We consider coupled waveguide lattices as an architecture that implement a wide range of multiport transformations. In this architecture, a particular transfer matrix is obtained through setting the step-wise profiles of the propagation constants seen by the field evolving in the lattice. To investigate the transformation capabilities, the implementation of a set of transfer matrices taken at random and particular cases of discrete Fourier transform, Hadamard and permutation matrices have been described. Because the waveguide lattices schemes are more compact than their traditional lumped-parameter counterparts, our architecture may be beneficial for using in photonic information processing systems of the future.
We consider evolution of multichannel excitations in longitudinally modulated waveguide arrays where refractive index either oscillates out-of-phase in all neighboring waveguides or when it is modulated in phase in several central waveguides surrounded by out-of-phase oscillating neighbors. Both types of modulations allow resonant inhibition of light tunneling, but only the modulation of latter type conserves the internal structure of multichannel excitations. We show that parameter regions where light tunneling inhibition is possible depend on the symmetry and structure of multichannel excita…
We report several major theoretical steps towards realizing stable long-distance multichannel soliton transmission in Kerr nonlinear waveguide loops. We find that transmission destabilization in a single waveguide is caused by resonant formation of radiative sidebands and investigate the possibility to increase transmission stability by optimization with respect to the Kerr nonlinearity coefficient $γ$. Moreover, we develop a general method for transmission stabilization, based on frequency dependent linear gain-loss in Kerr nonlinear waveguide couplers, and implement it in two-channel and thr…
We study transmission stability and dynamics of pulse amplitudes in $N$-channel soliton-based optical waveguide systems, taking into account second-order dispersion, Kerr nonlinearity, delayed Raman response, and frequency dependent linear gain-loss. We carry out numerical simulations with systems of $N$ coupled nonlinear Schrödinger (NLS) equations and compare the results with the predictions of a simplified predator-prey model for Raman-induced amplitude dynamics. Coupled-NLS simulations for single-fiber transmission with $2 \le N \le 4$ frequency channels show stable oscillatory dynamics of…
Robust multichannel bulk transport in a time-reversal-invariant insulator-free photonic waveguide array
Wuhan Textile University（武汉纺织大学）；Southern University of Science and Technology（南方科技大学）；Shantou University（汕头大学）；Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））
We demonstrate that a transformation device can be emulated using a gradient-index waveguide. The effective index of the waveguide is spatially varied by tailoring a gradient thickness dielectric waveguide. Based on this technology, we demonstrate a transformation device guiding visible light around a sharp corner, with low scattering loss and reflection loss. The experimental results are in good agreement with the numerical results.
We introduce continuous supersymmetric transformations to manipulate the modal content in systems of optical waveguides, providing a systematic method to design efficient and robust integrated devices such as tapered waveguides, single-waveguide mode filters, beam splitters and interferometers. These transformations connect superpartner profiles by smoothly modifying the transverse index profile along the propagation direction and, if the modification is performed adiabatically, the transverse electric modes evolve adapting their shape and propagation constant without being coupled to other gu…
We design compact waveguide couplers via impedance-tunable transformation optics. By tuning impedance coefficients in the original space, two-dimensional metallic and dielectric waveguide couplers are designed with a high efficiency. Through tuning refractive index simultaneously, we find that the transformation medium inside a designed metallic waveguide coupler can be a reduced-parameter material for coupling waves between waveguides with arbitrary different cross sections and embedded media. In the design of dielectric waveguide couplers, we apply two different schemes: one is that both cor…
Coupled waveguides are convenient at implementing useful optical transformations. In this letter, we investigate the uncertainty of transformation by two coupled waveguides that stems from the perturbations of waveguide's mode indices~--- the effect that may be imposed by a non-ideal fabrication process, in particular, those of femtosecond direct laser writing. In our analysis, the perturbations are assumed to be samples of a stationary random process, characterized by an intensity and a correlation scale parameter. We have derived analytical equations that link these parameters with relevant …
Silicon nitride ($Si_3N_4$) planar waveguide platform combined with silicon-on-insulator (SOI) devices offer a whole new generation of system-on-chip applications. Therefore, efficient coupling of an $Si_3N_4$ waveguide to an SOI waveguide is essential. We present a coupler to interface a 1.8 $μm$-wide $Si_3N_4$ waveguide to a 0.5 $μm$-wide SOI waveguide based on the focusing property of the Luneburg lens. In order to match the refractive indices of the waveguides with the edges of the lens, one side of the lens is flattened with quasi-conformal transformation optics. The designed coupler is i…
In this work, a plasmonic right-angled waveguide bend and divider are proposed. Using the Transformation Optics (TO) approach the transformation media of a bend and a T-shaped divider are obtained. Such media with continuous refractive index are realized with the help of graphene in the terahertz frequency range, key to effectively guiding the surface plasmon polariton (SPP) propagation on the 90 degree curves. Components with such capability are promising for THz device applications.
The absolute instruments like the Maxwell's fisheye (MFE) lens with aberration-free imaging properties have found interesting applications such as waveguide crossing. The flat wavefront of an optical wave in the waveguide does not match with the circular wavefront of the circular MFE lens at its edge, hence, we design and study the performance of a square MFE lens as photonic crystal waveguide crossing medium. We also have truncated the square MFE lens to a cross-shaped lens to squeeze it inside the crossing waveguides, therefore, practically no extra footprint is consumed by the truncated MFE…
Multimode waveguide crossings are crucial components for novel mode-division-multiplexing systems. One of the challenges of multimode waveguide routing in MDM systems is decreasing the inter-mode crosstalk and mode leakage of waveguide crossings. In this work, we present the intersections of three and four waveguides based on polygonal Maxwell's fisheye lens via transformation optics. The designed lenses are implemented by mapping their refractive index to the thickness of guiding Si layer. The three-dimensional finite-difference time-domain simulations are used to evaluate the performance of …
Multi-photon lithography allows to complement planar photonic integrated circuits (PIC) by in-situ 3D-printed freeform waveguide structures. However, design and optimization of such freeform waveguides using time-domain Maxwell's equations solvers often requires comparatively large computational volumes, within which the structure of interest only occupies a small fraction, thus leading to poor computational efficiency. In this paper, we present a solver-independent transformation-optics-(TO-) based technique that allows to greatly reduce the computational effort related to modeling of 3D free…
The construction of exactly solvable refractive indices allowing guided TE modes in optical waveguides is investigated within the formalism of Darboux-Crum transformations. We apply the finite-difference algorithm for higher-order supersymmetric quantum mechanics to obtain complex-valued refractive indices admitting all-real eigenvalues in their point spectrum. The new refractive indices are such that their imaginary part gives zero if it is integrated over the entire domain of definition. This property, called condition of zero total area, ensures the conservation of optical power so the refr…
The development of large-scale optical quantum information processing circuits ground on the stability and reconfigurability enabled by integrated photonics. We demonstrate a reconfigurable 8x8 integrated linear optical network based on silicon nitride waveguides for quantum information processing. Our processor implements a novel optical architecture enabling any arbitrary linear transformation and constitutes the largest programmable circuit reported so far on this platform. We validate a variety of photonic quantum information processing primitives, in the form of Hong-Ou-Mandel interferenc…
Transformation optics gives rise to numerous unusual optical devices, such as novel metamaterial lenses and invisibility cloaks. Very recently Mattheakis et al. have suggested theoretical design of an optical waveguide based on a network of Luneburg lenses, which may be useful in sensing and nonlinear optics applications. Here we report the first experimental realization of such Luneburg waveguides. We have studied wavelength and polarization dependent performance of the waveguides.
Reconfigurable Linear Optical Transformations in a Single Integrated Multimode Waveguide
MESA+ Institute for Nanotechnology, University of Twente（特文特大学 MESA+ 纳米技术研究所）；Institute of Photonics and Quantum Electronics (IPQ), Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院光子与量子电子学研究所）
Transformation optics (TO) has recently become a useful methodology in the design of unusual optical devices, such as novel metamaterial lenses and invisibility cloaks. Very recently Danner et al. [1] have suggested theoretical extension of this approach to birefrigent TO devices, which perform useful and different functions for mutually orthogonal polarization states of light. Theoretical designs which operate as invisibility cloak for one polarization while behaving as a Luneburg lens for another orthogonal polarization have been suggested. Here we report the first experimental realization o…
Micro-bending attenuation in an optical waveguide can be modeled by a Fokker-Planck equation. It is shown that a supersymmetric transformation applied to the Fokker-Planck equation is equivalent to a change in the refractive index profile, resulting in a larger or smaller attenuation. For a broad class of monomial index profiles, it is always possible to obtain an index profile with a larger micro-bending attenuation using a supersymmetric transformation. However, obtaining a smaller attenuation is not always possible and is restricted to a subset of index profiles.
We propose a method to efficiently pump an excited mode of a multimode optical waveguide starting from a fundamental-mode input by combining Stark-Chirped Rapid Adiabatic Passage (SCRAP) and Supersymmetry (SUSY) transformations. In a two-waveguide set, we implement SCRAP by modulating the core refractive index of one waveguide, which is evanescently coupled to its SUSY partner. SCRAP provides an efficient transfer of light intensity between the modes of different waveguides, while SUSY allows to control which modes are supported. Using both techniques allows to achieve fidelities above 99% for…
Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this letter, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided…
We perform phase-sensitive near-field scanning optical microscopy on photonic-crystal waveguides. The observed intricate field patterns are analyzed by spatial Fourier transformations, revealing several guided TE- and TM-like modes. Using the reconstruction algorithm proposed by Ha, et al. (Opt. Lett. 34 (2009)), we decompose the measured two-dimensional field pattern in a superposition of propagating Bloch modes. This opens new possibilities to study specific modes in near-field measurements. We apply the method to study the transverse behavior of a guided TE-like mode, where the mode extends…
We reveal and observe experimentally significant modifications undertaken by discrete solitons in waveguide lattices upon the continuous transformation of the lattice structure from one-dimensional to two-dimensional. Light evolution and soliton excitation in arrays with a gradually increasing number of rows are investigated, yielding solitons with an effective reduced dimensionality residing at the edge and in the bulk of the lattice.
Shortcut to adiabatic passage (STAP), initially proposed to accelerate adiabatic quantum state transfer, has been widely explored and applied in quantum optics and integrated optics. Here we bring STAP into the field of acoustics to design compact couplers and functional metamaterial. The space-varying coupling strengths of acoustic waveguides (WGs) are tailored by means of dressed states in a three-level system, accounting for the desirable acoustic energy transfer among three WGs with short length. We show that the acoustic coupler has one-way feature when loss is introduced into the interme…
We report quantitative experimental measurements of the Abraham force associated with a propagating optical wave. We isolate this force using a guided light wave undergoing an adiabatic mode transformation (AMT) along a liquid-filled hollow optical fiber (HOF). Utilizing this light intensity distribution within the liquid, we were able to generate a time-averaged non-vanishing Abraham force density, while simultaneously suppressing the Abraham-Minkowski force density. The incident laser field induced a linear axial displacement of the air-liquid interface inside the HOF, which provided a direc…
A method to generate the optical vortex beam with arbitrary superposition of different orders of orbital angular momentum (OAM) on a photonic chip is proposed. The distributed Fourier holographic gratings are proposed to convert the propagating wave in waveguides to a vortex beam in the free space, and the components of different OAMs can be controlled by the amplitude and phases of on-chip incident light based on the principle of Fourier transformation. As an example, we studied a typical device composed of nine Fourier holographic gratings on fan-shaped waveguides. By scalar diffraction calc…
Micro-bending is a well-known source of loss in optical waveguides. By treating the micro-bending as a stochastic process, the problem of loss mitigation can be modeled in terms of a Fokker-Planck equation. Given an initial refractive index profile, and taking micro-bending into account, we develop a formalism to derive a new refractive index profile which potentially results in less loss. Our formalism is based on applying the techniques of Supersymmetric Quantum Mechanics to a Fokker-Planck equation that is associated with a particular refractive index profile. We derive a non-linear differe…
Development of artificial materials exhibiting unusual optical properties is one of the major strands of current photonics research. Of particular interest are soft-matter systems reconfigurable by external stimuli that play an important role in research fields ranging from physics to chemistry and life sciences. Here, we prepare and study unconventional self-assembled colloidal optical waveguides (CWs) created from wavelength-size dielectric particles held together by long-range optical forces. We demonstrate robust non-linear optical properties of these CWs that lead to optical transformatio…
Transformation optics (TO) has been used to propose various novel optical devices. With the help of metamaterials, several intriguing designs, such as invisibility cloaks, have been implemented. However, as the basic units should be much smaller than the working wavelengths to achieve the effective material parameters, and the sizes of devices should be much larger than the wavelengths of illumination to work within the light-ray approximation, it is a big challenge to implement an experimental system that works simultaneously for both geometric optics and wave optics. In this letter, by using…
Recently the general linear transformation for point rotation coordinate frames was considered. A distinguishing feature of the frame, in contrast to the Cartesian one, is the existence of the rotation axis at every point. The frame coordinates are an angle and time, the frequency of rotation is a parameter. The concept of the frame originated from the optical indicatrix (index ellipsoid). Rotation of the optical indicatrix arises in three-fold electrooptical crystals under the action of the rotating electric field applied perpendicular to the optical axis \cite% {pat}. Such a rotation is poss…
Transformation optics has recently attracted extensive interest, since it provides a novel design methodology for manipulating light at will. Although transformation optics in principle embraces all forms of electromagnetic phenomena on all length scales, so far, much less efforts have been devoted to near-field optical waves, such as surface plasmon polaritons (SPPs). Due to the tight confinement and strong field enhancement, SPPs are widely used for various purposes at the subwavelength scale. Taking advantage of transformation optics, here we demonstrate that the confinement as well as prop…
Integrated Supermode Photonics Enabled by Supersymmetric Transformation
State Key Lab of Photonics and Communications, Department of Electronic Engineering, Shanghai Jiao Tong University（上海交通大学电子工程系光子与通信国家重点实验室）；School of Microelectronics Science and Technology, Sun Yat-Sen University（中山大学微电子科学与技术学院）；Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai)（南方海洋科学与工程广东省实验室（珠海））；Photonics Research Institute, Department of Electronic and Information Engineering, The Hong Kong Polytechnic University（香港理工大学电子及信息工程学系光子学研究所）
