Researchers have demonstrated an all-fiber mode division multiplexing reconstructive spectrometer that achieves high spectral reconstruction accuracy alongside fine resolution by manipulating spatial mode excitations within a multimode optical fiber. Developed by an engineering team including Junrui Liang, Jun Ye, Pu Zhou, and colleagues, the experimental system incorporates a custom-designed three-by-one mode-selective photonics lantern at the input stage of the fiber to launch distinct spatial modes. Traditional optical spectrometers have long faced an inescapable trade-off where achieving higher spectral resolution requires larger bench-top footprints and lengthened optical dispersion paths. Reconstructive spectrometers based on multimode optical fibers overcome footprint limitations by mapping complex spectral signals into spatial speckle patterns produced by multi-wave interference. However, conventional fiber speckle spectrometers frequently suffer from degraded reconstruction accuracy caused by information loss during spatial encoding. The reported architecture successfully recovered two thousand spectral channels across a two-picometer spectral resolution, reducing reconstruction errors by eighty-eight percent relative to single-mode excitation and fifty percent relative to two-mode excitation schemes.
In conventional bench-top optical spectrometers, instrument accuracy relies on the physical precision of dispersive gratings, optical alignment, and detector arrays, whereas reconstructive speckle systems rely on mathematical decoding of the light transmitted through scattering media. When light propagates through a multimode fiber, modal dispersion causes complex interference among guided modes, mapping input spectra into wavelength-dependent spatial intensity patterns. This encoding mechanism is represented mathematically by the linear system where observed speckle intensity vector I equals the fiber transmission matrix T multiplied by input spectrum vector S. In practice, recording this spatial intensity with an optical camera often results in information loss because the number of independent spatial channels fails to match the high dimensionality of continuous spectra. Earlier strategies sought to expand available channels through wavelength division multiplexing or space division multiplexing using multicore fibers and silicon waveguides. While prior simulation studies indicated that mode division multiplexing could potentially enhance channel capacity, earlier implementations were restricted to coarse spectral resolutions spanning several nanometers.
To overcome these performance barriers, the researchers turned to an all-fiber photonics lantern as a mode multiplexer capable of operating with low insertion losses and minimal crosstalk. Photonics lanterns have previously demonstrated utility across telecommunications for capacity expansion, computational optical imaging, and spatial mode manipulation, presenting seamless physical compatibility with existing all-fiber architectures. In prior speckle reconstructive configurations, planar-integrated lanterns were predominantly deployed at the output facet of waveguides to sample emerging modal fields. In contrast, the current design utilizes the photonics lantern at the input boundary to actively alter the initial modal launching conditions entering the multimode fiber. The custom three-by-one mode-selective lantern was fabricated by tapering a bundle of dissimilar single-mode optical fibers within a low-index capillary glass tube. By deliberately altering the input launching state, the device introduces multiple distinct scattering pathways through the fiber core, thereby encoding spectral information into speckle patterns with substantially greater completeness and preserving information that would otherwise be lost.
The complete experimental apparatus integrates specialized fiber components to ensure precise polarization control and stable mode generation throughout calibration and measurement. A tunable semiconductor laser with a tuning range spanning 1520 to 1567 nanometers, a three-decibel linewidth of five megahertz, and a linearly polarized output delivers narrow-band illumination. Light from the laser enters a segment of polarization-maintaining fiber to ensure linear polarization during the calibration procedure, followed by an in-line fiber polarizer and an additional polarization-maintaining fiber segment before fusing directly to the lantern. The three input single-mode fibers of the photonics lantern possess distinct core dimensions to synthesize specific spatial modes at the output end. Arm one features a fifteen-micrometer core diameter that produces a fundamental LP01 mode across a thirty-micrometer output core, while arms two and three possess ten-micrometer core diameters that yield near-LP11-odd and near-LP11-even mode fields, respectively. This output then couples directly into a one-hundred-meter step-index multimode fiber characterized by a one-hundred-and-five-micrometer core diameter and a numerical aperture of 0.22.
Light propagating through the one-hundred-meter multimode fiber undergoes modal dispersion and interference, generating complex near-field speckle patterns at the exit facet that change sensitively with optical wavelength. These output speckle fields are magnified by a fifty-times objective lens and recorded using an infrared camera featuring a pixel size of twenty by twenty micrometers. An optical attenuator is positioned before the camera sensor to avoid pixel saturation, while a linear polarizer is inserted into the imaging path to enhance speckle fringe contrast. During the calibration phase, the tunable laser steps through a two-nanometer range in precise increments of one picometer, acquiring a comprehensive calibration sequence covering two thousand discrete spectral channels. Because the calibration laser can switch wavelengths at ten kilohertz while the camera operates at approximately two hundred hertz, acquiring the entire transmission matrix requires approximately ten seconds. This rapid calibration cycle provides an effective practical solution to mitigate the temporal drift and environmental thermal fluctuations known to affect extended lengths of multimode optical fibers.
The theoretical foundation of the mode division multiplexing spectrometer rests on the mathematical coupling between incident beams and guided modes in the fiber core. The normalized power coupling coefficient eta-mn is defined by the spatial overlap integral between the incident electric field and the transverse electric field of each guided LP-mn mode divided by their normalized areas. Numerical calculations evaluated the power distributions of the first one hundred guided LP modes, sorted in descending order of effective refractive index from the fundamental LP01 mode down to the LP45-odd mode. The calculations confirmed that each of the three lantern arms excites markedly different initial modal weights, triggering distinct spatial power diffusion and intermodal scattering profiles along the fiber. Applying singular value decomposition to the resulting transmission matrices revealed that the number of nonzero singular values increases substantially when combining speckles generated by different launching modes. Across seven possible modal combinations, multi-mode excitation consistently produced new independent spatial channels rather than redundant data repetitions, directly expanding information-encoding capacity.
To evaluate spectral measurement accuracy, the authors calculated the reconstruction error mu, defined as the root-mean-square standard deviation between the reconstructed spectrum and ground-truth reference across all spectral channels. In a two-wavelength resolution test involving two sharp spectral lines separated by two picometers, single-mode LP01 excitation produced a reconstruction error of 0.0043 and a signal-to-noise ratio of seventeen decibels. Incorporating dual-mode excitation with LP01 and LP11-odd modes lowered the error to 0.0011 while increasing signal-to-noise ratio to twenty-three decibels. Three-mode excitation utilizing LP01, LP11-odd, and LP11-even modes achieved the best performance, yielding an error of 0.0005 and a signal-to-noise ratio of twenty-seven decibels, corresponding to error reductions of eighty-eight percent and fifty-five percent over single and dual excitation. When challenged with a continuous broadband Lorentzian spectrum having a full width at half maximum of 0.5 nanometers, three-mode excitation yielded an error of 0.0074, outperforming single-mode and two-mode errors of 0.0594 and 0.0140 by eighty-eight and forty-seven percent, while sustaining average error reductions of eighty-eight and fifty percent across broader linewidths.
Systematic evaluations confirmed that the three-mode excitation spectrometer successfully reconstructed complex multi-peak and continuous optical spectra across its working range. A comb of narrow spectral lines with full width at half maximum linewidths of 0.05 nanometers spanning 1550 to 1552 nanometers was reconstructed with an average error of 0.0022 and signal-to-noise ratios exceeding twenty decibels. Similarly, a continuous random spectrum formed from superposed Gaussian kernel functions was accurately recovered with a reconstruction error of 0.0097. However, the researchers noted fundamental physical limits governing speckle contrast and spectral bandwidth, since broad-band speckle represents an incoherent superposition of intensities across channels where contrast decreases inversely with the square root of the channel count. Mathematically, with K distinct launching modes, the observed intensity vector expands to KN elements and the transmission matrix becomes KN by M. When the ratio of spectral channels M to observational measurements KN exceeds one, augmenting K drastically reduces reconstruction uncertainty; however, when the ratio drops below one, accuracy gains saturate while modal switching adds time overhead.
Beyond multiplexing static measurements, the research team introduced an active alternating mode modulation technique designed to sharpen spectral resolution up to the physical limits of the multimode fiber. During calibration, consecutive spectral channels are assigned to alternating launch modes according to a structured lookup table, where channel indices matching three-i plus one, three-i plus two, and three-i plus three are excited by LP01, LP11-odd, and LP11-even modes, respectively. During measurement, the unknown test spectrum is injected under all three modal conditions to generate three corresponding speckle patterns labeled I-one, I-two, and I-three. Preliminary spectral estimates are calculated through matrix inversion and subsequently refined through nonlinear optimization algorithms that minimize the two-norm residual between observed speckles and matrix-spectrum products. Because individual channels yield nonzero solutions only when their pre-assigned calibration mode matches the applied launching state, concatenating the interleaved estimates exploits abrupt speckle pattern variations between adjacent modes to suppress inter-channel cross-talk and significantly enhance spectral discrimination.
The resolving power of the alternating mode modulation approach was verified by calculating the spectral correlation function C of the speckle patterns, whose half-width at half-maximum indicates achievable spectral resolution. In standard unmodulated configurations where all wavelengths are excited by an identical mode, the measured correlation function exhibited a half-width at half-maximum between three and four picometers. When alternating mode modulation was applied, the correlation curve showed distinct periodic modulation, compressing the half-width at half-maximum down to one picometer and matching the theoretical resolution limit obtained from numerical simulations of full-mode fiber excitation. This one-picometer limit corresponds directly to the finest tuning step size of the calibration laser used in the laboratory experiments. In validation trials, two spectral peaks separated by two picometers were successfully resolved with a reconstruction measurement of 0.0250. The authors concluded that future development will explore programmable mode excitations to widen operational bandwidth while balancing reconstruction accuracy against the temporal overhead of sequential mode switching.
Subject of Research: Mode division multiplexing reconstructive spectrometer using an all-fiber photonics lantern
Article Title: Mode division multiplexing reconstructive spectrometer with an all-fiber photonics lantern
Article References: Liang, J., Ye, J., Ma, X., Lu, Y., Li, J., Xu, J., Chen, Z., Leng, J., Jiang, Z., & Zhou, P. (2024). Mode division multiplexing reconstructive spectrometer with an all-fiber photonics lantern. Frontiers of Optoelectronics, 17(1), Article 23. https://doi.org/10.1007/s12200-024-00130-6
Image Credits: AI Generated
DOI: 10.1007/s12200-024-00130-6
Keywords: reconstructive spectrometer, mode division multiplexing, photonics lantern, multimode fiber, speckle patterns, transmission matrix, spectral resolution, polarization-maintaining fiber, tunable laser, singular value decomposition, alternating mode modulation, spectral correlation function, linearly polarized modes, infrared camera, optical fiber scattering, reconstruction error
News Source: Denise Maddox. (November 12, 2026). Mode Division Multiplexing Spectrometer Cuts Spectral Reconstruction Errors by Eighty-Eight Percent. Scienmag.
