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Invertible mapping between structured light and vector terahertz emission

This paper establishes a unified, invertible framework for generating and synthesizing vector terahertz beams by mapping the spatial and polarization properties of structured femtosecond optical fields onto coherent photocurrents in semiconductors, thereby enabling deterministic, inverse-designed control over terahertz emission patterns.

Original authors: Amirreza Sadeghpour, Daryoush Abdollahpour

Published 2026-08-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Amirreza Sadeghpour, Daryoush Abdollahpour

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Terahertz radiation occupies a quiet, often overlooked slice of the electromagnetic spectrum, sitting between the microwaves used in radar and the infrared light felt as heat. While this region holds great promise for seeing through clothing without harm, identifying hidden chemicals, or sending data at incredible speeds, it has long been difficult to master. The challenge lies not just in creating these waves, but in shaping them. Scientists have struggled to control the precise direction, intensity, and polarization of terahertz light, often finding that the waves emerge in messy, unpredictable patterns rather than the clean, focused beams needed for advanced technology. To solve this, researchers must find a way to command the very source of the radiation, turning a chaotic burst of energy into a carefully sculpted tool.

A team of physicists in Iran has now established a unified method to do exactly that, creating a bridge between the complex world of structured light and the generation of terahertz radiation. Their work centers on a semiconductor material called gallium arsenide, which acts as a highly sensitive canvas for light. When this material is hit by two specific pulses of laser light—one at a standard frequency and another at double that frequency—something remarkable happens inside the crystal. The electrons within the material do not simply absorb the energy; they are pushed into a state of quantum interference. Imagine two paths leading to the same destination, where the traveler's choice of path depends on the timing of their steps. In this case, the electrons can reach a higher energy state by absorbing one photon of the stronger light or two photons of the weaker light simultaneously. By carefully adjusting the relative timing, or phase, between these two light pulses, the researchers can force the electrons to move in a specific direction, creating a sudden, ultrafast surge of electric current.

This surge of current is the key. Because it happens in a fraction of a second, it acts like a tiny, transient antenna that flings out terahertz waves. The researchers discovered that the shape and polarization of the incoming laser light are directly copied onto this burst of current. If the laser light is shaped into a cylinder with a specific swirling pattern, the current inside the semiconductor flows in that same pattern. Consequently, the terahertz waves that fly out into the distance carry that same intricate structure. The team demonstrated this by using special laser beams known as cylindrical vector beams and full Poincaré beams, which have polarization that changes from point to point across the beam. When these beams hit the semiconductor, they generated terahertz waves with matching, complex shapes, including fields that rotate or form distinct lobes. In their simulations, these methods produced magnetic fields in the near vicinity of the material reaching up to 0.8 millitesla, and far-field electric fields strong enough to be useful for imaging and communication.

However, the most significant leap in this work is not just predicting what happens when a specific light hits the material, but reversing the process entirely. The researchers developed a new design strategy that starts with the desired outcome. Instead of asking, "What terahertz beam will this laser create?" they asked, "What laser do we need to create this specific terahertz beam?" By working backward from a target pattern—such as a beam that looks like two separate spots or a non-spreading ring—they calculated the exact distribution of electric current required to produce it. They then determined the precise shape and phase of the laser pulses needed to drive the electrons into that exact current pattern. This inverse design approach means that scientists can now program the terahertz source to emit any shape they desire, simply by adjusting the optical input.

The study confirms that this relationship is flexible and powerful. In one striking demonstration, the team showed that a complex terahertz field, which previously required a highly complicated laser beam with swirling polarization to create, could be reproduced using a much simpler, uniform laser beam. By only changing the timing and intensity of the light across the beam's face, they could force the semiconductor to generate the same intricate current pattern. This finding suggests that the complexity of the output does not strictly require a complex input; rather, the control lies in the precise coordination of the light's phase. The researchers validated these results through detailed computer simulations, showing that the method works for various beam shapes, including those that mimic the behavior of Bessel beams or create specific polarization patterns.

This work effectively turns the semiconductor into a reconfigurable antenna for terahertz waves. By mastering the quantum interference that drives the current, the researchers have provided a systematic way to engineer the amplitude, phase, and polarization of terahertz radiation. The implications are substantial for the future of this technology. It offers a route to compact, all-optical sources that can be tuned on the fly, potentially revolutionizing how we image materials, secure communications, or analyze chemical signatures. The ability to map a desired terahertz pattern directly back to the laser settings required to create it transforms the field from one of trial and error into a precise design discipline, opening the door to a new generation of programmable terahertz devices.

Technical Summary: Invertible Mapping Between Structured Light and Vector Terahertz Emission

Problem Statement
Terahertz (THz) radiation is a valuable tool for ultrafast spectroscopy, imaging, and communication; however, achieving deterministic control over the spatial and polarization structure of THz beams remains a significant challenge. While various generation methods exist (e.g., optical rectification, two-color filamentation), producing THz waves with tailored amplitude, phase, and polarization profiles in the far-field is difficult. Specifically, there is a gap in understanding how to systematically design the optical excitation required to synthesize a specific, complex vector THz field, particularly in the far-field region based on current distributions in semiconductors.

Methodology
The authors establish a unified framework linking structured optical fields to vector THz emission via coherent control of ultrafast photocurrents in low-temperature-grown Gallium Arsenide (LT-GaAs). The approach is divided into two complementary parts:

Forward Modeling (Part I):
- Physical Mechanism: The study utilizes quantum interference between one-photon ( $2\hbar\omega$ ) and two-photon ( $\hbar\omega + \hbar\omega$ ) excitation pathways. By illuminating the semiconductor with coherent fundamental ( $\omega$ ) and second-harmonic ( $2\omega$ ) pulses, the relative phase ( $\gamma$ ) between them controls the symmetry breaking of the carrier distribution, generating a directional photocurrent without external bias.
- Input Beams: The authors model the excitation using structured vector beams, specifically Cylindrical Vector Beams (CVBs) and Full Poincaré Beams (FPBs), which possess spatially varying polarization and phase profiles.
- Simulation: The photocurrent density is calculated using a current injection rate equation derived from quantum interference theory. This transient current is treated as a source for electromagnetic radiation. The near-field magnetic response and the far-field THz electric field are computed using retarded vector potentials and vector diffraction theory.
Inverse Design (Part II):
- Reconstruction Strategy: The authors introduce an inverse-design methodology to determine the necessary optical excitation for a desired far-field THz pattern.
- Process: Starting with a target far-field electric field distribution ( $E_{FF}$ ), the method back-propagates the field to the source plane to reconstruct the required near-field distribution and the corresponding source current density ( $J$ ).
- Synthesis: Using the relationship between current direction and the relative phase of the excitation fields, the authors derive the required spatial phase profile ( $\gamma(r)$ ) for the second-harmonic beam. They propose a simplified experimental configuration where a uniform, collimated fundamental beam acts as a global bias, while the spatial amplitude and phase of the second-harmonic beam are shaped to synthesize the target current.

Key Contributions

Unified Framework: The paper establishes a direct, invertible mapping between the spatial phase/polarization structure of femtosecond vector beams and the magnitude/orientation of injected photocurrents in semiconductors.
Forward Demonstration: The authors demonstrate that structured optical fields (CVBs and FPBs) can drive spatially structured photocurrents, resulting in vector THz emission that preserves the symmetry and topology of the input beams.
Inverse-Design Methodology: A systematic strategy is introduced to reconstruct the required current distribution and the corresponding optical excitation profiles from a desired THz field pattern. This transforms THz beam shaping from a predictive problem into a programmable design problem.
Non-Uniqueness of Mapping: The study reveals that the mapping between optical excitation and THz emission is non-unique. Complex vector THz fields originally generated by structured vector beams can be recreated using standard circularly polarized beams if the spatial amplitude and relative phase are appropriately modulated.

Results

Cylindrical Vector Beams (CVBs): Simulations show that azimuthally and radially polarized CVBs generate matching azimuthal and radial current distributions. The azimuthal current creates a transient circulating loop, producing a strong longitudinal magnetic field ( $>0.8$ mT) in the near-field and preserving the vector polarization symmetry in the far-field (peak amplitude $\approx 0.52$ kV/cm at 2 THz).
Full Poincaré Beams (FPBs): "Lemon" and "Star" FPBs generate complex, non-uniform current patterns. The study analytically explains the formation of current nodes (destructive interference) and the resulting topological inversion in the far-field polarization. FPBs yield higher peak electric fields ( $\approx 1$ kV/cm) compared to CVBs due to constructive interference of the dominant Gaussian core component.
Inverse Synthesis: The inverse framework successfully reconstructed the optical parameters needed to generate:
- A dual-Gaussian-lobe THz pattern with opposite circular polarizations.
- A non-diffracting zeroth-order Bessel-Gaussian THz beam.
- The complex vector field of a "lemon" FPB, but using a completely different optical input (uniform polarization with structured amplitude and phase).
Validation: The reconstructed current distributions in the inverse examples matched exactly with the forward-modeling results, confirming the internal consistency and validity of the inverse approach.

Significance
The paper claims to bridge structured light, quantum interference control, and THz photonics. By establishing a direct and invertible correspondence between optical excitation and vector THz emission, the work provides a route toward compact, all-optical, and reconfigurable THz sources with engineered amplitude, phase, and polarization profiles. The ability to decouple input polarization complexity from output vector topology allows for the generation of designer THz fields using standard optical components and phase modulation, offering a systematic design strategy for applications in ultrafast spectroscopy, polarization-resolved imaging, and structured THz communications. The authors position this as a step toward programmable ultrafast optoelectronic functionality.

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