Coupled Resonator Optical Waveguides Research Articles

On the spectral response of a taiji-CROW device

Physical systems with topological properties are robust against disorder. However, implementing them in integrated photonic devices is challenging because of the various fabrication imperfections and/or limitations that affect the spectral response of their building blocks. One such feature is strong backscattering due to the surface wall roughness of the waveguides, which can flip the propagating modes to counterpropagating modes and destroy the desired topological behavior. Here, we report a study on modeling, designing and testing an integrated photonic structure based on a sequence of two taiji microresonators coupled with a middle link microresonator (a taiji-CROW device, where CROW stands for coupled resonator optical waveguides). Our study provides design constraints to preserve the ideal operation of the structure by quantifying a minimum ratio between the coupling coefficients and the backscattering coefficients. This ratio is valuable to avoid surface roughness problems in designing topological integrated photonic devices based on arrays of microresonators.

Fully reconfigurable MEMS-based second-order coupled-resonator optical waveguide (CROW) with ultra-low tuning energy.

Integrated microring resonators are well suited for wavelength-filtering applications in optical signal processing, and cascaded microring resonators allow flexible filter design in coupled-resonator optical waveguide (CROW) configurations. However, the implementation of high-order cascaded microring resonators with high extinction ratios (ERs) remains challenging owing to stringent fabrication requirements and the need for precise resonator tunability. We present a fully integrated on-chip second-order CROW filter using silicon photonic microelectromechanical systems (MEMS) to adjust tunable directional couplers and a phase shifter using nanoscale mechanical out-of-plane waveguide displacement. The filter can be fully reconfigured with regard to both the ER and center wavelength. We experimentally demonstrated an ER exceeding 25 dB and continuous wavelength tuning across the full free spectral range of 0.123 nm for single microring resonator, and showed reconfigurability in second-order CROW by tuning the ER and resonant wavelength. The tuning energy for an individual silicon photonic MEMS phase shifter or tunable coupler is less than 22 pJ with sub-microwatt static power consumption, which is far better than conventional integrated phase shifters based on other physical modulation mechanisms.

Realization of a novel multimode waveguide with photonic band gap hopping based on coupled-resonator optical waveguide theory

Traditionally, in the application of photonic crystals, defect modes are mostly introduced in the photonic band gap to realize high-performance waveguides, and electromagnetic waves beyond the photonic band gap cannot be controlled in photonic crystals. Here we demonstrated a kind of deep subwavelength quasi-photonic crystal waveguide, named 2D closed surface-wave photonic crystal, by combining a photonic crystal with a spoof surface plasmon polaritons-based metal–insulator–metal structure. The closed surface-wave photonic crystal waveguide can realize the introduction of the defect mode in the frequency band where the first-order dispersion curve of the surface-wave photonic crystals is located, instead of being limited to the frequency range of the photonic band gap of surface-wave photonic crystals. At the same time, we confirmed the correctness of the coupled-resonator optical waveguide theory under the conditions of the first-order mode and the multi-order mode based on the closed surface-wave photonic crystal guided-wave mechanism. We have verified our work in 80–130 GHz through experiments, theory, and simulation, which are consistent. The closed surface-wave photonic crystals can be used as a kind of highly integrated waveguide and multi-bandpass/band-elimination filter in integrated optical circuits, and can adjust the working frequency band at very low cost.

Photonic band gaps and waveguide slow-light propagation in Bravais–Moiré two-dimensional photonic crystals

Photonic band gap widths and slow-light optical guided modes are theoretically investigated for Bravais–Moiré (BM) photonic crystals (PCs) made of cylindrical dielectric cores which are formed from the combination of two square Bravais lattices. The Moiré pattern forms due to a commensurable rotation of one of these lattices with respect to the other. The analysis of gap maps is made versus the radii of dielectric cores—both rotated and unrotated—contained in the BM unit cell (UC). Guided modes are considered within the framework of coupled-resonator optical waveguides (CROWs), built from the generation of a point defect chain along the direction of electromagnetic wave propagation. For the analyzed structures, rather wide photonic band gaps were found. It was noticed that changing the core radii can significantly affect the dielectric contrast in the UC, leading to wider gaps. In addition, due to the kind of crystal cell structure considered, guided modes with group velocities smaller than those typically observed in PCs with simple square lattices were found for the investigated CROWs.

Achieving Fano resonance with an ultra-high slope rate by silicon nitride CROW embedded in a Mach-Zehnder interferometer.

Fano resonance with asymmetric line shape is very promising in many applications such as optical switching, sensing, slow light, laser. Fano resonances based on some integrated structures have been demonstrated on the silicon on insulator platform. However, the extinction ratios and slope rates of the most proposed integrated Fano resonances are relatively low, which limits their applications. In this paper, a tunable silicon nitride coupled resonator optical waveguide (CROW) embedded in a Mach-Zehnder interferometer (MZI) is proposed to achieve Fano resonance. Benefiting from fine tuning supported by the low thermo-optic coefficient of the silicon nitride optical waveguide, the optical amplitudes and phases in the two arms of the MZI were accurately adjusted to achieve destructive interference, which gives an ultra-high extinction ratio. Furthermore, high quality factor CROW, supported by the native low loss silicon nitride optical waveguide, greatly shrinks the resonance bandwidth. Combining the above two superiorities, a Fano resonance with a very high extinction ratio of up to 57 dB and slope rate as high as 8.1 × 104 dB/nm was obtained, which is an order of magnitude larger than the reported integrated Fano resonances. We believe that the proposed structure would be a promising candidate for high-performance switching and high-sensitivity sensing.

Optical delay lines in topological microring resonator array

We use a periodic microring resonator array (MRRA) to realize photonic topological insulator. By tuning the coupling of resonators, two topological edge states can be observed in different bands in the dispersive band, normalized transmission spectrum and light field distribution. From the dispersion band structure, we calculate the group velocity, group velocity dispersion, normalized delay bandwidth product and other delay properties. It is demonstrated that optical delay lines (ODLs) in topological MRRA not only can obtain a comparable delay times, but also show a flatter transmission spectrum and more stable delay time, compared with the traditional coupled resonator optical waveguide. Our work may provide a theoretical reference for the topological ODLs with robust transmission.

Non-local scattering control in coupled resonator networks.

We demonstrate scattering control of Gaussian-like wave packets propagating with constant envelope velocity and invariant waist through coupled resonator optical waveguides (CROW) via an external resonator coupled to multiple sites of the CROW. We calculate the analytical reflectance and transmittance using standard scattering methods from waveguide quantum electrodynamics and show it is possible to approximate them for an external resonator detuned to the CROW. Our analytical and approximate results are in good agreement with numerical simulations. We engineer various configurations using an external resonator coupled to two sites of a CROW to show light trapping with effective exponential decay between the coupling sites, wave packet splitting into two pairs of identical Gaussian-like wave packets, and a non-local Mach-Zehnder interferometer.

General model of counterpropagating continuous-variable entangled states in lossy waveguides

We present a general theoretical approach to model an integrated source of counterpropagating continuous-variable entangled states in lossy waveguides pumped by a classical pulsed source incident from above the waveguide. We use a backward Heisenberg approach to model the generation of the entangled state and then solve the adjoint master equation to model the propagation of the state in the lossy waveguide. We employ a numerical method to implement the Schmidt decomposition method for the biphoton wave function rather than pursuing analytical methods. This approach allows us to model a wide variety of waveguide systems and pump configurations. We apply our model to the nonlinear generation and propagation of continuous-variable entangled states in a coupled resonator optical waveguide under a variety of different pump conditions and derive the optimal pumping conditions for our system.

Nonreciprocal Single-Photon Band Structure.

We study a single-photon band structure in a one-dimensional coupled-resonator optical waveguide that chirally couples to an array of two-level quantum emitters (QEs). The chiral interaction between the resonator mode and the QE can break the time-reversal symmetry without the magneto-optical effect and an external or synthetic magnetic field. As a result, nonreciprocal single-photon edge states, band gaps, and flat bands appear. By using such a chiral QE coupled-resonator optical waveguide system, including a finite number of unit cells and working in the nonreciprocal band gap, we achieve frequency-multiplexed single-photon circulators with high fidelity and low insertion loss. The chiral QE-light interaction can also protect one-way propagation of single photons against backscattering. Our work opens a new door for studying unconventional photonic band structures without electronic counterparts in condensed matter and exploring its applications in the quantum regime.

CROW-based Fano structures for all optical switching devices.

In this paper, an improved optical Fano switch based on coupled resonator optical waveguides (CROWs) is presented. The new topological design is employed to achieve steeper and highly asymmetric Fano resonances (FRs). Physically, in the proposed structures, due to the increase in the effective refractive index at the center of the CROW, a confined mode arises in the continuum background according to the variational theorem and leads to FR. The results show that in CROW-based Fano switches, the Fano spectrum is improved by tuning the number of nanocavities. The ratio between the slope ratio and linewidth shows an improvement of 55.25% from single to CROW5. As an important application of FR, an ultra-compact device with a CROW-based Fano structure is demonstrated. The results of the numerical finite difference time domain simulation agree well with the theoretical coupled mode theory.

Optical Arbitrary Waveform Measurement (OAWM) Using Silicon Photonic Slicing Filters

We demonstrate an optical arbitrary waveform measurement (OAWM) system that exploits a bank of silicon photonic (SiP) frequency-tunable coupled-resonator optical waveguide (CROW) filters for gapless spectral slicing of broadband optical signals. The spectral slices are coherently detected using a frequency comb as a multi-wavelength local oscillator (LO) and stitched together by digital signal processing (DSP). For high-quality signal reconstruction, we have implemented a maximum-ratio combining (MRC) technique based on precise calibration of the complex-valued opto-electronic transfer functions of all detection paths. In a proof-of-concept experiment, we demonstrate the viability of the scheme by implementing a four-channel system that offers an overall detection bandwidth of 140 GHz. Exploiting a femtosecond laser with precisely known pulse shape for calibration along with dynamic amplitude and phase estimation, we reconstruct 100 GBd QPSK, 16QAM and 64QAM optical data signals. The reconstructed signals show improved quality compared to that obtained with a single high-speed intradyne receiver, while the electronic bandwidth requirements of the individual coherent receivers are greatly reduced.

Variation-Aware Methods and Models for Silicon Photonic Design-for-Manufacturability

Methods for the generation and application of process variation-aware compact models for silicon photonics are presented. Three categories of process variations are considered. First, systematic variations, including die-to-die and spatial variations, are addressed with parameterized variation-aware compact models, and demonstrated for coupled resonator optical waveguide variation impact and yield analysis. Second, methods for random variation are presented, with ensemble and adjoint-based variation modeling methods. Third, particle defects are addressed with an extension to adjoint methods, enabling efficient analysis and identification of photonic component areas that are sensitive to defects. Finally, methods for extraction of variation models using variation test chip design and measurement are presented. Together, these methods are key components toward design-for-manufacturability approaches to achieve high yield and high performance in photonic integrated circuit design.

Moiré Effects in Silicon Photonic Nanowires

Photonic moiré lattices offer an attractive platform for manipulating the flow and confinement of light from remarkably simple device geometries. This emerging field draws inspiration from the rapid research progress observed in twisted bilayer van der Waals materials or “twistronics,” instead of applying moiré physics to photon propagation in wavelength-scale optical media. However, to date, only a limited number of experimental studies have been performed in this area, and there is strong interest in understanding how moiré effects can be tailored in compact and scalable optical technologies such as an integrated photonics platform. In this work, we map the moiré effects of one-dimensional (1D) photonic moiré lattices composed of width-modulated silicon nanowires, including the construction of a 1D experiment analogous to the twisting of a two-dimensional (2D) lattice. Although the twist angle Δθ and/or lattice mismatch ΔΛ are the sole defining parameters for infinite moiré crystals, we demonstrate how the crystal size, symmetry, and moiré fringe phase Δϕ also serve as important degrees of freedom. Through tailoring these parameters, we map a wide range of behaviors including the formation of moiré photonic crystal cavities, the onset of miniband formation and operation as a coupled resonator optical waveguide (CROW), widely tunable Q-factors and group velocities, suppression of grating sidebands, and persistent vs extinguishable tunneling. These results provide insight into the moiré physics of 1D optical systems and highlight various operating regimes relevant to the design of finite photonic moiré lattices and devices.

Mutlilayer Wedge Disks CROW for an Optical Delay Line

Optical delay lines are vital for the development of all optical telecommunications, optical computers and for many nonlinear and quantum optics processes. Periodic structures such as coupled resonator optical waveguides (CROW) achieve high delays in a compact manner and with a large bandwidth. Wedge disk resonators have demonstrated high quality factors compared to rectangular disks and rings while remaining integrable on chip. Vertical coupling is needed since the optical mode is pushed toward the disk center by the wedge. We propose an optical delay line made of wedge disks arranged in two overlapping layers. Disks are made of silicon dioxide on silicon pillars. Numerical calculations of the device performance and an experimental proof of concept are presented. A maximum delay of 85 ps for eleven disks is achieved with a loss per cavity of 3.91 dB. This is a first proof of concept of a CROW structure made of wedge disk coupled vertically.

An Analytical Method for Evaluating the Robustness of Photonic Integrated Circuits

We propose an efficient analytical method to evaluate the robustness of integrated photonic devices and circuits in the presence of independently-distributed random variations in the device parameters. By approximating the output of a photonic system in terms of a first or second-order Taylor series, we derive closed-form expressions for the mean and variance of the system output, which allow us to compute the one-standard-deviation (1-sigma) bounds on the expected system performance. Compared to other approaches for evaluating robustness, our method does not require computationally-intensive numerical simulations of the system output and can apply to any statistical distribution of parameter variations, including uniform and normal distributions. We demonstrate the method by analyzing the robustness of two coupled resonator systems: a fifth-order microring filter, and optical delay lines based on 1D Coupled Resonator Optical Waveguides and 2D Floquet topological microring lattice. Our method could provide a useful tool in the design and analysis of robust optical devices and circuits.

Wideband SiN pulse interleaver for optically-enabled analog-to-digital conversion: a device-to-system analysis with cyclic equalization.

We present the design and experimental characterization of a silicon nitride pulse interleaver based on coupled resonator optical waveguide filters. In order to achieve a targeted free spectral range of 1.44 THz, which is large given the reduced optical confinement of the silicon nitride platform, individual ring resonators are designed with tapered waveguides. Its application to time-interleaved photonically-assisted ADCs is analyzed by combining experimental characterization of the photonic integrated circuit with a comprehensive model of the entire ADC. The impact of fundamental signal distortion and noise sources affecting the converter is investigated and suitable equalization techniques at the digital signal processing level are evaluated. The novel application of a simple but powerful equalization filter in the DSP domain allows for a significant improvement of the digitized signal SNR. An ENOB of 5 over a 75 GHz bandwidth (150 GS/s) and an ENOB of 4.3 over a 100 GHz bandwidth (200 GS/s) are expected to be achievable with compact and off-the-shelf single-section semiconductor mode locked lasers, that can be further improved with lower noise light sources.

High-order nonreciprocal add-drop filter

Topological photonics have led to robust optical behavior of optical devices, which has alleviated the influence of manufacturing defects and perturbations on the device performance. Meanwhile, temporal coupled-mode theory (t-CMT) has been developed and applied widely. However, the t-CMT of cascaded coupled cavities (CCC) system and its corresponding high-order filter has yet to be established. Here, the t-CMT of CCC system is established based on the existing t-CMT. By combining the CCC with topological waveguides, a versatile design scheme of high-order nonreciprocal add-drop filter (HONAF) is proposed. The relationship between the coupling effect of cavities and transmission and the filtering performance of HONAF is analyzed quantitatively. Then, a method to improve the transmission efficiency and quality factor of the filter is given. The proposed HONAF is based on the combination of gyromagnetic photonic crystals and decagonal Penrose-type photonic quasicrystals. The transmission and filtering performance of the HONAF are numerically analyzed, which verifies the consistency between theoretical prediction and numerical simulation. The established t-CMT of CCC system can be widely used in coupled resonator optical waveguides and their related systems. The proposed HONAF with excellent performance can also be applied to wavelength division multiplexing/demultiplexing systems.

Compact high-contrast silicon optical filter using all-passive and CROW Fano nanobeam resonators.

We propose and experimentally demonstrate a high-order coupled-resonator optical waveguide (CROW) nanobeam filter with semi-symmetrical Fano resonance enhancement. Thanks to the tight arrangement of multiple nanobeams and assistance of the partial transmission element, the designed filter has a high-contrast transmission and low insertion loss. Finally, the fabricated filter has a compact size of 20µm×10µm, a high extinction ratio as much as 70 dB, and an insertion loss as low as 1 dB. This filter shows a passive structure without thermal control configuration for calibration on each resonator. This compact filter can be a basic building block for various applications requiring high extinction ratio filtering, such as single-photon source filtering of integrated photon chips.

Dispersive bands of bound states in the continuum

Abstract Bound states in the continuum (BICs), i.e. highly-localized modes with energy embedded in the continuum of radiating waves, have provided in the past decade a new paradigm in optics and photonics, especially at the nanoscale, with a range of applications from nanophotonics to optical sensing and laser design. Here, we introduce the idea of a crystal made of BICs, in which an array of BICs is indirectly coupled via a common continuum of states resulting in a tight-binding dispersive energy miniband embedded in the spectrum of radiating waves. The results are illustrated for a chain of optical cavities side-coupled to a coupled-resonator optical waveguide with nonlocal contact points.

Magnetically Controlled Assembly of Dielectric Microspheres toward Photonic Molecules

AbstractThe construction of “photonic molecules” with controlled sizes and shapes is of particular interest for the integration of miniaturized devices into optoelectronic chips. Here, a general approach is reported that allows the assembly of colloidal microspheres into coupled microcavities with high yield and large scale, utilizing magnetostatic interactions between diamagnetic building blocks dispersed in a ferrofluid under an external field. By precisely designing the local field gradient around diamagnetic microspheres, “virtual templates” can be formed to produce various coupled photonic structures, including diatomic heterogeneous molecules and polyatomic chain molecules. The diatomic structures can modulate the optical resonance modes upon the coherent coupling between microsphere cavities and serve as single‐mode wavelength‐tunable microlasers. The chain photonic molecules, as coupled resonator optical waveguides, could modulate the light propagation and store photons up to tens of picoseconds. The magnetically controlled assembly method is demonstrated, which provides a promising way for the facile and efficient fabrication of coupled microstructures for fascinating photonic and optoelectronic applications.