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Ultrashort pulsed laser atmospheric filament properties and microwave radiation inferred from S-band guided wave interaction and self-emission

This paper characterizes ultrashort pulsed laser-induced atmospheric filaments by measuring their electrical conductivity via S-band waveguide attenuation and self-emission to infer key plasma parameters, ultimately refining the inferred current decay rate by accounting for the filament's actual axial variation in microwave radiation.

Original authors: Edward. L. Ruden, James. E. Wymer, Jennifer. A. Elle, Alex C. Englesbe, Andrain P. Lucero, Erin A. Thornton, Andreas Schmitt-Sody

Published 2026-07-14

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CC BY 4.0

Original authors: Edward. L. Ruden, James. E. Wymer, Jennifer. A. Elle, Alex C. Englesbe, Andrain P. Lucero, Erin A. Thornton, Andreas Schmitt-Sody

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

Imagine a laser beam so fast it's like a blink of an eye that never happened, firing a pulse of light into the air. When this ultrashort pulse hits the atmosphere, it doesn't just pass through; it grabs a handful of air molecules, rips their electrons loose, and creates a glowing, ghostly tunnel of plasma called a "filament." This paper is a detective story about what happens inside that invisible tunnel and the strange radio waves it screams out.

The Main Mystery: The Invisible Highway
The researchers set up a giant, hollow copper pipe (a waveguide) and shot their laser right through the middle of it. As the laser zipped through, it left behind a hot, electrically charged trail. To figure out how "electric" this trail was, they sent a steady radio signal (3.2 GHz, which is in the S-band) down the pipe alongside the laser.

Think of the plasma filament like a sticky, electric sponge in the middle of a water hose. When the radio signal hits this sponge, it gets weaker. By measuring exactly how much the signal died down, the team could calculate the electrical conductivity of the plasma. They also took super-fast photos to measure the width of this glowing tunnel, finding it was incredibly thin—about the width of a human hair, or roughly 30 micrometers.

The Big Reveal: The "Scream" of the Electrons
Here is the coolest part: as the laser pulse zipped past, it left the electrons behind, and they didn't just sit there. They surged forward, creating a massive, fleeting electric current. This sudden movement acted like a giant antenna, blasting out microwave radiation.

The team measured this "self-emission" (the plasma's own radio scream) and found something surprising. The total amount of electrical charge moving in this current was surprisingly high—about 0.93 picocoulombs (that's a trillionth of a billionth of a coulomb) for a specific setup.

What They Ruled Out (The "Not-So-Simple" Answer)
You might think, "Okay, the electrons move, they lose energy to heat, and that's it." But the paper explicitly argues against this simple idea.

If the electrons just slowed down normally due to friction with air molecules (a process called Ohmic decay), the current would vanish almost instantly. The math shows that if this were the only thing happening, the radio waves they measured would be way too weak to explain what they saw. In fact, the energy in the radio waves would need to be more than the total energy the laser gave to the electrons to make the math work. Since you can't get more energy out than you put in, the paper rules out the idea that simple friction is the only thing slowing the current down.

Instead, the authors suggest that the current must be sticking around much longer than simple physics predicts. They propose that the electrons are somehow held in a "steady state" or that the current is being pushed to the edges of the filament and diffusing back in, which changes how fast it decays.

The Numbers and the Guesses
The team didn't just guess; they measured. They found that at different air pressures (from a near-vacuum of 1.11 Torr up to 630 Torr), the behavior changed.

At low pressure (1.11 Torr), the current decay rate was around 11 billion times per second.
At high pressure (630 Torr), it was much faster, around 16 billion times per second.

However, when they tried to predict the radio waves using these decay rates, the numbers didn't quite match the real-world measurements from other scientists (specifically a study by Englesbe). The paper suggests that to make the math match the real radio waves, the current must decay even slower than their best models predict. They calculated an "upper bound" decay rate (the slowest it could possibly be) that would result in a perfect energy match, but they admit this is a theoretical limit, not a proven fact.

The Final Picture
The paper concludes that while they can measure the size of the filament, its conductivity, and the total charge it carries, the exact mechanism of how that current fades away is still a bit of a mystery. The simple idea of "friction slowing it down" doesn't work. The current seems to live longer and radiate more efficiently than expected.

They compared their theoretical radio wave patterns to real measurements taken with the same equipment. The shapes matched up nicely, especially the timing of the wave's rise and fall (about 33 picoseconds). But the real-world waves had some extra "ringing" or wobbling that their model didn't capture, suggesting there might be other, more complex oscillations happening that they haven't fully figured out yet.

In short: The laser makes a plasma tunnel, the tunnel screams microwaves, and the scream is louder and lasts longer than simple friction would allow. The team has measured the scream and the tunnel, but the exact reason the current hangs on so long is still a puzzle they are working to solve.

Technical Summary: Ultrashort Pulsed Laser Atmospheric Filament Properties and Microwave Radiation

Problem Statement
Ultrashort pulsed laser (USPL) pulses propagating through air undergo geometric convergence and subsequent Kerr self-focusing, creating plasma filaments. These filaments have been observed to emit microwave radiation with a rotationally symmetric pattern, implying an axial current source. However, the filamentation process is inherently unstable, making the local laser intensity ( $I$ ) and resulting plasma properties difficult to determine directly. While previous studies have observed and simulated this radiation, there remains a need to experimentally infer local and far-field properties—specifically electrical conductivity ( $\sigma$ ), filament radius ( $R$ ), and the time integral of the axial current ( $Q$ )—across a wide range of atmospheric pressures ( $p$ ) to benchmark theoretical models.

Methodology
The authors employed a diagnostic setup involving a 30 mJ, 800 nm Ti:sapphire USPL focused into a pressure-controlled fused quartz tube (inner radius 3.92 mm) that passes orthogonally through an S-band (3.2 GHz) WR284 waveguide. The study utilized three primary measurement techniques:

Conductivity ( $\sigma$ ) via Waveguide Attenuation: The filament's electrical conductivity was measured by observing the attenuation of a TE $_{10}$ mode driven through the waveguide. A calibration table relating the attenuation factor ( $A$ ) to the unit-length conductance ( $G$ ) and filament radius ( $R$ ) was generated using 3-D continuous wave simulations. The actual filament conductivity profile was approximated as Gaussian rather than uniform, with conversion factors derived to match the inductance and conductance of the simulated uniform cylinder.
Filament Radius ( $R$ ) via Imaging: Fast-framing visible light imaging (2 ns gate) captured the filament's radial luminosity profile. These images were used to determine the standard deviation ( $s$ ) of the Gaussian intensity profile. An analytical relationship was derived to equate the inductance of a Gaussian current distribution to that of a uniform cylinder, allowing the determination of an effective radius $R = 1.9243s$ .
Current Time Integral ( $Q$ ) via Self-Emission: The filament's self-emission signal within the waveguide was isolated from the attenuated TE $_{10}$ signal. This signal was calibrated using time-domain simulations of a unipolar current pulse to determine the total charge $Q$ associated with the filament's axial current.

Inferred Properties and Models
Using the measured $\sigma$ , $R$ , and $Q$ , the authors inverted a physical model to infer:

Peak Laser Intensity ( $I_0$ ), Electron Densities ( $n_1, n_2$ ), and Temperature ( $T$ ): By combining the measured conductivity with ionization rate models for $O_2$ and $N_2$ and electron temperature models dependent on peak intensity, the authors determined the local plasma parameters along the filament.
Current Decay Rates ( $\nu$ ): Two theoretical estimates for the current decay rate were calculated:
- $\nu_1$ : Derived from a generalized Ohm's law assuming the current remains distributed throughout the filament cross-section (bulk decay).
- $\nu_0$ : Derived assuming the current is driven to the filament periphery during thermalization and diffuses back in (surface decay).
Far-Field Radiation: The far-field microwave radiation pattern was modeled as a collective effect of the entire filament, treating the axial variation of $Q(z)$ as a source. The model accounted for the time-dependent decay of the current using a convolution of the measured $Q(z)$ with an exponential decay function.

Key Results

Conductivity and Plasma Parameters: The study successfully mapped $\sigma$ , $I_0$ , $n_i$ , and $T$ along a 30 cm filament across pressures ranging from 1.11 to 630 Torr. The results indicated that electron-ion collisions dominate neutral collisions at high intensities ( $I_0 \gtrsim 10^{14}$ W/cm $^2$ ).
Current Decay and Radiation: The theoretical far-field radiation patterns calculated using the measured $Q(z)$ and the decay rates $\nu_1$ and $\nu_0$ resulted in radiated energies ( $K_R$ ) that significantly exceeded the available laser-imparted center-of-mass kinetic energy ( $K_0$ ) for most pressures. This discrepancy suggested that the simple steady-state decay models were insufficient.
Upper Bound on Decay Rate: By assuming 100% conversion of $K_0$ to radiation, the authors inferred a much lower upper bound on the decay rate, $\nu_{max}$ . When $\nu_{max}$ was used in the radiation model, the resulting far-field patterns showed favorable agreement with previously published experimental measurements (Englesbe et al.) taken with similar geometry but different laser energy.
Angle Dependence: The model predicted that radiation intensity drops rapidly as the emission angle $\theta$ increases beyond a minimum angle $\theta_{min}$ (where the principal frequency $f_1$ equals the effective collision frequency). This explains why radiation is strong at low angles for low pressures (where $\theta_{min}$ is large) but weak at the same angles for high pressures (where $\theta_{min}$ is very small, pushing the peak frequency into the THz range).

Significance and Claims
The paper positions itself primarily as a source of experimental benchmarks for 3-D time-domain simulations of laser filamentation and radiation. The authors claim that their direct measurements of $Q(z)$ and $\sigma$ provide a rigorous basis for inferring local plasma properties that are otherwise difficult to access.

The study highlights a critical physical insight: the decay rate $\nu$ required to match experimental radiation data is significantly lower than that predicted by standard Ohmic decay models ( $\nu_1$ or $\nu_0$ ). The authors suggest that a non-steady-state mechanism, which lowers $\nu$ without significantly altering the total charge transfer $Q$ , is necessary to reconcile the measured self-emission with the far-field radiation energy. They explicitly state that their model neglects oscillatory current modes and that the agreement with published data using $\nu_{max}$ serves as a baseline response, while discrepancies (such as "ringing" in experimental data) may be attributed to these neglected modes or horn dispersion.

Ultimately, the work demonstrates that while simple steady-state models can estimate plasma parameters, accurately predicting the far-field microwave emission from laser filaments requires accounting for complex, non-steady current decay dynamics that extend the current lifetime well beyond standard collisional expectations.

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