Three-dimensional Optical Waveguides Research Articles

Direct and inverse scattering in an optical waveguide*

Abstract In this paper, we study the direct and inverse scattering of the Schrödinger equation in a three-dimensional optical planar waveguide. For the direct problem, we derive a resonance-free region and resolvent estimates for the resolvent of the Schrödinger operator in such a geometry. Based on the analysis of the resolvent, several inverse problems are investigated. First, given the potential function, we prove the uniqueness of the inverse source problem with multi-frequency data. We also develop a Fourier-based method to reconstruct the source function. The capability of this method is numerically illustrated by examples. Second, the uniqueness and increased stability of an inverse potential problem from data generated by incident waves are achieved in the absence of the source function. To derive the stability estimate, we use an argument of quantitative analytic continuation in complex theory. Third, we prove the uniqueness of simultaneously determining the source and potential by active boundary data generated by incident waves. In these inverse problems, we only use the limited lateral Dirichlet boundary data at multiple wavenumbers within a finite interval.

Helical hollow channel waveguide in YAG fabricated by femtosecond laser enhanced wet etching.

Three-dimensional optical waveguides with hollow channels have many advantages, such as strong mode confinement and excellent dispersion control ability. Femtosecond laser enhanced wet etching is widely used to fabricate hollow channel waveguides in transparent dielectric materials. We propose a method for fabricating hollow channel waveguides in YAG using femtosecond laser enhanced wet etching with a simpler fabrication process and shorter etching time compared with the previous work. After 90 h of etching, a series of helical hollow channel waveguides with a length of 5 mm and a radius of 32 µm were successfully fabricated. At a pitch of 3 µm, the waveguide exhibited a loss (including coupling loss and transmission loss) as low as 0.68 dB at 1030 nm. The helical hollow channel waveguide also exhibited exceptional isotropic light confinement capability and remarkable supercontinuum-generating properties. Moreover, helical hollow channel waveguides with a radius of 2 µm were successfully fabricated. According to simulations, waveguides of such size can effectively control dispersion. Our work presents, to our knowledge, a novel approach to fabricating hollow channel waveguides with arbitrary lengths using femtosecond laser-enhanced wet etching.

Three-Dimensional Femtosecond-Laser Direct-Written Optical Waveguide: Advancements and Challenges (Invited)

Three-Dimensional Femtosecond-Laser Direct-Written Optical Waveguide: Advancements and Challenges (Invited)

Three-Dimensional Compacted Optical Waveguide Mode Converter/Splitter Designed by Invariant Engineering

In this paper we demonstrate an analytical method, basing on the invariant engineering, to solve the relevant coupled mode equations for designing various grating-assisted 3D optical waveguide mode converter/splitter. Our method is based on the quantum-optical analogy, i.e., the Maxwell equation for the electromagnetic wave propagating along a waveguide structure in the spatial domain is formally equivalent to the Schrödinger equation for the evolution of a quantum system in the time domain. It is found that, the spatial domain invariants can be effectively constructed to solve the 3D coupled-mode equations, analogously to solve the dynamical evolution for the quantum systems in the time domain. The present approach overcomes the complication of solving the coupled-mode equation by the usual numerical method. As a consequence, by appropriately setting the coupling parameters between the grating-assisted interconnected waveguides, the desired mode conversion/splitting based on 3D coupler can be designed conveniently. As the invariant method is a natural shortcut to the adiabaticity, the compacted devices designed by the invariant-based engineering are useful for the fabrications of various 3D integrated optical devices.

Efficient bidirectional marching solver for optical propagation in three-dimensional waveguide structures.

A novel bidirectional operator marching method based on the Dirichlet-to-Neumann (DtN) mapping for three-dimensional optical waveguide structures is developed and implemented using iterative methods. The backward propagation wave is integrated into the classical operator marching approach which represents the forward propagating wave. The bidirectional range marching formulas are exact for each range-independent piece and a large range step is possible in both directions. The validity and effectiveness of our proposed method are verified by analyzing uniform waveguides and longitudinal waveguides with varying refractive indices.

Function-expansion-based topology optimization of three-dimensional optical waveguide devices with multi-layered structure considering layer thickness

So far, as an optimal design method for 2D and 3D design of optical waveguide devices, topology optimization based on a function expansion method has been reported. In this paper, we improve the conventional function-expansion-based topology optimization method to design three-dimensional photonic devices with structural variation in the depth direction. In order to design realistic 3D optical waveguide devices, we consider a layered structure and design each layer by using function-expansion-based topology optimization method. In this approach, undesired floating structures are avoided and layer thickness can be optimized. The validity of this method is verified through design examples of a polarization splitter and rotator (PSR) and a crossing waveguide which have two-layer structure.

Compact Optical Switch Using the Tunability of a Au-Coated Hollow Core Waveguide

We design and fabricate a directional coupler type compact optical switch using the large variable characteristics of a hollow optical waveguide and use numerical simulations and experimentations to investigate the optical characteristics of the proposed directional coupler-type hollow waveguide optical switch. The optical switching operation is achieved by the optical power mode field distribution change and the coupling length in the directional coupler waveguide region because the air core thickness of the hollow waveguide is mechanically controlled by the electrical signal. The designed three-dimensional (3-D) optical hollow waveguide consists of a Au-coated reflector. The numerical simulation results show the possibility of a compact optical switch with a switch length of 1 mm when the air core thickness of the hollow optical waveguide is changed by 2 µm. The experimental device was a microstructured hollow optical waveguide coated with a thin Au film on a GaAs substrate using the same parameters as there used in the modeling. The experiment revealed a switching length of 0.9 mm and an extinction ratio of about 19 dB with a small change of air core thickness.

Full-vectorial analysis of optical waveguide discontinuities using a propagation operator method based on the finite element scheme

We propose an efficient numerical method for the full-vectorial analysis of three-dimensional (3-D) optical waveguide discontinuities. In this method, the finite element method with higher adaptability and flexibility is employed to discretize the waveguide cross section. In order to calculate the square root of the characteristic matrix, the Denman-Beavers iterative scheme is used. Applying this method to 3-D strongly guiding waveguide discontinuity problems, the modal reflectivities of the fundamental TE-like and TM-like modes are calculated. These results show unique vector properties and significantly differ from those of scalar analysis because various mode couplings between the field components occur at the discontinuity facet and they cannot be ignored.

Controlling upconversion luminescence patterns in space with red emission enhancement from a single fluoride microcrystal by tuning the excitation mode.

The ability to control the upconversion (UC) luminescence patterns in space from lanthanide-doped UC luminescence materials is very important for many applications including three-dimensional color displays, optical waveguides and optical communication. In this work, the fascinating UC luminescence patterns could be adjusted from the blue or green flower-like emission pattern to the red flame-like irradiation pattern with a red luminescence enhancement from a single β-NaYF4:Yb3+/(Tm3+ or Er3+) microcrystal (MC) by varying the excitation position. The red-to-blue (R/B) and the red-to-green (R/G) emission intensity ratios from the single MC particle that the focal point position of excitation NIR laser is on the side lace are much stronger than that in the case of the focused laser beam on the center. We think that the physical mechanism from the changes in the luminescence pattern and the emission intensity ratio is explained by the optical waveguide effect based on the total reflection effect. These results provide a new strategy for facilitating fundamental investigations of the UC micro/nano-materials, which will lead to promising applications in three-dimensional color display, optical waveguides and optical communication.

Size and host-medium effects on topologically protected surface states in bianisotropic three-dimensional optical waveguides

We study the optical properties of bi-anisotropic optical waveguides with nontrivial topological structure in wavevector space, placed in an ordinary dielectric matrix. We derive an exact analytical description of the eigenmodes of the systems with arbitrary parameters that allows us to investigate topologically protected surface states (TPSS) in details. In particular, we find that the TPSS on the waveguides would disappear (1) if their radius is smaller than a critical radius due to the dimensional quantization of azimuthal wavenumber, and also (2) if the permittivity of the host-medium exceeds a critical value. Interestingly, we also find that the TPSS in the waveguides have negative refraction for some geometries. We have found a TPSS phase diagram that will pave the way for development of the topological waveguides for optical interconnects and devices.

Efficient marching solver for a class of three-dimensional optical waveguides.

An efficient marching method of the wave propagation computation in the three-dimensional (3D) rectangular box is developed by solving the scalar Helmholtz equation with the weakly range-dependent refractive-index or wavenumber profile. The method is based on the application of the one-way formulation accompanied by a truncated technique that allows for the reduction of the number of eigenmodes and for quickly achieving reliable numerical results. The merits of the high accuracy and fast computation with a larger range step are shown to solve the equation. This treatment can be also applied to other complicated 3D waveguides.

Suppression of bend loss in writing of three-dimensional optical waveguides with femtosecond laser pulses

We provide a solution toward compact and low-loss three dimensional (3D) photonic circuits by femtosecond laser direct writing of 3D waveguides in fused silica. We suppress the bend loss by sandwiching the waveguide between a pair of walls formed by internal modification of glass. Our method allows to reduce the bend loss of a curved waveguide with a bending radius of 15 mm by more than one order of magnitude.

Transverse writing of three-dimensional tubular optical waveguides in glass with a slit-shaped femtosecond laser beam.

We report on fabrication of tubular optical waveguides buried in ZBLAN glass based on transverse femtosecond laser direct writing. Irradiation in ZBLAN with focused femtosecond laser pulses leads to decrease of refractive index in the modified region. Tubular optical waveguides of variable mode areas are fabricated by forming the four sides of the cladding with slit-shaped femtosecond laser pulses, ensuring single mode waveguiding with a mode field dimension as small as ~4 μm.

An Efficient Semivectorial Bidirectional Beam Propagation Method for 3-D Optical Waveguide Structures

An efficient semi-vectorial bidirectional beam propagation method (Bi-BPM) based on the complex Denman-Beavers iterative (C-DBI) scheme for three-dimensional (3-D) optical waveguide structures is constructed. Beside merely calculating the transition operators by the C-DBI scheme, like our previous paper, a new approximation for the bidirectional propagators by using the combination of Padé approximants and C-DBI scheme is proposed and developed. Such a treatment can be capable of correctly dealing with the evanescent waves generated in the transition processes, greatly improving the stability and accuracy of the Bi-BPM. Moreover, the efficiency of the present Bi-BPM can be also improved since the operators calculated by the C-DBI scheme can be simultaneously utilized for both processes of the Bi-BPM. In addition, the biconjugate gradient stabilized method is utilized to solve the resulting linear systems, further improving the efficiency. Numerical results from both single and multiple longitudinal discontinuity examples show that the present method can deal with evanescent waves properly with the accuracy comparable to that of the existing well-established methods.

Ultrafast-laser-inscribed 3D integrated photonics: challenges and emerging applications

AbstractSince the discovery that tightly focused femtosecond laser pulses can induce a highly localised and permanent refractive index modification in a large number of transparent dielectrics, the technique of ultrafast laser inscription has received great attention from a wide range of applications. In particular, the capability to create three-dimensional optical waveguide circuits has opened up new opportunities for integrated photonics that would not have been possible with traditional planar fabrication techniques because it enables full access to the many degrees of freedom in a photon. This paper reviews the basic techniques and technological challenges of 3D integrated photonics fabricated using ultrafast laser inscription as well as reviews the most recent progress in the fields of astrophotonics, optical communication, quantum photonics, emulation of quantum systems, optofluidics and sensing.

Full-Vectorial Analysis of Optical Waveguide Discontinuities Using Denman–Beavers Iterative Scheme

An accurate and efficient full-vectorial numerical approach for analyzing three-dimensional optical waveguide discontinuities is proposed, where the resulting square root of the characteristic matrix from the field-based operators is approximated by the Denman-Beavers iterative scheme with a branch-cut rotation in the complex plane. Both the magnetic and electric field formulations are rigorously derived along with the robust perfectly matched layer absorbing boundary conditions. Numerical results from a typical buried waveguide, a channel waveguide, and a rib waveguide show that the present scheme is more accurate and stable than the widely used Padé approximation, while the computational load is comparative.

Structure of modes of smoothly irregular three-dimensional integrated optical four-layer waveguide

An asymptotic method is used for researching an integrated optical multilayer waveguide satisfying the condition of the smooth modification of the shape of the studied three-dimensional structure. Three-dimensional fields of smoothly deforming modes of the integrated optical waveguide are described analytically. An evident dependence of the contributions that the first order of smallness makes to the amplitudes of the electrical and magnetic fields of the quasi-waveguide modes is obtained. The canonical type of equations describing the propagation of quasi-TE and quasi-TM modes in the smoothly irregular part of a four-layer integrated optical waveguide is represented for an asymptotic method. With the help of the method of coupled waves and the perturbation theory method, the shifts of complex propagation constants for quasi-TE and quasi-TM modes are obtained in an explicit form. The elaborated theory is applicable for an analysis of similar structures of dielectric materials, magnetic materials, and metamaterials over a wide enough range of electromagnetic wavelengths.

Multi-domain spectral method for modal analysis of optical waveguide

A multi-domain spectral method for scalar optical modal analysis is developed and presented. The method is mesh-free and is applicable to three-dimensional optical waveguide structures that are invariant in one direction. The mode profile is represented as a superposition of one-dimensional preselected basis functions with variable coefficients. As common to spectral methods, the presented method is inherently fast and efficient. Different optical waveguides are analyzed for comparison purpose to exhibit the validity and accuracy of the presented method.

Wide-angle beam propagation method without using slowly varying envelope approximation

A new wide-angle (WA) beam propagation method (BPM) is developed whereby the exact scalar Helmholtz propagator is replaced by any one of a sequence of higher-order (m,n) Pade approximant operators. Unlike the previous well-known WA-BPM proposed by Hadley [Opt. Lett.17, 1426 (1992)], the resulting formulations allow one a direct solution of the second-order scalar wave equation without having to make slowly varying envelope approximations so that the WA formulations are completely general. The accuracy and improvement of this approximate calculation of the propagator is demonstrated in comparison with the exact result and existing approximate approaches. The method is employed to simulate two-dimensional (2D) and three-dimensional (3D) optical waveguides and compared with the results obtained by the existing approach.

Single cell detection using a glass-based optofluidic device fabricated by femtosecond laser pulses

We demonstrate the fabrication of integrated three-dimensional microchannel and optical waveguide structures inside fused silica for the interrogation and processing of single cells. The microchannels are fabricated by scanning femtosecond laser pulses (523 nm) and subsequent selective wet etching process. Optical waveguides are additionally integrated with the fabricated microchannels by scanning the laser pulse train inside the glass specimen. Single red blood cells (RBC) in diluted human blood inside of the manufactured microchannel were detected by two optical schemes. The first involved sensing the intensity change of waveguide-delivered He-Ne laser light (632.8 nm) induced by the refractive index difference of a cell flowing in the channel. The other approach was via detection of fluorescence emission from dyed RBC excited by Ar laser light (488 nm) delivered by the optical waveguide. The proposed device was tested to detect 23 fluorescent particles per second by increasing the flow rate up to 0.5 microl min(-1). The optical cell detection experiments support potential implementation of a new generation of glass-based optofluidic biochip devices in various single cell treatment processes including laser based cell processing and sensing.