Coupled Waveguide System Research Articles

Chiral transmission by an open evolution trajectory in a non-Hermitian system

Exceptional points (EPs), at which two or more eigenvalues and eigenstates of a resonant system coalesce, are associated with non-Hermitian Hamiltonians with gain and/or loss elements. Dynamic encircling of EPs has received significant interest in recent years, as it has been shown to lead to highly nontrivial phenomena, such as chiral transmission in which the final state of the system depends on the encircling handedness. Previously, chiral transmission for a pair of eigenmodes has been realized by establishing a closed dynamical trajectory in parity-time- (PT-) or anti-PT-symmetric systems. Although chiral transmission of symmetry-broken modes, more accessible in practical photonic integrated circuits, has been realized by establishing a closed trajectory encircling EPs in anti-PT-symmetric systems, the demonstrated transmission efficiency is very low due to path-dependent losses. Here, we demonstrate chiral dynamics in a coupled waveguide system that does not require a closed trajectory. Specifically, we explore an open trajectory linking two infinite points having the same asymptotic eigenmodes (not modes in PT- and anti-PT-symmetric systems), demonstrating that this platform enables high-efficiency chiral transmission, with each eigenmode localized in a single waveguide. This concept is experimentally implemented in a coupled silicon waveguide system at telecommunication wavelengths. Our work provides a new evolution strategy for chiral dynamics with superior performance, laying the foundation for the development of practical chiral-transmission devices.

Acoustic chiral mode switching by dynamic encircling of exceptional points

Chiral mode switching initiated by dynamic encircling of an exceptional point (EP) has shown an extraordinary ability in wave controlling. In this work, we study the chiral mode transfer for acoustic waves in the coupled waveguide system that supports the non-adiabatic evolution of eigenstates. The system comprises a finite number of structural elements, which are constructed according to parametric conditions in the loop enclosing the EP and then stacked such that acoustic propagation in the waveguide system is equivalent to the dynamic encircling of the EP. An analytic model based on the spatial coupled-mode theory is developed, which provides a practical guide to design the system and makes predictions for dynamic evolution. Numerical simulation of the waveguide system is conducted to demonstrate the chiral mode switching for sounds.

See-through display based on commercial photopolymer: Optimization and shrinkage effects

Nowadays augmented reality, 3D Image, mixed reality and see-through applications are very attractive technologies due to their great potential. Holographic optical elements can provide interesting solutions for injection and extraction of the image in the waveguides that are part of the see-through devices. We have developed a coupled waveguide system based on slanted transmission gratings recorded in manufactured photopolymers. In this work we optimize our schedule to a commercial photopolymer for this high demanded application. We demonstrate that high diffraction efficiencies can be obtained if we optimize the recording geometry, recording intensity and recording time for this material. In addition, we study the effects of shrinkage in our holographic system. In general shrinkage is an important drawback for holographic applications, nevertheless we demonstrate how shrinkage can help these systems open new possibilities. Lastly, we show how to significantly improve the quality of the guided image.

Контрольоване нагрівання циліндричної плазми з використанням особливостей виняткової точки

The paper proposes a method of controlled heating of a cylindrical plasma using the features of the Exceptional point. It is shown that the coupled system of plasma and dielectric waveguides is capable of generating exceptional points where their dispersion curves cross. By controlling the connection (distance) between the waveguides, it is possible to control the distribution of the electromagnetic field, both in the plasma and in the dielectric waveguides around the exceptional point. It is also shown that in the presence of dissipative losses in the plasma, the degree of heating of the plasma waveguide can be controlled by tuning the distribution and intensity of the exciting electromagnetic field in the coupled waveguide system, which gives a potential advantage among other methods of plasma heating. The results obtained in the work can be considered as an example of a new method of controlled plasma heating, which can be used to overcome the existing problems of controlled thermonuclear fusion.

A topological nonlinear parametric amplifier

Topological boundary states are well localized eigenstates at the boundary between two different bulk topologies. As long as bulk topology is preserved, the topological boundary mode will endure. Here, we report topological nonlinear parametric amplification of light in a dimerized coupled waveguide system based on the Su-Schrieffer-Heeger model with a domain wall. The good linear transmission properties of the topological waveguide arising from the strong localization of light to the topological boundary is demonstrated through successful high-speed transmission of 30 Gb/s non-return-to-zero and 56 Gb/s pulse amplitude 4-level data. The strong localization of a co-propagating pump and probe to the boundary waveguide is harnessed for efficient, low power optical parametric amplification and wavelength conversion. A nonlinear tuning mechanism is shown to induce chiral symmetry breaking in the topological waveguide, demonstrating a pathway in which Kerr nonlinearities may be applied to tune the topological boundary mode and control the transition to bulk states.

Characteristic analysis of core radius, core refractive index, mismatched phase constant and coupling efficiency about 2 × 2 fiber directional coupler based on MATLAB

When two parallel waveguides are close to each other, the power of the two adjacent waveguides will be periodically converted to form a directional coupled waveguide system (). The transverse coupling between two parallel waveguides can be described by mode coupling theory. However, in practical application, due to the limitation of equipment or manual computing capacity, it is impossible to quickly calculate the coupling efficiency of two optical fibers through the current specific formula. Through the form of MATLAB programming, it can determine whether the fiber is a single-mode fiber, solve the characteristic equation to obtain the propagation constant, integrate the coupling coefficients K12 and K21, solve the coupling efficiency in the fiber, and finally output in the form of graphics. The results show that for the directional coupler composed of two fibers, if the core radius and core refractive index change, the mismatching phase constant and coupling efficiency will change correspondingly, and the calculated results are in good agreement with the predicted results. On this background, this paper proposes the form of MATLAB programming to calculate coupling efficiency. The coupling efficiency of fiber directional couplers is analyzed. The theory gives accurate results within the actual parameters.

Controllable multiple beam splitting in Hermitian and non-Hermitian symmetric coupled waveguide systems

We investigate high-fidelity multiple beam splitting in Hermitian and non-Hermitian (NH) symmetric coupled waveguides (WGs) with one input and 2 N output WG channels. In Hermitian systems, we realize adiabatically light splitting in resonant case based on the stimulated Raman adiabatic passage and arbitrary proportion from the middle WG to outer WGs in propagation coefficients mismatch case using shortcuts to adiabaticity (STA) technique. In NH systems with even WGs being dissipative, the compact and robust beam splitting can be achieved by eliminating the non-adiabatic coupling via the NH STA method. We further verify the feasibility of our theoretical predictions by means of the beam propagation method. The suggested multiple beam splitters open new opportunities for the realization of on-chip high-bandwidth photonics with high fidelity in short distances.

Three-band plasmon induced transparency effect based on four-disk resonator coupled waveguide system

In order to reduce power consumption and realize ultrafast response time and dynamic tunability, a plasmonic waveguide system based on four disk resonators is designed. A plasmon induced transparency effect is theoretically analyzed by using two different methods: one is the direct destructive interference between bright mode resonator and dark mode resonator, and the other is the indirect coupling through a plasmonic waveguide. Owing to the giant effective nonlinear Kerr coefficient of the graphene-Ag composite material structure and the enhancement characteristics of slow light response to optical Kerr effect, the pump intensity of PIT system for changing the phase shift of transmission spectrum is greatly reduced. An ultrafast response time of 1 ps is achieved, and 0.4π, 0.8π, 1.2π, 1.6π and 2π-phase shift of the transmission spectrum in the plasmon induced transparency system are achieved with the intensity of the pump light as low as 2.34, 4.68, 7.02, 9.36, 11.7 MW/cm<sup>–2</sup>, respectively. In this work, a plasmonic waveguide coupled directly by two small disk resonators is employed, because two small disk resonators play a role of the slit between the waveguide and the resonators, and also act as two separate resonators side-coupled with a plasmonic waveguide, which leads to the more efficient coupling of electromagnetic energy in the waveguide into the big disk resonators to form resonance and easier storage of light in the resonator. The triple-band plasmon induced transparency (PIT) effect and slow light properties of the model are analyzed by the expression of the deduced theoretical transmittance based on the coupled mode theory, indicating that they are very consistent with the finite-difference time-domain simulations. The results show that the transmission peak of the system is over 80% and the maximum group index is as high as 368. Furthermore, the disk resonators are easy to fabricate and the size of the entire PIT structure is < 0.5 μm<sup>2</sup>, which is beneficial to the design of optoelectronic device on-chip integration. The research results have important application prospects in highly integrating optical circuits and networks, and also provide the ideas for the design and fabrication of multi-channel optical filter and light storage devices with low power consumption, ultrafast nonlinear response, ultracompact and dynamical tunability.

Asymmetric guidance of multiple hybrid modes through a gain-loss-assisted planar coupled-waveguide system hosting higher-order exceptional points

The gain-loss-assisted optical systems have revealed an unconventional light manipulation tool by hosting exceptional points (EPs), which has lately a great deal of interest in the photonics community. Here, the emergence of higher-order EPs is investigated in a planar coupled-waveguide geometry, which has the potential to assemble additional degrees of freedom to explore EP-induced light dynamics. A planar form of waveguide array consisting of four high-indexed guides is designed to support multiple quasiguided hybrid modes. An inhomogeneous customized gain-loss profile to couple at least three chosen modes is introduced in such a way that the waveguide hosts an EP of order three with the simultaneous presence of two second-order EPs in the gain-loss parameter plane. We investigate the dynamical parametric encirclement schemes of embedded EPs of different orders and exclusively reveal both the chiral and nonchiral dynamics of light assisted by asymmetric conversions of hybrid modes. The implementation of our findings in discrete photonic systems hosting higher-order EPs indeed opens up a fertile platform to meet a wide range of enticing applications in the context of manipulation of modes including conversion and switching.

Transient growth and dissipative exceptional points.

In the context of non-Hermitian photonics, we study the physics of transient growth in coupled waveguide systems that exhibit higher-order exceptional points. We demonstrate the counterintuitive effect of transient growth despite the decaying spectrum, which is a direct consequence of the underlying modal nonorthogonality. Eigenvalue analysis fails to capture the power dynamics and thus we have to rely on methods of nonmodal stability theory, namely singular value decomposition and pseudospectra. The relation between the order of the exceptional point and transient growth is also examined. Our work provides a general methodology that can be applied to any non-Hermitian system that contains complex elements with more loss than gain, and exploits the boundaries of transient amplification in dissipative environments.

Quantum interference in anti-parity-time symmetric coupled waveguide system.

We theoretically demonstrate quantum interference in an anti-parity-time (anti-PT) symmetric system based on coupled waveguides. We calculate the coincidence probability in an input polarization-entangled two-photon state, which can be used to simulate different statistical particles. When the birefringence of the waveguides is negligible, our results indicate that the coincidence probabilities of the bosons and fermions decrease exponentially with the propagation distance in both the unbroken and broken anti-PT symmetry regions owing to the dissipation. Particularly, loss-induced transparency is observed for the bosons. Simultaneously, the statistical rule valid in the Hermitian system is violated and the antibunching of bosons is observed. When the birefringence of the waveguides is considered, the coincidence probability of the bosons and fermions is equalized at the exceptional point (EP), whereas that of the bosons is less(greater) than that of the fermions in the broken(unbroken) anti-PT symmetry region. Additionally, we observe the Hong-Ou-Mandel dip for bosons in the broken anti-PT phase. Our research provides a complementary technique for the manipulation of quantum interference compared with the PT symmetric system and may be applied in building quantum devices with anti-PT symmetric quantum mechanics.

Excitation of Ultrashort Spin Waves via Spin-Cherenkov Effect in Magnetic Waveguides

The excitation of ultrashort wavelength spin waves via the spin-Cherenkov effect in magnetic waveguides is investigated via a micromagnetic modeling. The proposed excitation method is relatively simple and easily tunable. The excitation efficiency of the proposed scheme is obtained for different excitation pulse velocities and widths. A coupled waveguide system is also considered. In this case, the spin waves are excited in the first waveguide and then are transferred to the second one due to the dipolar coupling between waveguides. It is also shown that the excitation and transfer of excited spin waves have some limitations related to the dipolar coupling mechanism between the waveguides.

Optical switch with ultra high extinction ratio using electrically controlled metal diffusion.

An optical switch with ultra high extinction ratio is proposed. Optical switching is realized using the resistive switching effect through the lateral coupling between the input nanophotonic waveguide and output waveguide at a wavelength of 1550 nm. The coupled waveguide system is engineered to increase the number of mode beats in a unit length of the device. An increase in the number of mode beats and controlled diffusion of metal ions through a thin dielectric layer with an applied electric field is responsible for a high optical extinction ratio of 27 dB for a 20 µm long device. Compared to electrical control by plasma dispersion in silicon, the resistive switching effect enables a reduction in the coupling length and an increase in the waveguide absorption, leading to an almost 100 times higher extinction ratio. The proposed compact on-chip silicon-based nanophotonic resistive device is a potential candidate for a large-scale integrated photonic circuit for applications in optical switching, modulation, memory, and computation.

Topological effects in integrated photonic waveguide structures [Invited

We review recent advances of topological photonics in coupled waveguide systems. To this end, we discuss the various prevalent platforms, as well as various implementations in one- and two-dimensional systems, including driven, static, nonlinear and quantum systems.

Generating path entangled states in waveguide systems with second-order nonlinearity.

Spontaneous parametric down-conversion in coupled nonlinear waveguides is a flexible approach for generating tunable path entangled states. We describe a formalism based on the Cayley-Hamilton theorem to compute the quantum states generated by waveguide arrays for arbitrary system parameters. We find that all four Bell states can be generated in directional couplers with non-degenerate photons. Our method enables one to efficiently explore the phase space of waveguide systems and readily assess the robustness of any given state to variations in the system's parameters. We believe it represents a valuable tool for quantum state engineering in coupled waveguide systems.

Deep learning based reconstruction of directional coupler geometry from electromagnetic near-field distribution

We demonstrate a method to retrieve the geometry of physically inaccessible coupled waveguide systems based solely on the measured distribution of the optical intensity. Inspired by recent advancements in computer vision, and by leveraging the image-to-image translation capabilities of conditional generative adversarial neural networks (cGANs), our method successfully predicts the arbitrary geometry of waveguide systems with segments of varying widths. As a benchmark, we show that our neural network outperforms nearest neighbor regression from both a runtime and accuracy point of view.

Numerical design of a high-performance polarization beam splitter assisted by composite subwavelength gratings.

We report a compact polarization beam splitter (PBS) consisting of slotted waveguides assisted by composite subwavelength gratings (CSWGs) on a silicon-on-insulator platform. By tailoring the material anisotropy of the CSWGs, coupling strengths of transverse-electric (TE) and transverse-magnetic (TM) polarization coupling strengths are respectively suppressed and enhanced significantly, achieving concurrent improvements in polarization extinction ratio (PER), device footprint, and working bandwidth (BW) compared with purely slotted waveguides. Differing in construction from mono-material SWGs, the CSWGs comprise silicon strips covered with a silicon dioxide (SiO2) layer of the same thickness as the slot layer of the slotted waveguides, simplifying the fabrication process and further reducing device length. Numerical simulations show significant improvement in PERTM from about 15 dB for the purely slotted waveguides to 28 dB for the proposed design, with a 40% reduction in device length at a wavelength of λ = 1550 nm. Within a BW of ∼60 nm, the proposed PBS achieves PERTM ∼25 dB, PERTE >15 dB, and insertion loss (ILs) <0.1 dB for TE and TM modes. Fabrication tolerance investigations are also described and discussed. The proposed idea paves the way for simultaneous improvements in PER, footprint, and working BW for PBSs comprising a variety of coupled-waveguide systems.

Monopole-antimonopole instability in non-Hermitian coupled waveguides

A non-Hermitian coupled waveguide system with periodically varying parameters, in which the Berry curvature is analogous to a hyperbolic magnetic monopole or antimonopole, is investigated. It is shown to have a purely imaginary Berry connection, and is consequently influenced by a geometric multiplier. It is possible for this multiplier to induce net gain or loss in the system, corresponding to the existence of the antimonopole or monopole in parameter space, respectively. For the right choice of parameters, the system will display an apparent non-adiabatic change in behaviour, which implies a switch between the dominant eigenstate in the waveguides, leading to a change in parameter space analogous to a charge reversal of the hyperbolic magnetic monopole.

Unbreakable -symmetry and its consequence in a -symmetric dimer

This article presents a finite dimensional unbreakable -symmetric waveguide system with linear and nonlinear coupling. In traditional -symmetric systems, a balance (or a symmetric state) among the waveguides with loss and gain can be achieved only when the coupling among the waveguides is sufficiently strong. But the coupled waveguide system that we report here obtains the balance (or symmetry preservation) as soon as the couplings are established and this symmetric nature is undisturbed even for arbitrarily large values of loss–gain strength. We here show that the -symmetry in the system is unbreakable in the presence of linear and nonlinear coupling. Interestingly, in the absence of linear coupling, the system shows contrast behavior where -symmetry is spontaneously broken for all parametric values. As the considered system is integrable, we illustrate the symmetry unbroken and broken nature of the system using their integrals of motion. Importantly, we illustrate the possibility to have high power oscillations by weakening the couplings among the waveguides.

Topological photonic crystals: a review.

The field of topological photonic crystals has attracted growing interest since the inception of optical analog of quantum Hall effect proposed in 2008. Photonic band structures embraced topological phases of matter, have spawned a novel platform for studying topological phase transitions and designing topological optical devices. Here, we present a brief review of topological photonic crystals based on different material platforms, including all-dielectric systems, metallic materials, optical resonators, coupled waveguide systems, and other platforms. Furthermore, this review summarizes recent progress on topological photonic crystals, such as higherorder topological photonic crystals, non-Hermitian photonic crystals, and nonlinear photonic crystals. These studies indicate that topological photonic crystals as versatile platforms have enormous potential applications in maneuvering the flow of light.