Modified Transfer Matrix Method for the Extraction of Material Properties via Terahertz Time-Domain Spectroscopy

Kamyar Rashidi; Matthew Y. Sfeir

REVIEW 3 major objections 7 minor 40 references

Modified Transfer Matrix Method for the Extraction of Material Properties via Terahertz Time-Domain Spectroscopy

T0 review · 3 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A modified transfer matrix method extracts accurate complex refractive indices from terahertz time-domain spectroscopy across 0.1–15 THz by modelling only the reflections that arrive within the measurement window.

desk verdict A genuinely useful TMM modification for THz-TDS, but the broad accuracy claim is undercut by missing error bars and an underspecified phase-branch selection. read the letter →

arxiv 2505.21924 v2 pith:KVLS2FMG submitted 2025-05-28 physics.optics cond-mat.mes-hallcond-mat.mtrl-sciphysics.chem-ph

Kamyar Rashidi , Matthew Y. Sfeir This is my paper

classification physics.opticscond-mat.mes-hallcond-mat.mtrl-sciphysics.chem-ph

keywords terahertztime-domainspectroscopytransfermatrixmethodrefractiveindexextractioncomplexgeneticalgorithmphaseambiguitymultilayerthinfilmsopticalconstants

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper introduces a modified Transfer Matrix Method (MTMM) that extracts the complex refractive index of materials from terahertz time-domain spectroscopy data. The key move is to zero out the backward-wave coupling terms in the interface transfer matrix for layers that are thick enough that their internal reflections arrive outside the measured time window, while keeping the full transfer matrix for thin layers where multiple reflections matter. Combined with a genetic algorithm whose search bounds are set by the analytic single-pass estimate, the method is claimed to recover physically meaningful refractive indices across a wide spectral range (0.1–15 THz) and across diverse sample geometries. The authors demonstrate the approach on water in a cuvette, a drop-cast conducting polymer film, a thick PA6 slab, and a photoexcited SnO2 film, benchmarking against existing methods such as Nelly, the single-pass method, and the full transfer matrix method.

What carries the argument

The central object is the modified interface transfer matrix, formed by replacing the second column of the standard TMM interface matrix with zeros: for a thick layer (thickness above $d_{\text{th},j} = c\Delta\tau/(2n_j)$), the matrix becomes $T'_{ij} = \begin{pmatrix} (n_i+n_j)/(2n_i) & 0 \\ (n_i-n_j)/(2n_i) & 0 \end{pmatrix}$. Setting the backward-wave coefficient to zero suppresses reflections that would fall outside the measurement time window while preserving the forward-propagating structure of the matrix product. The second load-bearing component is the genetic-algorithm optimizer, which searches for the complex refractive index that minimizes the cost function $C_f = |H_{\text{exp}}(\omega) - H_{\text{mod}}(\omega, \tilde{n})|$, with search bounds $[n_{\text{lb}}, n_{\text{ub}}]$ set to $± \pi c/(\omega d)$ around the analytic single-pass estimate so that at least one $2\pi$-phase-branch solution is included.

What would settle it

Construct a sample with a known high refractive index and moderate absorption (e.g., a silicon wafer at 0.1–1 THz, with independently calibrated refractive index) and run MTMM with the described bounds; if the extracted index is offset by an integer multiple of $2\pi c/(\omega d)$ relative to the known value, or if the GA converges to a solution outside the true branch, the central claim that the bounds always contain the physical solution is refuted. A systematic scan over frequency and thickness would reveal where branch ambiguity overwhelms the analytic estimate.

Watch

Extended reading notes

Core claim

The central claim is that a transfer function built from standard transfer matrices, with the second column of the interface matrix set to zero for layers exceeding a time-window-dependent thickness threshold (Eq. 8), correctly reproduces the experimental transmission function measured in THz-TDS. This modification is equivalent to neglecting back-propagating waves from thick layers that would arrive after the delay-line-limited time window, while still retaining all multiple reflections within thin layers. When paired with a genetic algorithm that minimizes the deviation between modelled and measured transfer functions, and whose search space is bounded around an analytic single-pass estimate according to the 2π phase ambiguity (Eq. 14), the method is shown to recover the true complex refractive index where full TMM fails because it includes unmeasurable reflections and where single-pass methods fail at low frequencies because they neglect thin-layer reflections. The paper demonstrates this on four distinct sample structures and reports agreement with benchmark methods while avoiding the spurious phase-jump solutions that plague unconstrained optimizers.

Load-bearing premise

The physical solution must lie within one 2π phase branch of the analytic single-pass estimate, so that the symmetric bounds around that estimate (Eq. 14) actually contain the true refractive index; if the sample is highly absorbing, high-index, or measured at very low frequency, the branch spacing is large relative to the estimate error and the true solution can fall outside the search range.

Editorial extensions

If this is right

If the central claim is correct, MTMM provides a single transfer-function model that works for both thin films and thick substrates, eliminating the need for case-specific approximations such as Fabry–Perot-only or single-pass-only models.
The method can be applied to photoexcited samples and other time-resolved configurations where a reference ground-state material replaces the usual air or vacuum reference, as demonstrated for SnO2.
Because the genetic algorithm explores a broad search space rather than relying on gradient information, it avoids the local-minimum convergence that limits simplex and gradient-based methods in the presence of multiple $2\pi$ phase solutions.
The authors state that the approach can be extended to reflection-mode THz-TDS and other configurations, broadening its use beyond transmission measurements.
Freely available source code and data let other groups apply the method directly to their own THz-TDS measurements.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The method's reliance on an analytic single-pass estimate for setting bounds means its accuracy at very low frequencies or for very high-index, high-absorption samples could be improved by an adaptive bound-selection scheme that accounts for the frequency-dependent branch spacing.
A natural extension would be to automate the threshold decision: instead of a sharp cutoff at $d_{\text{th},j}$, one could weight the backward-wave contributions by their temporal delay relative to the window, which might smooth the transition for samples with thicknesses near the threshold.
The success of the GA with constraints suggests a broader message for THz-TDS analysis: population-based optimizers paired with physically motivated bounds may replace the tree-based path enumeration used in Nelly, scaling more gracefully to multilayers with many interfaces.
The clear separation between the physical solution and spurious phase-offset solutions, visible when constraints are removed, could be exploited to estimate the confidence of the extraction by running the GA multiple times and examining the distribution of solutions.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a solid techniques paper with a genuinely useful modification to the transfer matrix method for THz-TDS. The core trick—zeroing the second column of the interface matrix for thick layers—is a clean way to enforce time-window truncation, and combining it with a genetic algorithm whose search bounds come from an analytical estimate is a sensible way to avoid the multiple-solution problem. The method deserves attention, but the headline claim of 'accurate results across 0.1–15 THz' is not supported by the evidence as presented.

What's actually new: I haven't seen the zeroed-column modification before. It gives a single matrix recipe that treats thin and thick layers uniformly, which is simpler than the tree-based Nelly approach or the hybrid Fabry–Perot approximations. The GA plus phase-bounded search is a practical recipe, and the four test cases—water cuvette, conducting polymer on glass, PA6 slab, photoexcited SnO2—cover a nice range of geometries. The promised code release is good practice.

The soft spots are real but manageable. First, there are no uncertainty intervals on any extracted n or k, and for the cuvette and SnO2 cases the benchmark is Nelly, which is itself a model. For PA6 there's no independent reference at all; the paper simply prefers its result to Nelly's jumps. Second, GA hyperparameters are not reported, so reproduction is harder than it should be. Third—and this is the stress-test point—the branch selection in Eq. 14 is only as good as the analytical estimate from Eq. 11. That estimate ignores multiple reflections and assumes low absorption; if it lands on the wrong 2π branch for a thick or high-index sample, the true solution is outside the bounds and cannot be found. The paper acknowledges the ambiguity in the supplemental (Fig. S1) and in the discussion, but it does not say when Eq. 11 can be trusted. That's a genuine limitation on the 'generally applicable' claim, though it doesn't undermine the examples shown.

Bottom line: a helpful method for practitioners, worth publishing after revision, but not the last word. I'd send it to peer review; a referee should push for quantification of uncertainty, reported hyperparameters, and an explicit statement of the branch-selection limits. I'd cite it as an alternative approach in my own work.

Referee Report

3 major / 7 minor

Summary. The paper proposes a modified transfer matrix method (MTMM) for extracting the complex refractive index of materials from terahertz time-domain spectroscopy (THz-TDS) measurements. The method accounts for multiple reflections within thin layers while excluding reflections from thick layers by zeroing the second column of the relevant interface transfer matrix (Eq. 8). The complex refractive index is obtained by minimizing the cost function in Eq. (10) with a genetic algorithm, initialized using analytical estimates (Eqs. 11-12) and constrained by phase-ambiguity bounds (Eq. 14). The authors demonstrate the approach on a water-filled cuvette, a drop-cast conjugated polymer film, a PA6 slab, photoexcited SnO2, and, in the supplemental document, PTFE and quartz samples, and they provide open-source code and data.

Significance. The core idea is useful and potentially practical: combining a time-window-aware transfer-matrix model with population-based optimization and analytical initialization is an intuitive contribution, and the public availability of source code and data is a clear strength. The transfer-matrix algebra in Eqs. (3)-(9) is internally consistent, and the paper correctly identifies the 2π phase ambiguity. However, the validation as presented is not yet strong enough for the abstract's wide-applicability claim. The PA6, PTFE, and quartz examples do not exercise the MTMM modification because the samples are below the thickness threshold, the main benchmarks are themselves model-based (Nelly), no independent reference values or error bars are supplied, and the branch-selection mechanism is not proven to recover the physical solution. The significance is thus conditional on additional validation and analysis.

major comments (3)

[§2.2, Eqs. (13)–(14)] The bounds in Eq. (14) are centered on the analytical estimate of Eq. (11) and have width 2πc/(ωd). The statement that this 'ensures the inclusion of at least one solution' is only true for the branch containing the analytical estimate; it does not guarantee that this branch is the physical one. Figure S1 shows that solutions differing by integer multiples of 2πc/(ωd) all fit the experimental transfer function, so the GA confined by Eq. (14) will select the branch chosen by Eq. (11). For high-index, strongly absorbing, or thick samples, and at frequencies where the branch spacing is small compared to the error of Eq. (11), the true refractive index can fall outside the bounds and cannot be recovered. The paper should quantify the range of validity of Eq. (11) (e.g., maximum n, k, thickness, or frequency such that the phase-unwrapped single-pass estimate is within half a branch spacing) and provide a diagnostic, such as comparing constrained and unconstrained solutions, to detect wrong-branch convergence.
[§3, Figs. 2–5 and S3–S4] The validation does not support the abstract's wide-range accuracy claim. The PA6 example (Fig. 4) is explicitly stated to use the full TMM because the 470 μm slab is below the 766 μm threshold, so MTMM and TMM are identical; the same holds for the 30 μm PTFE and 225 μm quartz examples in Figs. S3–S4. The only cases that actually exercise Eq. (8) are the water cuvette and the drop-cast film, and in both cases the benchmark is Nelly, which is itself a model-based extraction method. No independent reference values (e.g., published refractive indices for water, PA6, or PTFE) and no error bars from the stochastic GA are provided for any extracted curve. The authors should validate against materials with known optical constants or provide independent measurements, and report uncertainties from repeated optimizations.
[§2.1, Eq. (8)] The assertion that zeroing the second column of the interface matrix is mathematically equivalent to setting the backward wave in the thick layer to zero is asserted without a derivation. In particular, Eq. (9) modifies only T12 and T34 (the left interfaces of the thick layers) while leaving T23 and T45 unmodified; a reader cannot verify that this removes all round-trip paths in the thick layer rather than, for example, only the first returning echo. Please provide an explicit derivation or a simple two-interface example showing that the modified transfer-matrix product equals the time-windowed path sum, and state the general rule for which interfaces must be replaced.

minor comments (7)

[§2.1, Eq. (9)] The phrase 'since layers 2 and 4 are thick, we will replace them with T12 and T34' is ambiguous; it should read 'we replace the interface matrices at the left boundaries of the thick layers with their modified versions'.
[Fig. 3 caption] The caption refers to 'Fig. 2b and c' for the drop-cast CP film results, but the results appear in Fig. 3b and c.
[§3] The text contains several typographical errors: 'CF dye (7 μm)' should be 'CP film (7 μm)', 'calcualted' should be 'calculated', and 'usng' should be 'using'.
[§3, PA6 and PTFE discussion] The placeholder references 'Fig. ??' should be replaced with the correct supplemental figure numbers (S1, S2, and S3).
[§2.2] The statement that the phase 'is confined to the range -π/2 to π/2' is incorrect if the arctangent is computed with quadrant information (atan2); the range should be (-π, π]. This matters for the phase-unwrapping discussion.
[§2.2] The GA hyperparameters (population size, number of generations, crossover and mutation probabilities, tolerance) are not reported in the paper; they should be listed in the methods or referenced to specific lines of the provided source code.
[Table 1] Table 1 is difficult to read because the 'Sample Structure' row lists entries that do not align clearly with the four sample columns; please reformat so that each sample (cuvette, drop-cast film, PA6 slab, photoexcited SnO2) has its own column.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the extraction is a fit by design, benchmarks are external, and the branch-selection caveat is a correctness limitation, not a circular step.

full rationale

The central claim is that the MTMM transfer function model plus a constrained genetic algorithm recovers complex refractive indices from THz-TDS data. This is an inverse extraction problem: the refractive index is optimized to minimize a cost function against the measured transfer function (Eq. 10). That fitting procedure is not circular in the pejorative sense; it is the stated methodology. The modification in Eq. 8—zeroing the second column of interface matrices for thick layers—is a physical modeling approximation justified by time-window arguments, not a definition that presupposes the extracted index. The analytical initialization in Eqs. 11–12 and bounds in Eq. 14 are heuristic inputs that select a phase branch; the paper explicitly acknowledges the 2π ambiguity and shows multiple solutions in Fig. S1. The fact that the bounds are centered on an analytical estimate means the final solution depends on that estimate, but this is a robustness limitation rather than a circular reduction: the paper does not claim the bounds guarantee the physically correct branch, only that they include at least one solution. Validation is performed against Nelly, an external open-source implementation with prior validation against finite-element simulations (Ref. 14), and against previously published data from other groups (Refs. 40, 41), so the benchmarks are not the authors' own fitted outputs. The PA6 example lacks an absolute reference, but the comparison there is presented as a demonstration of phase-ambiguity consequences and the need for constraints, not as a self-derived ground truth. The self-citations in the reference list (Refs. 23, 24, 37, 38) concern TMM formalism and optimization heuristics and are not load-bearing for the paper's central claim. No step in the derivation reduces by construction to its own inputs, and no fitted parameter is renamed as a prediction. The branch-selection and physical-uniqueness concerns belong to correctness risk, not circularity. The paper's derivation chain is self-contained and its comparisons are externally anchored, so the circularity score is 0.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The ledger shows that the central claim rests on five assumptions: the validity of the one-dimensional transfer matrix model; the separability of the time window; the algebraic equivalence of the zeroed-column modification; the correctness of the analytical branch selection; and the global convergence of the genetic algorithm. No new physical entities are introduced. The genetic algorithm hyperparameters are the only hand-chosen numeric inputs not disclosed in the manuscript.

free parameters (1)

Genetic algorithm hyperparameters
Population size, crossover rate, mutation rate, termination tolerance, and maximum iterations are not specified in the manuscript; the reported convergence and accuracy depend on these choices, which are only available in the source code.

assumptions (5)

domain assumption A one-dimensional plane-wave transfer matrix model with known layer thicknesses describes the measured THz time-domain spectroscopy transfer function.
The entire method is built from Eqs. 3-6 under normal incidence, parallel interfaces, and homogeneous isotropic layers; no account is given for beam divergence, finite aperture, or thickness uncertainty.
domain assumption Reflections with round-trip delay longer than the measurement window Δτ do not contribute to the measured signal and can be discarded.
This is the physical basis for the threshold in Eq. 1 and the matrix modification in Eq. 8; it assumes the time window cleanly separates early and late reflections with no partial overlap.
ad hoc to paper Setting the second column of an interface transfer matrix to zero is equivalent to ignoring backward waves from thick layers without altering in-window paths.
Eq. 8 states 'This is valid' but no proof is given; the equivalence is only argued verbally, and for multilayer stacks with multiple thick layers the effect on all in-window paths is not demonstrated.
ad hoc to paper The initial analytical single-pass estimate lies within the same 2π phase branch as the true refractive index, so the bounds of Eq. 14 include the physical solution.
Supplemental Fig. S1 shows that multiple solutions differing by integer multiples of 2π satisfy the same transfer function, so without this assumption the optimization cannot distinguish physical from unphysical results.
domain assumption The genetic algorithm converges to the global minimum of the cost function within the prescribed bounds.
Population-based metaheuristics have no convergence guarantee; the paper observes local minimum problems in Nelly but does not prove that the genetic algorithm avoids them, so this is an assumed robustness property.

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Cite this review

Pith. "Pith review of Modified Transfer Matrix Method for the Extraction of Material Properties via Terahertz Time-Domain Spectroscopy." pith.science (2026). https://pith.science/paper/KVLS2FMG

@misc{pith2026250521924,
  author       = {Pith},
  title        = {Pith review of: Modified Transfer Matrix Method for the Extraction of Material Properties via Terahertz Time-Domain Spectroscopy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KVLS2FMG}},
  note         = {Machine review of arXiv:2505.21924}
}

read the original abstract

Terahertz Time-Domain Spectroscopy is a powerful technique for extracting the low-frequency optical properties of materials. However, the optical constants are difficult to determine directly from the experimental transfer function, such that various numerical approximations must be implemented to describe specific conditions. Here, we introduce a modified Transfer Matrix Method that uses a genetic algorithm for optimization to determine the refractive index of materials in the THz regime. We show that this approach is generally applicable across a wide range of refractive indices, structures, and frequency ranges. Our method is intuitive and yields accurate results compared to leading methods across a wide spectral range (0.1 - 15 THz).

Figures

Figures reproduced from arXiv: 2505.21924 by the authors.

**Figure 2.** (a) Illustration of THz wave propagation through an empty cuvette (reference) [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** (a) Schematic representation of THz wave propagation through a sample [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: (a) Schematic of a broadband THz wave propagation through PA6 and air, [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: (a) Illustration of the THz pulse propagating through an SnO [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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Works this paper leans on

40 extracted references · 40 canonical work pages

[1]

EXTRACTION OF REFRACTIVE INDEX IN BROADBAND AND THICK SAMPLES As illustrated in Eq. 14, the last term of the expression decreases with increasing ω or d, making it more difﬁcult to distinguish between the physical and non-physical solutions for thicker samples or higher frequencies. Optimization algorithms must navigate these ambiguities, as shown in Fig....

work page
[2]

Real-time terahertz imaging with a single-pixel detector,

R. I. Stantchev, X. Yu, T. Blu, and E. Pickwell-MacPherson, “Real-time terahertz imaging with a single-pixel detector,” Nat. communications 11, 2535 (2020)

work page 2020
[3]

Chemical recognition in terahertz time-domain spectroscopy and imaging,

B. Fischer, M. Hoﬀmann, H. Helm, et al., “Chemical recognition in terahertz time-domain spectroscopy and imaging,” Semicond. Sci. Technol. 20, S246 (2005)

work page 2005
[4]

Perspectives on terahertz honey bee sensing,

A. Prokscha, F. Sheikh, M. Jalali, et al., “Perspectives on terahertz honey bee sensing,” Sci. Reports 15, 10638 (2025)

work page 2025
[5]

A review on terahertz communications research,

T. Kleine-Ostmann and T. Nagatsuma, “A review on terahertz communications research,” J. Infrared, Millimeter, Terahertz Waves32, 143–171 (2011)

work page 2011
[6]

Ultrafast conductivity dynamics in pentacene probed using terahertz spectroscopy,

V . Thorsmølle, R. Averitt, X. Chi, et al., “Ultrafast conductivity dynamics in pentacene probed using terahertz spectroscopy,” Appl. physics letters 84, 891–893 (2004)

work page 2004
[7]

Biomedical applications of terahertz spectroscopy and imaging,

X. Y ang, X. Zhao, K. Y ang, et al., “Biomedical applications of terahertz spectroscopy and imaging,” Trends biotechnology 34, 810–824 (2016)

work page 2016
[8]

Eﬃcient metallic spintronic emitters of ultrabroadband terahertz radiation,

T. Seifert, S. Jaiswal, U. Martens, et al., “Eﬃcient metallic spintronic emitters of ultrabroadband terahertz radiation,” Nat. photonics 10, 483–488 (2016)

work page 2016

Show all 40 references

[9]

Phase-resolved detection of ultrabroadband thz pulses inside a scanning tunneling microscope junction,

M. Müller, N. Martín Sabanés, T. Kampfrath, and M. Wolf, “Phase-resolved detection of ultrabroadband thz pulses inside a scanning tunneling microscope junction,” ACS photonics 7, 2046–2055 (2020)

2020
[10]

A broadband thz-tds system based on dstms emitter and ltg ingaas/inalas photoconductive antenna detector,

Y . Zhang, X. Zhang, S. Li, et al., “A broadband thz-tds system based on dstms emitter and ltg ingaas/inalas photoconductive antenna detector,” Sci. Reports 6, 26949 (2016)

2016
[11]

Thz-tds time-trace analysis for the extraction of material and metamaterial parameters,

R. Peretti, S. Mitryukovskiy, K. Froberger, et al., “Thz-tds time-trace analysis for the extraction of material and metamaterial parameters,” IEEE transactions on Terahertz Sci. Technol. 9, 136–149 (2018)

2018
[12]

Terahertz conductivity analysis for highly doped thin-ﬁlm semiconductors,

A. M. Ulatowski, L. M. Herz, and M. B. Johnston, “Terahertz conductivity analysis for highly doped thin-ﬁlm semiconductors,” J. Infrared, Millimeter, Terahertz Waves 41, 1431–1449 (2020)

2020
[13]

M. C. Nuss and J. Orenstein, Terahertz time-domain spectroscopy (Springer Berlin Heidelberg, Berlin, Heidelberg, 1998), pp. 7–50

1998
[14]

Nelly: A user-friendly and open-source implementation of tree-based complex refractive index analysis for terahertz spectroscopy,

U. Tayvah, J. A. Spies, J. Neu, and C. A. Schmuttenmaer, “Nelly: A user-friendly and open-source implementation of tree-based complex refractive index analysis for terahertz spectroscopy,” Anal. Chem. 93, 11243–11250 (2021)

2021
[15]

Phase retrieval in terahertz time-domain measurements: a “how to

P . U. Jepsen, “Phase retrieval in terahertz time-domain measurements: a “how to” tutorial,” J. Infrared, Millimeter, Terahertz Waves40, 395–411 (2019)

2019
[16]

Uncertainty in terahertz time-domain spectroscopy measurement,

W . Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059–1072 (2008)

2008
[17]

Multilayer extraction of complex refractive index in broadband transmission terahertz time-domain spectroscopy,

N. Greenall, L. Li, E. Linﬁeld, et al., “Multilayer extraction of complex refractive index in broadband transmission terahertz time-domain spectroscopy,” in 2016 41st International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz), (IEEE, 2016), pp. 1–2

2016
[18]

Iterative tree algorithm to evaluate terahertz signal contribution of speciﬁc optical paths within multilayered materials,

Q. Cassar, A. Chopard, F. Fauquet, et al., “Iterative tree algorithm to evaluate terahertz signal contribution of speciﬁc optical paths within multilayered materials,” IEEE Trans. on Terahertz Sci. Technol. 9, 684–694 (2019)

2019
[19]

Reference-free thz-tds conductivity analysis of thin conducting ﬁlms,

P . R. Whelan, Q. Shen, D. Luo, et al., “Reference-free thz-tds conductivity analysis of thin conducting ﬁlms,” Opt. Express 28, 28819–28830 (2020)

2020
[20]

Applicability of the thin-ﬁlm approximation in terahertz photoconductivity measurements,

J. Neu, K. P . Regan, J. R. Swierk, and C. A. Schmuttenmaer, “Applicability of the thin-ﬁlm approximation in terahertz photoconductivity measurements,” Appl. Phys. Lett. 113 (2018)

2018
[21]

Transfer-matrix formalism for the calculation of optical response in multilayer systems: from coherent to incoherent interference,

M. C. Troparevsky, A. S. Sabau, A. R. Lupini, and Z. Zhang, “Transfer-matrix formalism for the calculation of optical response in multilayer systems: from coherent to incoherent interference,” Opt. express 18, 24715–24721 (2010)

2010
[22]

Terahertz optical thickness and birefringence measurement for thermal barrier coating defect location,

A. J. Waddie, P . J. Schemmel, C. Chalk, et al., “Terahertz optical thickness and birefringence measurement for thermal barrier coating defect location,” Opt. Express 28, 31535–31552 (2020)

2020
[23]

Eﬃcient and tunable photochemical charge transfer via long-lived bloch surface wave polaritons,

K. Rashidi, E. Michail, B. Salcido-Santacruz, et al., “Eﬃcient and tunable photochemical charge transfer via long-lived bloch surface wave polaritons,” arXiv preprint arXiv:2409.02067 (2024)

2024 arXiv
[24]

Addressing the dark state problem in strongly coupled organic exciton-polariton systems,

E. Michail, K. Rashidi, B. Liu, et al., “Addressing the dark state problem in strongly coupled organic exciton-polariton systems,” Nano Lett. 24, 557–565 (2024)

2024
[25]

General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference,

C. C. Katsidis and D. I. Siapkas, “General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference,” Appl. optics 41, 3978–3987 (2002)

2002
[26]

Fundamentals of measurement in terahertz time-domain spectroscopy,

W . Withayachumnankul and M. Naftaly, “Fundamentals of measurement in terahertz time-domain spectroscopy,” J. Infrared, Millimeter, Terahertz Waves 35, 610–637 (2014)

2014
[27]

Highly accurate thz time-domain spectroscopy of multilayer structures,

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly accurate thz time-domain spectroscopy of multilayer structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008)

2008
[28]

Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy,

L. Duvillaret, F. Garet, and J.-L. Coutaz, “Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy,” Appl. optics 38, 409–415 (1999)

1999
[29]

Application of terahertz time-domain spectroscopy in characterizing thin metal ﬁlm–substrate structures,

W. Ma, C. Li, Z. Wang, et al., “Application of terahertz time-domain spectroscopy in characterizing thin metal ﬁlm–substrate structures,” IEEE Trans. on Terahertz Sci. Technol. 10, 593–598 (2020)

2020
[30]

Convergence properties of the nelder–mead simplex method in low dimensions,

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P . E. Wright, “Convergence properties of the nelder–mead simplex method in low dimensions,” SIAM J. on optimization 9, 112–147 (1998)

1998
[31]

Highly accurate optical material parameter determination with thz time-domain spectroscopy,

I. Pupeza, R. Wilk, and M. Koch, “Highly accurate optical material parameter determination with thz time-domain spectroscopy,” Opt. express 15, 4335–4350 (2007)

2007
[32]

Review of performance optimization techniques applied to wind turbines,

A. Chehouri, R. Y ounes, A. Ilinca, and J. Perron, “Review of performance optimization techniques applied to wind turbines,” Appl. Energy 142, 361–388 (2015)

2015
[33]

Artiﬁcial neural networks for material parameter extraction in terahertz time-domain spectroscopy,

N. Klokkou, J. Gorecki, J. S. Wilkinson, and V . Apostolopoulos, “Artiﬁcial neural networks for material parameter extraction in terahertz time-domain spectroscopy,” Opt. Express 30, 15583–15595 (2022)

2022
[34]

Grey wolf optimizer,

S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey wolf optimizer,” Adv. engineering software 69, 46–61 (2014)

2014
[35]

Thz-tds: extracting complex conductivity of two-dimensional materials via neural networks trained on synthetic and experimental data,

B. Beddoes, N. Klokkou, J. Gorecki, et al., “Thz-tds: extracting complex conductivity of two-dimensional materials via neural networks trained on synthetic and experimental data,” Opt. Express 33, 14872–14884 (2025)

2025
[36]

Particle swarm optimization,

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN’95-international conference on neural networks, vol. 4 (ieee, 1995), pp. 1942–1948

1995
[37]

Design of single-mode single-polarization large-mode-area multicore ﬁbers,

K. Rashidi, D. Fathi, J. Maleki, et al., “Design of single-mode single-polarization large-mode-area multicore ﬁbers,” Micromachines 14, 1901 (2023)

2023
[38]

Optimal design of large mode area photonic crystal ﬁbers using a multiobjective gray wolf optimization technique,

K. Rashidi, S. M. Mirjalili, H. Taleb, and D. Fathi, “Optimal design of large mode area photonic crystal ﬁbers using a multiobjective gray wolf optimization technique,” J. Light. Technol. 36, 5626–5632 (2018)

2018
[39]

Optical waves in layered media,

P . Y eh and M. Hendry, “Optical waves in layered media,” (1990). 40. F. D’ Angelo, Z. Mics, M. Bonn, and D. Turchinovich, “Ultra-broadband thz time-domain spectroscopy of common polymers using thz air photonics,” Opt. express 22, 12475–12485 (2014)

1990
[41]

Ultrasensitive room temperature infrared photodetection using a narrow bandgap conjugated polymer,

C.-T. Liu, J. Vella, N. Eedugurala, et al., “Ultrasensitive room temperature infrared photodetection using a narrow bandgap conjugated polymer,” Adv. Sci. 10, 2304077 (2023). Modiﬁed Transfer Matrix Method for the Extraction of Material Properties via Terahertz Time-Domain Spe...

2023

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

EXTRACTION OF REFRACTIVE INDEX IN BROADBAND AND THICK SAMPLES As illustrated in Eq. 14, the last term of the expression decreases with increasing ω or d, making it more difﬁcult to distinguish between the physical and non-physical solutions for thicker samples or higher frequencies. Optimization algorithms must navigate these ambiguities, as shown in Fig....

work page

[2] [2]

Real-time terahertz imaging with a single-pixel detector,

R. I. Stantchev, X. Yu, T. Blu, and E. Pickwell-MacPherson, “Real-time terahertz imaging with a single-pixel detector,” Nat. communications 11, 2535 (2020)

work page 2020

[3] [3]

Chemical recognition in terahertz time-domain spectroscopy and imaging,

B. Fischer, M. Hoﬀmann, H. Helm, et al., “Chemical recognition in terahertz time-domain spectroscopy and imaging,” Semicond. Sci. Technol. 20, S246 (2005)

work page 2005

[4] [4]

Perspectives on terahertz honey bee sensing,

A. Prokscha, F. Sheikh, M. Jalali, et al., “Perspectives on terahertz honey bee sensing,” Sci. Reports 15, 10638 (2025)

work page 2025

[5] [5]

A review on terahertz communications research,

T. Kleine-Ostmann and T. Nagatsuma, “A review on terahertz communications research,” J. Infrared, Millimeter, Terahertz Waves32, 143–171 (2011)

work page 2011

[6] [6]

Ultrafast conductivity dynamics in pentacene probed using terahertz spectroscopy,

V . Thorsmølle, R. Averitt, X. Chi, et al., “Ultrafast conductivity dynamics in pentacene probed using terahertz spectroscopy,” Appl. physics letters 84, 891–893 (2004)

work page 2004

[7] [7]

Biomedical applications of terahertz spectroscopy and imaging,

X. Y ang, X. Zhao, K. Y ang, et al., “Biomedical applications of terahertz spectroscopy and imaging,” Trends biotechnology 34, 810–824 (2016)

work page 2016

[8] [8]

Eﬃcient metallic spintronic emitters of ultrabroadband terahertz radiation,

T. Seifert, S. Jaiswal, U. Martens, et al., “Eﬃcient metallic spintronic emitters of ultrabroadband terahertz radiation,” Nat. photonics 10, 483–488 (2016)

work page 2016