Polarimetric Dual-Comb Spectroscopy

• Polarimetric dual-comb spectroscopy is a method that reconstructs full wavelength-dependent Jones matrices by combining dual-comb techniques with spectroscopic polarimetry, eliminating mechanical polarization modulation.
• It leverages polarization multiplexing to generate mutually coherent comb pairs using architectures such as fiber Fabry–Perot resonators, all-PM erbium lasers, and solid-state oscillators.
• The technique enables rapid, high-resolution characterization of optical materials and biological samples while addressing challenges like phase stability and bandwidth limitations.

Searching arXiv for recent and directly relevant papers on polarimetric dual-comb spectroscopy and polarization-multiplexed dual-comb sources. {"query":"polarimetric dual-comb spectroscopy Jones-matrix dual-comb spectroscopic polarimetry polarization-multiplexed dual-comb source", "max_results": 10} I found directly relevant arXiv papers including "Jones-matrix dual-comb spectroscopic polarimetry" (Koresawa et al., 2023), "Detection of carbon monoxide using a polarization-multiplexed erbium dual-comb fiber laser" (Aldia et al., 2024), "Dual-Frequency Comb in Fiber Fabry-Perot Resonator" (Bunel et al., 11 Feb 2025), and "Dual-comb femtosecond solid-state laser with inherent polarization-multiplexing" (Kowalczyk et al., 2020). Polarimetric dual-comb spectroscopy denotes a class of measurements in which dual-comb spectroscopy is used to acquire polarization-resolved optical amplitude and phase spectra, so that a sample’s polarization response can be determined as a function of wavelength. In its most explicit form, represented by Jones-matrix dual-comb spectroscopic polarimetry, the method combines spectroscopic polarimetry, dual-comb spectroscopy, and Jones-matrix analysis to reconstruct the sample’s wavelength-dependent Jones matrix without mechanical polarization modulation (Koresawa et al., 2023). Related work on polarization-multiplexed dual-comb sources shows that orthogonally polarized combs can also be generated within a single cavity or resonator, providing mutually coherent sources that are directly relevant to polarimetric dual-comb implementations, even when the experiments themselves are not full polarization-resolved measurements of an unknown sample (Aldia et al., 2024, Bunel et al., 11 Feb 2025, Kowalczyk et al., 2020).

1. Definition and scope

Spectroscopic polarimetry is used for evaluation of thin film, optical materials, and biological samples because it can provide both spectroscopic characteristics and polarimetric characteristics of objects. Conventional implementations usually rely on mechanical polarization modulation, and the cited literature identifies two resulting constraints: mechanical instability and limited data acquisition speed (Koresawa et al., 2023). Dual-comb spectroscopy changes this operating regime because it can measure optical amplitude and phase spectra quickly and precisely without moving parts, and in dual-comb spectroscopic polarimetry the polarization behavior is extracted from the polarization-resolved dual-comb signal.

A recurrent distinction in the literature is between a full polarimetric measurement and a polarization-multiplexed dual-comb source. Jones-matrix dual-comb spectroscopic polarimetry measures a sample’s wavelength-dependent polarization response by reconstructing the Jones matrix from multiple known input polarizations and the corresponding complex output spectra (Koresawa et al., 2023). By contrast, the fiber Fabry–Perot resonator study explicitly states that it does not perform polarization-resolved spectroscopy in the sense of measuring an unknown sample’s polarization response, but establishes the key source architecture: two mutually coherent combs generated simultaneously in orthogonal polarization eigenmodes of the same cavity, with a small repetition-rate difference created by cavity birefringence (Bunel et al., 11 Feb 2025). The erbium single-cavity laser and the Yb:CNGS solid-state oscillator likewise demonstrate polarization multiplexing as a source strategy for dual-comb spectroscopy, rather than a complete Jones-matrix measurement of a sample (Aldia et al., 2024, Kowalczyk et al., 2020).

This suggests that polarimetric dual-comb spectroscopy encompasses both a measurement methodology and a source-architecture problem. The former concerns recovery of polarization-dependent amplitude and phase, while the latter concerns how to generate mutually coherent comb pairs in orthogonal polarization channels.

2. Jones-matrix formulation and measured observables

In the Jones-calculus formulation used for Jones-matrix dual-comb spectroscopic polarimetry, the polarization state of light is represented by a Jones vector (Koresawa et al., 2023):

$$\mathbf{J}= \begin{bmatrix} E_x e^{i\phi_x}\ E_y e^{i\phi_y} \end{bmatrix}.$$

After normalization, it is written as

$$\mathbf{J}= \begin{bmatrix} \sin\omega \, e^{i\Delta}\ \cos\omega \end{bmatrix},$$

where $\omega$ is the amplitude ratio between x- and y-polarized components and $\Delta$ is the phase difference between the two components. In the same framework, the sample is represented by

$$\mathbf{M}= \begin{bmatrix} J_{00} & J_{01}\ J_{10} & J_{11} \end{bmatrix},$$

and the output state is

$\mathbf{J}'=\mathbf{M}\mathbf{J}.$

The measured observables in dual-comb spectroscopic polarimetry are the complex spectra of the orthogonal polarization components. From Fourier transformation of the interferogram, one obtains complex spectra for each polarization component; from those spectra, the method derives the amplitude ratio spectrum $\omega(\lambda)$ and the phase difference spectrum $\Delta(\lambda)$ (Koresawa et al., 2023). In the paper’s terminology, DCSP acquires optical spectra of amplitude ratio and phase difference in p- and s-polarization components of the output light from simultaneous measurement of optical spectra of optical amplitude and phase in p- and s-polarization components without the need for mechanical polarization modulation.

The Jones-matrix formalism also supplies concrete model cases. The paper gives the Jones matrix of a birefringent material as

$$\mathbf{M}_B= \begin{bmatrix} 1 & 0\ 0 & e^{ib} \end{bmatrix},$$

that of an optically active material as

$$\mathbf{M}_r= \begin{bmatrix} \cos r & -\sin r\ \sin r & \cos r \end{bmatrix},$$

and a birefringent material with rotated axes as

$$\mathbf{J}= \begin{bmatrix} \sin\omega \, e^{i\Delta}\ \cos\omega \end{bmatrix},$$0

These examples define the interpretive framework for distinguishing birefringence, optical activity, and axis rotation in the wavelength-resolved measurements.

3. Measurement architecture without mechanical polarization modulation

The central experimental innovation in Jones-matrix dual-comb spectroscopic polarimetry is the use of polarization control pulse sequences with different polarizations and time delays, so that the incident light is multiplexed into multiple polarizations instead of a single polarization (Koresawa et al., 2023). A single optical-frequency-comb pulse is split into two optical paths. One becomes the first polarization-controlled pulse, the other becomes the second polarization-controlled pulse. The two pulses are engineered to have different polarizations and different time delays, and are recombined to form a polarization control pulse sequence. After a half-wave plate, the pair becomes, for example, a first pulse at $$\mathbf{J}= \begin{bmatrix} \sin\omega \, e^{i\Delta}\ \cos\omega \end{bmatrix},$$1 and a second pulse at $$\mathbf{J}= \begin{bmatrix} \sin\omega \, e^{i\Delta}\ \cos\omega \end{bmatrix},$$2. A third pulse, the reference pulse, is included to determine the absolute phase, so the signal contains a pulse train triple: first PCP, second PCP, and reference pulse.

The hardware reported for the demonstration used two phase-locked erbium-doped fiber optical frequency combs. The signal OFC had $$\mathbf{J}= \begin{bmatrix} \sin\omega \, e^{i\Delta}\ \cos\omega \end{bmatrix},$$3 MHz and $$\mathbf{J}= \begin{bmatrix} \sin\omega \, e^{i\Delta}\ \cos\omega \end{bmatrix},$$4 MHz, the local OFC had $$\mathbf{J}= \begin{bmatrix} \sin\omega \, e^{i\Delta}\ \cos\omega \end{bmatrix},$$5 MHz and $$\mathbf{J}= \begin{bmatrix} \sin\omega \, e^{i\Delta}\ \cos\omega \end{bmatrix},$$6 MHz, and therefore $$\mathbf{J}= \begin{bmatrix} \sin\omega \, e^{i\Delta}\ \cos\omega \end{bmatrix},$$7 Hz (Koresawa et al., 2023). The combs were phase-locked to a rubidium frequency standard, and coherent averaging was enabled via a narrow-linewidth CW intermediate laser. In pulse preparation, the PCPS branch was split into two pulses with a controlled delay of 0.63 ns between the first and second PCP, and the reference pulse was delayed by 0.15 ns relative to the second PCP. The reference pulse was set to $$\mathbf{J}= \begin{bmatrix} \sin\omega \, e^{i\Delta}\ \cos\omega \end{bmatrix},$$8 polarization.

The detection and processing workflow is also specified explicitly. The PCPS and the local comb interfere at a beam splitter. The interferogram is then separated into x-polarized and y-polarized components and detected by photodiodes. The processing sequence is: acquire the interferogram sequence; isolate the time windows corresponding to the first PCP, second PCP, and reference pulse; apply zero padding outside the selected window; Fourier-transform each extracted interferogram; obtain complex amplitude and phase spectra for x and y channels; use the reference pulse to determine absolute phase; and reconstruct the Jones matrix versus wavelength (Koresawa et al., 2023).

Conceptually, the reconstruction uses two known input Jones vectors,

$$\mathbf{J}= \begin{bmatrix} \sin\omega \, e^{i\Delta}\ \cos\omega \end{bmatrix},$$9

together with the two measured output vectors. The paper states that the known input polarizations of the two PCPs form the basis, the measured complex output spectra form the response, and solving the linear Jones equation yields the wavelength-dependent Jones matrix (Koresawa et al., 2023).

4. Experimental validation of wavelength-dependent Jones-matrix reconstruction

The reported validation program uses optical elements with known polarization property, and the experimental result is in good agreement with theoretical values (Koresawa et al., 2023). For a zero-order quarter-wave plate with the fast axis parallel to the y-polarization, only the Jones-matrix elements consistent with a birefringent retarder were nonzero; experimentally, $\omega$0 and $\omega$1 were dominant, with the others near zero, matching the theoretical Jones matrix. When the fast axis was rotated by $\omega$2, all matrix elements changed as expected from the rotated retarder model, and the experimental spectra remained in good agreement with theory.

For a multi-order quarter-wave plate with the fast axis parallel to y-polarization, the measured Jones-matrix spectra again matched the expected birefringent behavior, and wavelength dependence was clearly seen, especially in $\omega$3 and $\omega$4 (Koresawa et al., 2023). These measurements establish that the method is not limited to a single retardance model and can track spectral structure in the matrix elements themselves.

A Faraday rotator was measured as an optically active sample. Because the original $\omega$5/$\omega$6 input pair created a dead zone for this element, the incident polarizations were changed to a first PCP at $\omega$7 and a second PCP at $\omega$8 (Koresawa et al., 2023). The measured Jones matrix showed the expected rotation-type behavior and agreed well with theoretical values. Rotating the Faraday rotator itself by $\omega$9 did not change the matrix, consistent with the fact that Faraday rotation is not dependent on the sample orientation in the same way as a conventional rotated birefringent element. A combined system consisting of a Faraday rotator and a quarter-wave plate was also measured, and the combined Jones matrix matched the product of the individual matrices, as expected for serial optical elements.

These demonstrations address a common misconception: polarization-resolved spectra alone are not equivalent to a full wavelength-dependent Jones-matrix measurement. The JM-DCSP workflow requires multiple known incident polarizations and reconstruction of all matrix elements, not only a single amplitude-ratio or phase-difference trace.

5. Polarization-multiplexed dual-comb sources

Polarimetric dual-comb spectroscopy depends strongly on source architecture, and three cited papers show distinct ways to generate the two mutually coherent combs through polarization multiplexing rather than through two separate lasers.

Paper	Source architecture	Reported parameters
"Dual-Frequency Comb in Fiber Fabry-Perot Resonator" (Bunel et al., 11 Feb 2025)	Single birefringent fiber Fabry–Perot resonator; orthogonally polarized optical frequency combs in the same monolithic resonator	$\Delta$0 GHz, $\Delta$1 kHz, more than 40 nm optical span
"Detection of carbon monoxide using a polarization-multiplexed erbium dual-comb fiber laser" (Aldia et al., 2024)	Single-cavity all-polarization-maintaining erbium laser; fast and slow axes of PM fiber; polarization multiplexing with gain sharing	repetition rate $\Delta$2 MHz; tunable $\Delta$3 from 500 Hz to 200 kHz
"Dual-comb femtosecond solid-state laser with inherent polarization-multiplexing" (Kowalczyk et al., 2020)	Single-cavity Yb:CNGS solid-state oscillator; orthogonally polarized o- and e-beams in a birefringent gain crystal	repetition rate around 78.3 MHz; $\Delta$4 kHz; sub-100 fs pulses

In the fiber Fabry–Perot resonator work, the physical mechanism is cavity birefringence: the two orthogonal polarization modes, labeled $\Delta$5 and $\Delta$6, do not share identical round-trip times, so their free spectral ranges differ slightly (Bunel et al., 11 Feb 2025). The reported values are $\Delta$7 GHz and $\Delta$8 kHz, giving two orthogonally polarized combs with a 6 kHz repetition-rate difference. The cavity resonances are offset by about $\Delta$9 MHz at 1550 nm. The paper emphasizes excellent mutual coherence, beatnote linewidth below 15 Hz across the entire comb, low cross-talk, and a proof-of-concept spectroscopy measurement in which an RF comb with 6 kHz line spacing and 17 MHz span represents an optical span of about 5 THz. The broader significance stated in the paper is a route to single-resonator, orthogonally polarized, mutually coherent dual-comb generation in an all-fiber platform (Bunel et al., 11 Feb 2025).

In the all-PM erbium system, the two combs are generated in the same cavity on the fast and slow polarization axes of a PM fiber, and both combs share the same Er gain fiber and 116 cm of PM1550 fiber (Aldia et al., 2024). The source is explicitly operated without active stabilization. The reported standard deviation of the free-running drift of $$\mathbf{M}= \begin{bmatrix} J_{00} & J_{01}\ J_{10} & J_{11} \end{bmatrix},$$0 over 1 hour is 1.59 Hz, and dual-comb operation remained stable for months. The paper gives the non-aliasing condition

$$\mathbf{M}= \begin{bmatrix} J_{00} & J_{01}\ J_{10} & J_{11} \end{bmatrix},$$1

states that the center bursts in the interferogram are separated by

$$\mathbf{M}= \begin{bmatrix} J_{00} & J_{01}\ J_{10} & J_{11} \end{bmatrix},$$2

and reports theoretical tunability of non-aliasing bandwidth from 0.014 THz to 5.59 THz, equivalent to 0.12 nm to 45.93 nm at 1570 nm (Aldia et al., 2024).

In the Yb:CNGS solid-state oscillator, intrinsic polarization multiplexing arises from the birefringent active crystal itself (Kowalczyk et al., 2020). The source generates orthogonally polarized ordinary and extraordinary pulse trains, with $$\mathbf{M}= \begin{bmatrix} J_{00} & J_{01}\ J_{10} & J_{11} \end{bmatrix},$$3 MHz, $$\mathbf{M}= \begin{bmatrix} J_{00} & J_{01}\ J_{10} & J_{11} \end{bmatrix},$$4 MHz, and therefore $$\mathbf{M}= \begin{bmatrix} J_{00} & J_{01}\ J_{10} & J_{11} \end{bmatrix},$$5 kHz. The paper reports 93 fs pulses for the e-beam, 88 fs for the o-beam, about 30 mW per beam, and low relative noise sufficient for tooth-resolved free-running dual-comb spectroscopy over about 5 ms without correction; with computational phase correction, coherent averaging extends to 1 s and spectral SNR improves by more than 36 dB (Kowalczyk et al., 2020).

Taken together, these source papers suggest that polarization can function as the multiplexing degree of freedom at the source level, while Jones-matrix polarimetry uses polarization multiplexing at the measurement level to reconstruct the sample response.

6. Performance, limitations, and application space

The main advantages stated for Jones-matrix dual-comb spectroscopic polarimetry are no mechanical polarization modulation, rapid acquisition, high spectral resolution, direct complex amplitude/phase measurement, full Jones-matrix reconstruction, and suitability for dynamic samples and anisotropic materials (Koresawa et al., 2023). In the broader source literature, additional practical advantages are emphasized: all-PM fiber design, strong common-mode noise rejection in a single cavity, free-running operation without active stabilization for proof-of-principle spectroscopy, and wide tunability of $$\mathbf{M}= \begin{bmatrix} J_{00} & J_{01}\ J_{10} & J_{11} \end{bmatrix},$$6 (Aldia et al., 2024); a monolithic all-fiber source with excellent mutual coherence and tunable birefringence-controlled repetition-rate difference (Bunel et al., 11 Feb 2025); and unusually low relative noise from a bulk solid-state single-cavity source based on intrinsic polarization multiplexing (Kowalczyk et al., 2020).

The limitations are equally specific. In JM-DCSP, absolute phase is sensitive to environmental disturbances such as air turbulence and path-length fluctuations; the current setup uses separate optical paths, so phase stability is not perfect; common-path stabilization would help but is difficult because of long pulse delays; signal quality can depend on the sample and polarization basis, with some configurations leading to a dead zone; and bandwidth is limited by the optical bandpass filter used in the experiment (Koresawa et al., 2023). In the PM erbium source, the carrier-envelope-offset frequency is not actively controlled, so deliberate placement of the RF comb in the detector bandwidth is limited, and the demonstrated spectroscopy resolution is 3.6 GHz rather than comb-line-resolved (Aldia et al., 2024). In the fiber Fabry–Perot source, the spectral power in the wings is low, the proof-of-concept measurement is performed close to the pump where the SNR is best, and the RF span remains limited by the chosen $$\mathbf{M}= \begin{bmatrix} J_{00} & J_{01}\ J_{10} & J_{11} \end{bmatrix},$$7 and the detector/electronics bandwidth (Bunel et al., 11 Feb 2025). In the solid-state source, the spectroscopy reported is not itself a full polarimetric measurement of a polarization-anisotropic sample, the system still requires external polarization rotation and recombination for heterodyne readout, and long-duration performance benefits from computational phase correction (Kowalczyk et al., 2020).

The applications emphasized across the cited works include thin-film characterization, optical-material analysis, birefringence and optical activity measurements, dynamic polarization measurements, biological sample characterization, and any field needing fast wavelength-resolved polarization response (Koresawa et al., 2023). Gas sensing is demonstrated by spectroscopy of a $$\mathbf{M}= \begin{bmatrix} J_{00} & J_{01}\ J_{10} & J_{11} \end{bmatrix},$$8 reference cell at 790 Torr with a 30 cm effective path length in the free-running erbium system (Aldia et al., 2024). The fiber Fabry–Perot paper places its source in the broader dual-comb context of spectroscopy, ranging, and imaging (Bunel et al., 11 Feb 2025). A plausible implication is that polarimetric dual-comb spectroscopy will continue to develop along both axes already visible in the literature: more complete polarization-state reconstruction at the sample plane, and simpler single-cavity or single-resonator polarization-multiplexed comb sources with stronger passive mutual coherence.