Pith. sign in

REVIEW 3 major objections 5 minor 34 references

Strong Energy Dependent Transition Radiation in a Photonic Crystal

T0 review · 3 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A 1D photonic crystal can make transition radiation intensity grow as the fourth power of a particle's Lorentz factor, before saturating.

desk verdict A fresh Brewster-angle PhC configuration with a possible γ⁴ transition-radiation law, but the central frequency integral in the supplement is mishandled; the claim needs fixing and a numerical check before it carries weight. read the letter →

arxiv 2511.18863 v1 pith:23TFGAHI submitted 2025-11-24 physics.acc-ph cond-mat.mes-hallphysics.optics

V.Gareyan , Zh.Gevorkian This is my paper · ORCID
classification physics.acc-phcond-mat.mes-hallphysics.optics PACS 41.60.-m42.70.Qs
keywords transitionradiationphotoniccrystalBrewster'sangleLorentzfactordependencerelativisticparticledetection1DperiodicstackDiracconesresonance
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

The paper claims that a charged particle crossing a specially designed one-dimensional photonic crystal emits transition radiation at Brewster's angle whose intensity grows as the fourth power of the particle's Lorentz factor γ, before saturating at a value proportional to N_s². Ordinary transition radiation and Cherenkov radiation depend only weakly on particle energy, so this would be a new, sharp handle on particle energy. The key is choosing the thickness ratio of the two slab materials so that the crystal has a mode at Brewster's angle whose phase velocity is exactly c; then the radiation problem reduces to a finite geometric series that amplifies forward radiation. The authors also show that in the disordered 'Brewster randomness' stack the N² coherent enhancement is restored for both forward and backward Brewster angles, and they propose the periodic structure as a compact optical detector for ultra-relativistic particles.

What carries the argument

The load-bearing mechanism is the Brewster-angle condition ε⁻¹k_z^ε = b⁻¹k_z^b, which makes the single-period transfer matrix diagonal (Supplemental Eq. S.45). With the thickness-ratio design of Eq. (5), the crystal's Bloch mode at Brewster's angle has quasi-momentum q_z = ω/c exactly, so the particle's field-phase mismatch reduces to γ⁻²/2; the radiation amplitude becomes a geometric sum over N_s periods, and integrating its modulus squared over a wavelength window λ > 2l converts the 1/y² decay into the γ⁴ law.

What would settle it

Fabricate a periodic stack with the Eq. (5) ratio (e.g., b ≈ 3.4, ε = 1, N_s ≈ 10³) and measure the forward intensity at Brewster's angle for electron beams with Lorentz factors from about 10 to 200 in the wavelength window λ > 2l; if the integrated angular intensity does not track γ⁴ before flattening, or if the backward signal is not suppressed, the central claim fails. A second check is to vary the slab thickness by 1% and see whether the peak angle shifts as predicted by Supplemental Eq. S.95.

Watch

Extended reading notes

Core claim

Equations (5)–(6) and Supplemental §1.4.2 give the central result: for a periodic stack of N_s slabs with dielectric constant b separated by gaps with dielectric constant ε, with thickness ratio ab/aε = (√(ε+b) − ε)/(b − √(ε+b)), the forward spectral-angular intensity at Brewster's angle is I⁺(ω, θ_Br) ∼ |(1 − exp(iN_s ωlγ⁻²/2c))/(1 − exp(iωlγ⁻²/2c))|². Integrating over frequencies with λ > 2l in the window 1 ≪ γ ≪ √(N_s πl/λ) gives I⁺(θ_Br) ∼ γ⁴; beyond that, the intensity saturates at a plateau ∼ N_s². The backward Brewster intensity vanishes, and the band structure at Brewster's angle is gapless at every frequency, with a Dirac-cone-like linear dispersion; small angular deviations open a

Load-bearing premise

The design requires the photonic crystal's Brewster-angle mode to have phase velocity exactly c over a continuous range of optical frequencies, which needs lossless, non-dispersive materials and an exact thickness ratio; the additional requirement of N_s ∼ 10⁶–10⁸ for γ ∼ 10³–10⁴ pushes material absorption to the limit (Supplemental Eq. S.69).

Editorial extensions

If this is right

  • At a fixed detector angle (Brewster's angle), the radiated photon yield becomes a monotonic, steep function of particle energy in the pre-saturation window, enabling an energy-discriminating transition-radiation detector without moving the detector.
  • The saturation threshold γ_sat ∼ √(N_s l/λ) is tunable through the number of periods, so the detector can be centered on a desired Lorentz-factor range.
  • Because the backward Brewster intensity is suppressed, nearly all radiated energy is directed forward, giving a unidirectional signal.
  • The γ⁴ window appears for modest N_s at moderate γ (e.g., N_s = 10³ shows the law up to γ ∼ 100), so the effect is testable with existing multilayer fabrication.
  • The Dirac-cone-like band structure at Brewster's angle means the crystal supports an eigenmode at every frequency in that direction; no photonic band gap blocks the radiation.

Reading between the lines

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

  • A natural extension is to ask whether the γ⁴ law survives when the dielectric layers are weakly dispersive; the paper assumes non-dispersive materials over the whole integration window, and a controlled analysis with realistic Drude-Lorentz dispersion would likely shrink the usable γ range.
  • The same geometric-series mechanism might be transferred to other quasi-particles (e.g., neutron or atomic de Broglie waves crossing layered potentials) where a Brewster-like matching condition makes the transfer matrix diagonal, producing an analogous enhancement of the emitted wave.
  • If verified, the effect could complement silicon photomultipliers in beam instrumentation, potentially replacing centimeters-long X-ray transition-radiation detectors with micrometer-thick optical stacks.
  • A practical check of the tuning claim is to vary the slab thickness by about 1% and observe the predicted shift of the peak angle (Supplemental Eq. S.95), which would independently confirm the phase-velocity-matching mechanism.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper studies transition radiation from a charged particle crossing a 1D photonic crystal composed of alternating dielectric slabs. Using a transfer-matrix solution of the wave equation, the authors show that at Brewster's angle the transfer matrix becomes diagonal, allowing an exact treatment. For a periodic stack with a specific thickness ratio (Eq. 5), they claim that the forward radiation intensity at Brewster's angle, integrated over frequencies with λ>2l, scales as γ⁴ for 1≪γ≪√(N_s πl/λ), and then saturates as N_s² for larger γ. For a disordered stack satisfying 'Brewster randomness,' the paper re-establishes a N² intensity enhancement. The authors also draw an analogy between the band structure at Brewster's angle and Dirac cones in graphene, and propose using the structure as a detector for ultra-relativistic particles. The central derivation is in the Supplemental Material, with the key step being a frequency integral evaluated in §1.4.2.

Significance. If the γ⁴ scaling of the Brewster-angle transition radiation is correct, it would be a striking and practically relevant effect: optical transition radiation whose integrated intensity grows as the fourth power of the Lorentz factor, well beyond the weak γ-dependence of ordinary transition radiation. The paper is commendable for deriving the result from the standard Maxwell/transfer-matrix formalism rather than fitting to data, and for exhibiting an exact diagonalization condition at Brewster's angle. The thickness-ratio condition (Eq. S.76) is a genuine derived condition, not a fitted parameter. However, the key asymptotic evaluation leading to the γ⁴ law is not rigorous as written, and the practical applicability is limited by unaddressed loss constraints. The manuscript is therefore promising but requires substantial revision to establish the central claim.

major comments (3)
  1. [Supplemental §1.4.2, Eqs. (S.82)–(S.83)] The asymptotic evaluation of the frequency integral is incorrect. The identity in (S.82) is used to discard the term N_s∫ sin(N_s y)/y dy, but on a finite interval [y_min,y_max] with y_min>0 this term is not negligible; it is of the same order as the boundary terms and cancels the cos(N_s y_min)/y_min − cos(N_s y_max)/y_max parts that are kept in (S.83). A correct integration by parts gives the leading term 4cγ²/l (1/y_min − 1/y_max) ≡ 8c²γ⁴/l² (1/ω_min − 1/ω_max), not the expression in (S.83). Although this corrected result still exhibits γ⁴ scaling, the derivation as written does not establish it, and the smooth curves in Fig. S.3 cannot be reproduced by (S.83) because of the retained oscillatory terms. Please provide a rigorous estimate with convergence conditions or a numerical check of the exact integral.
  2. [Supplemental §1.4.2, Eq. (S.80) and replacement below] The replacement ∫ dω F(ω)C(ω) ≈ C(ω*) ∫ dω F(ω) is uncontrolled. The prefactor C(ω) in (S.71) contains factors of the form (1 − exp(i2πã_b β^{-1}) cos(...)) that vanish linearly as ω→0, and it varies substantially over the stated integration window (λ/l from 2 up to tens). Thus C(ω) is not slowly varying over the range where F(ω) has its main support, and the γ-scaling of the full integral could be altered (e.g., a factor C(ω)∝ω would introduce a logarithmic factor relative to the constant-C estimate). Please estimate the error or perform the integral with the actual C(ω) to confirm the γ⁴ law.
  3. [Supplemental §1.3, Eq. (S.69); Discussion, p.4] The loss constraint Eq. (S.69) limits the usable slab number by N_s ≪ √(1−Γ'²)/|Γ''|. For the proposed detector range γ∼10³–10⁴, the paper requires N_s∼10⁶–10⁸. For realistic optical materials with even tiny ε'', this condition is violated by orders of magnitude, yet the Discussion states that 'the only problem that remains is the precise angular spectroscopy.' This is an overstatement. Please quantify the maximum achievable N_s for candidate low-loss materials and discuss whether the proposed regime (γ∼10³–10⁴) is physically accessible.
minor comments (5)
  1. [Supplemental Eq. (S.80)] The intensity formula appears to be missing a square: it writes |[Ĉ(θ_Br)]_1|, whereas Eq. (S.72) has |α±|². Please correct the notation and ensure dimensional consistency.
  2. [Figs. 2, 4 and S.2–S.4] The parameter values used to produce the figures are not fully specified (dielectric constants ε and b, and the integration limits λ_max and λ_min). Fig. S.1 lists b=3.4, ε=1, but the other figures do not. Please state all parameters in the captions or text.
  3. [Main text, Eq. (6) and Fig. 2] The smooth γ⁴ curve in Fig. 2(a) appears inconsistent with the oscillatory terms retained in Eq. (S.83). Please clarify whether the plotted curve is the result of the approximate formula or of a numerical integration, and explain how the oscillations (if present) are averaged or removed.
  4. [Supplemental §1.4.2, text after Eq. (S.83)] The statement 'Thus, for the waves, propagating in the forward direction at Brewster's angle... we have I+(θ=θ_Br) ∼ γ⁴' is drawn from an expression that contains N_s-dependent oscillatory factors. A reader cannot infer a clean γ⁴ law without an additional averaging step. Please state explicitly the regime in which the oscillatory terms are negligible.
  5. [General] The paper would benefit from a direct numerical evaluation of the full transfer-matrix expression (without the approximations of §1.4.2) for a modest N_s (e.g., 10²–10³) to verify the claimed γ⁴ scaling. This would substantially increase confidence in the central result.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the gamma^4 law follows from a transfer-matrix derivation with a designed (not fitted) thickness ratio; the main skeptical concern is rigor of an asymptotic estimate, not circularity.

full rationale

The central derivation is self-contained. Starting from Maxwell's equations, the paper constructs the transfer matrix (Supplemental Eqs. S.24-S.30), evaluates the spectral-angular intensity (S.42), and specializes to the Brewster angle where epsilon^{-1} k_z^epsilon = b^{-1} k_z^b makes the one-period transfer matrix diagonal (S.45). Equation (6) is the resulting coherent sum f_Ns, not an input fitted to data. The thickness ratio ab/a_epsilon = (sqrt(epsilon+b)-epsilon)/(b-sqrt(epsilon+b)) (Eq. S.76) is a derived condition, imposed so that the photonic-crystal quasimomentum satisfies qtilde_z = 1 in the frequency range; it is a design parameter, not a fitted quantity, and it does not by itself force the integrated gamma^4 scaling. The gamma^4 scaling is obtained by an explicit frequency integral in Supplemental Sec. 1.4.2 (S.81-S.83) after the change of variable y = omega l/(2 c gamma^2), with the stated assumptions lambda > 2l and 1 << gamma << sqrt(pi N_s ltilde). Whether that integral is controlled - the boundary term and the slowly-varying-prefactor replacement questioned by the skeptic - is a validity/rigor question, not circularity: the result is not defined in terms of itself, and the paper does not tune parameters to reproduce a target intensity. The only self-citations, e.g. [24] on random-media radiation and [26] reporting earlier Brewster-angle observations, are background/support remarks and are not load-bearing: the derivation does not rest on a uniqueness theorem or on a prior ansatz from the authors. The Discussion's limitations - needed N_s ~ 10^6-10^8 for gamma ~ 10^3-10^4 and the loss bound of Supplemental Eq. S.69 - are feasibility/robustness constraints, not circular steps. Thus no circular step meets the required standard of an exhibited reduction of output to input.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No new physical entities are postulated. The paper's contribution is a specific constraint on existing geometric/material parameters (thickness ratio ab/aε), not a new force, particle, or conserved quantity. The free parameters listed are design choices of the proposed detector (thickness ratio, spectral window, angular window) rather than fitted constants, but the γ⁴ and N_s² claims are sensitive to them.

free parameters (3)
  • Thickness ratio ab/aε = Eq. (5): (√(ε+b) − ε)/(b − √(ε+b))
    Chosen to make the resonance condition q̃_z = 1 hold at all frequencies. This is a designed/fixed parameter, not fitted to any measurement, and the paper analyzes deviations from it (§1.4.4) as a robustness check. It is not a free parameter in the pejorative sense, but it is a hand-chosen constraint selected to produce the effect.
  • Frequency integration window λ > 2l (λ_max unspecified) = λ > 2(ab+aε), λ_max not fixed in main text; Supplemental uses λ/l up to 20 or 50
    The γ⁴ result is derived for an integral over a finite wavelength window λ > 2l. The specific choice of window affects the numerical prefactor and figures; it is an observational/design choice rather than a fundamental constant.
  • Observation angular window |δθ| = |δθ| < 4×10⁻³ in Fig. 4; ≤ ~0.1 arcsec in discussion
    The claimed intensity requires restricting observation to a narrow angular range around Brewster's angle; the quoted yield depends on this window size.
assumptions (5)
  • standard math The radiation problem is 1D and p-polarized: H lies in the plane parallel to slabs and the only surviving component is H_Φ along e_Φ = ez × q̂ (Supplemental §1.1.1).
    Standard transition-radiation treatment (Ginzburg–Tsytovich), justified by the source term being collinear to e_Φ. Not independently verified here.
  • domain assumption Materials are non-dispersive and lossless in the frequency window of interest (ε, b real constants).
    Invoked in Supplemental §1.4 ('Assume our photonic crystal consists of materials that are non-dispersive in the frequency region of interest') and used to set k_z = (ω/c)√(ε − c²q²/ω²). Losses are added perturbatively later, but the γ⁴ law is derived in the lossless limit.
  • domain assumption The observation point is far enough that the mixed (charge–radiation interference) term of the Poynting vector vanishes (Supplemental §1.1.3, Eq. S.43).
    The intensity formulas discard W_int assuming z ≫ z±(θ) and z ≪ 1/(2 Im k_z). The paper claims this is feasible at Brewster's angle due to bounded formation zone, but it is an essential assumption.
  • standard math The number of slabs N_s is large enough for the delta-function/peak approximation f_Ns ≈ (2π/l)δ((ω/v ∓ q_z) mod 2π/l) to hold (Supplemental §1.2.2).
    Standard Poisson-summation/asymptotic approximation for large N_s; used throughout to get N_s² and γ⁴ results.
  • ad hoc to paper The integral of a product of a rapidly oscillating function F(ω) and a slowly varying function C(ω) can be approximated as C(ω*) ∫dω F(ω) (Supplemental §1.4.2).
    This is the key approximation enabling the γ⁴ law. No rigorous error bound or stationary-phase justification is given; it is an unproven estimate, though plausible for large N_s.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Strong Energy Dependent Transition Radiation in a Photonic Crystal." pith.science (2026). https://pith.science/paper/23TFGAHI

@misc{pith2026251118863,
  author       = {Pith},
  title        = {Pith review of: Strong Energy Dependent Transition Radiation in a Photonic Crystal},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/23TFGAHI}},
  note         = {Machine review of arXiv:2511.18863}
}
abstract

Radiation of a charged particle crossing an alternating stack of slabs in the optical region is considered. Both disordered and periodic stacks are investigated. It is shown that for special type of alternating disordered and periodic stacks the radiation problem can be solved exactly for backward and forward Brewster observation angles. Strong $N^2$ dependence of radiation intensity on slab number is re-established in special case of the disordered stack. This leads to strong directivity either on forward or on backward Brewster angles depending on the type of stack randomness. In certain type of periodic photonic crystal, a strong energy dependence $E^4$ for relativistic particles of the radiation intensity, observed at Brewster's angle is found. Further increment of particle energy leads to saturation. The band structure of the corresponding photonic crystal (PhC) has a behavior, analogous to the Dirac cones in graphene. We suggest this special type $1D$ photonic crystal for application as a detector of relativistic particles.

Figures

Figures reproduced from arXiv: 2511.18863 by the authors.

Figure 1
Figure 1. FIG. 1: Illustration of the problem [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (a) Illustration of the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Band structure of the described PhC for the modes propagat [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Differential yield for the photons, radiated along the Brew [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

34 extracted references · 20 canonical work pages

  1. [1]

    Gong, Z., Chen, R., Wang, Z., Xi, X., Y ang, Y ., Zhang, B., Chen, H., Kaminer, I., & Lin, X. (2025). Free-electron resonance transition radiation via Brewster randomness. Pro- ceedings of the National Academy of Sciences, 122(6), e2413336122. https://doi.org/10.1073/pnas.2413336122

    work page doi:10.1073/pnas.2413336122 2025

  2. [2]

    X. L. Y ang, H. Peng, K. H. Liu, Z. W. Huang, K. X. Lin, T. W. Huang, C. T. Zhou; Numerical evidences of the target size effect on the coherent transition radiation from relativistic electron beams interacting with a solid plasma target. Phys. Plasmas 1 August 2025; 32 (8): 083905. https://doi.org/10.1063/5.0276668

    work page doi:10.1063/5.0276668 2025

  3. [3]

    V ., Davydov, E

    Fursaev, D. V ., Davydov, E. A., & Tainov, V . A. (2025). Fast Radio Bursts and Electromagnetic Transition Radiation on Gravitational Shockwaves. https://doi.org/10.1088/1475- 7516/2025/10/008

    doi:10.1088/1475- 2025

  4. [4]

    Ding, C., Geng, X., & Ji, L. (2025). Self-seeded photon acceleration by electron beam-driven tran- sition radiation. arXiv preprint arXiv:2506.06531. https://doi.org/10.48550/arXiv.2506.06531

    work page Pith review arXiv doi:10.48550/arxiv.2506.06531 2025

  5. [5]

    116, 205003,(2016)

    Guo-Qian Liao,Y u-Tong Li,Yi-Hang Zhang, et al Demonstration of Coherent Terahertz Transi- tion Radiation from Relativistic Laser-Solid In- teractions, Phys.Rev.Lett. 116, 205003,(2016). https://doi.org/10.1103/PhysRevLett.116.205003

    work page doi:10.1103/physrevlett.116.205003 2016

  6. [6]

    Casalbuoni, S., Schmidt, B., Schmüser, P ., Arsov, V ., & Wesch, S. (2009). Ultrabroadband terahertz source and beamline based on coherent transition radiation. Physical Re- view Special Topics-Accelerators and Beams, 12(3), 030705. https://doi.org/10.1103/PhysRevSTAB.12.030705

    work page doi:10.1103/physrevstab.12.030705 2009

  7. [7]

    Toshiharu Takahashi, Tomochika Matsuyama, Katsuhei Kobayashi, Y oshiaki Fujita, Y ukio Shibata, Kimihiro Ishi, Mikihiko Ikezawa; Utilization of coherent transition radiation from a linear accelerator as a source of millimeter-wave spectroscopy. Rev. Sci. Instrum. 1 November 1998; 69 (11): 3770-3775. https://doi.org/10.1063/1.1149177

    work page doi:10.1063/1.1149177 1998

  8. [8]

    Co- herent single-cycle pulses with MV/cm field strengths from a relativistic transition radiation light source,

    Matthias C. Hoffmann, Sebastian Schulz, Stephan Wesch, Stef- fen Wunderlich, Andrea Cavalleri, and Bernhard Schmidt, "Co- herent single-cycle pulses with MV/cm field strengths from a relativistic transition radiation light source," Opt. Lett. 36, 4473-4475 (2011). https://doi.org/10.1364/OL.36.004473

    work page doi:10.1364/ol.36.004473 2011

Show all 34 references
  1. [9]

    Low-velocity-favored transition radiation

    Chen Jialin, Chen Ruoxi, Tay Fuyang, Gong Zheng, Hu Hao, Y ang Yi, Zhang Xinyan, Wang Chan, Kaminer Ido, Chen Hong- sheng, Zhang Baile, Lin Xiao (2023). Low-velocity-favored transition radiation. Physical Review Letters, 131(11), 113002. https://doi.org/10.1103/PhysRevLett.131.113002

    2023 doi

  2. [10]

    A strong-field THz light source based on coherent transition radiation

    Kang Yin , Wang Ruoyu , Chen Wei , Tu Lingjun , Zhang Kaiqing , Feng Chao (2023). A strong-field THz light source based on coherent transition radiation. Frontiers in Physics, 11, 1252725. https://doi.org/10.3389/fphy.2023.1252725

    2023

  3. [11]

    Sei, N., Ogawa, H., Sakai, T., Hayakawa, K., Tanaka, T., Hayakawa, Y ., & Nogami, K. (2017). Millijoule terahertz coherent transition radiation at LEBRA. Japanese Journal of Applied Physics, 56(3), 032401. https://doi.org/10.7567/JJAP .56.032401

    2017 doi

  4. [12]

    Andronic, J.P

    A. Andronic, J.P . Wessels, Transition radiation detectors, Nu- clear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equip- ment, V olume 666, 2012, Pages 130-147, ISSN 0168-9002, https://doi.org/10.1016/j.nima.2011.09.041

    2012 doi

  5. [13]

    Dolgoshein, B. (1993). Transition radiation detectors. Nu- clear Instruments and Methods in Physics Research Sec- 6 tion A: Accelerators, Spectrometers, Detectors and Associated Equipment, 326(3), 434-469. https://doi.org/10.1016/0168- 9002(93)90846-A

    1993 doi

  6. [14]

    B., & Mennessier, G

    Artru, X., Y odh, G. B., & Mennessier, G. (1975). Practical theory of the multilayered transition ra- diation detector. Physical review d, 12(5), 1289. https://doi.org/10.1103/PhysRevD.12.1289

    1975 doi

  7. [15]

    Alice Collaboration. (2018). The ALICE Transition Radiation Detector: construction, operation, and performance. Nuclear Instruments and Methods in Physics Research Section A: Ac- celerators, Spectrometers, Detectors and Associated Equip- ment, 881, 88-127. https://doi.org/10.1...

    2018 doi

  8. [16]

    Ducros, Y

    Detoeuf, J.F. Ducros, Y . Feinstein, F. Hubbard, J.R. Mangeot, Ph. Mansoulie, B. Teiger, J. Zylberstejn, A. (1989). Status of the transition radiation detector for the D0 experiment. Nuclear In- struments and Methods in Physics Research Section A: Accel- erators, Spectrometers...

    1989 doi

  9. [17]

    & Archambault, L

    Cloutier, E., Beaulieu, L. & Archambault, L. Direct in- water radiation dose measurements using Cherenkov emis- sion corrected signals from polarization imaging for a clin- ical radiotherapy application. Sci Rep 12, 9608 (2022). https://doi.org/10.1038/s41598-022-12672-w

    2022 doi

  10. [18]

    A. L. Pokrovsky, A. E. Kaplan, P . L. Shkolnikov; Transition radiation in metal-metal multilayer nanostructures as a medical source of hard x-ray radiation. J. Appl. Phys. 15 August 2006; 100 (4): 044328. https://doi.org/10.1063/1.2335974

    2006 doi

  11. [19]

    identical, optically dense slabs - environment

    for the intensity, integrated over angles and frequencies W + ∼ γ and concentrated along the velocity of the particle with angular width θ ∼ γ −1, and also, for the length of the ra- diation formation zone we get ∼ γ, since the cutoff frequency ωmin ∼ ωpγ, where ωp is the plas...

  12. [21]

    Ter-Mikaelyan, M.L., High-Energy Electromagnetic Processes in Condensed Media (Wiley, New Y ork, 1972)

    1972

  13. [22]

    Potylitsyn, A. P . Electromagnetic Radiation of Electrons in Pe- riodic Structures (Springer, Heidelberg, 2011)

    2011

  14. [23]

    V . L. Ginzburg and V . N. Tsytovich, Transition Radiation and Transition Scattering (Adam Hilger, Bristol, 1990)

    1990

  15. [25]

    Zh. S. Gevorkian, Radiation of a relativistic charged particle in a system with one-dimensional randomness, 1998, Phys. Rev. E., v.57, p.2338. https://doi.org/10.1103/PhysRevE.57.2338; Zh.S. Gevorkian, C.P . Chen and Chi-Kun Hu, New mecha- nism of X-ray radiation from a relati...

    1998 doi

  16. [26]

    Ruoxi Chen, Zheng Gong, Jialin Chen, Xinyan Zhang, Xingjian Zhu, Hongsheng Chen, Xiao Lin, Recent advances of transi- tion radiation: Fundamentals and applications, Materials To- day Electronics, V olume 3, 2023, 100025, ISSN 2772-9494, https://doi.org/10.1016/j.mtelec.2023.100025

    2023

  17. [27]

    Zh.S.Gevorkian, S. R. Harutyunyan, N. S. Ananikian, V . H. Arakelian, R. B. Ayvazyan, V . B. Gavalyan, N. K. Grigoryan, H. S. V ardanyan, V . H. Sahakian, and A. A. Hakobyan ,Observation of Resonant Diffusive Radiation in Random Multilayered Systems,2006 Phys.Rev.Lett,97,04480...

    2006 doi

  18. [28]

    Andrei and Hughes, Taylor L

    Bernevig, B. Andrei and Hughes, Taylor L.. Topo- logical Insulators and Topological Superconduc- tors, Princeton: Princeton University Press, 2013. https://doi.org/10.1515/9781400846733

    2013 doi

  19. [29]

    Science276, 1401-1404 (1997)

    Miri Park et al., Block Copolymer Lithography: Periodic Arrays of ∼ 1011 Holes in 1 Square Centimeter. Science276, 1401-1404 (1997). DOI:10.1126/science.276.5317.1401. https://doi.org/10.1126/science.276.5317.1401

    1997

  20. [30]

    Review of Directed Self- Assembly Material, Processing, and Application in Advanced Lithography and Patterning

    Cheng, X.; Liang, D.; Jiang, M.; Sha, Y .; Liu, X.; Liu, J.; Cao, Q.; Shi, J. Review of Directed Self- Assembly Material, Processing, and Application in Advanced Lithography and Patterning. Micromachines 2025, 16, 667. https://doi.org/10.3390/mi16060667

    2025 doi

  21. [31]

    Angle amplification for nanoradian measurements,

    Marco Pisani and Milena Astrua, "Angle amplification for nanoradian measurements," Appl. Opt. 45, 1725-1729 (2006). https://doi.org/10.1364/AO.45.001725 - Supplemental Material - Strong Energy Dependent Transition Radiation in a Photonic Crystal V .Gareyan1 and Zh.Gevorkian 1,2...

    2006 doi

  22. [32]

    there is an observation along the Brewster’s angle, i. e. ε −1kε z = b−1kb z , or 2) for the given observation angle the slab thickness satisfies sin (kb z ab) = 0. Applying steps similar to the previous case, we get A+ ≈ − 2π l eiqzlNsC1δ ((ω/v − qz) mod 2π/l) , A− ≈ 2π l C2δ ...

    2000

  23. [33]

    G. M. Garibyan and Y an Shi, X-Ray Transition Radiation (Akad. Nauk Arm. SSR, Y erevan, 1983)

    1983

  24. [34]

    Jelley, Cerenkov Radiation and Its Applications (Pergamon, New Y ork, 1958)

    J.V . Jelley, Cerenkov Radiation and Its Applications (Pergamon, New Y ork, 1958)

    1958

  25. [35]

    Lin, X., Easo, S., Shen, Y . et al. Controlling Cherenkov angles with resonance transition radiation. Nature Phys 14, 816-821 (2018). https://doi.org/10.1038/s41567-018-0138-4

    2018 doi

  26. [36]

    Optical Properties of Photonic Crystals, K. Sakoda. Springer, Berlin (2001)

    2001

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.