Po-Jui Chiang

Subwavelength Dielectric-Fiber-Based THz Coupler

We demonstrate a terahertz (THz) directional coupler for future THz applications including THz power dividers, THz communications, and THz fiber-endoscopes. By using subwavelength polyethylene fibers, we successfully established a single-mode fiber-based THz directional coupler. Unlike traditional directional couplers, the demonstrated subwavelength directional fiber coupler shows less dependency on the overlapped length of two fibers and the delivered THz frequency in our interested minimal-attenuation wavelength regime. By tuning the geometry, we also show the feasibility to control the coupling ratio.

Robust Calculation of Chromatic Dispersion Coefficients of Optical Fibers From Numerically Determined Effective Indices Using Chebyshev–Lagrange Interpolation Polynomials

Numerical calculation of chromatic dispersion coefficients of optical fibers is conducted using a procedure involving Chebyshev-Lagrange interpolation polynomials. Only numerically determined effective indices at several wavelengths are needed for obtaining the dispersion curve, and no direct numerical differentiation of the effective refractive index is involved. A silica-filled metallic rectangular waveguide having analytical solutions for the effective refractive index and the chromatic dispersion is used as an example for confirming the accuracy and efficiency of the proposed method. The method is then also applied to the analysis of holey fibers

Pseudospectral Frequency-Domain Formulae Based on Modified Perfectly Matched Layers for Calculating Both Guided and Leaky Modes

We propose a new pseudospectral frequency-domain (PSFD) formulation within the modified perfectly matched layer (MPML) for absorbing both radiation losses and evanescent waves. By applying the improved PSFD method on Chebyshev-Gauss-Lobatto mesh points, both guided and leaky modes of optical waveguides can be solved from Helmholtzs equations for the transverse-magnetic components. To ensure the global accuracy of the PSFD-MPML method, new and appropriate boundary conditions are derived at each subdomain in the MPML region. By comparing the analytic solution of a step-index single-mode fiber and the results by adopting our method, the convergence behavior of the proposed method on the guided modes is examined. To demonstrate the validity and usefulness of our method on the leaky modes, the one-ring triangular holey fiber is taken as another example.

Frequency-domain formulation of photonic crystals using sources and gain

We present a formulation to analyze photonic periodic structures from viewpoints of sources and gain. The approach is based on a generalized eigenvalue problem and mode expansions of sources which sustain optical fields with phase boundary conditions. Using this scheme, we calculate power spectra, dispersion relations, and quality factors of Bloch modes in one-dimensional periodic structures consisting of dielectrics or metals. We also compare the results calculated from this scheme with those from the complex-frequency method. The outcomes of these two approaches generally agree well and only deviate slightly in the regime of low quality factors.

A high-accuracy pseudospectral full-vectorial leaky optical waveguide mode solver with carefully implemented UPML absorbing boundary conditions

The previously developed full-vectorial optical waveguide eigenmode solvers using pseudospectral frequency-domain (PSFD) formulations for optical waveguides with arbitrary step-index profile is further implemented with the uniaxial perfectly matched layer (UPML) absorption boundary conditions for treating leaky waveguides and calculating their complex modal effective indices. The role of the UPML reflection coefficient in achieving high-accuracy mode solution results is particularly investigated. A six-air-hole microstructured fiber is analyzed as an example to compare with published high-accuracy multipole method results for both the real and imaginary parts of the effective indices. It is shown that by setting the UPML reflection coefficient values as small as on the order of 10(-40) ∼ 10(-70), relative errors in the calculated complex effective indices can be as small as on the order of 10(-12).

Analysis of optical waveguides with ultra-thin metal film based on the multidomain pseudospectral frequency-domain method

Analysis of optical waveguides with thin metal films is studied by the multidomain pseudospectral frequency-domain (PSFD) method. Calculated results for both guiding and leaky modes are precise by means of the PSFD based on Chebyshev-Lagrange interpolating polynomials with modified perfectly matched layer (MPML). By introducing a suitable boundary condition for the dielectric-metallic interface, the stability and the spectrum convergence characteristic of the PSFD-MPML method can be sustained. The comparison of exact solutions of highly sensitive surface plasmon modes in 1D dielectric-metal waveguides and those calculated by our PSFD-MPML demonstrates the validity and usefulness of the proposed method. We also apply the method to calculate the effective refractive indices of an integrated optical waveguide with deposition of the finite gold metal layer which induces the hybrid surface plasmon modes. Furthermore, the 2-D optical structures with gold films are investigated to exhibit hybrid surface plasmon modes of wide variations. We then apply hybrid surface plasmon modes to design novel optical components-mode selective devices and the polarizing beam splitter.

Application of Pseudospectral Methods to Optical Waveguide Mode Solvers

A new full-vectorial multidomain pseudospectral mode solver based on pseudospectral methods for optical waveguides with arbitrary step-index profile is presented. The formulations are applied to optical fibers and rib waveguides and remarkable accuracy is demonstrated.

Design of metal-dielectric grating lasers only supporting surface-wave-like modes.

We present a prototype of semiconductor lasers with plasmonic periodic structures that only support transverse-magnetic modes at telecommunication wavelengths. The structure does not sustain transverse-electric guided modes which are irrelevant to surface-wave-enhanced applications, and lasing modes must be surface-wave-like. With thin low-index dielectric buffers near the metal surface, the threshold gain is kept at a decent level around the photonic band edge. Thin windows are then opened on the metal surface to let out significant surface fields. This facilitates usages of surface waves for the spectroscopy and sensing.

Efficient Photonic-Crystal Mode Solver: Eigenvalue Rather Than Generalized Eigenvalue Approach

We present an iterative scheme to obtain guided Bloch modes in lossy and dispersive photonic crystals. The formulation is based on the concept of sources and transforms the quadratic generalized eigenvalue problem of modes into simpler eigenvalue counterpart for iterations. This feature makes it particularly useful in computations with large matrix sizes. Fewer memories and less computation time than those of conventional methods are required in these cases. The robustness of iterations is rooted in the reciprocity theorem for periodic Bloch parts. Through repeated estimations of propagation constants, Bloch modes of periodic structures converge quickly. Using this method, we take sinusoidal metal gratings as examples and demonstrate advantages of the scheme.

The Effect of Choosing PML Reflection-Coefficient Value on Numerical Accuracy in the Pseudospectral Leaky Waveguide Mode Solver

It is shown that suitable choice of the reflection-coefficient value of uniaxial perfectly matched layers is essental for achieving high-accuaracy analysis of leaky waveguide modes using the full-vectorial multidomain pseudospectral mode solver.