Browsing by Author "Wu, Jing-Nuo"

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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.
Coherent Coupling Between a Three-Level Atom and a Structured Reservoir
(2008-12-01)
Wu, Jing-Nuo
;
Yang, Tzong-Jer
;
Cheng, Szu-Cheng
;
光電工程學系
;
Department of Photonics
We study the spontaneous emission (SE) spectra of a three-level A-type atom in photonic crystals. The air-band, the dielectric-band and the free-space vacuum reservoirs coupled with the atom are considered. With the consideration of the phase difference between the air-band and the dielectric-band fields, two band reservoirs become coherent and can interfere with each other. This interference effect depends on the embedded position of the atom and the band-gap width and can affect the SE spectrum. The effect of this interference on the SE spectrum is shown.
Dynamics of the Energy Relaxation and Decoherence of a Photon-Atom Bound State in an Anisotropic Photonic Crystal
(2013)
Wu, Jing-Nuo
;
Hsieh, Wen-Feng
;
Huang, Hsin-Chien
;
Cheng, Szu-Cheng
;
光電工程學系
An atom embedded inside photonic crystals can form a photon-atom bound state if the emission frequency of the excited atom is lying inside the photonic-band gap of photonic crystals. We studied the dynamics of the energy relaxation and decoherence of a QPAB, qubit made by a photon-atom bound state in photonic crystals. Dynamics of these measurements are solved analytically through the fractional calculus which has been shown to be appropriate mathematical method for the optical systems with non-Markovian dynamics. From these dynamics, we find that the losses of energy, coherence, and information of a QPAB are inhibited. As compared with those qubits without forming photon-atom bound states, the energy relaxation and decoherence rates of these QPABs are strongly suppressed. Other systems suitable for realizing these properties are discussed.
Effect of atomic position on the spontaneous emission of a three-level atom in a coherent photonic-band-gap reservoir
(2009-01-01)
Cheng, Szu-
;
Wu, Jing-Nuo
;
Yang, Tzong-Jer
;
Hsieh, Wen-Feng
;
光電工程學系
The effect of atomic position on the spontaneous emission and optical spectra of a three-level atom embedded in a photonic crystal was studied by considering the coherent two-band photonic-band-gap (PBG) reservoir. With the definite phase difference between the fields of the air band and dielectric band in this coherent PBG reservoir, we found that this coherent property grows stronger and results in the spectrum shift and the appearance of dark lines and kinks as the width of band gap gets smaller; and the variation of the atomic position leads to large shift of spectral peak. The averaged spectra of the system with an ensemble of atoms embedded in the dielectric region are blueshifted while those of atoms in the air region are redshifted. The spectra peaks can even shift more than 75% of the half width at half maximum. The feasible experimental systems composed of an ensemble of molecules (quantum dots or fluorescence dye) in photonic crystals are discussed.
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.
Spontaneous emission near the band edge of a three-dimensional photonic crystal: a fractional calculus approach
(2009-01-07)
Cheng, Szu-Cheng
;
Wu, Jing-Nuo
;
Tsai, Ming-Rung
;
Hsieh, Wen-Feng
;
光電工程學系
We suggest a better mathematical method, fractional calculus, for studying the behavior of the atom-field interaction in photonic crystals. By studying the spontaneous emission of an atom in a photonic crystal with a one-band isotropic model, we found that the long-time inducing memory of the spontaneous emission is a fractional phenomenon. This behavior could be well described by fractional calculus. The results show no steady photon-atom bound state for the atomic resonant transition frequency lying in the proximity of the allowed band edge which was encountered in a previous study (Woldeyohannes and John 2003 J. Opt. B: Quantum Semiclass. Opt.5 R43). The correctness of this result is validated by the 'cut-off smoothing' density of photon states (DOS) with fractional calculus. By obtaining a rigorous solution without the multiple-valued problem for the system, we show that the method of fractional calculus has a logically concise property.
Spontaneous emission of a three-level atom in a coherent photonic band gap reservoir
(2009)
Wu, Jing-Nuo
;
Yang, Tzong-Jer
;
Cheng, Szu-Cheng
;
Hsieh, Wen-Feng
;
光電工程學系
The optical spectra of a three-level atom embedded in a photonic crystal is studied by considering the coherent two-band photonic reservoir We find that the spectrum is shifting with respect to the atomic position.
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.