characterizing the proposed OPA is shown in Fig. 5(a), where a laser emitting 1 mW at 1502 nm is coupled into the chip input grating coupler using a single-mode optical fiber. Two digitally controlled 8-channel thermal phase modulator drivers were used to control the row and column phase shifters. A FJW FIND-R-Scope 85700A infrared camera with adjustable optics were used to monitor the far-field interference pattern of the OPA.

 figure: Fig. 5.

Fig. 5. (a) Measurement setup used to characterize the OPA chip. (b) Measured far-field interference pattern showing four grating lobes. (c) Demonstration of the 2-D far-field beam-steering. (d) Two consecutive resolvable spots while diagonal beam-steering is performed. The bottom figure shows the beam profiles.

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In order to demonstrate 2-D beam-steering, the thermal phase shifters were used to control the phase of the optical signals in each row and column.

To account for the different waveguide routing lengths and process variations, the OPA was first calibrated (using the procedure in [5]), where the far-field interference pattern is compared with the simulation result for the case that both row and column signals have zero phase offset. Then, by adjusting the currents of the thermal phase shifters around the corresponding calibration point, the 2-D beam-forming was performed. Figure 5(b) shows four grating lobes of the far-field interference pattern of the OPA. Figure 5(c) shows the 2-D beam-steering results (only one grating lobe is shown). By controlling the phase of the thermal phase modulators in the rows and columns, beam-steering range of about 7° is demonstrated, which is in agreement with the simulation results in Fig. 2(a). Figure 5(d) shows two consecutive resolvable spots as the main lobe is steered diagonally. The corresponding beam profiles are shown in the bottom section of Fig. 5(d).

The estimated output power for each grating coupler (emitter) is about 38 dB lower than the power coupled into the input grating coupler. Also, for the case that the optical power coupled into the chip is set to -2 dBm, the measured radiated power in the main lobe is about -45 dBm.

5. Conclusion

A novel architecture to perform 2-D beam-steering in an N × N OPA with only 2N phase shifters placed outside of the array aperture is presented. In this case, the number of phase shifters is reduced by a factor of N/2, which results in a significant power consumption reduction for a 2-D OPA with a large number of elements. As a proof of concept, an 8 × 8 OPA with 16 phase shifters outside of the aperture has been implemented and used to demonstrate robust 2-D beam-steering over a range of about 7°.

Funding

Defense Advanced Research Projects Agency (FA8650-18-1-7828).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

References

1. S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

2. 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), 3642–3663 (2019). [CrossRef]  

3. J. Sun, E. Timordugan, A. Yaacobi, E. Shah Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013). [CrossRef]  

4. C. V. Poulton, M. J. Byrd, P. Russo, E. Timordugan, M. Khandaker, D. 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), 1–8 (2019). [CrossRef]  

5. F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic projection system,” Opt. Express 23(16), 21012–21022 (2015). [CrossRef]  

6. F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic coherent imager,” Opt. Express 23(4), 5117–5125 (2015). [CrossRef]  

7. B. Abiri, F. Aflatouni, A. Rekhi, and A. Hajimiri, “Electronic two-dimensional beam steering for integrated optical phased srrays,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2K.7.

8. R. Fatemi, B. Abiri, and A. Hajimiri, “An 8×8 heterodyne lens-less OPA camera,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper JW2A.9.

9. S. Chung, H. Abediasl, and H. Hashemi, “15.4 A 1024-element scalable optical phased array in 0.18µm SOI CMOS,” in 2017IEEE International Solid-State Circuits Conference (ISSCC), San Francisco.

10. C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.

11. K. Van Acoleyen, H. Rogier, and R. Baets, “Two-dimensional optical phased array antenna on silicon-on-insulator,” Opt. Express 18(13), 13655–13660 (2010). [CrossRef]  

12. 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]  

13. D. N. Hutchison, J. Sun, J. K. Doylend, R. Kumar, J. Heck, W. Kim, C. T. Phare, A. Feshali, and H. Rong, “High-resolution aliasing-free optical beam steering,” Optica 3(8), 887–890 (2016). [CrossRef]  

14. J. C. Hulme, J. K. Doylend, M. J. R. Heck, J. D. Peters, M. L. Davenport, J. T. Bovington, L. A. Coldren, and J. E. Bowers, “Fully integrated hybrid silicon two dimensional beam scanner,” Opt. Express 23(5), 5861–5874 (2015). [CrossRef]  

15. T. Komljenovic, R. Helkey, L. Coldren, and J. Bowers, “Sparse aperiodic arrays for optical beam forming and LIDAR,” Opt. Express 25(3), 2511–2528 (2017). [CrossRef]  

16. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

17. A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. D. Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011). [CrossRef]  

18. Y. Zhang, S. Yang, A. E. Lim, G. Q. Lo, C. Galland, T. Baeher-Jones, and M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013). [CrossRef]  

References

  • View by:

  1. S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7
  2. 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), 3642–3663 (2019).
    [Crossref]
  3. J. Sun, E. Timordugan, A. Yaacobi, E. Shah Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
    [Crossref]
  4. C. V. Poulton, M. J. Byrd, P. Russo, E. Timordugan, M. Khandaker, D. 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), 1–8 (2019).
    [Crossref]
  5. F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic projection system,” Opt. Express 23(16), 21012–21022 (2015).
    [Crossref]
  6. F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic coherent imager,” Opt. Express 23(4), 5117–5125 (2015).
    [Crossref]
  7. B. Abiri, F. Aflatouni, A. Rekhi, and A. Hajimiri, “Electronic two-dimensional beam steering for integrated optical phased srrays,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2K.7.
  8. R. Fatemi, B. Abiri, and A. Hajimiri, “An 8×8 heterodyne lens-less OPA camera,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper JW2A.9.
  9. S. Chung, H. Abediasl, and H. Hashemi, “15.4 A 1024-element scalable optical phased array in 0.18µm SOI CMOS,” in 2017IEEE International Solid-State Circuits Conference (ISSCC), San Francisco.
  10. C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.
  11. K. Van Acoleyen, H. Rogier, and R. Baets, “Two-dimensional optical phased array antenna on silicon-on-insulator,” Opt. Express 18(13), 13655–13660 (2010).
    [Crossref]
  12. 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]
  13. D. N. Hutchison, J. Sun, J. K. Doylend, R. Kumar, J. Heck, W. Kim, C. T. Phare, A. Feshali, and H. Rong, “High-resolution aliasing-free optical beam steering,” Optica 3(8), 887–890 (2016).
    [Crossref]
  14. J. C. Hulme, J. K. Doylend, M. J. R. Heck, J. D. Peters, M. L. Davenport, J. T. Bovington, L. A. Coldren, and J. E. Bowers, “Fully integrated hybrid silicon two dimensional beam scanner,” Opt. Express 23(5), 5861–5874 (2015).
    [Crossref]
  15. T. Komljenovic, R. Helkey, L. Coldren, and J. Bowers, “Sparse aperiodic arrays for optical beam forming and LIDAR,” Opt. Express 25(3), 2511–2528 (2017).
    [Crossref]
  16. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  17. A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. D. Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
    [Crossref]
  18. Y. Zhang, S. Yang, A. E. Lim, G. Q. Lo, C. Galland, T. Baeher-Jones, and M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013).
    [Crossref]

2019 (2)

C. V. Poulton, M. J. Byrd, P. Russo, E. Timordugan, M. Khandaker, D. 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), 1–8 (2019).
[Crossref]

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), 3642–3663 (2019).
[Crossref]

2017 (1)

2016 (1)

2015 (3)

2013 (2)

J. Sun, E. Timordugan, A. Yaacobi, E. Shah Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

Y. Zhang, S. Yang, A. E. Lim, G. Q. Lo, C. Galland, T. Baeher-Jones, and M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013).
[Crossref]

2011 (2)

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]

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. D. Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

2010 (1)

Abediasl, H.

S. Chung, H. Abediasl, and H. Hashemi, “15.4 A 1024-element scalable optical phased array in 0.18µm SOI CMOS,” in 2017IEEE International Solid-State Circuits Conference (ISSCC), San Francisco.

Abiri, B.

F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic coherent imager,” Opt. Express 23(4), 5117–5125 (2015).
[Crossref]

F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic projection system,” Opt. Express 23(16), 21012–21022 (2015).
[Crossref]

B. Abiri, F. Aflatouni, A. Rekhi, and A. Hajimiri, “Electronic two-dimensional beam steering for integrated optical phased srrays,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2K.7.

R. Fatemi, B. Abiri, and A. Hajimiri, “An 8×8 heterodyne lens-less OPA camera,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper JW2A.9.

Aflatouni, F.

F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic coherent imager,” Opt. Express 23(4), 5117–5125 (2015).
[Crossref]

F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic projection system,” Opt. Express 23(16), 21012–21022 (2015).
[Crossref]

B. Abiri, F. Aflatouni, A. Rekhi, and A. Hajimiri, “Electronic two-dimensional beam steering for integrated optical phased srrays,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2K.7.

Baeher-Jones, T.

Baets, R.

Benney, L. D.

S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

Bovington, J. T.

Bowers, J.

Bowers, J. E.

Byrd, M. J.

C. V. Poulton, M. J. Byrd, P. Russo, E. Timordugan, M. Khandaker, D. 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), 1–8 (2019).
[Crossref]

C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.

Chung, S.

S. Chung, H. Abediasl, and H. Hashemi, “15.4 A 1024-element scalable optical phased array in 0.18µm SOI CMOS,” in 2017IEEE International Solid-State Circuits Conference (ISSCC), San Francisco.

Coldren, L.

Coldren, L. A.

Davenport, M.

Davenport, M. L.

Delva, J. G.

S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

Dobbelaere, P. D.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. D. Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Doylend, J. K.

Fatemi, R.

R. Fatemi, B. Abiri, and A. Hajimiri, “An 8×8 heterodyne lens-less OPA camera,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper JW2A.9.

Feshali, A.

Galland, C.

Gloeckner, S.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. D. Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Hajimiri, A.

F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic coherent imager,” Opt. Express 23(4), 5117–5125 (2015).
[Crossref]

F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic projection system,” Opt. Express 23(16), 21012–21022 (2015).
[Crossref]

B. Abiri, F. Aflatouni, A. Rekhi, and A. Hajimiri, “Electronic two-dimensional beam steering for integrated optical phased srrays,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2K.7.

R. Fatemi, B. Abiri, and A. Hajimiri, “An 8×8 heterodyne lens-less OPA camera,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper JW2A.9.

Hare, A. E.

S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

Hashemi, H.

S. Chung, H. Abediasl, and H. Hashemi, “15.4 A 1024-element scalable optical phased array in 0.18µm SOI CMOS,” in 2017IEEE International Solid-State Circuits Conference (ISSCC), San Francisco.

Heck, J.

Heck, M. J. R.

Helkey, R.

Hochberg, M.

Hosseini, E.

C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.

Hosseini, E. S.

S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

Huang, J.

Hulme, J. C.

Hutchison, D. N.

Kelsey, A. F.

S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

Khandaker, M.

C. V. Poulton, M. J. Byrd, P. Russo, E. Timordugan, M. Khandaker, D. 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), 1–8 (2019).
[Crossref]

Kim, W.

Komljenovic, T.

Kumar, R.

Laine, J. P.

S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

Lane, B. F.

S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

Lim, A. E.

Lo, G. Q.

Masini, G.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. D. Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Mekis, A.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. D. Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Mlynarczyk, J. M.

S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

Moss, B.

C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.

Narasimha, A.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. D. Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Peters, J. D.

Phare, C. T.

Pinguet, T.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. D. Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Pintus, P.

Poulton, C. V.

C. V. Poulton, M. J. Byrd, P. Russo, E. Timordugan, M. Khandaker, D. 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), 1–8 (2019).
[Crossref]

S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.

Rekhi, A.

F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic coherent imager,” Opt. Express 23(4), 5117–5125 (2015).
[Crossref]

F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic projection system,” Opt. Express 23(16), 21012–21022 (2015).
[Crossref]

B. Abiri, F. Aflatouni, A. Rekhi, and A. Hajimiri, “Electronic two-dimensional beam steering for integrated optical phased srrays,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2K.7.

Rogier, H.

Rong, H.

Russo, P.

C. V. Poulton, M. J. Byrd, P. Russo, E. Timordugan, M. Khandaker, D. 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), 1–8 (2019).
[Crossref]

C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.

Sahni, S.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. D. Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Shah Hosseini, E.

J. Sun, E. Timordugan, A. Yaacobi, E. Shah Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

Spector, S. J.

S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

Su, Z.

C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.

Sun, J.

D. N. Hutchison, J. Sun, J. K. Doylend, R. Kumar, J. Heck, W. Kim, C. T. Phare, A. Feshali, and H. Rong, “High-resolution aliasing-free optical beam steering,” Optica 3(8), 887–890 (2016).
[Crossref]

J. Sun, E. Timordugan, A. Yaacobi, E. Shah Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

Timordugan, E.

C. V. Poulton, M. J. Byrd, P. Russo, E. Timordugan, M. Khandaker, D. 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), 1–8 (2019).
[Crossref]

J. Sun, E. Timordugan, A. Yaacobi, E. Shah Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

Timurdogan, E.

C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.

Torres, A.

Tran, M.

Van Acoleyen, K.

Vermeulen, D.

C. V. Poulton, M. J. Byrd, P. Russo, E. Timordugan, M. Khandaker, D. 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), 1–8 (2019).
[Crossref]

C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.

Watts, M. R.

C. V. Poulton, M. J. Byrd, P. Russo, E. Timordugan, M. Khandaker, D. 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), 1–8 (2019).
[Crossref]

J. Sun, E. Timordugan, A. Yaacobi, E. Shah Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.

Whitson, M.

C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.

Xie, W.

Yaacobi, A.

J. Sun, E. Timordugan, A. Yaacobi, E. Shah Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

Yang, S.

Zhang, Y.

IEEE J. Sel. Top. Quantum Electron. (2)

C. V. Poulton, M. J. Byrd, P. Russo, E. Timordugan, M. Khandaker, D. 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), 1–8 (2019).
[Crossref]

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. D. Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Nature (1)

J. Sun, E. Timordugan, A. Yaacobi, E. Shah Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

Opt. Express (8)

Y. Zhang, S. Yang, A. E. Lim, G. Q. Lo, C. Galland, T. Baeher-Jones, and M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013).
[Crossref]

J. C. Hulme, J. K. Doylend, M. J. R. Heck, J. D. Peters, M. L. Davenport, J. T. Bovington, L. A. Coldren, and J. E. Bowers, “Fully integrated hybrid silicon two dimensional beam scanner,” Opt. Express 23(5), 5861–5874 (2015).
[Crossref]

T. Komljenovic, R. Helkey, L. Coldren, and J. Bowers, “Sparse aperiodic arrays for optical beam forming and LIDAR,” Opt. Express 25(3), 2511–2528 (2017).
[Crossref]

F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic projection system,” Opt. Express 23(16), 21012–21022 (2015).
[Crossref]

F. Aflatouni, B. Abiri, A. Rekhi, and A. Hajimiri, “Nanophotonic coherent imager,” Opt. Express 23(4), 5117–5125 (2015).
[Crossref]

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), 3642–3663 (2019).
[Crossref]

K. Van Acoleyen, H. Rogier, and R. Baets, “Two-dimensional optical phased array antenna on silicon-on-insulator,” Opt. Express 18(13), 13655–13660 (2010).
[Crossref]

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]

Optica (1)

Other (6)

S. J. Spector, B. F. Lane, M. R. Watts, L. D. Benney, J. G. Delva, A. E. Hare, A. F. Kelsey, J. M. Mlynarczyk, E. S. Hosseini, C. V. Poulton, and J. P. Laine, “Broadband imaging and wireless communication with an optical phased array,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SM3I.7

B. Abiri, F. Aflatouni, A. Rekhi, and A. Hajimiri, “Electronic two-dimensional beam steering for integrated optical phased srrays,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2K.7.

R. Fatemi, B. Abiri, and A. Hajimiri, “An 8×8 heterodyne lens-less OPA camera,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper JW2A.9.

S. Chung, H. Abediasl, and H. Hashemi, “15.4 A 1024-element scalable optical phased array in 0.18µm SOI CMOS,” in 2017IEEE International Solid-State Circuits Conference (ISSCC), San Francisco.

C. V. Poulton, P. Russo, E. Timurdogan, M. Whitson, M. J. Byrd, E. Hosseini, B. Moss, Z. Su, D. Vermeulen, and M. R. Watts, “High-performance integrated optical phased arrays for chip-scale beam steering and LiDAR,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper ATu3R.2.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (5)

Fig. 1.
Fig. 1. Conceptual schematic of the proposed N × N OPA, where optical signals traveling in the row and column waveguides have (a) different phases and amplitudes and (b) different phases but the same amplitude.
Fig. 2.
Fig. 2. (a) The far-field interference pattern of an 8 × 8 OPA with 64 per-element phase control (top row) and that of an 8 × 8 OPA with identical element structure and spacing but implemented based on the proposed architecture (bottom row). The diagonal beam-steering (with same relative phase between the elements in rows and columns) is performed. (b) The peak intensity of the main lobe in the far-field pattern for the conventional and proposed 8 × 8 OPAs.
Fig. 3.
Fig. 3. (a) The structure of the implemented 8 × 8 OPA with 16 phase shifters placed outside of the array aperture. (b) The structures of the grating couplers (as OPA elements) and directional couplers with varying lengths. (c) The microphotograph of the implemented 8 × 8 OPA chip fabricated in the IME 180 nm SOI process.
Fig. 4.
Fig. 4. (a) The structure and the microphotograph of the implemented thermal phase shifter. (b) The structures of the nanophotonic waveguides, the waveguide crossing, directional couplers with varying length, the Y-junction [18], and the grating coupler serving as the OPA element. (c) Finite-Difference Time-Domain (FDTD) simulation results for the directional couplers with varying length and different silicon etch levels within the coupling region.
Fig. 5.
Fig. 5. (a) Measurement setup used to characterize the OPA chip. (b) Measured far-field interference pattern showing four grating lobes. (c) Demonstration of the 2-D far-field beam-steering. (d) Two consecutive resolvable spots while diagonal beam-steering is performed. The bottom figure shows the beam profiles.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

E m n = 1 N ( a m 2 + b n 2 + 2 a m b n cos ( ϕ m θ n ) ) exp [ j tan 1 ( a m sin ϕ m + b n sin θ n a m cos ϕ m + b n cos θ n ) ] .
Δ ϕ m + 1 , m , n = tan 1 ( a m + 1 sin ϕ m + 1 + b n sin θ n a m + 1 cos ϕ m + 1 + b n cos θ n ) tan 1 ( a m sin ϕ m + b n sin θ n a m cos ϕ m + b n cos θ n ) .
Δ θ m , n + 1 , n = tan 1 ( a m sin ϕ m + b n + 1 sin θ n + 1 a m cos ϕ m + b n + 1 cos θ n + 1 ) tan 1 ( a m sin ϕ m + b n sin θ n a m cos ϕ m + b n cos θ n ) .
E m n = 2 N a 0 | cos ( ϕ m θ n 2 ) | e j ( ϕ m + θ n 2 )

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