Modeling Coherent Nonlinear Microscopy of Axially Layered Anisotropic Materials Using FDTD

Abstract

Providing quantitative interpretation of coherent nonlinear microscopy images, such as third-harmonic generation (THG), is generally hampered by the complex phase-matching conditions, especially in the presence of sample linear heterogeneity. We recently presented a numerical pipeline using the finite-difference time-domain (FDTD) method to take this heterogeneity into account. However, due to software restrictions, we only considered nonlinear materials with diagonal nonlinear susceptibilities. We now expand the recently developed FDTD approach to model nonlinear microscopy for anisotropic materials that obey Kleinman Symmetry, organized in layers along the optical axis, and validate our simulations on well-described geometries.

Figures (5)

• Figure 1: THG on a slab of isotropic $\chi^{(3)}$ material in water as a function of the polarization state. (a) geometry considered (b) Spectrum measured in the simulation with $\varphi=0$ (linear polarization) at the center of the detector array, showing the fundamental frequency and the THG signal. In green, the region over which the signal is integrated. (c) Intensity of the third harmonic field on the detector array, with from top to bottom total intensity, intensity along the x polarization, and along the y-polarization. (d) Simulated integrated THG as a function of the phase between the two polarizations.
• Figure 2: Non-degenerate third order nonlinear processes in a slab of isotropic $\chi^{(3)}$ material as a function of the polarization state. (a) geometry considered (b1) Spectrum measured in the simulation at the center of the detector array shown on a log scale, showing the fundamental frequency, the two THG signals, the two 4-wave mixing signals at $2\omega_1-\omega_2$ and $2\omega_2-\omega_1$, and the 2 TSFG signals at $2\omega_1-\omega_2$ (b2) zoom on the region highlighted in blue in (b1) where we the four third-order sum-frequency signals using a linear scale, with 4 signals at $3\omega_1$, $2\omega_1+\omega_2$, $\omega_1+2\omega_2$, and $3\omega_2$. (c) Intensity of the THG and TSFG fields on the detector array, along the $x$ polarization (left), and along the $y$ polarization (right)
• Figure 3: SHG in an anisotropic material mimicking a 2$\mu$m layer of the corneal stroma oriented along $x$ as a function of the incident linear polarization angle (a) geometry considered, with the nonlinear signal detected in transmission (b) Spectrum measured in the simulation at the center of the detector array shown in a log scale, where we can identify the fundamental frequency at 1.2$\mu$m ($\omega$), the SHG signal at 600 nm (2$\omega$) and a cascaded SHG peak at 400 nm (3$\omega$). In green, the spectral region over which the SHG signal is integrated. (c) The intensity of the SHG field on the detector array, with from top to bottom: the total intensity, the intensity along the $x$ polarization, and the intensity along the $y$ polarization (d) Integrated SHG intensity as a function of the linear polarization angle from the $x$ axis (so 0 is $x$ polarized, 90 is $y$ polarized)
• Figure 4: SHG and SFG in an anisotropic material mimicking the layer of the corneal stroma (a) geometry considered, with two incoming Gaussian beams at $\lambda_1=1000$ nm polarized along $x$ and $\lambda_1=1200$ nm polarized along $y$. (b1) Spectrum measured in the simulation at the center of the detector array on a log scale, showing the fundamental frequencies, and the nonlinear signals. In blue, a region corresponding to second-order processes displayed on a linear scale in (b2), where we can identify 3 peaks corresponding to the 2 SHG signals and the SFG signal, and in red to cascaded processes displayed on a linear scale in (b3) with 4 peaks corresponding to $3\omega_1$,$2\omega_1+\omega_2$,$\omega_1+2\omega_2$, and $3\omega_2$
• Figure 5: SHG and THG in an anisotropic material mimicking the layer of the corneal stroma as a function of the incident linear polarization angle (a) geometry considered (b) Spectrum measured in the simulation at the center of the detector array, showing the fundamental frequency, the SHG signal at 600 nm (and a weak cascaded SHG peak at 300 nm) and thg THG signal at 400 nm. In green, the region over which the SHG signal is integrated, and in purple, the region where THG is integrated. (c) simulated integrated SHG and THG signal as a function of the linear polarization direction