Contra-directional Coupling Research Articles

Suppressing the crosstalk between racetrack resonators by grating assisted couplers for WDM sensing

We proposed a uniform racetrack resonators based sensor for bio-chemical WDM sensing. The sensing channels are assigned by grating assisted contra-directional couplers. Each resonator only occupies one sensing channel. The crosstalk between sensing channels can be suppressed by aligning the center coupling wavelength of one resonator with the weak coupling wavelength of the others. Based on the simulation results obtained from transfer matrix method, the sensing channel gap can be reduced down to 2 FSRs (∼1.5 nm) of the resonator. The total crosstalk can be as low as 2.5 × 10−2 dB in a sensor with 23 channels covering the whole C band. This sensor with high throughput will be very important for analyzing a wide range of analytes, such as organic compounds or biological materials.

Spectral engineering of subwavelength-grating-based contradirectional couplers.

We tailor the spectral characteristics of silicon photonic contradirectional couplers (Contra-DCs), where the design of the coupler is based on placing a subwavelength grating (SWG) waveguide next to a strip waveguide. By tapering the gap distance between the SWG and strip waveguides, we demonstrate a compromise between sidelobe suppression and pass-band/stop-band extinction ratio such that the performance of the device as a potential optical (de)multiplexer is improved. The designs with different pass-band bandwidths of 12 nm, 9 nm, and 6 nm show 10 dB to 20 dB sidelobe suppression ratio and 15 dB to 35 dB extinction ratio. We also obtain a resonant transmission peak in the stop-band of the spectral response of the device by introducing a π phase shift into the gratings of the SWG waveguide. The resonant peak has 1 nm bandwidth and 7 dB extinction ratio, where the use of the SWG waveguide in the structure of such coupler allows the characteristics of the resonant peak to be highly sensitive to the cladding material, which is of strong desire in integrated sensing applications.

Design and modeling of highly tunable filters based on the linear electro-optic effect in strained silicon waveguides

Design and modeling of wavelength tunable filters based on the linear electro-optic (Pockels) effect in strained silicon waveguides is presented. The structure is based on the silicon grating-assisted contradirectional couplers. The basic idea is to utilize a silicon nitride (Si3N4) layer on top of the silicon waveguides to induce a relatively large Pockels effect in the waveguides by breaking the centrosymmetry of the Si crystal due to the surface strain. Wavelength tuning is obtained by applying DC voltages to the device contacts on top of the Si3N4 layer. Based on the presented structure, a wavelength tunable filter at the C-band communication window is designed and its characteristics were investigated by full-vectorial finite-element and finite-difference time-domain methods for electrostatic and optical responses. A 3.5-nm wavelength shift for an applied voltage of 1 V and a 7.5-nm shift for an applied voltage of 5 V are obtained with negligible loss. The presented device is superior to the previously reported structures in terms of tunability and loss.

Design of low-energy on-chip electro-optical 1 × M wavelength-selective switches

A theoretical design is presented for a 1×M wavelength-selective switch (WSS) that routes any one of N incoming wavelength signals to any one of M output ports. This planar on-chip device comprises of a 1×N demultiplexer, a group of N switching “trees” actuated by electro-optical or thermo-optical means, and an M-fold set of N×1 multiplexers. Trees utilize 1×2 switches. The WSS insertion loss is proportional to [log2 (M+N+1)]. Along with cross talk from trees, cross talk is present at each cross-illuminated waveguide intersection within the WSS, and there are at most N−1 such crossings per path. These loss and cross talk properties will likely place a practical limit of N=M=16 upon the WSS size. By constraining the 1×2 switching energy to ∼1 fJ/bit, we find that resonant, narrowband 1×2 switches are required. The 1×2 devices proposed here are nanobeam Mach–Zehnders and asymmetric contra-directional couplers with grating assistance.

Coupled-mode theory for the interaction between acoustic waves and spin waves in magnonic-phononic crystals: Propagating magnetoelastic waves

We have investigated co-directional and contra-directional couplings between spin wave and acoustic wave in one-dimensional periodic structure (magphonic crystal). The system consists of two ferromagnetic layers alternating in space. We have taken into consideration materials commonly used in magnonics: yttrium iron garnet, CoFeB, permalloy, and cobalt. The coupled mode theory (CMT) formalism have been successfully implemented to describe magnetoelastic interaction as a periodic perturbation in the magphonic crystal. The results of CMT calculations have been verified by more rigorous simulations by frequency-domain plane wave method and time-domain finite element method. The presented resonant coupling in the magphonic crystal is an active in-space mechanism which spatially transfers energy between propagating spin and acoustic modes, thus creating propagating magnetoelastic wave. We have shown, that CMT analysis of the magnetoelastic coupling is an useful tool to optimize and design a spin wave - acoustic wave transducer based on a magphonic crystals. The effect of spin wave damping has been included to the model to discuss the efficiency of such a device. Our model shows that it is possible to obtain forward conversion of the acoustic wave to the spin wave in case of co-directional coupling and backward conversion in case of contra-directional coupling.

Silicon photonic bandpass filter based on apodized subwavelength grating with high suppression ratio and short coupling length.

A compact silicon bandpass filter with high sidelobe suppression is proposed and experimentally demonstrated using an apodized subwavelength grating (SWG) coupler. The device is implemented by placing a SWG waveguide next to a strip waveguide, and apodization is employed with a Gaussian profile to taper the gap between the two waveguides. A high sidelobe suppression ratio of 27 dB can be obtained with a 3-dB bandwidth of 8.8 nm and an insertion loss of 2.5 dB. Owing to the large optical phase mismatch between the two waveguides and the presence of the SWG waveguide, the coupling length of the device is reduced to 100.3 μm. The experimental results validate our proposed apodized-SWG-based contradirectional coupler (contra-DC) as a promising device in suppressing out-of-band components in coarse wavelength division multiplexed (CWDM) optical communication systems.

Silicon Add-Drop Filter Based on Multimode Bragg Sidewall Gratings and Adiabatic Couplers

A silicon photonic add-drop filter is demonstrated with sidewall Bragg gratings in a multimode strip waveguide. The operating principle is based on the contradirectional coupling between the TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> mode and different higher-order modes inside the multimode waveguide, which depends on the symmetry property of the periodic refractive-index perturbations. In order to relax the fabrication tolerance, a pair of adiabatic couplers is used to add/drop the optical signal at the output/input ports of the multimode waveguide. Experimental results show that the functionality of add/drop filtering is successfully achieved with a low insertion loss of 0.6 dB. We also show that by sweeping the multimode waveguide width from 700 to 1400 nm, the bandwidth can be flexibly tuned from 16 to 2 nm.

Two-mode contra-directional coupler based on superposed grating.

We propose and demonstrate a novel two-mode grating assisted contra-directional coupler (TGACC), which is capable of filtering two modes channels simultaneously by superposed grating with two superposed grating components. Finite-difference time-domain simulation is employed to study the structure. The influences of main structural parameters are analyzed, and apodization is employed to reduce the band sidelobes, crosstalk and back-reflections. We experimentally present a mode-channel switchable TGACC for 2.54nm-wide wavelength band centered at 1548.0nm by 50K thermal-optic tuning. With two channels combined into one device, the TGACC can help to enrich the functionality and reduce the footprint of mode-division multiplexing (MDM) systems.

First-Order Grating Coupling Coefficients in Asymmetric Three-Layer Waveguides for Transverse Electric Modes

An equivalent surface current method is used to derive an analytic expression that approximates the coupling coefficient, reflectivity bandwidth, and group velocity for coupling between identical and nonidentical TE modes in an asymmetric three-layer waveguide with a sinusoidal grating at one waveguide interface. The analytic expression for the coupling coefficient agrees with expressions derived by two other methods for contradirectional coupling between identical modes. The results from the analytical expressions are compared to results from a numerically accurate Floquet–Bloch solution. The analytical expressions, which do not depend on which interface contains the grating, provide almost identical results obtained by the accurate solution for shallow grating depths and small index changes at the grating interface, a case typical of single-mode distributed feedback lasers. However, the accurate numerical solution, unlike the analytic solution, shows that in waveguides with only a large index step at the grating interface, increasing the grating depth can result in decreasing the coupling coefficient, a case typical of some distributed Bragg reflector lasers. In highly confined silicon photonic waveguides (large index steps at both interfaces), the analytic expression gives accurate results even for deep gratings. The derivation of the analytical expression for the coupling coefficient in this paper using the equivalent surface current method extends the application of the previous analytic formulas to nonidentical mode coupling where the forward and backward modes are not identical, which has application to gratings in multimode broadened waveguide lasers and amplifiers.

Subwavelength grating waveguide devices in silicon-on-insulators for integrated microwave photonics (Invited Paper)

We provide an overview of our recent work on developing subwavelength grating (SWG) waveguide devices as an enabling technology for integrated microwave photonics. First, we describe wavelength-selective SWG waveguide filters, including ring resonators, Bragg gratings, and contradirectional couplers. Second, we discuss the development of an index variable optical true time delay line that exploits spatial diversity in an equal-length waveguide array. These SWG waveguide components are fundamental building blocks for realizing more complex structures for advanced microwave photonic signal processing.

FSR-free silicon-on-insulator microring resonator based filter with bent contra-directional couplers.

High-speed optical interconnects drive the need for compact microring resonators (MRRs) with wide free spectral ranges (FSRs). A silicon-on-insulator MRR based filter with bent contra-directional couplers that exhibits an FSR-free response, at both the drop and through ports, while achieving a compact footprint is both theoretically and experimentally demonstrated. Also, using bent contra-directional couplers in the couping regions of MRRs allowed us to achieve larger side-mode suppressions than MRRs with straight CDCs. The fabricated filter has a minimum suppression ratio of more than 15 dB, a 3dB-bandwidth of ~23 GHz, an extinction ratio of ~18 dB, and a drop-port insertion loss of ~1 dB. High-speed data transmission through our filter is also demonstrated at data rates of 12.5 Gbps, 20 Gbps, and 28 Gbps.

Silicon Add-Drop Filter Based on Multimode Grating Assisted Couplers

We demonstrate the design, fabrication, and characterization of a two-mode silicon add-drop filter, which is based on multimode grating-assisted contra-directional couplers. The mode conversions between two asymmetry strip waveguides are realized by using spatially periodic corrugations in one side wall of a multimode waveguide at the phase-match condition. Experimental results show that the fundamental mode of a single-mode waveguide is successfully coupled to the first two modes of the multimode waveguide in the opposite direction. The corresponding mode conversion bandwidths and extinction ratios are also measured. The demonstrated add-drop filter may find their applications in a hybrid multiplexing system by combing wavelength-division multiplexing technology and mode-division multiplexing technology for on-chip optical interconnect.

Large-mode-volume multiwaveguide distributed feedback resonator

We propose a multiwaveguide cavity which can significantly enlarge the mode volume of distributed feedback (DFB) cavity without increasing the cavity length. The cavity is constructed by combining λ/4 shifted DFB cavity with contra-directional couplers. Different from single-waveguide DFB cavity, the resonant mode is oscillating in multiple waveguides. A smaller threshold gain density is also obtained compared to single-waveguide DFB cavity. Theory model of the multiwaveguide cavity is established and finite-difference time-domain simulation is performed to verify the model.

Silicon photonic contradirectional couplers using subwavelength grating waveguides.

We propose and demonstrate a novel design of contradirectional couplers in which a subwavelength grating (SWG) waveguide replaces one of the asymmetric waveguides of the conventional designs. The fabricated devices in silicon-on-insulator (SOI) platform show over 35 dB suppression of undesired codirectional coupling and larger than 120 nm operating range free from the interference of intrawaveguide reflections thanks to the large optical phase-mismatch between the segmented SWG waveguide and its nearby continuous waveguide. We study the effects of tailoring the period of the SWG waveguide, the gap distance between the two waveguides, and the coupling length on the spectral characteristics of the device where changing the gap distance from 100 nm up to 500 nm allows for bandwidths from 18.2 nm down to 0.9 nm.

Silicon band-rejection and band-pass filter based on asymmetric Bragg sidewall gratings in a multimode waveguide.

A silicon photonic wire filter based on an asymmetric sidewall Bragg grating in a multimode silicon-on-insulator strip waveguide is demonstrated. The operating principle is based on the contra-directional coupling between the transverse electric fundamental (TE0) and first-order (TE1) modes, which is enabled by the asymmetric spatially periodic refractive-index perturbations. An asymmetric Y-junction is cascaded at the input port of the filter so as to drop the Bragg reflection. Compared with conventional Bragg grating-based filters, this device eliminates the back reflection at the input port and the 6dB inherent insertion loss at the drop port; moreover, a narrow 3dB bandwidth can be obtained with a large critical dimension as a result of the weak coupling strength between the TE0 and TE1 modes inside the multimode waveguide. Experimental results show that a bandwidth of ∼2.8 nm is achieved by a large corrugation width of 150nm. The insertion loss at the drop port is -2.1 dB, and the extinction ratio is -33 dB at the through port.

High-extinction-ratio silicon polarization beam splitter with tolerance to waveguide width and coupling length variations.

We demonstrate a compact silicon polarization beam splitter (PBS) based on grating-assisted contradirectional couplers (GACCs). Over 30-dB extinction ratios and less than 1-dB insertion losses are achieved for both polarizations. The proposed PBS exhibits tolerance in width variation, and the polarization extinction ratios remain higher than 20 dB for both polarizations when the width variation is adjusted from + 10 to -10 nm. Benefiting from the enhanced coupling by the GACCs, the polarization extinction ratio can be kept higher than 15 dB and the insertion loss is lower than 2 dB for both polarizations when the coupling length varies from 30.96 to 13.76 μm.

Backward spoof surface wave in plasmonic metamaterial of ultrathin metallic structure.

Backward wave with anti-parallel phase and group velocities is one of the basic properties associated with negative refraction and sub-diffraction image that have attracted considerable interest in the context of photonic metamaterials. It has been predicted theoretically that some plasmonic structures can also support backward wave propagation of surface plasmon polaritons (SPPs), however direct experimental demonstration has not been reported, to the best of our knowledge. In this paper, a specially designed plasmonic metamaterial of corrugated metallic strip has been proposed that can support backward spoof SPP wave propagation. The dispersion analysis, the full electromagnetic field simulation and the transmission measurement of the plasmonic metamaterial waveguide have clearly validated the backward wave propagation with dispersion relation possessing negative slope and opposite directions of group and phase velocities. As a further verification and application, a contra-directional coupler is designed and tested that can route the microwave signal to opposite terminals at different operating frequencies, indicating new application opportunities of plasmonic metamaterial in integrated functional devices and circuits for microwave and terahertz radiation.

On-Chip Silicon Two-Mode (De)Multiplexer for OFDM/OQAM Data Transmission Based on Grating-Assisted Coupler

We fabricate and demonstrate on-chip two-mode (de)multiplexing using a tapered asymmetrical grating-assisted contradirectional coupler-based $\text{TE}_{0}$ and $\text{TE}_{2}$ mode multiplexer and demultiplexer on the silicon-on-insulator platform. The designed silicon photonic device is composed of apodized grating couplers, a narrow waveguide, a bus waveguide, and an asymmetrical multimode grating-assisted contradirectional coupler. The operation principle of such a mode (de)multiplexer is analyzed according to the coupled mode theory. System experiments of orthogonal-frequency-division-multiplexing-based offset quadrature amplitude modulation (OFDM/OQAM) 256-ary QAM data transmission have been carried out for two-mode (de)multiplexing application at 23.89 Gbit/s. The bit error rate (BER) performance for the signal transmission through the fabricated two-mode (de)multiplexer is evaluated. The optical signal-to-noise ratio (OSNR) penalties of data transmission through the fabricated two-mode (de)multiplexer are less than 2 dB at a BER of $2\mathrm{e}^{-2}$ (20% forward error correction threshold).

Widely bandwidth-tunable silicon filter with an unlimited free-spectral range.

Next-generation high-capacity optical networks require flexible allocation of spectrum resources, for which low-cost optical filters with an ultra-wide bandwidth tunability beyond 100 GHz are desired. We demonstrate an integrated band-pass filter with the bandwidth continuously tuned across 670 GHz (117-788 GHz) which, to the best of our knowledge, is the widest tuning span ever demonstrated on a silicon chip. The filter also features simultaneous wavelength tuning and an unlimited free spectral range. We measured an out-of-band contrast of up to 55 dB, low in-band ripples of less than 0.3 dB, and in-band group delay variation of less than 8 ps. This result was achieved using cascaded Bragg-grating-assisted contra-directional couplers and micro-heaters on the 220 nm silicon-on-insulator platform with a very compact footprint of less than 7000 μm2. Another design with the bandwidth continuously tunable from 50 GHz to 1 THz is also presented.

Modeling of Inline Transitions Between Different Waveguides as Impedance Inverters for the Use in Novel Filter Designs

In this paper, a novel approach for field coupled inline transitions between different waveguides is proposed. The immittance inverting characteristics of these transitions are simultaneously utilized for filter design. Based on scattering parameters, an exact relation is derived between the desired inverter constants and the even and odd mode characteristic impedances. The well-known approximation introduced by Cohn is improved. Further it will be shown that the introduced inline transitions can be effectively modeled with a contra-directional symmetrical coupler. The description of the field coupled waveguide transitions as inverters allows a “straight on design method” for general field coupled structures and accelerates the optimization process. The integration of the inline transitions into the filter design is applied for two different types of transitions, namely, the transition between a parallel-plate waveguide and a rectangular waveguide (RWG) and the transition between a microstrip line and a RWG, using a ridged waveguide section for the coupling. For both configurations a third-order bandpass filter was realized by using three coupled waveguide resonators. Two of the coupling structures were made up of inline transitions. To verify the approach and quantify losses, a filter was fabricated and its scattering parameters measured. With this new approach low-loss waveguide filters can be integrated into a planar RF circuit while minimizing space. No delicate manufacturing processes are required.