# Route to Intelligent Imaging Reconstruction via Terahertz Nonlinear Ghost Imaging

*ic*) Laboratory, Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Time-Resolved Nonlinear Ghost Imaging: A Conceptual Overview

## 3. Compressed and Adaptive Sensing Applications

## 4. Performance of Field-Based Ghost-Imaging Detection in the Fourier Plane

## 5. A Route towards Thinner THz Emitters: Surface Emission from Quasi-2D Semiconductor Structures

^{2}), InAs is probably considered the benchmark surface emitter. In this case, the generation is driven by the very large difference in mobility between holes and electrons via the photo-Dember effect (Figure 5c,d): when a high density of photogenerated pairs is induced in the proximity of the surface, electrons quickly diffuse away from the surface, leaving uncompensated carriers of the opposite sign. Such a charge unbalance creates a fast stretching dipole, or equivalently, a local current transient that is the source of the terahertz emission [46].

^{2}), this phenomenon becomes critically saturated due to the electromagnetic screening role of dense carrier densities. Conversely, the optical surface rectification (SOR) dominates the emission [43]. The optical surface rectification is a quadratic phenomenon induced by the contribution of a local static field at the surface, which is induced by surface states within the bulk cubic nonlinear response (Figure 5a,b). The DC field effectively plays the role of a field contribution in a four-wave mixing process in a mechanism commonly referred to as a field-induced quadratic response [45,47] and is described using:

## 6. Discussions and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Conceptual description of time-resolved nonlinear ghost imaging (TIMING). (

**a**) Schematic of the experimental setup. (

**b**,

**c**) Simulation of the TIMING reconstruction of a semi-transparent sample, including the average field transmission (panel b) and the full spatiotemporal image of the sample (panel c). The simulated object size was 10.24 cm × 10.24 cm, sampled with a spatial resolution of 512 × 512 pixels (Δx = 200 µm) and a temporal resolution of Δt = 19.5 fs. The nonlinear crystal thickness was ${z}_{0}$= 10 μm. n.u.: normalised units, TDS: Time-domain spectroscopy.

**Figure 2.**Walsh–Hadamard image reconstruction. (

**a**) Generation of incident patterns from the Walsh–Hadamard matrix. Each pattern is defined as the tensor product between two columns of the generating matrix. The patterns can be generated from different configurations of a Hadamard matrix: we show the Walsh, or “sequency”, order (top, used in TIMING) and the standard Hadamard, or “natural”, order (bottom). (

**b**,

**c**) Reconstructed Walsh spectrum of the peak-field object transmission. Interestingly, only a fraction of the patterns (8.1%) were associated with a spectral amplitude exceeding the −60 dB threshold (with 0 dB being the energy correlation of the fittest pattern—panel c). Nevertheless, these patterns were sufficient to provide a high-fidelity reconstruction of the image (insets). (

**d**,

**e**) Pearson correlation coefficients between reconstructed and original images as a function of the number of patterns employed in the reconstruction. The results refer to the entire scan (panel d) and the initial 10% of patterns (panel e).

**Figure 3.**Influence of the pinhole size on the Fourier detection of TIMING reconstruction coefficients.

**(a**–

**d**) The spatial average of the transmitted field (

**b**) associated with each incident pattern (

**a**) could be measured by performing a point-like detection in the centre of the Fourier plane (

**c**,

**d**). In realistic implementations, the centre of the Fourier plane is sampled using a sampling function PH of finite diameter d. (

**e**) Spatial correlation between the reconstructed and original image as a function of the sampling function diameter. A departure from the point-like approximation led to a significant corruption of the reconstructed image (insets). Interestingly, the typical image degradation did not necessarily involve the total disappearance of highly resolved details.

**Figure 4.**Influence of the pinhole displacement on the Fourier detection of TIMING reconstruction coefficients. (

**a**) Spatial correlation between the reconstructed and original image as a function of the sampling function position in the focal plane. The displacement (Δx, Δy) was measured with respect to the lens axis and the sampling function diameter was set to d = 0.36 mm, corresponding to a spatial correlation of 100% at the centre of the Fourier plane (cf. Figure 3e). (

**b**–

**d**) Examples of image reconstruction with off-axis detection, illustrating the appearance of spurious spatial frequencies. Interestingly, the object morphology was still noticeable, even at a relatively large distance from the optical axis.

**Figure 5.**Surface emission driving mechanisms. (

**a**) Surface optical rectification—a surface field at the air–semiconductor barrier combines with the optical field in a four-wave mixing process (cubic), generating a terahertz mixing product (see Equation (7)). (

**b**) Measurement of the terahertz emission using surface optical rectification with an optical pulsed excitation fluence of 7 mJ/cm

^{2}(1 kHz repetition rate) and a pulse with a wavelength of 800 nm and a duration of 90 fs. (

**c**) Simplified sketch of the photo-Dember process in InAs. The absorption of an ultrashort pulse generates a high density of photogenerated hole–electron pairs within the optical penetration depth (140 nm). The fast diffusion of the electrons induces a transient current J

_{THz}, which is the source of the terahertz emission. (

**d**) Measurement of the terahertz emission by photo-Dember mechanism with an optical pulsed excitation fluence of 0.28 µJ/cm

^{2}(80 MHz repetition rate) and pulse with a wavelength of 800 nm and a duration of 140 fs.

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**MDPI and ACS Style**

Totero Gongora, J.S.; Olivieri, L.; Peters, L.; Tunesi, J.; Cecconi, V.; Cutrona, A.; Tucker, R.; Kumar, V.; Pasquazi, A.; Peccianti, M.
Route to Intelligent Imaging Reconstruction via Terahertz Nonlinear Ghost Imaging. *Micromachines* **2020**, *11*, 521.
https://doi.org/10.3390/mi11050521

**AMA Style**

Totero Gongora JS, Olivieri L, Peters L, Tunesi J, Cecconi V, Cutrona A, Tucker R, Kumar V, Pasquazi A, Peccianti M.
Route to Intelligent Imaging Reconstruction via Terahertz Nonlinear Ghost Imaging. *Micromachines*. 2020; 11(5):521.
https://doi.org/10.3390/mi11050521

**Chicago/Turabian Style**

Totero Gongora, Juan S., Luana Olivieri, Luke Peters, Jacob Tunesi, Vittorio Cecconi, Antonio Cutrona, Robyn Tucker, Vivek Kumar, Alessia Pasquazi, and Marco Peccianti.
2020. "Route to Intelligent Imaging Reconstruction via Terahertz Nonlinear Ghost Imaging" *Micromachines* 11, no. 5: 521.
https://doi.org/10.3390/mi11050521