Pith. sign in

REVIEW 4 major objections 5 minor 32 references

A study of cross-relaxation and temporal dynamics of lasing at 2 microns in Thulium doped ceramic

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read Thulium ceramic laser's cross-relaxation nears its theoretical ceiling.

desk verdict Competent characterization of a Tm:Lu2O3 ceramic laser whose headline cross-relaxation value is plausible but whose error bars undersell the model uncertainty in the absorbed-power calibration. read the letter →

arxiv 2506.08948 v1 pith:O3PKYRQ6 submitted 2025-06-10 physics.optics

Alessandro Fregosi , Fernando Brandi , Luca Labate , Federica Baffigi , Gianluca Cellamare , Mohamed Ezzat , Daniele Palla , Guido Toci
show 2 more authors
Alex Whitehead Leonida A. Gizzi
This is my paper
classification physics.optics
keywords Thuliumcross-relaxationTm:Lu2O3ceramiclaser2micronslopeefficiencyrateequationmodelpulsedpumpingsolid-state
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 reports a diode-pumped thulium ceramic laser (Tm:Lu2O3, 4 at.% doping) emitting near 2 microns, and uses its measured slope efficiency of 73% to infer how efficiently thulium ions share excitation through cross-relaxation. The central claim is that cross-relaxation, the mechanism where one excited ion passes part of its energy to a neighboring ground-state ion so both end up in the laser upper level, operates at a coefficient of about 1.89–1.91, close to the theoretical maximum of 2. If correct, this means the material can convert pump photons into stored laser energy at nearly the best rate allowed by its energy-level scheme, which matters for building high-average-power, high-repetition-rate 2-micron lasers for applications like pumping titanium-sapphire amplifiers and driving plasma accelerators. The paper validates its model by matching both continuous-wave output power and millisecond-scale pulsed dynamics with a set of macroscopic rate equations.

What carries the argument

The central mechanism is thulium cross-relaxation (CR): an ion initially excited to the 3H4 level transfers part of its energy to a neighboring ground-state 3H6 ion, leaving both ions in the 3F4 upper laser level, so one pump photon can ultimately create two stored excitations. The quantity that measures this is η_CR, roughly the ratio of the upper-level population with CR active to the population when CR is forced off. The extraction path is the slope efficiency relation η_sl ≃ η_CR (λ_P/λ_L) R1/(R1+L), which connects the measured output-versus-pump slope to the CR coefficient through the wavelength ratio and cavity losses; the paper also uses a set of four coupled rate equations for the population densities N1–N4, coupled to a Fabry–Perot cavity equation, and an overlap integral that converts incident pump power to effective absorbed power P_eff in the laser mode.

What would settle it

A calorimetric measurement of the absorbed pump power in the same crystal under the same lasing conditions that differs from the overlap-corrected value χ = 0.47 ± 0.06 by more than its stated uncertainty would shift the retrieved η_CR beyond its quoted ±0.05 error bars.

Watch

Extended reading notes

Core claim

The paper claims that in a 4 at.% Tm:Lu2O3 ceramic, cross-relaxation is almost fully exploited. From the slope of laser output power versus effective absorbed pump power, m = 0.73 ± 0.02, and the relation η_sl ≃ η_CR (λ_P/λ_L) R1/(R1+L), the authors obtain η_CR = 1.89 ± 0.05 at 23 °C (1.91 ± 0.05 at 13 °C), while the numerical rate-equation solution gives 1.91 and an independent calculation from the formula η_CR = P41N/(1/τ40 + P41N) yields 1.97. These values approach the maximum theoretical η_CR of 2. The paper also demonstrates that the same rate-equation model reproduces the pulsed laser output over millisecond time scales, including the roughly 100 µs delay between pump onset and the first laser pulse, thereby establishing both the high efficiency and the validity of the model used to extract it.

Load-bearing premise

The extraction of η_CR relies on converting measured incident pump power into the effective power absorbed inside the laser mode using a Gaussian-beam overlap factor χ = 0.47 ± 0.06, and the systematic errors in that factor and in the assumed negligible ground-state depletion are not propagated into the quoted ±0.05 uncertainties.

Editorial extensions

If this is right

  • If cross-relaxation really runs at η_CR ≈ 1.9, a single 796 nm pump photon can store nearly two 2 µm excitations, so Tm:Lu2O3 lasers can approach the theoretical maximum quantum conversion for this scheme.
  • The rate-equation model's agreement with both cw slope data and millisecond pulsed dynamics makes it a predictive tool for designing Tm:Lu2O3 cavities, such as amplifiers for 2 µm short-pulse lasers.
  • The measured slope efficiency of 73% implies the ceramic sample had small cavity losses, about 1.3%, so the material's quality supports scaling to larger pumped volumes.
  • The model's reproduction of the roughly 100 µs first-pulse delay, and its shortening on later pulses, gives a quantitative basis for timing pulsed pump diodes in burst-mode operation.

Reading between the lines

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

  • The quoted ±0.05 uncertainty on η_CR does not include systematic errors in the overlap factor χ = 0.47 ± 0.06 or the assumed negligible ground-state depletion; an independent calibration of P_eff could tighten or shift the central value.
  • Applying the same slope-efficiency extraction across a series of Tm doping concentrations would map where cross-relaxation saturates and where the inverse process (P22 upconversion) starts to degrade the two-for-one advantage.
  • The model's success on millisecond dynamics suggests it could be extended to the multi-pulse extraction regime at kilohertz repetition that the paper names as the target for high-average-power systems, but that regime is not explored in this work.
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

4 major / 5 minor

Summary. The paper reports an experimental and numerical study of a Tm:Lu2O3 ceramic laser pumped at ~795 nm and lasing at 2 µm. The authors measure the output power versus effective absorbed pump power, obtain a slope efficiency of ~73%, and convert this into a cross-relaxation coefficient η_CR ≈ 1.9, which they interpret as approaching the theoretical maximum of 2. They also present rate-equation simulations that reproduce the continuous-wave power curve and the pulsed temporal dynamics, and they compare the retrieved η_CR with a value computed from literature parameters.

Significance. The result is of practical interest for high-average-power 2 µm lasers based on thulium-doped ceramics, because an efficient cross-relaxation mechanism directly improves the quantum efficiency of the pump process. The paper combines a detailed rate-equation model, measurements of absorption and emission cross sections, and comparisons in both quasi-CW and pulsed regimes. The measurement of the slope efficiency itself is straightforward, and the pulsed-dynamics comparison is a useful validation of the modeling framework. However, the headline quantitative claim (η_CR ≈ 1.9, approaching the maximum of 2) currently depends on an effective pump-power calibration whose systematic uncertainty is not propagated, and the paper contains a formula error in the definition of η_CR. These issues are repairable, so the manuscript merits revision rather than rejection.

major comments (4)
  1. [Section 4, final paragraph] The expression η_CR = P41N/(1/τ40+P41N) is printed without a factor of 2 (or an added unity) and cannot produce the stated result η_CR = 1.97, because the denominator exceeds the numerator. With the given parameters (P41N ≈ 7.0×10^−2 µs^−1, 1/τ40 ≈ 1.7×10^−3 µs^−1), the printed formula yields ~0.98, not 1.97. The correct expression for the number of upper-laser-level ions per absorbed pump photon is η_CR = 1 + P41N/(1/τ40 + P41N), equivalently (1/τ40 + 2P41N)/(1/τ40 + P41N). Please correct the formula and ensure a consistent definition of η_CR is used throughout.
  2. [Section 4, Eqs. (6)-(7)] The slope efficiency m is defined with respect to P_eff, which is obtained via P_eff = χ P_Inc with χ = 0.47 ± 0.06. Because η_CR = (λ_L/λ_P) m and m ∝ 1/χ, the ±13% relative uncertainty in χ propagates directly into η_CR, giving a systematic error of roughly ±0.24, which is five times the quoted statistical error of ±0.05. The paper acknowledges the Gaussian approximation of a strongly multimode pump (M²≈150) and the assumption of negligible ground-state depletion as limitations, but these are not included in the reported uncertainties. Please propagate these systematic effects and discuss how they affect the claim that η_CR approaches the theoretical maximum of 2.
  3. [Section 2 vs. Section 4] The theoretical relation η_sl ≃ η_CR (λ_P/λ_L) R1/(R1+L) presented in Section 2 is not the relation used to retrieve η_CR in Section 4, where η_CR = (λ_L/λ_P) m is used without the factor R1/(R1+L). While the missing factor is close to unity (~0.987), the inconsistency should be resolved by using the same formula in both places, and the approximate nature of the relation should be stated.
  4. [Section 4 and Table 1] The numerical simulation is adjusted to the measured power data by fitting the cavity loss L, stated as L=1.3% in Table 1 and in the Fig. 7 caption, but as L=1.1% in the text of Section 4. Because L is fitted to the same slope-efficiency data, the simulated value η_CR = 1.91 is not an independent confirmation of the experimental value 1.89; it is a consistency check of the model with one free parameter. Please reconcile the two values of L and clarify that the simulation does not independently predict η_CR.
minor comments (5)
  1. [Table 1 and Section 4] The cavity loss is given as L=0.013 in Table 1 but as L=1.1% in the text of Section 4; these values should be reconciled.
  2. [Figs. 6 and 7] Fig. 6 reports slope efficiencies of 0.75 and 0.74 for the two temperatures, while Fig. 7 gives m=0.73 for what appears to be the same dataset; the relationship between the two figures should be clarified.
  3. [Section 2] The sentence 'The limit is given by η_sl ≤ 0.8 for η_CR = 2' is inconsistent with the formula preceding it, which with the given values yields about 0.76.
  4. [Abstract and Section 4] The abstract and conclusion state a slope efficiency of 73%, while Section 4 reports 74–75% for the individual temperature datasets; please make the reported values consistent.
  5. [General] There are several grammatical and typographical errors, e.g., 'in order for the model to match the data' and 'we’re not accounting for this short timescale behavior'; a careful proofread is recommended.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the slope-to-eta_CR conversion is an explicit measurement inversion, and the simulation's eta_CR uses literature P41/tau40 rather than the fitted slope.

full rationale

The central chain is: measure P_L vs P_eff; fit slope m; convert via eta_sl ~ eta_CR (lambda_P/lambda_L) R1/(R1+L) to retrieve eta_CR; and compare with a rate-equation simulation whose eta_CR comes from literature P41(4%) and tau40, not from the measured slope. This is a measurement inversion plus an independent cross-check, not a prediction from the fitted data. The only fitted model parameter in the CW comparison is the cavity loss L=1.1%, used to match the output-power curve; eta_CR itself is not fit. The paper explicitly acknowledges the P_eff model limitations in Section 4, stating: "It is worth noting at this point the main limitations of the above procedure... Eq. (7) holds in the case of a negligible depletion of the ground state"; this is a systematic-error caveat rather than a circular reduction. The final printed formula eta_CR = P41N/(1/tau40+P41N) with result 1.97 is arithmetically inconsistent as written (the expression evaluates to about 0.98 unless a factor of 2 is intended), but this is a typographical/correctness issue, not a circularity. Self-citations ([14,15,25]) are contextual and not load-bearing for the eta_CR claim; no uniqueness theorem or ansatz is smuggled via self-citation. The quoted eta_CR uncertainty does not propagate the 13% systematic uncertainty in chi, which is an incomplete error budget but not circularity. Overall, the derivation is self-contained against the external literature values and does not reduce to its own inputs by construction.

Assumptions & free parameters 1 free parameters · 7 assumptions · 0 invented entities

The model depends heavily on literature values for lifetimes, branching ratios, and P41(Tm) concentration scaling. The only parameter fitted to the data is the cavity loss L. No new physical entities are introduced.

free parameters (1)
  • cavity residual loss L = 1.1% or 1.3% (inconsistent)
    Fitted so the simulation matches the measured laser power in Fig. 7; the text gives L=1.1% while the figure caption and Table 1 give 1.3%.
assumptions (7)
  • domain assumption Macroscopic rate equations with levels 3H6, 3F4, 3H5, 3H4 and cross-relaxation terms P41 and P22 describe Tm:Lu2O3 dynamics.
    Taken from Ref. [17]; used as the model basis in Eqs. (1)-(4).
  • domain assumption Lifetime quenching follows τ_i(ηd) = τ_i0/(1 + A_i η_d^2).
    From Refs. [17,19]; gives τ2(4%)≈1.22 ms and τ4(4%)≈63 µs.
  • domain assumption Cross-relaxation coefficient P41 depends on concentration as P41(ηd) = B η_d^2 / (η_d^2 + η_0^2), with B and η0 from Refs. [22,23,24].
    Used to compute P41(4%) = 6.28e-29 m3 µs-1.
  • domain assumption The cross-relaxation coefficient is given by η_CR = P41N / (1/τ40 + P41N), citing Refs. [20,32].
    This formula as printed is inconsistent with the stated result of 1.97; a factor of 2 appears to be missing if the max is 2.
  • domain assumption Slope efficiency relates to η_CR by η_sl ≈ η_CR (λ_P/λ_L) R1/(R1+L).
    Used in Section 2 to convert measured slope efficiency to cross-relaxation coefficient; approximate and ignores other losses.
  • domain assumption Pump beam with M²≈150 is well approximated by a Gaussian for overlap calculations.
    Used in Eq. (6); the authors note the potential uncertainty from this approximation.
  • domain assumption Ground-state depletion is negligible when computing absorbed pump power via Eq. (7).
    Acknowledged by the authors as a limitation in Section 4; the transmission measurement with and without lasing shows up to 10% difference.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A study of cross-relaxation and temporal dynamics of lasing at 2 microns in Thulium doped ceramic." pith.science (2026). https://pith.science/paper/O3PKYRQ6

@misc{pith2026250608948,
  author       = {Pith},
  title        = {Pith review of: A study of cross-relaxation and temporal dynamics of lasing at 2 microns in Thulium doped ceramic},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O3PKYRQ6}},
  note         = {Machine review of arXiv:2506.08948}
}
read the original abstract

We report the characterization of the pump absorption and emission dynamic properties of a \tulio{} ceramic lasing medium using a three mirrors folded laser cavity. We measured a slope efficiency of 73\%, which allowed us to retrieve the cross-relaxation coefficient. The behavior of our system was modeled via a set of macroscopic rate equations in both the quasi continuous wave and the pulsed pumping regime. Numerical solutions were obtained, showing a good agreement with the experimental findings. The numerical solution also yielded a cross-relaxation coefficient in very good agreement with the measured one, showing that the cross-relaxation phenomenon approaches the maximum theoretical efficiency.

Figures

Figures reproduced from arXiv: 2506.08948 by the authors.

Figure 1
Figure 1. The scheme of the energy levels used to model the laser dynamics, from[17] . W41 (t) = σeIp (t) /hνp, where σa and σe are respectively the absorption and emission pump cross section obtained from the measurements reported in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Example of the measured absorption cross-section in the center of the Tm: Lu2O3 ceramic sample used [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Scheme (not to scale) of the experimental apparatus: the achromatic doublets (AD) are used to focus the pump beam emerging from the optical fiber on the sample; the cavity is composed by three mirrors: the dichroic entry mirror (EM) and the spherical mirror (SM) transmit the pump light while they reflect the 2 µm radiation. 90% and 97% reflectivity output coupler mirrors (OM) are used. Both the pump and the laser be… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Laser spectra for the two 90% and 97% reflectivity output coupler mirrors. With the 97% reflectivity we observe a change in the emission spectra as a function of the cavity losses due to its alignment. decrease in the radiation absorbed by the sample that is taken into…
Figure 5
Figure 5. Figure 5: Pump laser power transmitted as a function of the incident pump laser power for the two different working temperatures of 13 and 23 ◦C. Straight lines are the results of a best fit calculation that we use to obtain the pump absorption ratio g in Eq. (9). Using the meas…
Figure 6
Figure 6. Figure 6: Laser power as a function of the effective absorbed pump power for the two working temperature of 13 and 23 ◦C; the straight lines are the results of a best fit calculation that provide both the laser threshold power and slope efficiency. Exp. Sim. 0.2 0.5 1 1.5 2 3 4 …
Figure 8
Figure 8. Figure 8: Experimental and theoretical laser power as a function of time obtained for pump pulse width of 150 µs in the top panel and 700 µs in the bottom panel. The resulting laser power is reported in [PITH_FULL_IMAGE:figures/full_fig_p005_8.png]
Figure 7
Figure 7. Figure 7: Experimental and theoretical laser power as a function of Peff . The dashed line is a linear fit of the data while the solid line is obtained with the model in Eq. 1—5. The cavity energy loss L is tailored to 1.3% in order for the model to match the data. the whole vol…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

32 extracted references · 31 canonical work pages

  1. [1]

    N., Haefner, C., Bromage, J., Butcher, T., Chanteloup, J.-C

    Danson, C. N., Haefner, C., Bromage, J., Butcher, T., Chanteloup, J.-C. F., Chowdhury, E. A., Galvanauskas, A., Gizzi, L. A., Hein, J., Hillier, D. I., Hopps, N. W., Kato, Y ., Khazanov, E. A., Kodama, R., Korn, G., Li, R., Li, Y ., Limpert, J., Ma, J., Nam, C. H., Neely, D., Papadopoulos, D., Penman, R. R., Qian, L., Rocca, J. J., Shaykin, A. A., Siders,...

    work page 2019

  2. [2]

    K., Akhter, T., Alesini, D., Alexandrova, A

    Assmann, R., Weikum, M. K., Akhter, T., Alesini, D., Alexandrova, A. S., Anania, M. P., Andreev, N. E., Andriyash, I., Artioli, M., Aschikhin, A., Audet, T., Bacci, A., Barna, I. F., Bartocci, S., Bayramian, A., Beaton, A., Beck, A., Bellaveglia, M., Beluze, A., Bernhard, A., Biagioni, A., Bielawski, S., Bisesto, F. G., Bonatto, A., Boulton, L., Brandi, F...

    work page 2020

  3. [3]

    Mason, N

    P. Mason, N. Stuart, J. Phillips, R. Heathcote, S. Buck, A. Wojtusiak, M. Galimberti, T. de Faria Pinto, S. Hawkes, S. Tomlinson, R. Pattathil, T. Butcher, C. Hernandez-Gomez, and J. Collier, Progress on Laser Development at the Extreme Photonics Applications Centre, in2023 Conf. Lasers Electro-Optics Eur . Eur . Quantum Electron. Conf., page 1, 2023

    work page 2023

  4. [4]

    C. M. Werle, C. Braun, T. Eichner, T. H ¨ulsenbusch, G. Palmer, and A. R. Maier, Opt. Express31, 37437 (2023)

    work page 2023

  5. [5]

    E. Adli, W. An, N. Andreev, O. Apsimon, R. Assmann, J.-L. Babiegeon, R. Bingham, T. Blackburn, C. Brady, M. Bussmann, B. Carlsten, J. Chappell, J. B. B. Chen, S. Corde, L. Corner, B. Cowan, B. Cros, J. England, E. Esarey, R. Fonseca, B. Foster, S. Gessner, L. A. Gizzi, D. Gordon, E. Gschwendtner, A. Hartin, B. Hidding, M. Hogan, S. Hooker, T. Hughes, A. K...

    work page 2019

  6. [6]

    Sistrunk, D

    E. Sistrunk, D. A. Alessi, A. Bayramian, K. Chesnut, A. Erlandson, T. C. Galvin, D. Gibson, H. Nguyen, B. Reagan, K. Schaffers, C. W. Siders, T. Spinka, and C. Haefner, Laser Technology Development for High Peak Power Lasers Achieving Kilowatt Average Power and Beyond, inShort-pulse High-energy Lasers Ultrafast Opt. Technol., edited by P. Bakule and C. L....

    work page 2019

  7. [7]

    Tamer, B

    I. Tamer, B. A. Reagan, T. Galvin, J. Galbraith, E. Sistrunk, A. Church, G. Huete, H. Neurath, and T. Spinka, Opt. Lett.46, 5096 (2021)

    work page 2021

  8. [8]

    T. C. Galvin, A. Bayramian, K. D. Chesnut, A. Erlandson, C. W. Siders, E. Sistrunk, T. Spinka, and C. Haefner, Scaling of petawatt-class lasers to multi- kHZ repetition rates, inHigh-Power , High-Energy, High-Intensity Laser Technol. IV, edited by J. Hein and T. J. Butcher, volume 11033, page 1103303, International Society for Optics and Photonics, SPIE, 2019

    work page 2019

Show all 32 references
  1. [9]

    Behnke, R

    L. Behnke, R. Schupp, Z. Bouza, M. Bayraktar, Z. Mazzotta, R. Meijer, J. Sheil, S. Witte, W. Ubachs, R. Hoekstra, and O. O. Versolato, Opt. Express29, 4475 (2021)

    2021

  2. [10]

    Behnke, E

    L. Behnke, E. J. Salumbides, G. G ¨oritz, Y . Mostafa, D. Engels, W. Ubachs, and O. Versolato, Opt. Express 31, 24142 (2023)

    2023

  3. [11]

    Mostafa, L

    Y . Mostafa, L. Behnke, D. J. Engels, Z. Bouza, J. Sheil, W. Ubachs, and O. O. Versolato, Applied Physics Letters123, 234101 (2023)

    2023

  4. [12]

    Tamer, Z

    I. Tamer, Z. Hubka, L. Kiani, J. Owens, A. Church, F. Batysta, T. Galvin, D. Willard, A. Yandow, J. Galbraith, D. Alessi, C. Harthcock, B. Hickman, C. Jackson, J. Nissen, S. Tardiff, H. Nguyen, E. Sistrunk, T. Spinka, and B. A. Reagan, Opt. Lett. 49, 1583 (2024)

    2024

  5. [13]

    Rastogi and S

    V . Rastogi and S. Chaurasia, Photonics11(2024)

    2024

  6. [14]

    Palla, L

    D. Palla, L. Labate, F. Baffigi, G. Cellamare, and L. A. Gizzi, Opt. Laser Technol.156, 108524 (2022)

    2022

  7. [15]

    Cellamare, L

    G. Cellamare, L. Labate, F. Baffigi, D. Palla, and L. A. Gizzi, Preliminary design of a Tm:Lu2O3-based amplifier for J-scale ultra-short pulses at a kW average power, inProc.SPIE, volume 11777, 2021

    2021

  8. [16]

    R. C. Powell and G. Blasse, Energy transfer in concentrated systems, inLuminescence and Energy Transfer, pages 43–96, Berlin, Heidelberg, 1980, Springer Berlin Heidelberg

    1980

  9. [17]

    Albalawi, S

    A. Albalawi, S. Varas, A. Chiasera, H. Gebavi, W. Albalawi, W. Blanc, R. Balda, A. Lukowiak, M. Ferrari, and S. Taccheo, Opt. Mater. Express7, 3760 (2017). 8

    2017

  10. [18]

    Baylam, F

    I. Baylam, F. Canbaz, and S. A., IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS24, 1601208 (2018)

    2018

  11. [19]

    Gebavi, D

    H. Gebavi, D. Milanese, R. Balda, S. Chaussedent, M. Ferrari, J. Fernandez, and M. Ferraris, Journal of Physics D: Applied Physics43, 135104 (2010)

    2010

  12. [20]

    Loiko, P

    P. Loiko, P. Koopmann, X. Mateos, V . Serres, J. S. Jambunathan, A. Lucianetti, T. Mocek, M. Aguil´o, F. D´ıaz, U. Griebner, V . Petrov, and C. Kr¨ankel, IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS24, 1601208 (2018)

    2018

  13. [21]

    O. L. Antipov, S. Y . Golovkin, O. N. Gorshkov, N. G. Zakharov, A. P. Zinov’ev, A. P. Kasatkin, M. V . Kruglova, M. O. Marychev, A. A. Novikov, N. V . Sakharov, and E. V . Chuprunov, Quantum Electronics 41, 863 (2011)

    2011

  14. [22]

    Falconieri, A

    M. Falconieri, A. Lanzi, G. Salvetti, and A. Toncelli, Optical Materials7, 135 (1997)

    1997

  15. [23]

    M. Tao, Q. Huang, T. Yu, P. Yang, W. Chen, and X. Ye, Cross relaxation in Tm-doped fiber lasers, in Proceedings of SPIE - The International Society for Optical Engineering, volume 8796, 2013

    2013

  16. [24]

    Rustad and K

    G. Rustad and K. Stenersen, IEEE Journal of Quantum Electronics32, 1645 (1996)

    1996

  17. [25]

    Y . Feng, G. Toci, B. Patrizi, A. Pirri, Z. Hu, X. Chen, J. Wei, H. Pan, X. Li, X. Zhang, S. Su, M. Vannini, and J. Li, Journal of the American Ceramic Society103, 1819 (2020)

    2020

  18. [26]

    P. F. Moulton, IEEE JOURNAL OF QUANTUM ELECTRONICSQE-21, 073505 (1985)

    1985

  19. [27]

    A. E. Siegman, How to (maybe) measure laser beam quality, inDPSS (Diode Pumped Solid State) Lasers: Applications and Issues, page MQ1, Optica Publishing Group, 1998

    1998

  20. [28]

    Koopmann, R

    P. Koopmann, R. Peters, K. Petermann, and G. huber, Appl. Phys. B102, 19–24 (2011)

    2011

  21. [29]

    Kogelnik and T

    H. Kogelnik and T. Li, Appl. Opt.5, 1550 (1966)

    1966

  22. [30]

    Svelto,Principles of Lasers, Springer US, 2010

    O. Svelto,Principles of Lasers, Springer US, 2010

    2010

  23. [31]

    Zheng, H

    L. Zheng, H. Wu, L. Zhang, Y . Luo, G.-H. Pan, X.-J. Wang, Z. Hao, and J. Zhang, Ceramics International 49, 11060 (2023)

    2023

  24. [32]

    van Dalfsen, S

    K. van Dalfsen, S. Aravazhi, C. Grivas, S. M. Garc ´ıa- Blanco, and M. Pollnau, Opt. Lett.39, 4380 (2014)

    2014

Pith tools

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