Coupled Resonator Optical Waveguides Research Articles

Photoconductive heaters enable control of large-scale silicon photonic ring resonator circuits

A multitude of large-scale silicon photonic systems based on ring resonators have been envisioned for applications ranging from biomedical sensing to quantum computing and machine learning. Yet, due to the lack of a scalable solution for controlling ring resonators, practical demonstrations have been limited to systems with only a few rings. Here, we demonstrate that large systems can be controlled by using only doped waveguide elements inside their ringswhile preserving their area and cost. We measure the large photoconductive changes of the waveguides for monitoring the rings' resonance conditions across high-dynamic ranges and leverage their thermo-optic effects for tuning. This allows us to control ring resonators without requiring additional components, complex tuning algorithms, or additional electrical I/Os. We demonstrate automatic resonance alignment of 31 rings of a 16 x 16 switch and of a 14-ring coupled resonator optical waveguide, making them the largest, yet most compact, automatically controlled silicon ring resonator circuits to date, to the best of our knowledge.

Topological properties of coupled resonator array based on accurate band structure

The topological edge states of the coupled-resonator optical waveguide (CROW) system have been widely researched. Without breaking time-reversal symmetry nor needing to construct complicated optical modes as pseudospins, the CROW system offers characteristics that are effective for exploration of photonic topological effects and has potential for applications in nanodevices. We extend the previous method by using specific coupling conditions to calculate the system's actual band structure, thereby providing a new perspective of this system. Two types of topological properties, one with and the other without an artificial magnetic field, are identified based on the band diagrams. Fractal spectra including the Hofstadter butterfly spectrum are obtained, revealing the abundant physics associated with the CROW system. By connecting the band diagrams with the corresponding structural parameters, we propose a triangular lattice array with reduced losses at the corners and propose a scheme with the potential for use as a reconfigurable multipath platform.

A 300-mm Silicon Photonics Platform for Large-Scale Device Integration

A 300-mm silicon photonics platform for large-scale device integration was developed, leveraging 40-nm complementary metal-oxide-semiconductor technology. Through fabrication using this technology platform, wire waveguides were obtained with low propagation losses for the C-band (0.4 dB/cm) and O-band (1.3 dB/cm). Several types of wavelength filters, including a coupled resonator optical waveguide (CROW), an arrayed waveguide grating, and a cascaded Mach–Zehnder interferometer, were also demonstrated, with low crosstalk and low insertion loss. A polarization rotator Bragg grating with multiple reflection peaks having polarization independence was also obtained. In terms of wafer-scale uniformity, a small standard deviation of 0.7 nm in resonant wavelength for the CROW was confirmed. A grating coupler also exhibited low wafer-scale variations in the maximum coupling efficiency and the diffraction wavelength in optical coupling with a single-mode fiber. Extraction of fabrication deviations for the waveguides was performed using the spectral variation of microring resonators and grating couplers. The extracted wafer-scale variations in waveguide width and height and grating depth well reproduced the results of physical measurements, with subnanometer-level accuracy. The developed technology can thus enable manufacturing of high-speed, low-power optical interconnects.

Coherent virtual absorption for discretized light.

Coherent virtual absorption (CVA) is a recently introduced phenomenon for which exponentially growing waves incident on a conservative optical medium are neither reflected nor transmitted, at least transiently. CVA has been associated with complex zeros of the scattering matrix and can be regarded as the time reversal of the decay process of a quasi-mode sustained by the optical medium. Here we consider CVA for discretized light transport in coupled resonator optical waveguides or waveguide arrays and show that a distinct kind of CVA, which is not related to the complex zero excitation of quasi-modes, can be observed. This result suggests that a scattering matrix analysis cannot fully capture CVA phenomena.

Photonic Delay Lines Based on Silicon Coupled Resonator Optical Waveguide Structures

We propose a Coupled Resonator Optical Waveguide Structure based on silicon microring resonators. The proposed structure is designed on Silicon on Insulator platform so as to scale down the device dimensions as silicon on insulator platform provides the advantage of large index contrast, miniaturization of device dimensions. Tunability is incorporated on the structure in the simulation environment by placing thermal heaters on the top of the rings which change the refractive indices of the rings thereby changing the resonance wavelength. Finite difference time domain method is used to simulate the structure. Variable delays are achieved by tuning the necessary number of ring structures to their resonant wavelengths. This structure can be helpful in realizing optical delay lines for on chip optical interconnects.

Giant Resonance and Anomalous Quality Factor Scaling in Degenerate Band Edge Coupled Resonator Optical Waveguides

We propose a novel scheme for enhancing the quality factor of coupled resonators optical waveguides (CROWs) when operating near a degenerate band edge (DBE). A DBE is a four-mode exceptional point of degeneracy (EPD) occurring when four Bloch eigenmodes coalesce providing a resonance condition with a giant enhancement in fields. We report an unprecedented scaling law of quality factor of CROWs when operating at the DBE, even in the presence of losses and structural perturbations. Remarkably, the Q factor of the proposed CROW can be engineered to exceed that of a single ring resonator having a diameter equal to the CROW length, hence having an overall strong area reduction. The findings reported in this letter are critical for enhancing fields amplitudes to giant levels and the Q factor of ring resonators and are very beneficial for various applications including four wave mixing, Q switching, lasers, and highly sensitive sensors.

Squeezed-state evolution and entanglement in lossy coupled-resonator optical waveguides

We investigate theoretically the temporal evolution of a squeezed state in lossy coupled-cavity systems. We present a general formalism based upon the tight binding approximation and apply this to a two-cavity system as well as to a coupled resonator optical waveguide in a photonic crystal. We derive analytical expressions for the number of photons and the quadrature noise in each cavity as a function of time when the initial excited state is a squeezed state in one of the cavities. We also analytically evaluate the time dependant cross correlation between the photons in different cavities to evaluate the degree of quantum entanglement. We demonstrate the effects of loss on the properties of the coupled-cavity systems and derive approximate analytic expressions for the maximum photon number, maximum squeezing and maximum entanglement for cavities far from the initially excited cavity in a lossless coupled resonator optical waveguide.

Wideband multi-stage CROW filters with relaxed fabrication tolerances.

We present wideband and large free spectral range optical filters with steep passband edges for the selection of adjacent WDM communication channels that can be reliably fabricated with mainstream silicon photonics technology. The devices are based on three cascaded stages of coupled resonator optical waveguides loaded on a common bus waveguide. These stages differ in the number of resonators but are implemented with exactly identical unit cells, comprised of a matched racetrack resonator layout and a uniform spacing between cells. The different number of resonators in each stage allows a high rejection in the through port response enabled by the interleaved distribution of zeros. Furthermore, the exact replication of a unique cell avoids the passband ripple and high lobes in the stopband that typically arise in apodized coupled resonator optical waveguide based filters due to fabrication and coupling induced variations in the effective path length of each resonator. Silicon photonics filters designed for the selection of 9 adjacent optical carriers generated by a 100 GHz free spectral range comb laser have been successfully fabricated with 248 nm DUV lithography, achieving an out-of-band rejection above 11 dB and an insertion loss of less than 0.5 dB for the worst channels.

Induced high-order resonance linewidth shrinking with multiple coupled resonators in silicon-organic hybrid slotted two-dimensional photonic crystals for reduced optical switching power in bistable devices

Shrinking the linewidth of resonances induced by multiple coupled resonators is comprehensively analyzed using the coupled-mode theory (CMT) in time. Two types of coupled resonators under investigation are coupled resonator optical waveguides (CROWs) and side-coupled resonators with waveguide (SCREW). We examine the main parameters influencing on the spectral response such as the number of resonators (n) and the phase shift (φ) between two adjacent resonators. For the CROWs geometry consisting of n coupled resonators, we observe the quality (Q) factor of the right- and left-most resonant lineshapes increases n times larger than that of a single resonator. For the SCREW geometry, relying on the phase shift, sharp, and asymmetric resonant lineshape of the high Q factor a narrow linewidth of the spectral response could be achieved. We employ the finite-difference time-domain (FDTD) method to design and simulate two proposed resonators for practical applications. The proposed coupled resonators in silicon-on-insulator (SOI) slotted two-dimensional (2-D) photonic crystals (PhCs) filled and covered with a low refractive index organic material. Slotted PhC waveguides and cavities are designed to enhance the electromagnetic intensity and to confine the light into small cross-sectional area with low refractive index so that efficient optical devices could be achieved. A good agreement between the theoretical CMT analysis and the FDTD simulation is shown as an evidence for our accurate investigation. All-optical switches based on the CROWs in the SOI slotted 2-D PhC waveguide that are filled and covered by a nonlinear organic cladding to overcome the limitations of its well-known intrinsic properties are also presented. From the calculations, we introduce a dependency of the normalized linewidth of the right-most resonance and its switching power of the all-optical switches on number of resonator, n. This result might provide a guideline for all-optical signal processing on a silicon PhC chip design.

Improved 2 × 2 Mach-Zehnder switching using coupled-resonator photonic-crystal nanobeams.

Design and simulation results are presented for an on-chip 2×2 Mach-Zehnder-based optical switch where each arm of the interferometer is composed of a coupled-resonator optical waveguide. The individual resonators are one-dimensional photonic crystal nanobeam cavities, and switching occurs through thermally induced changes in the refractive index of the silicon structure using integrated heating pads. The performance of the coupled-resonator device is directly compared to its single resonator counterpart, and significant improvement is found in the bar-state CT metric.

Theory of coupled resonator optical waveguides exhibiting high-order exceptional points of degeneracy

We present a novel approach and a theoretical framework for generating high order exceptional points of degeneracy (EPD) in photonic structures based on periodic coupled resonators optical waveguides (CROWs). Such EPDs involve the coalescence of Floquet-Bloch eigenwaves in CROWs, without the presence of gain and loss, which is in contrast to the requirement of Parity-Time (PT) symmetry to develop exceptional points based on gain and loss balance. The EPDs arise here by introducing symmetry breaking in a conventional chain of coupled resonators through coupling the chain of resonators to an adjacent uniform optical waveguide, which leads to unique modal characteristics that cannot be realized in conventional CROWs. Such remarkable characteristics include high quality factors (Q-factor) and strong field enhancement, even without any mirrors at the two ends of a cavity. We show for the first time the capability of CROWs to exhibit EPDs of various order; including the degenerate band edge (DBE) and the stationary inflection point (SIP). The proposed CROW of finite length shows enhanced quality factor when operating near the DBE, and the Q-factor exhibits an anomalous scaling with the CROW's length. We develop the theory of EPDs in such unconventional CROW using coupled-wave equations, and we derive an analytical expression for the dispersion relation. The proposed unconventional CROW concepts have various potential applications including Q-switching, nonlinear devices, lasers, and extremely sensitive sensors.

Slow light effect with high group index and wideband by saddle-like mode in PC-CROW

Slow light with high group index and wideband is achieved in photonic crystal coupled-resonator optical waveguides (PC-CROWs). According to the eye-shaped scatterers and various microcavities, saddle-like curves between the normalized frequency f and wave number k can be obtained by adjusting the parameters of the scatterers, parameters of the coupling microcavities, and positions of the scatterers. Slow light with decent flat band and group index can then be achieved by optimizing the parameters. Simulations prove that the maximal value of the group index is > 104, and the normalized delay bandwidth product within a new varying range of n g > 102 or n g > 103 can be a new and effective criterion of evaluation for the slow light in PC-CROWs.

PT -Symmetric Coupled-Resonator Waveguide Based on Buried Heterostructure Nanocavities

The authors study coupled resonator optical waveguides (CROWs) to extend control of light propagation in photonic devices. Exploiting parity-time ($\mathcal{P}\phantom{\rule{0}{0ex}}\mathcal{T}$) symmetry of the waveguide allows selection of the group velocity and its dispersion for cavity modes. The researchers describe a scalable, controllable CROW with $\mathcal{P}\phantom{\rule{0}{0ex}}\mathcal{T}$ symmetry, which is induced by periodic and balanced amplification and absorption, and analyze its potential for switching from slow to fast light transport. With suitable tweaking, even superluminal propagation could be within reach.

Photon-pair generation in lossy coupled-resonator optical waveguides via spontaneous four-wave mixing

We theoretically model pair generation and evolution via the nonlinear process of spontaneous four-wave mixing in a coupled-resonator optical waveguide in a photonic crystal slab. Using the adjoint master equation for a system of lossy coupled cavities, we calculate a symmetrized second-order coherence function to determine pair detection probability. We find that the scattering loss can have as large an effect on pair generation as waveguide dispersion. In particular, the wave-vector dependence of the loss can shift the frequency of the maximum detection probability and therefore cannot, in general, be ignored or treated via a simple overall loss factor.

Performance Comparison of Grating-Assisted Integrated Photonic Delay Lines

Incorporation of grating waveguides in optical delay lines based on integrated microring resonator structures is proposed. Specifically, transmittive apodized grating waveguides are implemented in two common microring configurations, namely, coupled-resonator optical waveguides (CROWs) and side-coupled integrated spaced sequence of resonators (SCISSORs). The performance of these proposed devices is compared with standard CROWs and SCISSORs (i.e., with no gratings), as well as with grating-assisted waveguides (cascaded complementary apodized grating waveguides). It is shown that, for the same minimum bit rate operation, the proposed grating-assisted SCISSORs exhibit the best performance in terms of delay tunability and delay per footprint. However, the maximum true time delay of grating-assisted waveguides possesses a close to linear dependence on length, while the true delay in mircoresonator-type structures (with or without gratings) do not increase efficiently with the number of rings. Also, it is argued that the grating-assisted waveguides are expected to have the lowest insertion loss per delay time.

Realizing topological edge states in a silicon nitride microring-based photonic integrated circuit.

Topological edge states in a photonic integrated circuit based on the platform of silicon nitride are demonstrated with a two-dimensional coupled resonator optical waveguide array involving the synthetic magnetic field for photons at near-infrared wavelengths. Measurements indicate that the topological edge states can be observed at certain wavelengths, with light travelling around the boundary of the array. Combined with the induced disorders in fabrication near the edge, the system shows the defect immunity under the topological protection of edge states.

Photonic molecules with a tunable inter-cavity gap

Optical micro-resonators have broad applications. They are used, for example, to enhance light–matter interactions in optical sensors or as model systems for investigating fundamental physical mechanisms in cavity quantum electrodynamics. Coupling two or more micro-cavities is particularly interesting as it enlarges the design freedom and the field of application. In this context, achieving tunability of the coupling strength and hence the inter-cavity gap is of utmost importance for adjusting the properties of the coupled micro-resonator system. In this paper, we report on a novel coupling approach that allows highly precise tuning of the coupling gap of polymeric micro-resonators that are fabricated side by side on a common substrate. We structure goblet-shaped whispering-gallery-mode resonators on an elastic silicone-based polymer substrate by direct laser writing. The silicone substrate is mechanically stretched in order to exploit the lateral shrinkage to reduce the coupling gap. Incorporating a laser dye into the micro-resonators transforms the cavities into micro-lasers that can be pumped optically. We have investigated the lasing emission by micro-photoluminescence spectroscopy, focusing on the spatial localization of the modes. Our results demonstrate the formation of photonic molecules consisting of two or even three resonators, for which the coupling strengths and hence the lasing performance can be precisely tuned. Flexibility and tunability are key elements in future photonics, making our approach interesting for various photonic applications. For instance, as our coupling approach can also be extended to larger cavity arrays, it might serve as a platform for tunable coupled-resonator optical waveguide devices.

Quantum and thermal noise limits of coupled resonator optical waveguide and resonant waveguide optical rotation sensors

We analyze theoretically the performance limitations of coupled resonator optical waveguides (CROWs) and a single passive resonator of the same area for rotation sensing applications. We show that when the dominant noise sources are of quantum (shot) or thermal origin, the single passive resonator outperforms the CROW regardless the propagation loss in the waveguides. We also show that optimizing the design parameters of the CROW and the single ring cavity according to the dominant noise source can improve the minimal detectable rotation rate by almost 50%.

Photonic crystal power combiner based on hexagonal waveguides

A new 2×1 power combiner scheme based on two-dimensional photonic crystal has been designed using hexangular waveguides. These waveguides are created by reducing the radius of inner rods in alternate manner which subsequently leads to coupled resonator optical waveguide structure. In this design, the outer hexagon has two input ports and the output port is embedded in the inner hexagonal. Due to geometrical and metallurgical engineering, the photonic bandgap locates in the THz region. Three different radii of coupled resonator optical waveguide rods have been studied. It has been shown that the structure with largest inner rods provides better power output.

Analysis of coupled resonator optical waveguide gyroscope based on periodically modulated coupling and circumferences

Based on periodically modulated coupling and circumferences, we developed a new structure for coupled resonator optical waveguide (CROW) gyroscopes. Its sensitivity and resolution were significantly improved. With our new structure, which overcomes the individual limitations of the previous schemes, the sensitivity and resolution of our gyroscope are higher than those with coupling-coefficient modulation alone and circumference modulation alone. The resolution of the gyroscope gradually declines with increasing resonator propagation loss; when the quality factor Q≤2×106, the height of the center resonance peak of the transmission band decreases by more than 90%. Fortunately, this effect can be weakened by increasing the circumference difference. We also numerically analyzed the influence of manufacturing errors on the performance of the gyroscope. We found that the fluctuations of radius have a greater influence than the fluctuations of quality factor.