Eigenmodes Of Waveguide Research Articles

Cryogenic Thermo-Optical Coefficient of SU-8 Measured Using a Racetrack Resonator at 850 nm

SU-8 is an emerging polymer material for integrated optical circuits that has demonstrated good structural properties in a cryogenic environment. In this article, we investigate the thermo-optical properties of SU-8 for a wavelength λ = 850 nm, from room temperature to cryogenic temperature down to 14 K. To measure the material properties, we designed and fabricated SU-8 racetrack resonators via electron beam lithography. While cooling the device in a closed-cycle cryostat, we measured the resonance spectrum as a function of the temperature from which we determined the temperature-induced variations of the group and effective indices of the waveguide. With the aid of waveguide eigenmode simulations, we used these data to derive the temperature dependence of the SU-8 refractive index nSU−8 (T). At room temperature (T~295 K), the thermo-optic coefficient dnSU−8/dT = −5.3 ± 0.2 × 10−5 K−1. At low temperature (T~14 K), dnSU−8/dT = −1.27 ± 0.05 × 10−4 K−1. Our research shows the potential of SU-8 photonics in a cryogenic environment, suitable for the integration with quantum light sources emitting in the near infrared (NIR).

Coupling Nanowire Quantum Dots to Optical Waveguides by Microsphere-Induced Photonic Nanojet

Silica-on-silicon is a major optical integration platform, while the emergent class of the integrated laser-written circuits’ platform offers additionally high customizability and flexibility for rapid prototyping. However, the inherent waveguides’ low core/cladding refractive index contrast characteristic, compared to other photonic platforms in silicon or silicon nitride, sets serious limitations for on-chip efficient coupling with single photon emitters, like semiconductor nanowires with quantum dots, limiting the applications in quantum computing. A new light coupling scheme proposed here overcomes this limitation, providing means for light coupling >50%. The scheme is based on the incorporation of an optical microsphere between the nanowire and the waveguide, which is properly optimized and arranged in terms of size, refractive index, and the distance of the microsphere between the nanowire and waveguide. Upon suitable design of the optical arrangement, the photonic nanojet emitted by the illuminated microsphere excites efficiently the guided eigenmodes of the input channel waveguide, thus launching light with high-coupling efficiency. The method is tolerant in displacements, misalignments, and imperfections and is fabricationally feasible by the current state of art techniques. The proposed method enables the on-chip multiple single photon emitters’ integration, thus allowing for the development of highly customizable and scalable quantum photonic-integrated circuits for quantum computing and communications.

Solitary high-Q resonance in a grating waveguide via parity symmetry breaking at mode crossing

A phenomenon of a solitary narrow high-Q resonance in a planar grating waveguide associated with a bound state in the continuum (BIC) is revealed analytically. BICs appear when dispersion curves of the leaking even-parity and non-leaking odd-parity infinite-grating eigenmodes intersect. These intersections engender a parity symmetry break of the leaking eigenmode, causing it to decouple from a spatial Fourier harmonic that is emitted out of the waveguide. As a result, the otherwise low-Q waveguide eigenmode, comprised of those two aforementioned and some other infinite-grating eigenmodes, acquires a very high quality factor in a narrow vicinity of the mode-crossing frequency. Implementation of such a mechanism can be instructive for designing BICs in other photonic crystals and structures.

Creation and preservation of superoscillation in a dielectric optical waveguide.

Superoscillation refers to a phenomenon where a band-limited wave locally oscillates faster than its highest Fourier component. Current research on optical superoscillations predominantly lies on the basis of free-space waves. As the optical waveguides play a key role in energy and information transportation, guided waves with precisely controlled deep-subwavelength features offers unprecedented flexibility for applications. In this Letter, we numerically show that, by superimposing eigenmodes of a multimode SiO2 waveguide and forcing the resultant field to pass through a set of predetermined points, superoscillatory fields in various shapes can be formed in preset cross-sectional planes. Furthermore, by padding prescribed intensities in multiple cross sections, we successfully create a persistent superoscillatory saddle.

Towards Watt-Level THz Sources for High-Resolution Spectroscopy Based on 5th-Harmonic Multiplication in Gyrotrons

We propose the concept of high-power THz radiation sources based on five-fold frequency multiplication in gyrotrons intended for plasma applications. The efficient excitation at the 5th cyclotron harmonic is due to the specific property of the eigenmodes of cylindrical waveguides, as a result of which, the conditions of simultaneous electrodynamic resonance at two selected TE modes are satisfied asymptotically with very high accuracy. Previously, we have verified this principle in experiments with a low-frequency kilowatt-level gyrotron in which, due to the low-density spectrum, the operating mode is excited with no competition from parasitic oscillations. The novel concept is a development of this idea applied to the systems with a denser spectrum, which is inevitable in higher frequency and power devices. Simulations within the averaged time-domain model demonstrate that, despite the mode competition, it is possible to excite Watt-level 1.25 THz 5th cyclotron harmonic in a recently developed sub-MW 0.25 THz gyrotron with TE19,8 operating mode. The obtained results open a possibility for implementation of radiation sources with output power/frequency combination, practically inaccessible using other THz generation methods and highly sought for a number of applications, including high-resolution molecular spectroscopy.

Simple yet effective analysis of waveguide mode symmetry: generalized eigenvalue approach based on Maxwell's equations.

Particular waveguide structures and refractive index distribution can lead to specified degeneracy of eigenmodes. To obtain an accurate understanding of this phenomenon, we propose a simple yet effective approach, i.e., generalized eigenvalue approach based on Maxwell's equations, for the analysis of waveguide mode symmetry. In this method, Maxwell's equations are reformulated into generalized eigenvalue problems. The waveguide eigenmodes are completely determined by the generalized eigenvalue problem given by two matrices (M, N), where M is 6 × 6 waveguide Hamiltonian and N is a constant singular matrix. Close examination shows that N usually commute with the corresponding matrix of a certain symmetry operation, thus the waveguide eigenmode symmetry is essentially determined by M, in contrast to the tedious and complex procedure given in the previous work [Opt. Express25, 29822 (2017)10.1364/OE.25.029822]. Based on this new approach, we discuss several symmetry operations and the corresponding symmetries including chiral, parity-time reversal, rotation symmetry, wherein the constraints of symmetry requirements on material parameters are derived in a much simpler way. In several waveguides with balanced gain and loss, anisotropy, and geometrical symmetry, the analysis of waveguide mode symmetry based on our simple yet effective approach is consistent with previous results, and shows perfect agreement with full-wave simulations.

Boosted excitation of the fifth cyclotron harmonic based on frequency multiplication in conventional gyrotrons.

We discovered a specific property of the eigenmodes of a cylindrical waveguide, due to which efficient mode excitation at ultrahigh (s=4n+1, n is integer) multiples of the gyrofrequency can be provided by a polyhelical weakly relativistic electron beam, standardly used for gyrotron operation. In the proof-of-principle experiment with a V-band gyrotron driven by a 25-keV, 2-A beam, about 100 mW radiation power at the fifth cyclotron harmonic (0.22 THz) has been detected in the cw regime. Based on the gyrotron theory, we demonstrate in simulations that, using parameters of existing gyrotrons, this method can be applied for producing cw radiation at a power level of up to several watts in the terahertz gap.

3-D NMM Method for Fully Anisotropic and Nonreciprocal Media

A new 3-D spectral numerical mode-matching (SNMM) method is developed to simulate electromagnetic waves in multilayered structures with fully anisotropic and nonreciprocal media. The SNMM method reduces the original 3-D layered structure into a series of 2-D waveguide eigenvalue problems plus a 1-D layered medium problem, which can be analytically solved by a recursion procedure. These waveguide eigenvalue problems with fully anisotropic and nonreciprocal media are solved numerically by the mixed spectral element method (MSEM) with exponential convergence. Based on the waveguide eigenmodes, the local reflection and transmission matrices and the global reflection matrices are expanded so that the new NMM method is suitable for fully anisotropic and nonreciprocal structures. The NMM method is applied to solve three models, including a three-layer symmetrical structure with inhomogeneous nonreciprocal media, the negative refraction of a YVO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> bicrystal, and a 3-D multilayer structure with nonreciprocal media. Numerical experiments indicate that this new NMM method is highly efficient and accurate for these models for fully anisotropic and nonreciprocal media.

Compact silicon-based polarization-independent 1.55/2 μm wavelength diplexer based on a multimode interference coupler with multiple shallow grooves

Faced with the rapid growth of internet traffic demand, which has posed a huge challenge to the current fiber-based communications systems, expanding the telecommunications bands from traditional near-infrared (NIR) region to mid-infrared (MIR) region is emerging as an attractive solution. And on-chip wavelength division multiplexing (WDM) application for NIR/MIR wavelengths is an essential element in future optical telecommunication systems. Here, we propose a compact silicon-based polarization-independent wavelength diplexer for the NIR/MIR wavelengths of 1.55/2 μm, where multiple rectangular grooves are shallowly etched on the silicon MMI waveguide for introducing the refractive-index perturbations on the MMI waveguide eigenmodes. And this refractive-index perturbation scheme provides a simple and scalable method to manipulate the four beat lengths of the two wavelengths at TE- or TM-polarization in a single waveguide via self-imaging effect, leading to a compact footprint. By optimizing the structural parameters, both NIR/MIR wavelength demultiplexing and polarization independence, for the first time, are obtained simultaneously in the present single device. From the results, the proposed diplexer is only 21.6 μm in length, and shows a wide bandwidth of ∼ 100/120 nm around the wavelength of 1.55/2 μm for insertion loss (IL) < 1 dB and extinction ratio (ER) > 15 dB. Moreover, we also realize a compact and polarization-independent wavelength diplexer for 1.31/2 μm by flexibly changing the dimensions, showing the flexibility and extensibility of our refractive-index perturbation scheme. Besides, fabrication tolerances are analyzed and mode propagation profiles are also demonstrated.

Compact, spatial-mode-interaction-free, ultralow-loss, nonlinear photonic integrated circuits

Multi-mode waveguides are ubiquitously used in integrated photonics. Although interaction among different spatial waveguide eigenmodes can induce novel nonlinear phenomena, spatial mode interaction is typically undesired. Adiabatic bends, such as Euler bends, have been favoured to suppress spatial mode interaction. Here, we adapt and optimize Euler bends to build compact racetrack microresonators based on ultralow-loss, multi-mode, silicon nitride photonic integrated circuits. The racetrack microresonators feature a footprint of only 0.21 mm2 for 19.8 GHz free spectral range, suitable for tight photonic integration. We quantitatively investigate the suppression of spatial mode interaction in the racetrack microresonators with Euler bends. We show that the low optical loss rate (15.5 MHz) is preserved, on par with the mode interaction strength (25 MHz). This results in an unperturbed microresonator dispersion profile. We further generate a single dissipative Kerr soliton of 19.8 GHz repetition rate without complex laser tuning schemes or auxiliary lasers. The optimized Euler bends and racetrack microresonators can be building blocks for integrated nonlinear photonic systems, as well as linear circuits for programmable processors or photonic quantum computing.

Waves guided by metasurfaces with non-local impedance boundary conditions

Non-local impedance boundary conditions (IBCs), which consider the spatial dispersion of impedance, simulate material and surface effects in scattering and propagation. These non-local IBCs are often used to describe various metasurfaces. The use of non-local IBCs leads to some problems and contradictions, limiting the areas of their application. In this article, we demonstrate that eigenmodes in a parallel-plate waveguide with non-local IBCs are non-orthogonal. To restore the orthogonality of the waveguide’s eigenmodes, we derive equations for calculating active power flowing along a surface with non-local IBCs. An unambiguous relationship between impedance spatial dispersion and the active power is demonstrated. We also consider the problem of excitation of the parallel-plate waveguide with non-local IBCs. We show that the use of the eigenmode expansion method leads to incorrect results, which can be corrected by an expression of the Lorentz form obtained in this article.

Scattering of eigenmodes of planar dielectric waveguide with PEC wall by graphene strip grating at THz

The H-polarized eigenmodes of dielectric waveguide scattering by a finite system of graphene strips are considered in the THz frequency range. The waveguide has one perfectly electric conducting wall. The solution is based on the singular integral equations with Nystrom discretization. Such an approach is efficient and has guaranteed convergence. Dependences of the scattering characteristics on the frequency and the radiation patterns are presented. We study the properties of periodic graphene strip grating with the same values of the chemical potential on every strip and with different values of the chemical potential on every strip. In the first case, the radiation patterns with relatively high side-lobe level are obtained. In the second case, the side-lobe level is reduced to −20 dB.

Compact silicon three-mode multiplexer by refractive-index manipulation on a multi-mode interferometer.

Mode-division multiplexing can scale the capacity of optical communications and optical interconnects. We demonstrate an ultra-compact and fabrication-error tolerant silicon three-mode multiplexer by shallowly etching rectangular trenches on a multi-mode interferometer. Depending on the selected input port, the TE0 mode is converted to the eigenmodes of the bus waveguide. These modes are coupled to each other owing to the refractive-index perturbation induced by the shallow trenches and finally converted to a selected spatial mode at the output. A three-mode multiplexing device is experimentally demonstrated with a footprint of 2.00 × 17.05 µm2. The bandwidths for the three channels are >70 nm with crosstalk values below -10 dB.

Modal Network Formulation for the Analysis and Design of Mode-Converting Metasurfaces in Cylindrical Waveguides

Modal network theory has proven to be a useful tool in analyzing waveguide discontinuities. Ports of a modal network correspond to waveguide eigenmodes on either side of the discontinuity. In this work, modal network theory is extended beyond conventional/geometrical waveguide discontinuities. We use the modal network formulation to analyze discontinuities resulting from metasurfaces. Specifically, we analyze azimuthally invariant cascaded sheet metasurfaces placed in a cylindrical waveguide excited by TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0n</sub> modes. The metasurface comprises multiple radially varying electric admittance sheets separated by dielectric spacers. We derive the modal representation of a single inhomogeneous, electric sheet admittance using two approaches: a conventional numerical integration approach and a discrete Hankel transform (DHT) approach. We show that the DHT approach is more efficient. Subsequently, the modal matrices of cascaded sheet metasurfaces are derived using the DHT. Finally, we propose an optimization-based procedure to synthesize transparent metasurface-based mode converters. The mode converters transform a set of incident modes on one side to another set of desired modes on the opposite side of the metasurface. Two designs are synthesized at 10 GHz: a single-mode converter, and a mode splitter. The designs are verified using the commercial finite element electromagnetic solvers.

Nanowire Oligomer Waveguide Modes towards Reduced Lasing Threshold.

Semiconductor nanowires offer a promising route of realizing nanolasers for the next generation of chip-scale optoelectronics and photonics applications. Established fabrication methods can produce vertical semiconductor nanowires which can themselves act both as a gain medium and as a Fabry–Pérot cavity for feedback. The lasing threshold in such nanowire lasers is affected by the modal confinement factor and end facet reflectivities, of which the substrate end reflectivity tends to be limited due to small refractive index contrast between the nanowire and substrate. These modal properties, however, also depend strongly on the modal field profiles. In this work, we use numerical simulations to investigate waveguide modes in vertical nanowire oligomers (that is, arrangements of few vertical nanowires close to each other) and their modal properties compared to single nanowire monomers. We solve for the oligomer waveguide eigenmodes which are understood as arising from interaction of monomer modes and further compute the reflectivity of these modes at the end facets of the nanowires. We consider either the nanowires or an additional coating layer as the gain medium. We show that both types of oligomers can exhibit modes with modal properties leading to reduced lasing threshold and also give directions for further research on the topic.

Waves in Diagonally-Oriented EBG Waveguides in Electromagnetic Crystals with a Square Lattice

Abstract—EBG waveguides in an electromagnetic crystal are studied in the form of a two-dimensionally periodic array of metal cylinders located between conducting screens. The dispersion characteristics of waveguides formed by removing one, two, and three rows of cylinders along the diagonal of a square crystal lattice are obtained. As a result of analyzing the frequency dispersion of the fundamental waveguide modes and eigenmodes of a homogeneous crystal, the factors limiting the operating frequency bands of the waveguides are determined and the lattice parameters optimal from the aspect of the band properties are obtained. The characteristics of waveguides oriented along the diagonal of the crystal lattice are compared with similar characteristics of waveguides formed along the principal axes in crystals with a square lattice.

Theoretical analysis of mode conversion by refractive-index perturbation based on a single tilted slot on a silicon waveguide.

We propose a compact mode converter operating at the mid-infrared wavelength of 3.4 µm, comprising an etched parallelogram slot filled with silicon nitride on a silicon-on-calcium fluoride platform. The tilted slot introduces transverse and longitudinal index perturbations on the waveguide eigenmodes, achieving mode conversion in the propagation direction. Differing from previous reports using massive parameter sweep, we provide analytical formulas to determine geometry parameters by considering the modified phase-matching condition and the profiles of coupling coefficient of coupled-mode theory. Rigorous 3D numerical examples demonstrate the transverse electric (TE)0-to-TE1, TE0-to-TE2, TE0-to-TE3, and TE0-to-TE4 converters to achieve conversion efficiencies (inter-modal crosstalk [CT] values) of >92.7% (<-27 dB), >91.7% (<-16 dB), >88.2% (<-13 dB), and >75.8% (<-10 dB), respectively, with a total transmitted power of >93%. Converter device lengths range from 16.84 to 24.61 µm for TE0-to-TE1 to TE0-to-TE4, respectively. Over a broadband wavelength of 100 nm, the conversion efficiency, power transmission, and maximum inter-modal CT are almost >80%, >90%, and <-10 dB, respectively. Also, the fabrication tolerance of the proposed structure is addressed. The proposed model can not only realize arbitrary mode-order conversion but extend to other wavelength bands. To validate the feasibility of our model, the numerical results of our device operating at the wavelength of 1.55 µm are also offered and compared with those of other reports. The proposed idea may pave a new approach to designing mode converters with arbitrary geometries.

FOCUSING OF MODES WITH AN INHOMOGENEOUS SPATIAL POLARIZATION OF THE DIELECTRIC RESONATOR OF A TERAHERTZ LASER

Wave beams with non-uniform spatial polarization of radiation are necessary for solving important fundamental and applied problems related to the interaction of electromagnetic waves of the terahertz range with matter - surface diagnostics of materials, thin films, biological objects, information transmission, and processing systems, achieving subwave resolution in tomography, communication systems, etc. The results are presented in the literature on focusing on pulsed radiation beams in the terahertz range. Data on the focusing of continuous radiation beams are practically absent. The spatial-energy characteristics of laser beams having an inhomogeneous spatial polarization at their moderate and sharp focusing are theoretically investigated. As the radiation understudy, in the numerical simulation of the focusing of wave beams in the terahertz range, we used the modes of a laser waveguide dielectric resonator that coincide with the eigenmodes of a hollow dielectric waveguide. Symmetric and asymmetric modes with both spatially inhomogeneous azimuthal, radial, and homogeneous linear field polarizations are studied. The components of the electric field of laser beams during their propagation in free space were studied using the Rayleigh-Sommerfeld integrals in the nonparaxial approximation. The effect of the focusing lens on laser radiation was taken into account using the amplitude-phase correction function. The distributions of the total intensity of the resonator modes and their individual field components in the focal region of the lens are studied. The obtained results expand the knowledge about the features of focusing terahertz laser beams.

Leaky waves in planar dielectric waveguide

A new analytical and numerical solution of the electrodynamic waveguide problem for leaky modes of a planar dielectric symmetric waveguide is proposed. The conditions of leaky modes, corresponding to the Gamow-Siegert model, were used as asymptotic boundary conditions. The resulting initial-boundary problem allows the separation of variables. The emerging problem of the eigen-modes of open three-layer waveguides is formulated as the Sturm-Liouville problem with the corresponding boundary and asymptotic conditions. In the case of guided and radiation modes, the Sturm-Liouville problem is self-adjoint and the corresponding eigenvalues are real quantities for dielectric media. The search for eigenvalues and eigenfunctions corresponding to the leaky modes involves a number of difficulties: the problem for leaky modes is not self-adjoint, so the eigenvalues are complex quantities. The problem of finding eigenvalues and eigenfunctions is associated with finding the complex roots of the nonlinear dispersion equation. To solve this problem, we used the method of minimizing the zero order. An analysis of the calculated distributions of the electric field strength of the first three leaky modes is given, showing the possibilities and advantages of our approach to the study of leaky modes.

Studies of a Gyrotron Traveling-Wave Tube with Helically Corrugated Waveguides at IAP Ras: Results and Prospects

The gyrotron traveling-wave tube (gyro-TWT) is a wideband version of gyrotron amplifiers, which produce pulsed or continuous-wave radiation in the millimeter-wavelength band at a power level that exceeds the powers produced by conventional TWTs with slow-wave structures and rectilinear beams by 1–2 orders of magnitude. Since 1996, researchers at the Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS) have been developing the concept of the gyro-TWT based on the use of a waveguide with a helically corrugated surface, which changes the dispersion of one of the eigenmodes in a circular waveguide radically. In this paper, we discuss several problems that arise in implementation of such devices, which many years of experimental studies have revealed, present the parameters of gyro-TWTs developed with allowance for specific applications of their end users, and discuss lines of further perfection of such amplifiers.