Stochastic and multi-objective design of photonic devices with machine learning.

Compact and highly performing photonic devices are characterized by non-intuitive geometries, a large number of parameters, and multiple figures of merit. Optimization and machine learning techniques have been explored to handle these complex designs, but the existing approaches often overlook stochastic quantities. As an example, random fabrication uncertainties critically determines experimental device performance. Here, we present a novel approach for the stochastic multi-objective design of photonic devices combining unsupervised dimensionality reduction and Gaussian process regression. The proposed approach allows to efficiently identify promising alternative designs and model the statistic of their response. Incorporating both deterministic and stochastic quantities into the design process enables a comprehensive analysis of the device and of the possible trade-offs between different performance metrics. As a proof-of-concept, we investigate surface gratings for fiber coupling in a silicon-on-insulator platform, considering variability in structure sizes, silicon thickness, and multi-step etch alignment. We analyze 86 alternative designs presenting comparable performance when neglecting variability, discovering on the contrary marked differences in yield and worst-case figures for both fiber coupling efficiency and back-reflections. Pareto frontiers demonstrating optimized device robustness are identified as well, offering a powerful tool for the design and optimization of photonic devices with stochastic figures of merit.

Highly efficient ultra-broad beam silicon nanophotonic antenna based on near-field phase engineering.

Optical antennas are a fundamental element in optical phased arrays (OPA) and free-space optical interconnects. An outstanding challenge in optical antenna design lies in achieving high radiation efficiency, ultra-compact footprint and broad radiation angle simultaneously, as required for dense 2D OPAs with a broad steering range. Here, we demonstrate a fundamentally new concept of a nanophotonic antenna based on near-field phase-engineering. By introducing a specific near-field phase factor in the Fraunhofer transformation, the far-field beam is widened beyond the diffraction limit for a given aperture size. We use transversally interleaved subwavelength grating nanostructures to control the near-field phase. A Bragg reflector is used at the end of the grating to increase both the efficiency and the far-field beam width. The antenna has a compact footprint of 3.1 µm × 1.75 µm and an ultra-broad far-field beam width of 52° and 62° in the longitudinal and transversal direction, respectively, while the radiation efficiency reaches 82% after incorporating a bottom reflector to further improve the directionality. This unprecedented design performance is achieved with a single-etch grating nanostructure in a 300-nm SOI platform.

Broadband behavior of quadratic metalenses with a wide field of view.

Metalenses are attracting a large interest for the implementation of complex optical functionalities in planar and compact devices. However, chromatic and off-axis aberrations remain standing challenges. Here, we experimentally investigate the broadband behavior of metalenses based on quadratic phase profiles. We show that these metalenses do not only guarantee an arbitrarily large field of view but are also inherently tolerant to longitudinal and transverse chromatic aberrations. As such, we demonstrate a single-layer, silicon metalens with a field of view of 86° and a bandwidth up to 140 nm operating at both 1300 nm and 1550 nm telecommunication wavelength bands.

Athermal echelle grating and tunable echelle grating demultiplexers using a Mach-Zehnder interferometer launch structure.

We present a comparative experimental study of three silicon photonic echelle grating demultiplexers that are integrated with a Mach-Zehnder interferometer (MZI) launch structure. By appropriate choice of the MZI configuration, the temperature induced shift of the demultiplexer channel wavelengths can be suppressed (athermal) or enhanced (super-thermal) or be controlled by an on-chip micro-heater. The latter two configurations allow the channel wavelengths to be actively tuned using lower power than possible by temperature tuning a conventional echelle demultiplexer. In the athermal configuration, the measured channel spectral shift is reduced to less than 10 pm/°C, compared to the 83 pm/°C shift for an unmodified echelle device. In super-thermal operation an enhanced channel temperature tuning rate of 170 pm/°C is achieved. Finally, by modulating the MZI phase with an on-chip heater, the demultiplexer channels can be actively tuned to correct for ambient temperature fluctuations up to 20 °C, using a drive current of less than 20 mA.

Mid-infrared Fourier-transform spectrometer based on metamaterial lateral cladding suspended silicon waveguides.

Integrated mid-infrared micro-spectrometers have a great potential for applications in environmental monitoring and space exploration. Silicon-on-insulator (SOI) is a promising platform to tackle this integration challenge, owing to its unique capability for large volume and low-cost production of ultra-compact photonic circuits. However, the use of SOI in the mid-infrared is restricted by the strong absorption of the buried oxide layer for wavelengths beyond 4 µm. Here, we overcome this limitation by utilizing metamaterial-cladded suspended silicon waveguides to implement a spatial heterodyne Fourier-transform (SHFT) spectrometer operating at wavelengths near 5.5 µm. The metamaterial-cladded geometry allows removal of the buried oxide layer, yielding measured propagation loss below 2 dB/cm at wavelengths between 5.3 and 5.7 µm. The SHFT spectrometer comprises 19 Mach-Zehnder interferometers with a maximum arm length imbalance of 200 µm, achieving a measured spectral resolution of 13 cm-1 and a free spectral range of 100 cm-1 at wavelengths near 5.5 µm.

Metamaterial-Engineered Silicon Beam Splitter Fabricated with Deep UV Immersion Lithography.

Subwavelength grating (SWG) metamaterials have garnered a great interest for their singular capability to shape the material properties and the propagation of light, allowing the realization of devices with unprecedented performance. However, practical SWG implementations are limited by fabrication constraints, such as minimum feature size, that restrict the available design space or compromise compatibility with high-volume fabrication technologies. Indeed, most successful SWG realizations so far relied on electron-beam lithographic techniques, compromising the scalability of the approach. Here, we report the experimental demonstration of an SWG metamaterial engineered beam splitter fabricated with deep-ultraviolet immersion lithography in a 300-mm silicon-on-insulator technology. The metamaterial beam splitter exhibits high performance over a measured bandwidth exceeding 186 nm centered at 1550 nm. These results open a new route for the development of scalable silicon photonic circuits exploiting flexible metamaterial engineering.

Efficient Bloch mode calculation of periodic systems with arbitrary geometry and open boundary conditions in the complex wavevector domain.

We show how existing iterative methods can be used to efficiently and accurately calculate Bloch periodic solutions of Maxwell's equations in arbitrary geometries. This is carried out in the complex-wavevector domain using a commercial frequency-domain finite-element solver that is available to the general user. The method is capable of dealing with leaky Bloch mode solutions, and is extremely efficient even for 3D geometries with non-trivial material distributions. We perform independent finite-difference time-domain simulations of Maxwell's equations to confirm our results. This comparison demonstrates that the iterative mode finder is more accurate, since it provides the true solutions in the complex-wavevector domain and removes the need for additional signal processing and fitting. Due to its efficiency, generality and reliability, this technique is well suited for complex and novel design tasks in integrated photonics, and also for a wider range of photonics problems.

Anti-reflection subwavelength gratings for InP-based waveguide facets.

We demonstrate the anti-reflection properties of lithographically defined subwavelength gratings applied to the facets of integrated waveguides realized in the InP membrane-on-silicon platform. The subwavelength gratings are based on the gradient index effect to create a smooth index transition between the core material and air, making it possible to obtain reflections below -30dB at a wavelength of 1550 nm for both TE and TM polarized modes, as shown by 3D finite-difference time-domain simulations. Characterizations performed using Mach-Zehnder interferometers as test structures show relative reflections as low as -25dB, confirming the effectiveness of the technique.

Compact and highly-efficient broadband surface grating antenna on a silicon platform.

We present a compact silicon-based surface grating antenna design with a high diffraction efficiency of 89% (-0.5 dB) and directionality of 0.94. The antenna is designed with subwavelength-based L-shaped radiating elements in a 300-nm silicon core, maintaining high efficiency with a compact footprint of 7.6 µm × 4.5 µm. The reflectivity remains below -10 dB over the S, C and L optical communication bands. A broad 1-dB bandwidth of 230 nm in diffraction efficiency is achieved with a central wavelength of 1550 nm.

Highly efficient optical antenna with small beam divergence in silicon waveguides.

Optical antennas are key components in optical phased arrays for light detection and ranging technology requiring long sensing range and high scanning resolution. To achieve a narrow beam width in the far-field region, antenna lengths of several millimeters or more are required. To date, such long antennas have been impossible to achieve in silicon waveguides because currently demonstrated technologies do not allow accurate control of grating strength. Here, we report on a new type of surface-emitting silicon waveguide with a dramatically increased antenna length of L=3.65mm. This is achieved by using a subwavelength metamaterial waveguide core evanescently coupled with radiative segments laterally separated from the core. This results in a far-field diffracted beam width of 0.025°, which is a record small beam divergence for a silicon photonics surface-emitting device. We also demonstrate that by using a design with L-shaped surface-emitting segments, the radiation efficiency of the antenna can be substantially increased compared to a conventional design, with an efficiency of 72% at the wavelength of 1550 nm.

Spectrum-free integrated photonic remote molecular identification and sensing.

Absorption spectroscopy is widely used in sensing and astronomy to understand remote molecular compositions. However, dispersive techniques require multichannel detection, reducing detection sensitivity while increasing instrument cost when compared to spectrophotometric methods. We present a novel non-dispersive infrared molecular detection and identification scheme that performs spectral correlation optically using a specially tailored integrated silicon ring resonator. We show experimentally that the correlation amplitude is proportional to the number of overlapping ring resonances and gas lines, and that molecular specificity can be achieved from the phase of the correlation signal. This strategy can enable on-chip detection of extremely faint remote spectral signatures.

Photonic temperature and wavelength metrology by spectral pattern recognition.

Spectral pattern recognition is used to measure temperature and generate calibrated wavelength/frequency combs using a single silicon waveguide ring resonator. The ring generates two incommensurate interleaving TE and TM spectral combs that shift independently with temperature to create a spectral pattern that is unique at every temperature. Following an initial calibration, the ring temperature can be determined by recognizing the spectral resonance pattern, and as a consequence, the wavelength of every resonance is also known. Two methods of pattern-based temperature retrieval are presented. In the first method, the ring is locked to a previously determined temperature set-point defined by the coincidence of only two specific TE and TM cavity modes. Based on a prior calibration at the set-point, the ring temperature and hence all resonance wavelengths are then known and the resulting comb can be used as a wavelength calibration reference. In this configuration, all reference comb wavelengths have been reproduced within a 5 pm accuracy across an 80 nm range by using an on-chip micro-heater to tune the ring. For more general photonic thermometry, a spectral correlation algorithm is developed to recognize a resonance pattern across a 30 nm wide spectral window and thereby determine ring temperature continuously to 50 mK accuracy. The correlation method is extended to simultaneously determine temperature and to identify and correct for wavelength calibration errors in the interrogating light source. The temperature and comb wavelength accuracy is limited primarily by the linewidth of the ring resonances, with accuracy and resolution scaling with the ring quality factor.

Perfectly vertical surface grating couplers using subwavelength engineering for increased feature sizes.

We present perfectly vertical grating couplers for the 220 nm silicon-on-insulator platform incorporating subwavelength metamaterials to increase the minimum feature sizes and achieve broadband low back-reflection. Our study reveals that devices with high coupling efficiencies are distributed over a wide region of the design space with varied back-reflections, while still maintaining minimum feature sizes larger than 100 nm and even 130 nm. Using 3D-finite-difference time-domain simulations, we demonstrate devices with broadband low back-reflection of less than -20dB over more than 100 nm bandwidth centered around the C-band. Coupling efficiencies of 72% and 67% are achieved for minimum feature sizes of 106 nm and 130 nm, respectively. These gratings are also more fabrication tolerant compared to similar designs not using metamaterials.

Empirical model for the temperature dependence of silicon refractive index from O to C band based on waveguide measurements.

An accurate model for the silicon refractive index including its temperature and wavelength dependence is critically important for many disciplines of science and technology. Currently, such a model for temperatures above 22°C in the optical communication bands is not available. The temperature dependence in the spectral response of integrated echelle grating filters made in silicon-on-insulator is solely determined by the optical properties of the slab waveguide, making it largely immune to dimensional uncertainties. This feature renders the echelle filters a reliable tool to evaluate the thermo-optic properties of silicon. Here we investigate the temperature dependence of silicon echelle filters for the wavelength range of both O and C bands, measured between 22°C to 80°C. We show that if a constant thermo-optic coefficient of silicon is assumed for each band, as is common in the literature, the predictions show an underestimate of up to 10% in the temperature-induced channel wavelength shift. We propose and assess a model of silicon refractive index that encompasses both the wavelength and temperature dependence of its thermo-optic coefficients. We start from literature data for bulk silicon and further refine the model using the echelle filter measurement results. This model is validated through accurate predictions of device channel wavelengths and their temperature dependence, including the quadratic term, over a wide wavelength and temperature range. This work also demonstrates a new high-precision method for characterizing the optical properties of a variety of materials.

Mapping the global design space of nanophotonic components using machine learning pattern recognition.

Nanophotonics finds ever broadening applications requiring complex components with many parameters to be simultaneously designed. Recent methodologies employing optimization algorithms commonly focus on a single performance objective, provide isolated designs, and do not describe how the design parameters influence the device behaviour. Here we propose and demonstrate a machine-learning-based approach to map and characterize the multi-parameter design space of nanophotonic components. Pattern recognition is used to reveal the relationship between an initial sparse set of optimized designs through a significant reduction in the number of characterizing parameters. This defines a design sub-space of lower dimensionality that can be mapped faster by orders of magnitude than the original design space. The behavior for multiple performance criteria is visualized, revealing the interplay of the design parameters, highlighting performance and structural limitations, and inspiring new design ideas. This global perspective on high-dimensional design problems represents a major shift in modern nanophotonic design and provides a powerful tool to explore complexity in next-generation devices.

Bragg filter bandwidth engineering in subwavelength grating metamaterial waveguides.

Bragg gratings are fundamental building blocks for integrated photonic circuits. In the high-index contrast silicon-on-insulator material platform, it is challenging to accurately control the grating strength and achieve narrow spectral bandwidths. Here we demonstrate a novel Bragg grating geometry utilizing a silicon subwavelength grating (SWG) waveguide with evanescently coupled periodic Bragg loading segments placed outside the SWG core. We report experimental 3 dB filter bandwidths in a range from 8 nm to 150 pm by adjusting the distance of the Bragg loading segments from the core and the relative phase shift of the segments on the two sides of the waveguide, with a structure that has a minimum feature size of 100 nm.

Athermal echelle grating filter in silicon-on-insulator using a temperature-synchronized input.

Athermal design of integrated photonic devices can reduce the need for active temperature stabilization and consequently the energy required to operate photonic integrated circuits. For silicon photonic filters such as AWGs which employ wire or ridge waveguides, temperature insensitivity can be achieved using cladding materials with negative thermo-optic coefficients. On the other hand, in echelle grating filters the inteference takes place in the slab free-propagation region, and therefore the modal overlap with the cladding is small, rendering this method ineffective. In this work we present an approach to design an athermal echelle grating filter exploiting a temperature-synchronized Mach-Zehnder interferometer as input. This reduces the spectral shift over a temperature range of 20 K to less than ±45 pm compared to the 1.6 nm shift for the same echelle grating with a conventional waveguide input. Furthermore, the proposed design relies exclusively on a standard fabrication process for silicon-on-insulator photonic devices and exhibits a good tolerance to fabrication uncertainties.

Stochastic process design kits for photonic circuits based on polynomial chaos augmented macro-modelling.

Fabrication tolerances can significantly degrade the performance of fabricated photonic circuits and process yield. It is essential to include these stochastic uncertainties in the design phase in order to predict the statistical behaviour of a device before the final fabrication. This paper presents a method to build a novel class of stochastic-based building blocks for the preparation of Process Design Kits for the analysis and design of photonic circuits. The proposed design kits directly store the information on the stochastic behaviour of each building block in the form of a generalized-polynomial-chaos-based augmented macro-model obtained by properly exploiting stochastic collocation and Galerkin methods. Using these macro-models, only a single deterministic simulation is required to compute the stochastic moments of any arbitrary photonic circuit, without the need of running a large number of time-consuming circuit simulations thereby dramatically improving simulation efficiency. The effectiveness of the proposed approach is verified by means of classical photonic circuit examples with multiple uncertain variables.

Integrated all-optical MIMO demultiplexer for mode- and wavelength-division-multiplexed transmission.

A photonic integrated circuit performing simultaneous mode and wavelength demultiplexing for few-mode-fiber transmission is demonstrated for the first time. The circuit is realized on an InP-based technological platform; it can handle up to eight mode- and wavelength-division-multiplexed (MDM/WDM) channels and allows all-optical multiple-input-multiple-output processing to unscramble mode mixing generated by fiber propagation. A single arrayed waveguide grating is used to demultiplex the WDM channels carried by all the propagating modes, optimizing circuit complexity, chip area, and operational stability. Combined with an integrated wideband mode multiplexer the circuit is successfully exploited for the transmission of 10 Gbit/s on-off-keying non-return-to-zero channels with a residual cross talk of about -15 dB.

Reconfigurable photonic integrated mode (de)multiplexer for SDM fiber transmission.

Spatial division multiplexing in multi-mode fibers allows to largely enhance transmission capacity compared to single-mode links. Photonic integrated circuits can provide solutions for mode multiplexing at the transmitter and demultiplexing at the receiver but have to generally face high losses and inter-modal cross-talk issues. Here a photonic circuit for efficient mode multiplexing and demultiplexing in few-mode fibers is presented and demonstrated. Two 10 Gbit/s channels at the same wavelength and polarization are simultaneously transmitted over modes LP01 and LP11a of a few-mode fiber relying only on integrated mode MUX and DEMUX. The proposed Indium-Phosphide-based circuits have a good coupling efficiency with fiber modes and mode-dependant loss smaller than 1 dB. Measured mode excitation cross-talk is as low as -20 dB and a channel cross-talk after propagation and demultiplexing of -15 dB is achieved. An operational bandwidth of the full transmission system of at least 10 nm is demonstrated. Both mode MUX and DEMUX are fully reconfigurable and allow a dynamic switch of channel routing in the transmission system. These results enable fully-integrated fiber mode handling for high-bandwidth flexible optical networks.