Retrieving nonlinear refractive index of nanocomposites using finite-difference time-domain simulations

Andrey V. Panov

Author Affiliations

Andrey V. Panov

^{}Institute of Automation and Control Processes, Far East Branch of Russian Academy of Sciences, 5, Radio st., Vladivostok 690041, Russia (panov@iacp.dvo.ru)

Andrey V. Panov, "Retrieving nonlinear refractive index of nanocomposites using finite-difference time-domain simulations," Opt. Lett. 43, 2515-2518 (2018)

In this Letter, a method is proposed that utilizes three-dimensional finite-difference time-domain simulations of light propagation for restoring the effective Kerr nonlinearity of nanocomposite media. In this approach, a dependence of the phase shift of the transmitted light on the input irradiance is exploited. The reconstructed values of the real parts of the nonlinear refractive index of a structure of randomly arranged spheres are in good agreement with the predictions of the effective medium approximations.

İlker R. Çapoğlu, Craig A. White, Jeremy D. Rogers, Hariharan Subramanian, Allen Taflove, and Vadim Backman Opt. Lett. 36(9) 1596-1598 (2011)

References

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Results of the Reconstruction of Linear Refractive Index ${n}_{0}$, Nonlinear Susceptibility ${\chi}^{(3)}$, and Its Standard Deviation for the Homogeneous Specimens^{a}

The nonlinear susceptibility is linearly related to the second-order nonlinear refractive index ${n}_{2}$. The first and the third columns display the true values of ${n}_{0}$ and ${\chi}^{(3)}$, and the second and fourth columns exhibit the retrieved magnitudes. Here ${n}_{0\mathrm{ref}}$ is the refractive index of the reference specimen. The ambient medium with ${n}_{b}=2$ was used for the FDTD simulations of transmission through the layer with ${n}_{0}>2$.

Table 2.

Linear Refractive Indexes and Nonlinear Susceptibilities ${\chi}^{(3)}$ of Mixtures Retrieved with the Modeling and Predicted by the Effective Medium Theories^{a}

Here $f$ is the volume fraction (concentration) of inclusions, ${n}_{0\mathrm{rec}}$ is the reconstructed linear refractive index, ${n}_{0\mathrm{MG}}$ and ${n}_{0B}$ are ones calculated using the Maxwell Garnett [14] or Bruggeman [15] approximations, and ${\chi}_{\mathrm{rec}}^{(3)}$ is the nonlinear susceptibility retrieved by the FDTD method; for comparison, there are presented third-order susceptibilities of mixtures obtained using the nonlinear effective medium approximations ${\chi}_{\mathrm{SH}}^{(3)}$ [1], ${\chi}_{\mathrm{AG}}^{(3)}$ [2], and ${\chi}_{\mathrm{RZPA}}^{(3)}$ [3]; ${\chi}_{\mathrm{in}}^{(3)}$ is the third-order susceptibility of the inclusions. The retrieved values for $f=0.1306$ were calculated for the aligned cubic inclusions with the edge size of 32 nm. The last row for ${w}_{0}=600\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{nm}$ was calculated using $3.2\times 3.2\times 8\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{\mu m}$ size of the computational domain.

Tables (2)

Table 1.

Results of the Reconstruction of Linear Refractive Index ${n}_{0}$, Nonlinear Susceptibility ${\chi}^{(3)}$, and Its Standard Deviation for the Homogeneous Specimens^{a}

The nonlinear susceptibility is linearly related to the second-order nonlinear refractive index ${n}_{2}$. The first and the third columns display the true values of ${n}_{0}$ and ${\chi}^{(3)}$, and the second and fourth columns exhibit the retrieved magnitudes. Here ${n}_{0\mathrm{ref}}$ is the refractive index of the reference specimen. The ambient medium with ${n}_{b}=2$ was used for the FDTD simulations of transmission through the layer with ${n}_{0}>2$.

Table 2.

Linear Refractive Indexes and Nonlinear Susceptibilities ${\chi}^{(3)}$ of Mixtures Retrieved with the Modeling and Predicted by the Effective Medium Theories^{a}

Here $f$ is the volume fraction (concentration) of inclusions, ${n}_{0\mathrm{rec}}$ is the reconstructed linear refractive index, ${n}_{0\mathrm{MG}}$ and ${n}_{0B}$ are ones calculated using the Maxwell Garnett [14] or Bruggeman [15] approximations, and ${\chi}_{\mathrm{rec}}^{(3)}$ is the nonlinear susceptibility retrieved by the FDTD method; for comparison, there are presented third-order susceptibilities of mixtures obtained using the nonlinear effective medium approximations ${\chi}_{\mathrm{SH}}^{(3)}$ [1], ${\chi}_{\mathrm{AG}}^{(3)}$ [2], and ${\chi}_{\mathrm{RZPA}}^{(3)}$ [3]; ${\chi}_{\mathrm{in}}^{(3)}$ is the third-order susceptibility of the inclusions. The retrieved values for $f=0.1306$ were calculated for the aligned cubic inclusions with the edge size of 32 nm. The last row for ${w}_{0}=600\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{nm}$ was calculated using $3.2\times 3.2\times 8\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{\mu m}$ size of the computational domain.