Topological Hall effect in nonlinear optics

Abstract

We present an experimental evidence of \emph{topological} Hall-effect in an all-optical third-order nonlinear optical process via spatial symmetry-breaking in pseudo-spin textures created by a spatially-structured pump laser beam. The experimental configuration consists of a moderately-focused pump laser beam undergoing a parametric interaction with an organic solvent (toluene) and an off-resonant laser beam probes the non-trivial spatial magnetization textures created by the pump beam. The phase-profile of the transmitted probe beam is extracted using phase-retrieval algorithms for ascertaining the topological charge which is shown to be consistent with the estimation of Berry's curvature that we obtain via paraxial approximation-based modeling of third-order nonlinear interaction.

Figures (5)

• Figure 1: (a)-(c) represents elliptic pump beam profiles for $w_{x} = 1100~\mu m, ~500~\mu m, 150~\mu m$ and $w_{y} = 1200~\mu m$ corresponding to ellipticity of $0.90$ (a), $0.40$ (b), $0.12$ (c) respectively. (d)-(f) represents a force field ($|\vec{\mathcal{F}}|$) intensity map for pump beam with ellipticity of $0.90$ (a), $0.40$ (b), $0.12$ (c) respectively.
• Figure 2: (a)-(d) represents simulated probe beam profiles at the exit face nonlinear medium ($z = +\frac{T}{2}$) for $w_{x} = ~500~\mu m$ and $w_{y} = 1200~\mu m$ at average pump beam power of (a) $30~mW$, (b) $150~mW$, (c) $300~mW$, (d) $500~mW$ respectively. (e)-(h) represents simulated probe beam profiles at the exit face nonlinear medium ($z = +\frac{T}{2}$) for $w_{x} = ~150~\mu m$ and $w_{y} = 1200~\mu m$ at average pump beam power of (a) $30~mW$, (b) $150~mW$, (c) $300~mW$, (d) $500~mW$ respectively.
• Figure 3: shows the collinear pump-probe based experimental configuration for observing topological Hall effect (THE) in an asymmetric synthetic magnetic field ($\vec{\mathcal{B}}$). B1: Polarizing beam-splitter; B2: Non-polarizing beam-splitter; S: sample; D1-D3: Power meter; H: Half-wave plate; P: Polarizer; M1-M5: Steering mirror; M6 & M7: Dichroic mirrors for realizing collinear arrangement; L: cylindrical lens;C: CCD camera. Inset: $T = 1~cm$ thick cuvette filled with toluene that exhibits $\chi^{(3)} < 0$ (defocusing) for $700~ps$ pulsed laser centered at $532~nm$ wavelength.
• Figure 4: (a)-(d) represents experimentally measured probe beam profiles at the far field ($z = \frac{T}{2}+30~cm$) for $w_{x} = ~500~\mu m$ and $w_{y} = 1200~\mu m$ at average pump beam power of (a) $30~mW$, (b) $150~mW$, (c) $300~mW$, (d) $500~mW$ respectively. (e)-(h) experimentally measured probe beam profiles at the far field ($z = \frac{T}{2}+30~cm$) for $w_{x} = ~150~\mu m$ and $w_{y} = 1200~\mu m$ at average pump power of (e) $30~mW$, (f) $150~mW$, (g) $300~mW$, (h) $500~mW$ respectively.
• Figure 5: (a)-(d) represents the subtracted pattern of interfering beams from the interference pattern (see supplementary) for $w_{x} = ~150~\mu m$ and $w_{y} = 1200~\mu m$ at average pump power of (a) $30~mW$, (b) $150~mW$, (c) $300~mW$, (d) $500~mW$ respectively. (e)-(h) represents computationally retrieved unwrapped phase profile from the subtracted fringe pattern, for $w_{x} = ~150~\mu m$ and $w_{y} = 1200~\mu m$ at average pump power of (e) $30~mW$, (f) $150~mW$, (g) $300~mW$, (h) $500~mW$ respectively.