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.

Albert S. Reyna and Cid B. de Araújo Adv. Opt. Photon. 9(4) 720-774 (2017)

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.