## Comparative Study of FDTD-Adopted Numerical Algorithms for Kerr Nonlinearities

Publication: Research - peer-review › Journal article – Annual report year: 2011

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**Comparative Study of FDTD-Adopted Numerical Algorithms for Kerr Nonlinearities.** / Maksymov, Ivan S.; Sukhorukov, Andrey A.; Lavrinenko, Andrei; Kivshar, Yuri S.

Publication: Research - peer-review › Journal article – Annual report year: 2011

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*I E E E Antennas and Wireless Propagation Letters*, vol 10, pp. 143-146. DOI: 10.1109/LAWP.2011.2114319

### APA

*I E E E Antennas and Wireless Propagation Letters*,

*10*, 143-146. DOI: 10.1109/LAWP.2011.2114319

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*I E E E Antennas and Wireless Propagation Letters*. 2011, 10. 143-146. Available: 10.1109/LAWP.2011.2114319

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TY - JOUR

T1 - Comparative Study of FDTD-Adopted Numerical Algorithms for Kerr Nonlinearities

AU - Maksymov,Ivan S.

AU - Sukhorukov,Andrey A.

AU - Lavrinenko,Andrei

AU - Kivshar,Yuri S.

PY - 2011

Y1 - 2011

N2 - Accurate finite-difference time-domain (FDTD) modeling of optical pulse propagation in nonlinear media usually implies the use of auxiliary differential equation (ADE) techniques. The updating of electric field in full-vectorial 3-D ADE FDTD modeling of the optical Kerr effect and two-photon absorption in optical media is proceeded conventionally through the iterative solution of nonlinear algebraic equations. Here, we study three approaches for the field update including simple noniterative explicit schemes. By comparing them to the analytical results for optical pulse propagation in long nonlinear media (nonlinear phase incursion for the pump wave of about $\pi$ radians), we demonstrate convincingly that simple noniterative FDTD updating schemes, which are commonly believed to be inaccurate and unstable, produce accurate results and drastically speed up the computation as compared to ADE approaches. Such schemes can significantly reduce the CPU time for nonlinear computations, especially in 3-D models.

AB - Accurate finite-difference time-domain (FDTD) modeling of optical pulse propagation in nonlinear media usually implies the use of auxiliary differential equation (ADE) techniques. The updating of electric field in full-vectorial 3-D ADE FDTD modeling of the optical Kerr effect and two-photon absorption in optical media is proceeded conventionally through the iterative solution of nonlinear algebraic equations. Here, we study three approaches for the field update including simple noniterative explicit schemes. By comparing them to the analytical results for optical pulse propagation in long nonlinear media (nonlinear phase incursion for the pump wave of about $\pi$ radians), we demonstrate convincingly that simple noniterative FDTD updating schemes, which are commonly believed to be inaccurate and unstable, produce accurate results and drastically speed up the computation as compared to ADE approaches. Such schemes can significantly reduce the CPU time for nonlinear computations, especially in 3-D models.

KW - Finite-difference time domain (FDTD)

KW - Optical Kerr effect

KW - Four-wave mixing (FWM)

KW - Nonlinearity

U2 - 10.1109/LAWP.2011.2114319

DO - 10.1109/LAWP.2011.2114319

M3 - Journal article

VL - 10

SP - 143

EP - 146

JO - I E E E Antennas and Wireless Propagation Letters

T2 - I E E E Antennas and Wireless Propagation Letters

JF - I E E E Antennas and Wireless Propagation Letters

SN - 1536-1225

ER -