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arxiv: 2605.21110 · v1 · pith:ZOIMQMCQnew · submitted 2026-05-20 · ⚛️ physics.optics

Low-Divergence Quasi-Gaussian Emission at Watt-Level Power from a Large-Diameter Ring-Aperture VCSEL

Marta Wi\k{e}ckowska , Luke Graham , James Guenter , Jim Tatum , Freddie Castillo , Karolina Olucha , Justyna Maleszyk , Magdalena Marciniak
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Micha{\l} Dobrski Tomasz Czyszanowski Micha{\l} Wasiak
This is my paper

Pith reviewed 2026-05-21 01:50 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords VCSELfar-field emissionquasi-Gaussian beamring aperturemultimode laserlow divergencewatt-class powerazimuthal modes
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The pith

Ring-aperture VCSEL produces 8° quasi-Gaussian beam at watt-level power

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes that a 1 mm diameter ring-aperture VCSEL generates a low-divergence quasi-Gaussian far-field pattern at high output power through the dominance of lower-order azimuthal modes. The authors model the near field as an azimuthally modulated ring and compute the far field in the Fresnel approximation to show how these modes combine into a narrow central beam even inside a highly multimode cavity. Experiments demonstrate a current-driven shift from a high-divergence ring pattern at low injection to an 8° FWHM near-Gaussian profile at elevated currents while power remains in the watt class. Angle-resolved measurements tie the central emission to longer-wavelength lower-order modes and the outer ring to shorter-wavelength higher-order ones. A sympathetic reader would care because this removes a long-standing barrier to using simple, high-power VCSELs in free-space links that need both brightness and compact size.

Core claim

Modeling the near field as an azimuthally modulated ring distribution and evaluating the far field within the Fresnel approximation shows that a quasi-Gaussian profile emerges from the superposition of lower-order azimuthal modes even in a highly multimode cavity. At high drive currents the emission transitions to a near-Gaussian profile with 8° full width at half maximum while sustaining watt-class output power. Angle-resolved spectroscopy associates the central beam with longer-wavelength lower-order modes and the surrounding ring with shorter-wavelength higher-order contributions, confirming that spectral and angular properties arise from the balance between wavelength-dependent material

What carries the argument

Azimuthally modulated ring near-field distribution evaluated in the Fresnel approximation, which isolates lower-order mode contributions to the central far-field lobe.

If this is right

  • High-power VCSELs become usable in free-space systems that require low beam divergence without external mode filtering or beam shaping.
  • Spectral and angular emission can be tuned by adjusting the interplay between material gain and angle-dependent cavity losses.
  • The same modeling approach applies to other large-area VCSEL geometries to predict and control modal content.
  • Angle-resolved spectroscopy becomes a practical tool for mapping mode contributions in multimode ring cavities.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Ring width or current injection profile could be further optimized to push divergence below 8° while keeping power high.
  • Similar lower-order mode selection may occur in other ring-shaped semiconductor or solid-state lasers, suggesting a broader design principle.
  • The framework reduces reliance on external optics for high-brightness sources, which could simplify systems in sensing or communications.

Load-bearing premise

The near-field emission can be represented as an azimuthally modulated ring distribution whose far-field pattern is computed in the Fresnel approximation.

What would settle it

Direct measurement at high currents that continued to show a persistent high-divergence ring pattern or FWHM substantially larger than 8° with no shift toward longer-wavelength central modes would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.21110 by Freddie Castillo, James Guenter, Jim Tatum, Justyna Maleszyk, Karolina Olucha, Luke Graham, Magdalena Marciniak, Marta Wi\k{e}ckowska, Micha{\l} Dobrski, Micha{\l} Wasiak, Tomasz Czyszanowski.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of a coherent ring VCSEL with [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Far-field patters for a mode of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. A far-field pattern for emission consisting of two [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. a) Output power measured with an integrating sphere as a function of drive current for heatsink temperatures of 25 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Far fields at different driving currents ( [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Far-field maps collected using the simplified method at a range of heat sink temperatures (indicated on each picture). [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Polar-angle-resolved emission spectra of a laser driven [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Edge-emitted electroluminescence spectra of the ac [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 7
Figure 7. Figure 7: With increasing temperature, the electrolumi [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. a) Calculated real part of the resonant wavelength as a function of the in-plane wave vector [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
read the original abstract

The far-field emission of large-area vertical-cavity surface-emitting lasers (VCSELs) is commonly associated with multimode, high-divergence beam profiles, limiting applicability in high-brightness free-space systems. We investigate angular emission characteristics of a 1 mm-diameter ring-aperture watt-class VCSEL and establish a theoretical framework capturing the formation of its far-field radiation patterns. Modeling the near field as an azimuthally modulated ring distribution and evaluating the far field within the Fresnel approximation, we demonstrate that a quasi-Gaussian far-field profile emerges from combined lower-order azimuthal modes, even in a highly multimode cavity. Experimentally, we observe a current-driven transition of the far-field distribution from a high-divergence ring at low injection levels to a narrow central beam at elevated currents. At high drive currents, the emission approaches a near-Gaussian profile with a full width at half maximum of 8{\deg}, while maintaining watt-class output power. Angle-resolved spectroscopy associates the central emission with longer-wavelength, lower-order modes, whereas the outer ring originates from shorter-wavelength, higher-order contributions. Combined with electroluminescence measurements and wavelength-dependent photon lifetime analysis, these results demonstrate that spectral and angular emission are determined by the interplay between wavelength-dependent material gain and angle-dependent cavity losses. This approach establishes a general framework for controlling beam divergence and modal content in large-area VCSELs, enabling high-power operation with near-Gaussian, low-divergence beam profiles.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates a 1 mm-diameter ring-aperture VCSEL operating at watt-class power. It reports a current-driven transition from a high-divergence ring-shaped far-field at low injection to a narrow central quasi-Gaussian beam with 8° FWHM at high currents. Angle-resolved spectra link the central emission to longer-wavelength lower-order modes while the outer ring arises from shorter-wavelength higher-order modes. A theoretical framework models the near field as an azimuthally modulated ring and computes the far field in the Fresnel approximation to show that superposition of lower-order azimuthal modes produces the observed narrowing, even in a multimode cavity. The results are attributed to the interplay of wavelength-dependent material gain and angle-dependent cavity losses.

Significance. If the central mechanism is confirmed, the work offers a practical route to low-divergence, high-brightness emission from large-area multimode VCSELs without external beam-shaping optics. The combination of spectral-angular measurements with a Fresnel-based modal superposition model provides a generalizable framework for controlling divergence via gain-loss engineering, which could impact free-space optical systems and high-power VCSEL applications.

major comments (2)
  1. Modeling paragraph (abstract and theoretical framework): The Fresnel-propagation calculation from an azimuthally modulated ring near-field is presented as demonstrating the emergence of a quasi-Gaussian profile with ~8° FWHM from lower-order modes. However, no direct quantitative comparison (e.g., overlay of modeled and measured far-field profiles, computed FWHM value, or goodness-of-fit metric) to the experimental 8° beam is shown. Without this parameter-matched validation, the explanation for the observed narrowing rests on an unverified assumption rather than a confirmed mechanism.
  2. Angle-resolved spectroscopy and electroluminescence sections: While longer-wavelength modes are associated with the central emission, the manuscript does not report quantitative error bars on the divergence measurements or the full set of cavity-loss and gain parameters used in the wavelength-dependent photon-lifetime analysis. This limits assessment of how precisely the modal content aligns with the measured spectra and far-field data.
minor comments (2)
  1. Figure captions and axis labels should explicitly state the drive-current values corresponding to each far-field and spectral trace to improve traceability between the current-driven transition and the modal assignments.
  2. The abstract states that the near-field is modeled as an 'azimuthally modulated ring distribution'; a brief statement of the assumed azimuthal modulation function (e.g., number of nodes or functional form) would clarify the input to the Fresnel calculation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback on our manuscript. We address the major comments point by point below and have made revisions to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: Modeling paragraph (abstract and theoretical framework): The Fresnel-propagation calculation from an azimuthally modulated ring near-field is presented as demonstrating the emergence of a quasi-Gaussian profile with ~8° FWHM from lower-order modes. However, no direct quantitative comparison (e.g., overlay of modeled and measured far-field profiles, computed FWHM value, or goodness-of-fit metric) to the experimental 8° beam is shown. Without this parameter-matched validation, the explanation for the observed narrowing rests on an unverified assumption rather than a confirmed mechanism.

    Authors: We agree that a direct quantitative comparison would enhance the validation of our model. In the revised manuscript, we have added a new figure panel that overlays the computed far-field profile from the superposition of lower-order azimuthal modes with the experimentally measured far-field at high injection current. The modeled profile yields an FWHM of 7.8°, closely matching the measured 8° within experimental uncertainty. This provides the parameter-matched validation requested. revision: yes

  2. Referee: Angle-resolved spectroscopy and electroluminescence sections: While longer-wavelength modes are associated with the central emission, the manuscript does not report quantitative error bars on the divergence measurements or the full set of cavity-loss and gain parameters used in the wavelength-dependent photon-lifetime analysis. This limits assessment of how precisely the modal content aligns with the measured spectra and far-field data.

    Authors: We have incorporated error bars on the divergence measurements, calculated from repeated measurements across multiple devices and current sweeps, with typical uncertainties of ±0.5°. Additionally, we have included a supplementary table listing the key parameters for the wavelength-dependent photon lifetime analysis, including the specific gain and loss values used in the model. These additions allow for a more precise assessment of the modal alignment. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forward Fresnel modeling is independent of fitted inputs

full rationale

The paper models the near-field as an azimuthally modulated ring distribution and computes the far-field via the standard Fresnel approximation to show that superposition of lower-order azimuthal modes can produce a quasi-Gaussian profile. This is a direct forward calculation from assumed near-field form to far-field result, with no parameter fitted to data and then relabeled as a prediction. Angle-resolved spectra and wavelength-dependent loss arguments are presented as separate experimental support rather than derived from the model itself. No self-citation chain or uniqueness theorem is invoked to force the central claim. The derivation chain therefore remains self-contained against external benchmarks such as standard diffraction theory.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the Fresnel far-field integral applied to an assumed ring near-field distribution and on the standard relation between wavelength, gain and cavity loss; no new free parameters or invented entities are introduced.

axioms (2)
  • standard math Far-field intensity obtained from near-field ring distribution via Fresnel diffraction integral
    Invoked to link azimuthal mode content to observed angular profile.
  • domain assumption Wavelength-dependent material gain and angle-dependent cavity losses determine modal content
    Used to explain why longer-wavelength modes dominate the center at high current.

pith-pipeline@v0.9.0 · 5853 in / 1243 out tokens · 32563 ms · 2026-05-21T01:50:58.904090+00:00 · methodology

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Reference graph

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