Codirectional Coupler Research Articles

Coupling Dynamics and Linear Polarization Phenomena in Codirectional Polariton Waveguide Couplers

AbstractIn this work, the previous studies investigating the potential of integrated devices using polariton waveguides that form codirectional couplers is extended. For suitable coupler parameters, a transfer of condensates between the arms of the coupler occurs leading to the observation of previously predicted Josephson‐like oscillations. The ability to tune the periodicity of these oscillations opens the way to the design of polaritonic circuits in which the directionality of the signal towards the output terminals can be controlled, for a fixed separation between the arms, varying the coupling length. The response of the devices to linearly polarized excitation is also investigated, delving into the dynamics of linear polarization at the output terminals of long couplers, providing valuable insights into their potential applications, including polariton switches and logic gates with efficient operation. The results are supported by numerical simulations based on the generalized Gross–Pitaevskii equation describing the dynamics of coherent polaritons in spatially non‐uniform systems, reproducing the polariton distribution on the output terminals and an oscillatory dependence of the corresponding emission as a function of the polarization azimuth. How the coupling and the controllable polarization degree of freedom in polariton couplers opens avenues for innovative optical architectures and functionalities is shown here.

Subwavelength grating-based silicon photonic TE mode division multiplexer for C + L band operation

This paper reports a subwavelength grating (SWG) based multiplexer (MUX) on a silicon photonics platform capable of multiplexing three transverse electric modes. The designed MUX is simulated using a commercial 3D finite-difference time-domain solver and shows broadband operation over the whole C and L optical telecom bands from 1530 nm to 1625 nm wavelength range. The effective indices of the Bloch modes in the SWG waveguides are extracted from the band structure plot. The designed MUX consists of two co-directional coupling regions for fundamental to higher-order mode coupling, with each coupling stage consisting of single-mode and multimode SWG waveguides. The transmission characteristics, viz. transmittance, insertion loss, and return loss, are presented and discussed. The coupling lengths without the tapering regions for TE0–TE1 and TE0–TE2 mode couplings are 14μm and 1.48μm, respectively. The transmittance is >78% with the highest insertion loss and return loss of 1.1 dB and –15 dB, respectively. At 1550 nm, the transmission is >88%, insertion loss is <0.6 dB, and return loss is <−15 dB. A uniform under-etch and over-etch of 5 nm are taken for the fabrication tolerance study, which shows a maximum variation of 0.58 dB for the insertion loss with return loss <−14.6 dB at 1550 nm. Over the whole simulated range, the insertion loss is <1.4 dB, and return loss is <−14.6 dB with ±10 nm change in device dimension. A temperature tolerance study with 50 °C and 100 °C rise in temperature has been done, and the device retains its broadband operation over the simulated range. The maximum increase in insertion loss is 0.1 dB for the TE0–TE2 coupling, while the overall return loss of the device decreases to <−20 dB for the TE0–TE1 coupling.

Study on Interleaved Three-Switch Buck-Boost Converters with Co-directional Coupling Inductor

Study on Interleaved Three-Switch Buck-Boost Converters with Co-directional Coupling Inductor

Angled Flip-Chip Integration of VCSELs on Silicon Photonic Integrated Circuits

An investigation of angled flip-chip integration of a singlemode 850 nm vertical-cavity surface-emitting laser (VCSEL) on a silicon nitride photonic integrated circuit (PIC) is presented. Using numerical FDTD simulations, we consider the conditions under which the VCSEL can be integrated at an angle over a grating coupler with high coupling efficiency and low optical feedback. With both coupling efficiency and feedback decreasing with increasing angle, there is a trade-off. With co-directional coupling, first-order diffraction loss sets in at a critical angle, which further reduces the coupling efficiency. No such critical angle exists for contra-directional coupling. We also experimentally demonstrate angled flip-chip integration of GaAs-based 850 nm single transverse and polarization mode VCSELs over grating couplers on a silicon-nitride PIC. At the output grating coupler, light is either collected by an optical fiber or converted to a photocurrent using a flip-chip integrated GaAs-based photodetector. The latter forms an on-PIC optical link. We measured an insertion loss of 21.9, 17.6 and 20.1 dB with a singlemode fiber, multimode fiber and photodetector over the output grating coupler, respectively.

Tunable narrow band add-drop filter design based on apodized long period waveguide grating assisted co-directional coupler.

Tunable add/drop filter based optical interconnects are an integral part of data centers as well as optical communications. Although add/drop filters based on ring resonators and waveguide Bragg gratings are well developed, long period waveguide grating (LPWG) based add/drop filters have little been investigated so far. In this article, we propose an apodized LPWG assisted co-directional coupler for narrow band add/drop filtering by combining silicon (Si) waveguide with titanium dioxide (TiO2) waveguide geometry. The proposed structure has been analyzed by combining the finite element method (FEM) and transfer matrix method (TMM), showing a good side lobe suppression ratio (SLSR) equal to 25.7 dB and an insertion loss of 0.6 dB. Owing to the high group index difference of Si and TiO2 waveguides, a narrow band response of 1.4 nm has been achieved with 800µm long LPWG. The opposite thermo-optic coefficients of Si and TiO2 ensures a good thermal tunability of the central wavelength. Considering a thin metallic heater of titanium nitride (TiN) the thermal tuning efficiency is found to be 0.07 nm/mW. Further, two LPWGs have been cascaded to realize a tunable dual channel filter with a minimum channel spacing of 185 GHz and a channel crosstalk better than 20 dB, showing its potential application towards dense wavelength division multiplexing.

Directional microwave coupled-line couplers with high lateral coupling level

Classic сoupled-line couplers with a high lateral coupling level by type of directivity are counterdirectional. Restrictions on their synthesis are imposed by the gap between transmission lines, which must be extremely small (tens of microns), the difference in the phase velocities of even and odd modes, which must be compensated and others. This makes it difficult of manufacturing couplers. Described in technical literature сoupled-line couplers with a high lateral coupling level with changed types of directivity are either quite bulky or have small dimensions due to the use of discrete inductors and capacitances, which complicates the technological process with surface mounting when implementing the final device. In this article we propose a compact сoupledline coupler with a high lateral coupling level, which implements power transfer to a single port (0 dB, crossover). The coupler topology uses periodic loops that are located between сoupled-line. The equivalent circuit of the coupled lines was calculated and analyzed for a single periodic stub. This allowed us to determine the necessary parameters and dimensions of the topology. The device is narrow-band (3 GHz ± 5 %), transmission coefficient minus 0.44 dB at the center frequency of 3 GHz, isolation for isolated ports is not less than 35 dB. The proposed compact coupler with a coupling level of 0 dB suits building distribution circuits in which it is necessary to exclude the intersection of transmission lines. The information on the synthesis of the 3 dB co-directional microwave coupler on coupled strip lines with lateral electromagnetic coupling is given. The coupler is characterized by a high isolation level with an isolated port, not less than 40 dB. The imbalance of the amplitudes between the working (through and connected) and the input port is minus (3.4 ± 0.8) dB.

Solitons in a -symmetric grating-assisted co-directional coupler

We explore a co-directional coupling arrangement between two waveguides mediated by a PT-symmetric sinusoidal grating characterized by an index-modulation parameter κ and a gain/loss parameter g. We show that the device supports soliton-like solutions for both the -conserving regime g < κ and the -broken regime g > κ. In the first case the coupler exhibits a gap in wave-number k and the solitons can be regarded as an extension of a previous solution found for pure index modulation. In the second case the coupler exhibits a gap in frequency ω and the solutions are entirely new.

Duty cycle variation methods for Bragg gratings: comparative study and optimal design

An analysis of spectral response apodization by duty cycle methods for grating-assisted optical filters is presented. The study is performed for the case of codirectional couplers, Bragg reflectors, and mirrors. The modeling results show that the supersymmetric duty cycle (SDC) modulation method, initially considered for parity–time symmetric gratings in Lupu et al. [IEEE J. Sel. Top. Quantum Electron. 22, 35 (2016)10.1109/JSTQE.2016.2542791IJSQEN1077-260X], performs better than the other methods. An analytical approach to the transfer matrix of the modulated grating explains the better performance of the SDC method.

Effects of the Linear Polarization of Polariton Condensates in Their Propagation in Codirectional Couplers

We report on the linear polarization of polariton condensates in a codirectional coupler that allows evanescent coupling between adjacent waveguides. During the condensate’s formation, polaritons usually acquire a randomly oriented polarization, however, our results reveal a preferential orientation of the linear polarization along the waveguide propagation path. Furthermore, we observe polarization-dependent intensity oscillations in the output terminal of the coupler, and we identify the mode beating between the linear-polarized eigenmodes as the origin of these oscillations. Our findings provide an insight into the control of the polarization of polariton condensates, paving the way for the development of spin-based polaritonic architectures where condensates propagate over macroscopic distances.

Coupled-line co-directional coupler with inherent harmonic suppression and its wideband implementation

In the study, a novel implementation of the coupled-line co-directional (CL-COD) coupler is proposed for the first time, and the wideband realizations are also demonstrated. The CL-COD coupler, which is composed of inductor loaded parallel coupled line and a pair of open-circuited stubs, has the advantages of smaller size and inherent harmonics suppression compared with the traditional λ/4 branch line coupler. Design equations of the single-section CL-COD coupler are derived by the even-odd mode decomposition analysis and a prototype is designed for validation. The experimental results indicate that compared with the traditional single-section λ/4 branch line coupler, the designed single-section CL-COD coupler shows a size reduction of 64.1%, a bandwidth enhancement of 13%, and a second harmonic suppression of more than 20 dB. By cascading multi-sections of the CL-COD couplers, wideband CL-COD coupler with harmonics suppression is also realized. A computer-aided program is applied for solving the circuit parameters of the multi-section cascaded CL-COD coupler. Besides, the two- and three-section cascaded 3-dB CL-COD couplers are designed for guidance. Finally, a 3-dB three-section cascaded CL-COD coupler is fabricated and measured. Compared with the traditional three-section cascaded λ/4 branch line coupler, the prototype shows a size reduction of 61.9% with an additional second order harmonic suppression.

Strain-Insensitive Simultaneous Measurement of Bending and Temperature Using Long-Period Fiber Grating Inscribed on Double-Clad Fiber with CO₂ Laser.

Here we report an optical fiber sensor capable of performing strain-insensitive simultaneous measurement of bending and temperature using a long-period fiber grating (LPFG) inscribed on doubleclad fiber (DCF) with a CO₂ laser at ˜10.6 μm. The LPFG inscribed on DCF, referred to as a DC-LPFG, was fabricated by scanning CO₂ laser pulses on an unjacketed DCF with a specific period. Due to co-directional mode coupling, the fabricated DC-LPFG has discrete attenuation bands widely distributed over hundreds of nanometers. Among these wavelength-dependent loss dips, adjacent two dips with different resonance wavelengths were selected as sensor indicators for the measurement of bending and temperature. For these two indicator dips designated as dips A and B, their bending and temperature responses were investigated in a curvature range of 4.90 to 21.91 m-1 and a temperature range of 30 to 110 °C. With increasing bending applied to the DC-LPFG at room temperature, dips A and B showed different blue shifts. The bending sensitivities of dips A and B were measured to be approximately -0.77 and 0.51 nm/m-1, respectively. Unlike the bending response, they showed red shifts of different amounts with increasing ambient temperature, while the sensor head (i.e., the DC-LPFG) remained straight without any applied bending. The temperature sensitivities of dips A and B were measured to be ˜0.094 and ˜0.078 nm/°C, respectively. Owing to their linear and independent responses to bending and temperature, bending and temperature changes applied to the DC-LPFG could be simultaneously estimated from the measured wavelength shifts of the two indicator dips using their pre-determined bending and temperature sensitivities. Moreover, in a strain range of 0 to 2200 με (step: 200 με), strain-induced spectral variations of dips A and B were also measured, and the strain sensitivities of dips A and B were evaluated as approximately -0.028 and -0.013 pm/με, respectively. These strain-induced wavelength shifts were so small that they had little effect on the measurement results of bending and temperature. Thus, it is concluded that the fabricated DC-LPFG can be employed as a cost-effective sensor head for strain-insensitive separate measurement of bending and temperature.

Propagative Oscillations in Codirectional Polariton Waveguide Couplers.

We report on novel exciton-polariton routing devices created to study and purposely guide light-matter particles in their condensate phase. In a codirectional coupling device, two waveguides are connected by a partially etched section that facilitates tunable coupling of the adjacent channels. This evanescent coupling of the two macroscopic wave functions in each waveguide reveals itself in real space oscillations of the condensate. This Josephson-like oscillation has only been observed in coupled polariton traps so far. Here, we report on a similar coupling behavior in a controllable, propagative waveguide-based design. By controlling the gap width, channel length, or propagation energy, the exit port of the polariton flow can be chosen. This codirectional polariton device is a passive and scalable coupler element that can serve in compact, next generation logic architectures.

Gain spectral narrowing of semiconductor laser based on dual-core vertical coupler structure

Semiconductor FP ridge waveguide lasers based on dual-core vertical coupler structure with different ridge height were fabricated. Their modal gain of these devices around the threshold current were extracted and investigated using the Hakki–Paoli (H–P) method. It is observed that the gain spectrum profile and its 3 dB bandwidth vary with the ridge height. The narrower gain bandwidth of 12 nm was achieved when the ridge height was 4.59 μm, which is smaller than a quarter of that for the laser with the ridge height of 1.6 μm. This phenomenon is attributed to the narrowed gain spectrum induced by wavelength filtering effect of the dual-core vertical coupler (DCVC) structure induced by their co-directional coupling, which further shrinks its amplified spontaneous emission (ASE) spectrum. In addition, further simulation results show that the coupling length also affects the bandwidth of the DCVC structure. Within a single coupling length, the longer the coupling length, the narrower the bandwidth, and the larger the coupling efficiency. Such narrow-spectrum gain characteristic of DCVC structure will enable one to fabricate single longitudinal mode lasers with no need of fabricating gratings.

Wavelength-Switchable Fiber Laser Based on Long-Period Fiber Grating Written on Polarization-Maintaining Photonic Crystal Fiber.

Here we propose a wavelength-switchable erbium-doped fiber ring laser using a temperatureinsensitive spectral polarization-dependent loss (PDL) element and two fiber Bragg gratings (FBGs). The fiber PDL element was fabricated by inscribing a long-period grating (LPG) on polarizationmaintaining photonic crystal fiber (PMPCF) with a 10.6 μm CO₂ laser. The LPG fabricated on PMPCF, referred to as PMPCF-LPG, has the characteristics of a fiber polarizer at two specific wavelengths due to the birefringence of PMPCF and the co-directional mode coupling of the LPG. The two wavelengths at which the fabricated PMPCF-LPG acts as a polarizer are two resonance wavelengths (~1528.58 and ~1555.90 nm) of the PMPCF-LPG, obtained for orthogonal input polarization states. By considering these two resonance wavelengths of the PMPCF-LPG, the Bragg wavelengths of two FBGs, which determine lasing wavelengths in our wavelength-switchable laser, were selected as ~1527.71 and ~1554.74 nm. As the temperature sensitivity of the PMPCF birefringence is 30 times lower than that of the birefringence of conventional polarization-maintaining fiber (PMF), the fabricated PMPCF-LPG could facilitate more stable switching operation between the two lasing wavelengths in comparison with a previous fiber laser employing an LPG inscribed on conventional PMF as a wavelength-switching filter. The lasing wavelengths of our laser could be switched by controlling input polarization of the PMPCF-LPG with a polarization controller, and temperature-insensitive wavelength switching operation was experimentally demonstrated over a temperature range of 25-100 °C.

Spatial eigenmodes conversion with metasurfaces engraved in silicon ridge waveguides.

We explore the discrete nature of waveguide modes and the effective medium concept to achieve an ultra-compact highly efficient mode conversion device in a high-index platform such as a silicon waveguide. The proposed device is based on a co-directional coupler that has a periodic variation in its refractive index along the propagation direction. The transverse variation of the index profile is calculated based on the interference pattern between the modes of interest. We show that mode conversion can be realized with dielectric metasurfaces engraved in the silicon waveguide. We derive the equation for effective index and show proof-of-concept numerical results of the device performance. We obtain conversion efficiencies of 95.4% between the TE0-TE1 modes over 8.91μm interaction distance and 96.4% between the TE0-TE2 over 6.32μm. The resulting coupling coefficient changes as a function of the interaction distance in a sinusoidal manner, which is crucial for constructive energy transfer from one mode to another. Such mode coupling devices have the potential for application in dispersion compensations, wavelength division multiplexing systems, and sensing.

Grating assisted glass fiber coupler for mode selective co-directional coupling.

To keep pace with the increasing demand of transmission capacity, space division multiplexing technologies are currently intensively investigated. In this context, mode selective glass fiber couplers are of great interest due to their compatibility with existing glass fiber networks. In this work, we present a novel type of mode selective glass fiber coupler for co-directional coupling based on fiber gratings and fused asymmetric fibers. The achieved mode selective coupling efficiency agrees well with numerical simulations performed for comparison. The benefits of the grating approach are a lower mode crosstalk and a simple adaption of the propagation constants through changing of the grating-period.

Silicon photonic add-drop filter based on a grating-assisted co-directionally coupled vertical hybrid structure.

Add-drop filters (ADFs) are an essential component in optical interconnection using dense wavelength-division multiplexing. Silicon photonic ADFs based on contra-directional coupling have been well developed, but those based on grating-assisted co-directional coupling (GACC) have never been studied. This paper reports an ADF based on GACC in a vertical hybrid structure (VHS). which consists of two width-modulated silicon strip waveguides with a large lateral gap and a wide silicon nitride strip waveguide above them. The VHS makes it possible for the ADF to have a narrow 3-dB bandwidth as well as a short grating length. An efficient analysis method for design is explained, and the ADF is designed. Theoretical investigation of the ADF demonstrates that the ADF has a 3-dB bandwidth of 1.16 nm and a grating length of 1.13 mm, which are similar to those of ADFs based on contra-directional coupling. As an application, the ADF is used for a nonvolatile switchable ADF by adding an optical phase change material strip above the silicon nitride waveguide. The nonvolatile switchable ADF is shown to have an extinction ratio larger than 30 dB. The investigated ADF requires neither waveguides in close proximity nor grating teeth with dimensions close to the resolution of deep UV lithography. In this regard, it has the advantage of ease of fabrication as compared to ADFs based on contra-directional coupling. Therefore, the ADF is expected to play a key role in optical interconnection using dense wavelength-division multiplexing, prevailing over ADFs based on contra-directional coupling.

Experimental demonstration of active phasers based on codirectional coupling for real‐time analog signal processing

AbstractA phaser based on codirectional coupling is proposed and experimentally investigated to achieve a flat transmission magnitude while maintaining strong frequency‐dependent group delay response. This is the first experimental demonstration of such devices for real‐time radio analog signal processing applications, which are readily scalable to mm‐wave frequencies. While shielding improved the transmission performance by mitigating the radiation, a gain element is introduced to achieve a perfectly flat transmission magnitude response. The proposed structure thus forms the fundamental building block of engineering more complex dispersion profiles without compromising transmission magnitude response.

On-chip unidirectional dual-band fiber-chip grating coupler in silicon nitride

We report, for the first time, a single state polarization (TE) dual-band grating fiber-chip coupler on a 700 nm thick silicon nitride platform that couples to both O and C band channels. Dual-band coupling with a single grating coupler is achieved using cross mode k-space equalization. By phase matching the first-order vertical TE01 mode and the fundamental TE00 mode in two distinct bands, we observe simultaneous co-directional dual-band coupling to a single waveguide. Experimental peak efficiency per coupler is measured to be −7.3 dB in the O-band and −8.2 dB in the C-band and the combined 1 dB bandwidth is observed to be 82 nm.

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.