A new full-vectorial FD-BPM scheme: application to the analysis of magnetooptic and nonlinear saturable media

Alcantara, Licinius Dimitri Sá de; Teixeira, F.L.; Cesar, A.C.; Borges, Ben‐Hur V.

doi:10.1109/jlt.2005.850811

Cited by 20 publications

(4 citation statements)

References 23 publications

(28 reference statements)

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“…For example, the constitutive relation for a (local, instantaneous) nonlinear medium can be expressed as , with each component of given by (13) where is the linear susceptibility and are nonlinear susceptibilities. Important special cases of the above are isotropic models of the form [232], [233] (14)…”

Section: Nonlinear Mediamentioning

confidence: 99%

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

Teixeira

2008

IEEE Trans. Antennas Propagat.

197

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Section: Nonlinear Mediamentioning

confidence: 99%

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

Teixeira

2008

IEEE Trans. Antennas Propagat.

197

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“…Such modifications to enhance its capability have been proposed in [10], [11]. The finite-difference time-domain (FDTD) method has been previously applied to analyzing problems in nonlinear optics, including solitons [9], [12]- [17].…”

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confidence: 99%

FDTD Computational Study of Ultra-Narrow TM Non-Paraxial Spatial Soliton Interactions

Lubin

Greene

Taflove

2011

IEEE Microw. Wireless Compon. Lett.

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Abstract-We consider the interaction between two (1+1)D ultra-narrow optical spatial solitons in a nonlinear dispersive medium using the finite-difference time-domain (FDTD) method for the transverse magnetic (TM) polarization. The model uses the general vector auxiliary differential equation (GVADE) approach to include multiple electric-field components, a Kerr nonlinearity, and multiple-pole Lorentz and Raman dispersive terms. This study is believed to be the first considering narrow soliton interaction dynamics for the TM case using the GVADE FDTD method, and our findings demonstrate the utility of GVADE simulation in the design of soliton-based optical switches.Index Terms-Finite-difference time-domain method, FDTD, GVADE, nonlinear optics, spatial solitons. SPATIAL optical solitons are self-trapped optical beams balancing diffraction and self-focusing due to intensity-induced modifications in the local refractive index. One fascinating feature of solitons is their deflection behavior when in the vicinity of other solitons. This can be exploited for applications in optical routing and guiding or in switching applications in all optical-based interconnects and nanocircuits (for example, [1]).The work by Aitchison, et al. first reported experimental observations that solitons either repel or attract each other with a periodic evolution over propagation, depending on the relative phase between them [2]. Subsequent studies extended the findings and explored applications; slight variation on the launch angle and relative phase was found to cause a soliton pair to merge into one of the original trajectories [3]. More recent efforts considered interactions in semiconductor media [4], incoherent interactions [5], all-optical switching [6], long-range interactions [7], and the dynamics of interacting, self-focusing beams [8].An effective numerical technique known as the beam propagation method (BPM) can be used to model soliton interaction. It is a Fourier-based algorithm that solves the nonlinear Schrodinger equation (NLSE) for the envelope of the field. It typically requires low memory for computer implementation. Some limitations, however, are that it makes a scalar approximation, relies on paraxiality, and also depends on slowly-varying envelope conditions for validity without proper modifications Recently, a new FDTD algorithm was described, which can accommodate more than one electric-field component in media possessing both instantaneous and dispersive nonlinearities, as well as linear material dispersion. Known as the general vector auxiliary differential equation (GVADE) method [15], it has been applied to the study of soliton interactions with nanoscale air gaps embedded in glass [16]. Ultra-narrow solitons involve significant interactions between both longitudinal and transverse electric-field components [14] and the GVADE method accounts for this physics.In this study, we consider the problem of modeling interacting spatial solitons with beamwidths on the order of one wavelength using the GVADE FDTD metho...

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“…It is well-known that the FR effect is caused by a periodic power transfer between the transverse components E x and E y [24]. Here, at z = 0, the transverse component is only along the x direction, i.e., E y = 0.…”

Section: Structure Principle and Numerical Resultsmentioning

confidence: 99%

Nonreciprocal TE–TM Mode Conversion Based on Photonic Crystal Fiber of Air Holes Filled With Magnetic Fluid Into a Terbium Gallium Garnet Fiber

Otmani

Bouchemat

et al. 2015

IEEE Trans. Magn.

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In this work, we study the nonreciprocal TE-TM mode conversion phenomenon, by the simulation of magneto photonic crystal fibre (MPCF). This MPCF consists of a periodic triangular lattice of air-holes filled with magnetic fluid (Fe 3 O 4 ) into a Terbium Gallium Garnet (TGG) fibre. It is well known that, owing to its excellent transparency properties and its resistant character to laser damage, TGG is always selected as a Faraday rotator material. Also, TGG has a high Verdet constant related with the Faraday rotation (FR) effect. Here, with the consideration of the effect of gyrotropy, our simulations are associated with some calculations of the FR and modal birefringence. In this MPCF, the light is guided by internal total reflection, like classical fibres. However, it was shown that the designed MPCF could function as a mode converter with much stronger conversion efficiency than those of the conventional fibres.

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A new full-vectorial FD-BPM scheme: application to the analysis of magnetooptic and nonlinear saturable media

Cited by 20 publications

References 23 publications

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

FDTD Computational Study of Ultra-Narrow TM Non-Paraxial Spatial Soliton Interactions

Nonreciprocal TE–TM Mode Conversion Based on Photonic Crystal Fiber of Air Holes Filled With Magnetic Fluid Into a Terbium Gallium Garnet Fiber

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