# A model of optical pump-terahertz probe by ultrafast terahertz near-field microscopy

## TL;DR

This paper introduces a new model to speed up the analysis of ultrafast optical pump-terahertz probe signals at the nanoscale.

## Contribution

A generalized evolutionary model (GEM) is proposed to rapidly extract transient permittivity without full spectral acquisition.

## Key findings

- GEM enables rapid permittivity retrieval from near-field OPTP signals.
- Validation on SRAM, GaAs, and Bi2Te3 showed high accuracy and a 25x speedup.
- The method avoids full-time-domain spectral acquisition at every delay step.

## Abstract

Terahertz scattering-type scanning near-field optical microscopy (THz s-SNOM) has emerged as a powerful tool for capturing information beyond the diffraction limit. Adding an external pumping laser enables nanoscale optical pump-THz probe (OPTP) spectroscopy, extending ultrafast dynamics studies to the nanoscale. However, unlike the thin-film approximation in far-field transmission, the relation between transient permittivity and the near-field OPTP signal remains computationally demanding to solve. Here, we introduce a generalized evolutionary model (GEM) derived from the physical independence between the ultrafast pump delay and the mechanical tip oscillation. By assuming a multiplicative evolution of the spectral response, GEM establishes a direct analytical link that decouples the transient permittivity from the complex near-field scattering integral. This approach allows for the rapid prediction of permittivity evolution without the need for full-time-domain spectral acquisition at every delay step. Our findings demonstrate that GEM significantly accelerates the extraction of transient permittivity during the pumping process, as validated on typical semiconductor samples.

•Our method allows rapid permittivity retrieval from near-field OPTP signals•No need for full-time-domain spectral acquisition at every delay step•Validated on SRAM, GaAs, and Bi2Te3 with high accuracy and 25x speedup

Our method allows rapid permittivity retrieval from near-field OPTP signals

No need for full-time-domain spectral acquisition at every delay step

Validated on SRAM, GaAs, and Bi2Te3 with high accuracy and 25x speedup

Photonics; Radiation physics; Applied sciences