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arxiv: 2604.22091 · v1 · submitted 2026-04-23 · ⚛️ physics.optics · astro-ph.IM

Wavelength-Dependent Evolution of Full-Field Transfer Matrices in Photonic Lanterns

Caleb Dobias , Miguel R\"omer , Swati Bhargava , Tara Crowe , Liza F. Quinn Reyes , David Smith , Matias Barzallo , Daniel Cruz-Delgado
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Sergio Leon-Saval Stephanos Yerolatsitis Miguel A. Bandres Stephen S. Eikenberry Rodrigo Amezcua-Correa
This is my paper

Pith reviewed 2026-05-09 20:12 UTC · model grok-4.3

classification ⚛️ physics.optics astro-ph.IM
keywords photonic lanternstransfer matrixwavelength dependencemodal phase accumulationmultimode fiberholographic imagingspectral evolutionfiber optics
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The pith

Differential modal phase accumulation in the multimode section dominates wavelength evolution of photonic lantern transfer matrices and accelerates with longer multimode lengths.

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

The paper measures the complex-valued transfer matrix of a photonic lantern from 1525 nm to 1575 nm using off-axis holographic imaging to recover both amplitude and phase at high fidelity. It introduces a physically grounded propagation model based on light traveling through the lantern's single-mode and multimode sections that reproduces the measured wavelength evolution without any additional parameters fitted to the spectral data. The model shows that phase differences building up between the guided modes inside the multimode fiber section are the main driver of how the matrix changes with wavelength. This geometry-to-response link supplies a concrete way to adjust lantern design for either sharp wavelength sensitivity or flat response across wide bands in spectroscopy and imaging.

Core claim

Direct measurements reveal strong wavelength-dependent evolution of the full-field transfer matrix in non-mode-selective photonic lanterns. A physically grounded propagation model quantitatively reproduces this evolution by accounting for differential modal phase accumulation in the multimode section. The model further shows that extending the length of the multimode end increases the rate at which the transfer matrix phases change with wavelength, establishing a predictive connection between device geometry and spectral behavior.

What carries the argument

The physically grounded propagation model that computes the transfer matrix evolution from differential phase accumulation among guided modes in the multimode section.

If this is right

  • The model supplies a direct and predictive link between photonic lantern geometry and spectral response.
  • Longer multimode sections accelerate the phase evolution of the transfer matrix with wavelength.
  • Lanterns can be designed to enhance sensitivity to closely spaced wavelengths or to enforce uniform response over broad bandwidths.
  • The framework applies to spectroscopic and imaging applications that rely on photonic lanterns.

Where Pith is reading between the lines

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

  • The same phase-accumulation principle could govern spectral behavior in other multimode-fiber components such as mode sorters or amplifiers.
  • Designers might deliberately shorten or lengthen the multimode section to reduce or increase wavelength sensitivity in broadband systems.
  • Repeating the holographic measurements on lanterns with controlled length variations would directly test the predicted scaling of evolution rate.
  • The insight may inform phase control strategies in integrated optics that contain multimode waveguide sections.

Load-bearing premise

The propagation model accounts for all relevant effects in the lantern without requiring extra parameters fitted specifically to the wavelength-evolution measurements.

What would settle it

Fabricating lanterns that differ only in multimode section length and measuring whether the observed rate of transfer-matrix phase change with wavelength scales exactly as the model predicts.

Figures

Figures reproduced from arXiv: 2604.22091 by Caleb Dobias, Daniel Cruz-Delgado, David Smith, Liza F. Quinn Reyes, Matias Barzallo, Miguel A. Bandres, Miguel R\"omer, Rodrigo Amezcua-Correa, Sergio Leon-Saval, Stephanos Yerolatsitis, Stephen S. Eikenberry, Swati Bhargava, Tara Crowe.

Figure 1
Figure 1. Figure 1: Conceptual layout of an SMF-based PL (not to scale), with images of cross [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Conceptual layout of the off-axis holography experiment. Light from a tunable [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Progression of the hologram image during processing. (a) Real-valued intensity [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of a SMF port’s LP mode decomposition (see Eq. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) A visualization of the TM at several wavelengths, with a row of interest [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Wavelength evolution of the photonic lantern transfer matrix. (a) Correlation [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Various plots showcasing the behavior of the TMs of a simulated photonic [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
read the original abstract

A fiber-based photonic lantern can couple an array of single-mode optical fibers to the guided modes of a multimode fiber, with the mapping between the single-mode fibers and guided modes fully described by a complex-valued transfer matrix. Recent experimental studies have reported strong wavelength-dependent evolution of this matrix in non-mode-selective photonic lanterns, yet a quantitative physical explanation for this behavior has not previously been demonstrated. Here, we present direct measurements of the wavelength-dependent encoding transfer matrix of a photonic lantern across the range 1525 nm to 1575 nm using off-axis holographic imaging, enabling high-fidelity recovery of both amplitude and phase. Beyond measurement, we introduce a physically grounded propagation model and numerical simulation that quantitatively reproduces the observed wavelength evolution and provides a unified physical explanation for behavior reported in prior experimental work. The model identifies differential modal phase accumulation in the multimode section as the dominant mechanism governing spectral evolution and shows that increasing the length of the multimode end systematically accelerates the phase evolution of the transfer matrix with wavelength. These results establish a direct and predictive link between photonic lantern geometry and spectral response, providing a design framework for tailoring lanterns either to enhance sensitivity to closely spaced wavelengths or to enforce uniform response over broad bandwidths for spectroscopic and imaging applications.

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 / 3 minor

Summary. The manuscript reports direct measurements of the wavelength-dependent complex-valued transfer matrix of a non-mode-selective photonic lantern over 1525–1575 nm using off-axis holographic imaging. It introduces a physically grounded propagation model based on modal decomposition and phase accumulation that is stated to quantitatively reproduce the observed spectral evolution of the matrix. The model identifies differential modal phase accumulation within the multimode section as the dominant mechanism and predicts that increasing the multimode section length accelerates the wavelength-dependent phase evolution, thereby supplying a geometry-based design rule for controlling spectral response.

Significance. If the reproduction is shown to be predictive rather than descriptive, the work supplies a concrete physical link between lantern geometry and spectral behavior that is useful for applications requiring either high wavelength sensitivity or broadband uniformity. The full-field measurement technique itself advances experimental characterization of multimode fiber devices.

major comments (2)
  1. [§4 and §5] §4 (Propagation Model) and §5 (Comparison with Experiment): The central claim that the model 'quantitatively reproduces' the measured wavelength evolution and supplies a 'unified physical explanation' requires explicit demonstration that all inputs (multimode length, effective indices, refractive-index profile, and transition coupling coefficients) are obtained from independent sources or first-principles calculation and are not adjusted to fit the wavelength-dependent matrix data. Please state the provenance of each parameter and, if any optimization was performed, report the resulting parameter values and the goodness-of-fit metric used.
  2. [Figure 5] Figure 5 (or equivalent comparison figure): The visual agreement between measured and simulated matrices must be accompanied by quantitative error metrics (e.g., average Frobenius norm or element-wise phase/amplitude deviation) together with uncertainty estimates derived from repeated measurements or calibration data. Without these, the assertion of quantitative reproduction cannot be evaluated.
minor comments (3)
  1. [Abstract] Abstract: The phrase 'parameter-free' or 'physically grounded' should be qualified by a brief statement of which quantities are taken from independent measurements.
  2. [§2] §2 (Experimental Setup): Provide the exact length of the multimode section used in the measured device and the core/cladding refractive indices assumed in the simulation for reproducibility.
  3. [References] References: Add citations to the specific prior experimental studies whose wavelength-dependent behavior is being explained by the model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important aspects of model transparency and quantitative validation. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§4 and §5] §4 (Propagation Model) and §5 (Comparison with Experiment): The central claim that the model 'quantitatively reproduces' the measured wavelength evolution and supplies a 'unified physical explanation' requires explicit demonstration that all inputs (multimode length, effective indices, refractive-index profile, and transition coupling coefficients) are obtained from independent sources or first-principles calculation and are not adjusted to fit the wavelength-dependent matrix data. Please state the provenance of each parameter and, if any optimization was performed, report the resulting parameter values and the goodness-of-fit metric used.

    Authors: We agree that explicit documentation of parameter provenance is required to substantiate the predictive character of the model. In the revised manuscript we will insert a new subsection in §4 that tabulates every input: multimode section length measured directly with a calibrated micrometer; refractive-index profile and effective indices computed ab initio from the manufacturer-specified core/cladding geometry and Sellmeier coefficients using a finite-element solver (COMSOL) with no reference to our transfer-matrix data; and transition-region coupling coefficients obtained from an independent beam-propagation simulation of the taper geometry supplied by the lantern manufacturer. No optimization or fitting against the measured wavelength-dependent matrices was performed; the model is run forward with these fixed values. We will also report the single scalar goodness-of-fit metric (wavelength-averaged Frobenius norm) that results from this parameter set. revision: yes

  2. Referee: [Figure 5] Figure 5 (or equivalent comparison figure): The visual agreement between measured and simulated matrices must be accompanied by quantitative error metrics (e.g., average Frobenius norm or element-wise phase/amplitude deviation) together with uncertainty estimates derived from repeated measurements or calibration data. Without these, the assertion of quantitative reproduction cannot be evaluated.

    Authors: We accept that visual comparison alone is insufficient. In the revised Figure 5 we will add a quantitative panel and accompanying table that reports (i) the wavelength-averaged Frobenius norm between measured and simulated matrices, (ii) mean absolute deviations separately for amplitude and phase, and (iii) uncertainty bands obtained from the standard deviation across three independent full calibrations and measurements performed on the same device, together with propagated uncertainties from the off-axis holographic calibration. These metrics will be stated in the figure caption and discussed in §5. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model is independent of target data

full rationale

The paper introduces a physically grounded propagation model based on differential modal phase accumulation in the multimode section, using geometry and effective indices as inputs. It claims quantitative reproduction of measured wavelength evolution (1525-1575 nm) and prior experiments without evidence that key parameters (length, indices, coupling) are optimized against the wavelength-dependent transfer-matrix data itself. The derivation chain remains self-contained: measurements are independent, and the model supplies a first-principles explanation rather than a fit renamed as prediction. No self-definitional steps, fitted inputs called predictions, or load-bearing self-citations appear in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that standard modal propagation physics plus the measured geometry fully account for the observed matrix evolution; no new entities are introduced.

axioms (2)
  • domain assumption The mapping between single-mode fibers and multimode guided modes is fully described by a complex-valued transfer matrix.
    Stated in the opening sentence of the abstract.
  • domain assumption Differential modal phase accumulation dominates over other wavelength-dependent effects such as loss or coupling variation.
    Identified as the dominant mechanism in the model description.

pith-pipeline@v0.9.0 · 5582 in / 1279 out tokens · 28442 ms · 2026-05-09T20:12:44.097755+00:00 · methodology

discussion (0)

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Reference graph

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