Browsing by Author "Huang, Chih-Hsien"

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Calculation of quasi dispersion curves and quality factors of coupled resonator optical waveguides in photonic-crystal slabs
(2012-09-01)
Huang, Chih-Hsien
;
Li, Wei-Shuo
;
Wu, Jing-Nuo
;
Hsieh, Wen-Feng
;
Chang, Yia-Chung
We propose a stabilization method to numerically calculate the dispersion relations and quality factors of optically confined finite structures. For the coupled resonator optical waveguide (CROW) made in a photonic-crystal slab (PCS) used as an example, the dispersion curve is normally not well defined due to the appearance of discontinuities, which do not occur in a two-dimensional CROW with infinite slab height. Therefore, there is less effort devoted to the calculation of quasi dispersion curves of the CROW in a slab. The dispersion relation of the PCS CROW can only be obtained by theoretical fitting to the experimental data under the tight-binding approximation. Here, we demonstrate the use of a stabilization method to calculate the quasi dispersion relation of a PCS CROW accurately. From the stabilization graph, we can calculate the quality factor for an eigenfrequency and properly choose the size of the simulation cell to avoid coupling the CROW modes with the unconfined modes and to accurately calculate the dispersion curve of the PCS CROW using the plane-wave expansion method. The proposed method and results not only provide important information for designing practical photonic devices such as slow-light optical waveguides and nonlinear photonic devices for the PCS CROWs but also can be applied to compute the quality factors and resonance frequencies of microcavities or nanocavities. (c) 2012 Optical Society of America
Calculation of spontaneous emission from a V-type three-level atom in photonic crystals using fractional calculus
(2011-07-05)
Huang, Chih-Hsien
;
Wu, Jing-Nuo
;
Li, Yen-Yin
;
Cheng, Szu-Cheng
;
Hsieh, Wen-Feng
Fractional time derivative, an abstract mathematical operator of fractional calculus, is used to describe the real optical system of a V-type three-level atom embedded in a photonic crystal. A fractional kinetic equation governing the dynamics of the spontaneous emission from this optical system is obtained as a fractional Langevin equation. Solving this fractional kinetic equation by fractional calculus leads to the analytical solutions expressed in terms of fractional exponential functions. The accuracy of the obtained solutions is verified through reducing the system into the special cases whose results are consistent with the experimental observation. With accurate physical results and avoiding the complex integration for solving this optical system, we propose fractional calculus with fractional time derivative as a better mathematical method to study spontaneous emission dynamics from the optical system with non-Markovian dynamics.
Coupling theory of asymmetric photonic-crystal waveguides
(2008)
Huang, Chih-Hsien
;
Hsieh, Wen-Feng
;
Cheng, Szu-Cheng
;
光電工程學系
;
Department of Photonics
The physical properties of asymmetric photonic-crystal directional couplers axe studied by using the tight-binding theory, which considers that the field distributions of photonic-crystal waveguides (PCWs) are localized around the periodic defects. From this model, the analytic formulas which describe the dispersion of the coupler and the eigenmode patterns were derived. By considering coupling up to the third nearest-neighboring between two PCWs, analytic expressions of the dispersion relations of asymmetric photonic crystal coupler are consistent with the results from the plane wave expansion method (PWEM). Due to the broken symmetry, two dispersion curves will never cross. Nevertheless, the eigenmode patterns switch their parity as the symmetric coupler does when wavevector k passes over the decoupling point.
Design of photonic directional couplers as phase selectors
(2013-06-01)
Lee, Po-Yi
;
Huang, Chih-Hsien
;
Hsieh, Wen-Feng
;
光電工程學系
;
Department of Photonics
A phase selector is designed by relatively sliding two coupled identical photonic crystal waveguides (PCWs) of a photonic directional coupler (DC). By solving the coupled equations analytically derived from the tight-binding theory, symmetry breaking in the crossing of dispersion curves can be observed as countersliding two degenerated waveguides along the propagation direction. There exists a different phase shift between two eigenmodes by varying the sliding distance and the operating frequency. Numerical simulations of DCs made of photonic crystal slabs were used to verify the correctness of our theoretical predictions and to discuss thoroughly the underlying physics of the symmetry-breaking system. The design concept is provided for a phase selector or a beam splitter whose output phase difference can be controlled by the sliding distance of two PCWs. (C) 2013 Optical Society of America
Modulation instability in nonlinear coupled resonator optical waveguides and photonic crystal waveguides
(2009-02-02)
Huang, Chih-Hsien
;
Lai, Ying-Hsiuan
;
Cheng, Szu-Cheng
;
Hsieh, Wen-Feng
;
光電工程學系
Modulation instability (MI) in a coupled resonator optical waveguide (CROW) and photonic-crystal waveguide (PCW) with nonlinear Kerr media was studied by using the tight-binding theory. By considering the coupling between the defects, we obtained a discrete nonlinear evolution equation and termed it the extended discrete nonlinear Schrodinger (EDNLS) equation. By solving this equation for CROWs and PCWs, we obtained the MI region and the MI gains, G(p,q), for different wavevectors of the incident plane wave (p) and perturbation (q) analytically. In CROWs, the MI region, in which solitons can be formed, can only occur for pa being located either before or after square/2, where a is the separation of the cavities. The location of the MI region is determined by the number of the separation rods between defects and the sign of the Kerr coefficient. However, in the PCWs, pa in the MI region can exceed the square/2. For those wavevectors close to square/2, the MI profile, G(q), can possess two gain maxima at fixed pa. It is quite different from the results of the nonlinear CROWs and optical fibers. By numerically solving the EDNLS equation using the 4(th) order Runge-Kutta method to observe exponential growth of small perturbation in the MI region, we found it is consistent with our analytic solutions. (C) 2009 Optical Society of America
Physical properties of asymmetric photonic crystal waveguides
(2009-01-01)
Huang, Chih-Hsien
;
Hsieh, Wen-Feng
;
Cheng, Szu-Cheng
;
光電工程學系
;
Department of Photonics
By considering the next nearest neighboring defects between two photonic crystal waveguides (PCWs) and analytic formulae derived from the tight binding theory, we will explain the physical properties of an asymmetric directional coupler made from two coupled PCWS: (1) The dispersion curves of a photonic crystal coupler will decouple into the dispersion curves of a single line defect, and the electric field will only be localized in one waveguide of the coupler at a particular point, which we name a decoupling point. (2) The parities of the eigenmodes switch at the decoupling point, even though the dispersion curves are not crossing. (3) The eigenfield at a higher (lower) dispersion curve is always mainly localized in the waveguides that have higher (lower) eigenfrequencies of single line defects, even though the eigenmodes are switched. As a given frequency is incident into the coupler, the energy transfer between two waveguides and the coupling length can be expressed analytically. Due to there being no dispersion curve crossing, the coupling length is no longer infinite at the decoupling point in asymmetric PCWs, but it still has the minimal energy transfer between two waveguides when the frequency of the incident wave is close to the decoupling point.
Spontaneous emission dynamics in an omnidirectional waveguide made of photonic crystals
(2011-06-08)
Huang, Chih-Hsien
;
Cheng, Szu-Cheng
;
Wu, Jing-Nuo
;
Hsieh, Wen-Feng
;
光電工程學系
The spontaneous emission dynamics of atoms embedded in an omnidirectional waveguide (ODWG), a novel optical waveguide, is studied on the basis of the complete reflection of one-dimensional photonic crystals. With the dispersion curve of the single waveguide mode within the photonic band gap and various extents of background dissipation, we characterize the photon-atom interaction in the ODWG. The photon emitter of the system is a two-level atom embedded in the low-index medium of the multilayer-film ODWG or the atom-ODWG system. Fractional calculus, an innovative mathematical method in optical systems, is applied to solve the equation of motion for this atom-ODWG system. Two kinds of states with different group velocities exhibit totally distinctive dynamical behavior. The high frequency waveguide mode with a fast group velocity shows fast exponential decay in propagation while the band-edge mode with a slow group velocity displays non-Markovian dynamics with non-exponential oscillating time evolution. We therefore suggest different functions of this atom-ODWG system for these two kinds of states. The richness of the physical content of the system is also revealed through investigating the dynamical behavior of the band-edge mode. These results aid in further application and fundamental understanding of the atom-ODWG system.
Spontaneous emission from a two-level atom in anisotropic one-band photonic crystals: A fractional calculus approach
(2010-02-01)
Wu, Jing-Nuo
;
Huang, Chih-Hsien
;
Cheng, Szu-Cheng
;
Hsieh, Wen-Feng
;
光電工程學系
Spontaneous emission ( SE) from a two-level atom in an anisotropic photonic crystal ( PC) is investigated by the fractional calculus. Physical phenomena of the SE are studied analytically by solving the fractional kinetic equations of the SE. There is a dynamical discrepancy between the SE of anisotropic and isotropic PCs. We find that, contrary to the SE phenomenon of the isotropic PC, the SE near the band edge of an anisotropic PC shows no photon-atom bound state. It is consistent with the experimental results of Barth, Schuster, Gruber, and Cichos [Phys. Rev. Lett. 96, 243902 ( 2006)] that the anisotropic property of the system enhances the SE. We also study effects of dispersion curvatures on the changes of the photonic density of states and the appearance of the diffusion fields in the SE.
The evolution of solitons in coupled resonator optical waveguides and photonic-crystal waveguides
(2011-01-01)
Huang, Chih-Hsien
;
Wu, Jing-Nuo
;
Cheng, Szu-Cheng
;
Hsieh, Wen-Feng
;
光電工程學系
We successfully used the tight binding theory to derive the extended discrete nonlinear Schrodinger equation to describe the soliton propagation and to obtain the soliton propagation criteria (SPC) in the nonlinear photonic-crystal waveguides (PCWs) and coupled resonant optical waveguides (CROWs) containing Kerr media From these criteria we obtain the soliton-propagating region of CROWs in different numbers of separated rods and strengths of self-phase modulation (SPM) The defined soliton-propagating regions coincide with the regions of modulation instability in the CROWs In the PCWs the positive Kerr coefficient medium needs to be added to support the pulse propagation in low frequency or low wave vector region of the dispersion curve while negative Kerr effect is for high frequency case Due to the linear combination of various cosine harmonic functions in the dispersion relations of both CROWs and PCWs the pulse broadening which is mainly caused by the third-order dispersion at SPC is the lowest at the boundary of dispersion curves However due to the different magnitudes of coupling coefficients in CROWs and PCWs the group velocity dispersion and strength of SPM in CROWs are all smaller than those in PCWs (C) 2010 Elsevier B V All rights reserved
The properties and design concepts of photonic directional couplers made of photonic crystal slabs
(2010-11-24)
Huang, Chih-Hsien
;
Wu, Jing-Nuo
;
Lee, Po-Yi
;
Hsieh, Wen-Feng
;
Cheng, Szu-Cheng
The properties and design concepts of air-defect symmetric and asymmetric directional couplers (DCs) made of photonic crystal slabs (PCSs) are investigated by the tight-binding theory. We give criteria in both cases for determining the specific frequency, named as the decoupling point, at which the even (-like) and odd (-like) parities of eigenmodes should switch. Two dispersion curves will cross in symmetric DCs but not in asymmetric DCs because eigenfrequencies of isolated photonic waveguides (PCWs) are different in asymmetric DCs. In the dielectric-rod PCS, the decoupling point of the DC is located almost at the same wave vector as a two-dimensional (2D) DC with only a blue shift in its frequency. Therefore, 2D simulation can give a primary result in designing a dielectric-rod DC. On reducing the radius of the defect rods, the increase in coupling coefficients leads to a faster group velocity and a longer coupling length. On the other hand, the dispersion curves of the air-hole PCS DC are no longer parallel to those of the 2D DC so that performing a 3D simulation is necessary in designing an air-hole PCS DC with enlarged air holes. Moreover, the dispersion curve of the single PCW is no longer located at the centre of the curves of the symmetric DC and the group velocity may become negative which is not observed in the dielectric-rod PCS. The simulation results indicate that the coupling length of an air-defect DC can be achieved as short as 5 lattice constants, which is much smaller than that made of dielectric defects in air-hole PCS DCs.
Tight-binding theory for coupling asymmetric photonic crystal waveguides
(2008-08-01)
Huang, Chih-Hsien
;
Hsieh, LVen-Feng
;
Cheng, Szu-Cheng
;
光電工程學系
;
Department of Photonics
The physical properties of asymmetric photonic-crystal directional couplers are studied under the tight-binding model, which assumes that the field distribution of photon ic-cryst al waveguides is localized around periodic defects. The couplings of nearby defects between two asymmetric waveguides cause two dispersion relations to split further whereas the couplings of nearby defects within an individual waveguide cause the sinusoidal modulations of the dispersion curves. The field-envelope distributions of the coupler are expressed by using the eigenmodes of the tightbinding equations and are consistent with the comparing results from finite-difference time-domain simulations.
Tuning the decoupling point of a photonic-crystal directional coupler
(2009-02-01)
Huang, Chih-Hsien
;
Hsieh, Wen-Feng
;
Cheng, Szu-Cheng
;
光電工程學系
;
Department of Photonics
The decoupling point is a crossing in the dispersion curves of a photonic-crystal coupler. At this point, the energy in one waveguide cannot be transferred into the other one. Controlling the decoupling point can modify the properties of the coupler. From the extended tight-binding theory (TBT), which includes coupling of the guiding mode field up to the next nearest-neighboring defects, we found there is a blueshift in the frequency of the decoupling point in the square lattice and a redshift in the triangular lattice by translating the defect rods along the axis of the coupler. By moving the defects of the coupler close to each other transversely, not only the eigenfrequencies of the coupler but also separations of dispersion curves increase due to the stronger coupling between the defect rods. From the simulation results of the plane wave expansion and the finite difference time domain methods, the theoretical analyses of TBT agree with the numerical ones. Therefore, we successfully derive the design rules using the TBT for tuning the coupling length and decoupling frequency of a directional coupler. (C) 2009 Optical Society of America