[Paper Review] Generation of spatiotemporal optical vortices with partial temporal coherence

Amal Mirando, Yimin Zang+2 more|arXiv (Cornell University)|Mar 23, 2021

Orbital Angular Momentum in Optics27 references31 citations

TL;DR

This paper demonstrates the generation of spatiotemporal optical vortices (STOVs) with transverse orbital angular momentum using partially coherent light sources, such as amplified spontaneous emission (ASE) or noise-like pulses, instead of expensive mode-locked lasers. By applying a spiral phase to broadband, temporally incoherent pulses via a spatial light modulator, the authors experimentally verify STOVs with topological charges l = ±1 and l = +2 through interference-based phase transition measurements, proving that partial temporal coherence enables stable, low-cost STOV generation.

ABSTRACT

Recently, a spatiotemporal optical vortex (STOV) with a transverse orbital angular momentum (OAM) has been generated from coherent ultrafast pulses using mode-locked lasers. In contrast, we demonstrate theoretically and experimentally that a STOV can be generated from a light source with partial temporal coherence with fluctuating temporal phase. By eliminating the need of mode-locked laser sources, the partially coherent STOV will serve as a convenient and cost-effective transverse OAM source.

Motivation & Objective

• To develop a low-cost alternative to mode-locked lasers for generating spatiotemporal optical vortices (STOVs) with transverse orbital angular momentum (OAM).
• To investigate whether STOVs can be generated from partially coherent temporal sources such as ASE or noise-like pulses (NLPs), which lack stable phase relationships.
• To experimentally verify the existence of phase singularities and topological charge in partially coherent STOVs using interference-based detection with a time-delayed reference beam.
• To demonstrate that higher-order STOVs (l > 1) spontaneously split into multiple fundamental vortices due to random phase fluctuations, even without propagation.

Proposed method

• Modeling partially coherent pulses using a Gaussian spectrum with randomly distributed spectral phase, where the variance σ² controls the degree of temporal incoherence.
• Applying a spiral phase 𝑒𝑖𝑙𝜙 in the spatial-frequency domain via a 2D spatial light modulator (SLM) to generate STOVs from broadband, partially coherent sources.
• Numerically simulating STOVs using a 2D Fourier transform of the pulse envelope with random spectral phase, using equation 𝐴(𝑡) = 𝐹𝑇{𝑒−𝜔²/𝑟² 𝑒^{𝑗𝜙𝑟𝑎𝑛𝑑(𝜔)}}, where 𝜙𝑟𝑎𝑛𝑑(𝜔) ~ 𝑁(𝜇, 𝜎²).
• Measuring phase singularities via interference fringes between a reference beam and the object STOV, using a time-delayed reference beam and CCD detection, as described by the interference integral in equation (3).
• Using the time-averaged Poynting vector <𝑺> ∝ 𝑖(𝑢∇𝑢∗ − 𝑢∗∇𝑢)/2 + 𝑘|𝑢|²𝒛 to visualize vortex structures and singularities in the spatiotemporal domain.
• Experimentally generating STOVs using ASE from a Yb-doped fiber laser operated below threshold and from a noise-like pulse (NLP) state, both exhibiting high spatial and partial temporal coherence.

Experimental results

Research questions

• RQ1 Can spatiotemporal optical vortices (STOVs) be generated using partially coherent light sources instead of mode-locked lasers?
• RQ2 How does random temporal phase fluctuation affect the stability and structure of STOVs with topological charge l > 1?
• RQ3 Can phase singularities in partially coherent STOVs be experimentally verified using interference-based detection with a time-delayed reference beam?
• RQ4 What is the impact of increasing temporal incoherence (σ²) on the formation and morphology of STOVs?
• RQ5 Can STOVs with topological charge l = 2 be generated and resolved into multiple fundamental vortices due to intrinsic phase randomness?

Key findings

• Partially coherent STOVs with topological charge l = 1 were successfully generated and experimentally verified using ASE and NLP sources, with clear phase transitions observed in interference patterns.
• For l = 1, a single π phase transition was observed in interference fringes, confirming the presence of a single phase singularity, with coherent time ~450 fs based on 8 nm bandwidth.
• For l = 2, two distinct π phase transitions were observed in the interference pattern, confirming the splitting of the high-order vortex into two fundamental vortices due to random phase fluctuations.
• Numerical simulations showed that increasing σ² from 0.2π² to π² severely distorts the ring-shaped STOV profile, introducing multiple amplitude peaks and singularities across the temporal domain.
• The experimental phase transition patterns for l = +1 and l = +2 matched theoretical predictions, with time delays of -68 fs, 0 fs, and 32 fs (l = +1), and multiple delays spanning -216 fs to 180 fs (l = +2), confirming vortex order.
• The method enables low-cost STOV generation using broadband sources like LEDs or fiber laser ASE, eliminating the need for expensive mode-locked lasers.