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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - A Simple Approach, Based on Coupled Mode Theory, to Study PhC Lasers
摘要： PhC lasers have attracted large interest as efficient light-sources in on-chip and chip-to-chip interconnections. They allow for scaling the active volume while maintaining the high cavity Q-factor, thus exhibiting low threshold current and operating energy [1,2]. Methods for studying these laser cavities are typically based on FDTD simulations, which are often time-consuming and do not allow to catch the most relevant physics of these devices. We propose here an alternative and simple approach to analyze active PhC waveguides and lasers. Our approach is based on coupled-mode theory, which has proved to be an effective tool to study lasers with periodic gain and/or refractive index perturbation, as standard DFB lasers. We apply this method to PhC line-defect waveguides and lasers with a small complex refractive index perturbation (to account for gain and refractive index variation) with respect to a reference, unpumped PhC line-defect waveguide [3]. The optical electric field of the TE-like guided mode is expanded as sum of the forward- and backward-propagating Bloch modes of the passive waveguide; the equation governing the evolution (cid:549)+,-(z) of the Bloch modes along the perturbed waveguide are: (cid:2034)(cid:1878)(cid:2032)+ = (cid:1861)(cid:2018)11,(cid:1869)=0((cid:2033)) (cid:2032)++ (cid:1861)(cid:2018)12,(cid:1869)=1((cid:2033)) (cid:1857)+2(cid:1861)(cid:2012)((cid:2033))(cid:1878)(cid:2032)(cid:3398) (cid:3398)(cid:2034)(cid:1878)(cid:2032)(cid:3398) = (cid:1861)(cid:2018)21,(cid:1869)=(cid:3398)1((cid:2033))(cid:1857)(cid:3398)2(cid:1861)(cid:2012)((cid:2033))(cid:1878)(cid:2032)++ (cid:1861)(cid:2018)11,(cid:1869)=0((cid:2033)) (cid:2032)(cid:3398) (1) where k11,q=0 and k12,q=1;21q=-1 are the self- and cross- coupling coefficients calculated as in [3]. An example is in Fig. 1 for refractive index perturbation ((cid:507)(cid:81)s(cid:143)(cid:19)) and positive gain g0. This figure proves that, differently from standard DFB lasers, the cross-coupling coefficient is always comparable to the self-coupling coefficient. This is because of the strong z-component of the TE-like electric field of the fundamental guided mode. The coupling coefficients are gain-dependent since gain, not present in the holes, is also a periodic perturbation; k11,q=0 and k12,q=1;21q=-1 are also frequency-dependent because of the slow-light effect and they significantly increase as frequency approaches the band edge. Therefore, Bloch modes at shorter frequency and/or with higher gain of the active waveguide will go through a stronger distributed feedback effect with respect to longer frequency Bloch modes and/or lower active waveguide gain. Based on this model, we have simulated a laser cavity with the geometry as in Fig. 2a, consisting of a pumped active section, a rear passive mirror with material refractive index smaller than the active section and a front passive buffer with material refractive index equal (Type A) , slightly larger (Type B) or smaller (Type C) than the active region. Based on the model of eq. (1), we have calculated the rear and buffer mirror reflection coefficients (S11) (Fig.2a). Threshold condition, found searching for frequency and gain g0 satisfying rL(cid:11)(cid:550)(cid:12)(cid:194) rR(cid:11)(cid:550)(cid:15)(cid:74)0)=1, is in Fig.2b as function of the front buffer number of cells. The different trends of the threshold gain with the number of buffer cells can be explained by the interplay, in determining rR(cid:11)(cid:550)(cid:15)(cid:74)0), between the distributed feedback in both the active region and the front buffer. In Type C, the latter is dominant (nearly doubled with respect to the active region feedback); therefore, threshold gain diminishes as the front buffer reflection increases (similar to a FP laser with increase of the front mirror reflection). On the contrary, in Type A and Type B the role of distributed feedback in the active region plays a major role and the threshold depends on the interference between the active region distributed feedback and the front buffer back reflection. For this reason, Type B shows an optimum number of cells minimizing threshold gain.
关键词： coupled-mode theory,FDTD simulations,PhC lasers,distributed feedback,Bloch modes
更新于2025-09-12 10:27:22
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Magneto-optical properties of asymmetric one-dimensional magneto-photonic crystals
摘要： We analytically investigate the magneto-optical properties of asymmetric one-dimensional magneto-photonic crystals (MPCs) by using our previously presented coupled mode description. We show that an MPC with one magnetic defect, placed asymmetrically, provides the same number of degrees of freedom as a symmetric double-defect MPC. Consequently, an asymmetric single-defect MPC allows arbitrary transmittance and Faraday rotation at the central frequency, just as a symmetric double-defect MPC, and hence a desired performance can be obtained by the more compact single-defect structure. However, the possible ranges of performance are more restricted than the possible ranges of a double-defect MPC. We present the synthesis relations to design the single-defect MPC. In a similar manner, we show that an asymmetric double-defect MPC provides more degrees of freedom than either a symmetric double-defect or an asymmetric single-defect MPC. The excessive degree allows us to design a more compact MPC than the symmetric double-defect MPCs for a desirable central frequency performance, in the wide possible range that double-defect structures provide.
关键词： Faraday rotation,Synthesis,Magneto-photonic crystals,Coupled mode theory
更新于2025-09-09 09:28:46
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Resonance || Fano Resonance in High-Permittivity Objects
摘要： In this chapter, Fano resonances in simple structures with high permittivity such as spheres or core-shell particles are analyzed by Mie theory. The Mie scattering coefficients can be decomposed into slow varying backgrounds and narrow resonances, which cause the Fano resonances in scattered field. For structures of arbitrary shapes, temporal coupled-mode theory is applied to explain the Fano resonances found in the scattering cross section. At last, we analyze the periodic structures by using band diagram, and it shows that the Fano resonances can be viewed as the superposition of the Bloch wave and the Mie scattering wave.
关键词： sensor,temporal coupled-mode theory,Mie theory,Fano resonance,photonic crystal
更新于2025-09-09 09:28:46
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Optical spatial differentiator for a synthetic three-dimensional optical field
摘要： We propose a grating-based spatial differentiator to process a synthetic three-dimensional optical field, where several conventional two-dimensional optical images are stacked at multiple wavelengths. The device simultaneously enables both spatial differentiation and demultiplexing during light diffraction. We show the spatial differentiation resulting from coupling and interference of spatial modes and derive the theoretical condition for spatial differentiation based on spatial coupled-mode theory. We numerically investigate field transformation during diffraction and demonstrate spatial differentiation with image processing of edge detection for a synthetic three-dimensional optical field, where four images are stored at different wavelengths.
关键词： demultiplexing,coupled-mode theory,grating-based,spatial differentiation,optical spatial differentiator,synthetic three-dimensional optical field
更新于2025-09-09 09:28:46