{"id":"452754c4-2aca-416a-baed-d8a11136d609","arxiv_id":"2608.13288","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A Floquet quasi-phase-matching theory and truncated multimode simulations show that nonlinear gas-filled multipass cells can exhibit geometric parametric instability, generating tunable discrete sidebands from a Gaussian pump.","lead":"This paper uses theory and simulations to show that gas-filled multipass cells, a standard tool for compressing high-power laser pulses, can develop discrete spectral sidebands through a geometric parametric instability previously seen mainly in special optical fibers. The sideband frequencies are tunable through cavity geometry and gas pressure, which matters for beam quality and for generating multiple colors from a single pulse.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The load-bearing idealization is the diagonal radial-mode truncation: pump-mediated FWM between different radial indices (nonzero S_{p_s,0,0,p_i}) is omitted, so the predicted spectrum may not be the full GPI spectrum.","rationale":"The reader's weakest assumption was direct nonlinear interaction at crossing points; I find that assumption well-justified by the timing (temporal separation 24–900× the pulse duration), so I do not rest the concern there. The more load-bearing idealization is the diagonal radial truncation, which the paper explicitly admits in the Conclusion. It is load-bearing because the linear stability analysis is the foundation of Eqs. (12), (16), and (21); restricting the signal and idler to equal radial indices is not justified by any symmetry, and the off-diagonal overlaps are numerically comparable to the diagonal ones. The MMGNLSE equations in Appendix C implement exactly the same restriction, so the simulations cannot falsify the omitted physics. This does not disprove the claim that some GPI can occur: the diagonal p_s=1 branch will likely survive in a full treatment. However, the quantitative sideband spectrum and gain structure are not established until the cross-radial terms are included. I therefore keep the reader's CONDITIONAL verdict, with a sharper condition attached. Credit is due for an internally consistent analytical derivation, closed-form gain and depletion expressions, and an explicit statement of the model's limitations. The proposed test settles whether the predicted spectrum is complete or only an artifact of the diagonal truncation.","tokens_in":17676,"tokens_out":16278,"duration_ms":188287,"concrete_test":"Implement a five-mode radial MMGNLSE with the full pump-mediated overlap tensor S_{p,0,0,q} for p,q=0,...,4 (including p≠q) and rerun the small-signal Floquet linearization with the same tensor. Keep the parameters of Table I. Compare the sideband center frequencies and per-pass gains with Eqs. (12) and (16). If branches with ΔN=6,10,... dominate or the p_s=1,h=0 gain changes by more than ~20%, the diagonal-only spectrum is not representative and the numerical claim needs revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on a linearized Floquet analysis whose eigenmodes are assumed to be isolated LG_{0p} sideband pairs with equal radial indices. This is not a selection rule. Equation (5) allows µ_s≠µ_i, and for the radial branch the mismatch is ΔN=N_s+N_i−2N_p=2(p_s+p_i), not necessarily 4p_s. The overlaps S_{p_s,0,0,p_i} are nonzero for p_s≠p_i; e.g. S_{1,0,0,2}=3/8, comparable to S_{1,0,0,1}=1/2. Equations (23) and (C1)–(C2) nevertheless restrict the nonlinear sum to diagonal overlaps S_{p,0,0,p}, so the small-signal matrix and the MMGNLSE both exclude pump-mediated cross-radial FWM terms A_0^2 A_{p_i}^* with p_i≠p_s. The numerical agreement with Eq. (14) therefore confirms the reduced model, not the full multimode physics. Including the full tensor would introduce additional Floquet branches at ΔN=6,10,... and can change the fastest-growing radial composition. The manuscript's Conclusion admits 'Direct energy transfer between different higher-order radial modes is not included,' which is the load-bearing assumption. The crossing-point approximation is less critical: for L_cav=1.95 m and 0.05 m the time between successive center crossings is ≈6.5 ns and ≈0.17 ns versus a 7 ps pulse, i.e. 24–900× longer.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes that geometric parametric instability (GPI) can occur in gas-filled nonlinear multipass cells (MPCs). The authors map a mode-matched symmetric MPC onto an equivalent waveguide with Laguerre–Gaussian modes, take each mirror-to-mirror pass as one period of a Floquet map, and derive a quasi-phase-matching condition governed by the single-pass Gouy-phase imbalance of the signal–idler pair relative to the pump pair. The central spectral prediction is Eq. (14), giving the sideband detuning Δf_SB ≈ (1/2π)√((4p_sΦ0 + 2πh)/(β2 L_cav)). They derive the small-signal gain (Eq. 16), bandwidth (Eq. 20), and a pump-depleted coupled-mode model (Eq. 21) with a maximum converted fraction u_max = 1 − |D_h|/2. A truncated MMGNLSE retaining five radial modes and diagonal pump–sideband overlaps is used to simulate the process; the simulations reproduce the predicted sideband positions and show pump depletion and competition among radial channels. The paper concludes that GPI may limit spatial beam quality in nonlinear pulse compression while offering a tunable mechanism for broadband multicolor generation.","tokens_in":18058,"tokens_out":6024,"duration_ms":65860,"significance":"If the central prediction holds, the paper describes a new physical mechanism in a technologically relevant platform: a mode-matched MPC would act as a discrete parametric amplifier whose sideband spectrum is set by geometry and gas pressure. The analytical derivation is parameter-free in an important sense: the dispersion uses literature Sellmeier data for argon, the Gouy phase and overlap integrals are computed analytically, and no free parameters are tuned to match the simulated sideband positions. The numerical data do reproduce the predicted frequencies and the gain hierarchy, which is a meaningful internal consistency check. However, the validation is not independent of the theory: the MMGNLSE is built from the same diagonal-overlap and path-averaged Gouy-phase assumptions as the analytical model and truncates to five radial modes. The load-bearing idealization is the omission of pump-mediated FWM between sideband modes with different radial indices. This limitation is explicitly acknowledged in the Conclusion, but it is central to the claim that the full multimode GPI spectrum has been described.","major_comments":[{"comment":"The phase-matching and gain analysis restricts the signal–idler pair to equal radial indices, μ_s = μ_i = (0, p_s), giving ΔN = 4p_s in Eq. (6). The overlap tensor in Eq. (5) does not enforce p_s = p_i: for example, S_{1,0,0,2} = 3/8 is comparable to S_{1,0,0,1} = 1/2, so the degenerate-FWM tensor contains additional pump-mediated couplings A_0^2 A_{p_i}^* with p_i ≠ p_s. Equations (23) and (C1)–(C2) drop all such cross-radial terms, and Eq. (12) consequently predicts only branches with ΔN = 4p_s. Including the full tensor would introduce additional Floquet branches at ΔN = 6, 10, ... (e.g., from p_s = 1, p_i = 2), which can change the fastest-growing radial composition and the sideband spectrum. The Conclusion states that direct energy transfer between different higher-order radial modes is not included; my reading is that this is the load-bearing assumption of the paper. I request a quantitative estimate of the magnitude of the omitted cross-radial terms relative to the retained γ_FWM(p_s) at the parameters of Figs. 5–8, or a simulation that includes them.","section":"Sec. II.3 and Appendix C (Eqs. 6, 12, 23, C1–C2)"},{"comment":"The numerical verification is not independent of the analytical model. The MMGNLSE in Eq. (23) uses the same diagonal-overlap restriction S_{p,0,0,p}, the same path-averaged γ_eff(C), and the same Gouy-phase term as the theory, and it retains only five radial modes. The agreement between the simulated sideband positions and Eq. (14) therefore demonstrates internal consistency of the reduced model, but it does not test the full multimode GPI spectrum. I recommend either extending the MMGNLSE to include the full overlap tensor (or a controlled subset with p_s ≠ p_i), or providing an analytic estimate of the omitted cross-radial FWM terms. This distinction matters because the manuscript's abstract and conclusion claim that a Gaussian pump will amplify discrete sidebands at Floquet quasi-phase-matching frequencies set by the Gouy-phase imbalance; if the cross-radial terms introduce additional branches or modify the dominant radial order, the central spectral prediction is incomplete.","section":"Sec. III.1 and III.2 (Figs. 5–8)"},{"comment":"The pump-depleted coupled-mode model fixes the nonlinear phase mismatch δϕ_NL at the input pump power and neglects depletion-induced changes of pump SPM and sideband XPM; the authors disclose this in Appendix A. In the large-signal simulations of Fig. 7, the gain saturation and the 'competition' among radial channels are therefore derived from a model that also uses the diagonal truncation. If cross-radial FWM is present, energy can be transferred directly between p_s = 1 and p_s = 2 channels, so the interpretation of higher-order channels as independent competitors driven by a common pump may change. I ask the authors to clarify, at least quantitatively, whether the omitted cross-radial terms could alter the predicted conversion dynamics or the pump-depletion scenario in Fig. 7.","section":"Sec. II.4.2 and Appendix A (Eqs. 21, A1–A6)"}],"minor_comments":[{"comment":"The text says that Floquet orders with 4p_sΦ0 + 2πh ≤ 0 have no positive-detuning solution, but the figures include negative h. Please state explicitly the allowed h range for the branches shown in Figs. 3 and 9 so that readers can map the notation onto the plotted bands.","section":"Sec. II.3 (Eq. 14)"},{"comment":"The caption describes the color scale as '(20/ln 10)G' and the text says '10 log10 e^{2G}'; these are equivalent, but the caption could be simplified to 'gain in dB' to avoid confusion about the factor of two.","section":"Fig. 9 caption"},{"comment":"The effective pass number J_eff(J) = (1−R^J)/(1−R) is introduced without derivation. A brief sentence explaining how mirror loss per pass is folded into the gain expression would help the reader assess the 18 dB discrepancy in Fig. 6(b).","section":"Eq. (24)"},{"comment":"The final sentence, 'Direct energy transfer between different higher-order radial modes is not included in the present model,' is an important limitation that appears only at the end of the paper. I recommend stating this assumption explicitly in the abstract or in a dedicated model-assumptions paragraph in Sec. II so that readers do not over-interpret the numerical confirmation.","section":"Sec. IV (Conclusion)"},{"comment":"The expression Φ0(C) = 2 arctan[√(C/(2−C))] assumes the beam waist is at the cavity center (ζ = 0) and that the mirrors are at ζ = ±L_cav/2. This is stated in the text, but it would be helpful to repeat it in the caption of Fig. 1(a) where the geometry is illustrated.","section":"Sec. II.1 (Eq. 2)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is technically careful and the analytical framework is internally consistent. The main risk is the diagonal-overlap truncation: the authors explicitly omit cross-radial FWM and acknowledge it only in the final sentence of the Conclusion. Because the numerical validation uses the same truncation, the present evidence supports the reduced model rather than the full multimode claim. This is a fixable issue within the manuscript's scope—either by adding a quantitative estimate of the omitted terms or by running a full-tensor simulation—so I recommend major revision rather than rejection. I would not want the paper rejected on the current evidence because the limitation is disclosed and the derivation is sound as far as it goes."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this paper claims a new instability class in multipass cells: geometric parametric instability driven by the discrete Gouy-phase imbalance per pass. The Floquet quasi-phase-matching condition, Eq. (14), is clean and new, and the small-signal gain, bandwidth, pump-depleted analysis, and tunability maps are all carefully worked out. The authors use literature Sellmeier data and analytic overlap integrals with no fitted parameters, and their MMGNLSE simulations reproduce the predicted sideband positions. That is real work and deserves credit.\n\nThe soft spot is load-bearing. The linearized Floquet analysis and the MMGNLSE both restrict the nonlinear sum to diagonal radial overlaps S_{p,0,0,p}. But Eq. (5) allows p_s ≠ p_i; for example S_{1,0,0,2} = 3/8, which is not negligible compared to S_{1,0,0,1} = 1/2. Excluding those pump-mediated cross-radial FWM terms is not a selection rule. It drops additional Floquet branches at ΔN = 6, 10, ... and can change which radial mode grows fastest. The paper's own conclusion admits \"Direct energy transfer between different higher-order radial modes is not included.\" Because the MMGNLSE uses the same truncation, the simulation is not an independent test of the full multimode physics. I would like the authors to show whether the diagonal branches survive once the full tensor is included, even just in the linearized analysis, and ideally release the code and data. The crossing-point approximation, by contrast, is fine: the time between crossings is many pulse durations even in the quasi-concentric case.\n\nSo, who is this for? Anyone working on high-power pulse compression or multicolor generation in gas-filled MPCs. The paper deserves a serious referee. The right outcome is probably major revision: keep the theory, but either extend the multimode treatment to include off-diagonal radial coupling or explicitly characterize the regime where it is negligible.","headline":"A well-derived Floquet theory for a new MPC instability, with a diagonal-radial truncation that should not be mistaken for a selection rule.","tokens_in":18550,"tokens_out":2390,"would_cite":true,"duration_ms":25091,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Geometric parametric instability can occur in gas-filled nonlinear multipass cells, driven by the single-pass Gouy-phase imbalance of the signal-idler pair.","keywords":["geometric parametric instability","multipass cells","Gouy phase","Floquet quasi-phase-matching","four-wave mixing","multimode nonlinear optics","nonlinear pulse compression","Laguerre-Gauss modes"],"falsifier":"Measure the first $p_s=1$, $h=0$ sideband pair in an argon-filled MPC at 5 bar, pumped at 1030 nm, for $C=0.05$ and $C=1.95$; Eq. (14) predicts detunings near 96 THz and 46 THz, respectively. If no sidebands emerge at the predicted detunings, or their dependence on $C$ and pressure deviates from $\\sqrt{(4\\Phi_0+2\\pi h)/(\\beta_2 L_{\\mathrm{cav}})}$ scaling, the Floquet quasi-phase-matching picture fails.","tokens_in":17502,"feed_emoji":"🪞","tokens_out":15056,"duration_ms":137647,"temperature":0.7,"pith_summary":"This paper claims that geometric parametric instability--the resonant growth of discrete, symmetrically detuned spectral sidebands--can arise in a gas-filled nonlinear multipass cell, not only in graded-index fibers. The mechanism is Floquet quasi-phase-matching with each mirror-to-mirror pass as one period: the single-pass Gouy-phase imbalance between the signal-idler pair and the pump pair, $4p_s\\Phi_0$, adds to an integer Floquet phase $2\\pi h$ to balance the material-dispersion phase, giving a sideband detuning $\\Delta f_{\\mathrm{SB}}\\approx(1/2\\pi)\\sqrt{(4p_s\\Phi_0+2\\pi h)/(\\beta_2 L_{\\mathrm{cav}})}$ (Eq. 14). The paper derives small-signal gain, bandwidth, and a pump-depleted conversion limit, and reproduces the sideband frequencies in multimode generalized nonlinear Schrödinger simulations. If correct, this makes MPCs both a potential source of beam-quality degradation in pulse compression and a tunable platform for multicolor and vortex sideband generation.","feed_headline":"Gas-filled multipass cells can amplify discrete sidebands","feed_subtitle":"A mirror-pass geometric phase imbalance sets sideband frequencies that cavity shape and pressure can tune.","key_machinery":"The load-bearing object is the single-pass Gouy phase $\\Phi_0(C)=2\\arctan\\sqrt{C/(2-C)}$ of the fundamental Laguerre-Gaussian mode in a symmetric MPC with $C=L_{\\mathrm{cav}}/R_0$, along with the mode-order multiplier $N_{\\ell p}=1+2p+|\\ell|$. The MPC is mapped to an equivalent waveguide whose effective propagation constants $\\tilde{\\beta}_{\\ell p}=N_{\\ell p}\\Phi_0/L_{\\mathrm{cav}}$ are uniformly spaced by $2\\Phi_0/L_{\\mathrm{cav}}$ between adjacent radial modes, mimicking the self-imaging spectrum of a graded-index fiber. This machinery turns each mirror-to-mirror pass into one Floquet period: the phase-matching condition $\\delta\\phi=0$ with integer Floquet order $h$ selects discrete sideband frequencies (Eq. 14), determines the gain (Eq. 16) and bandwidth (Eq. 20), and through the normalized mismatch $D_h$ sets the pump-depleted conversion ceiling (Eq. 22).","core_discovery":"The paper's central claim is that a mode-matched, rotationally symmetric gas-filled MPC pumped by a Gaussian beam in a normally dispersive gas is parametrically unstable: photon-seeded sideband pairs grow at discrete frequencies selected by a Floquet quasi-phase-matching condition. With $\\mu_p=(0,0)$ and $\\mu_s=\\mu_i=(0,p_s)$, the single-pass residual mismatch is $\\delta\\phi=\\phi_D(\\Omega)-4p_s\\Phi_0+\\Delta\\phi_{NL}-2\\pi h$, and setting it to zero gives the sideband detuning; retaining only $\\beta_2$ yields $\\Delta f_{\\mathrm{SB}}\\approx(1/2\\pi)\\sqrt{(4p_s\\Phi_0+2\\pi h)/(\\beta_2 L_{\\mathrm{cav}})}$. The small-signal amplitude gain is $g=\\sqrt{|\\kappa(p_s)|^2-[\\delta\\phi/(2L_{\\mathrm{cav}})]^2}$, and the pump-depleted coupled-mode model gives a maximum converted fraction $u_{\\max}=1-|D_h|/2$ with exponential instability only for $|D_h|<2$. Truncated MMGNLSE simulations seeded with one photon per spectral mode reproduce the predicted sideband frequencies and show the $p_s=1$ channel growing fastest, depleting the shared pump, and competing with higher radial orders.","pith_inferences":["If the crossing-separation assumption is violated--shorter pulses or tighter cavities--the single-pass Floquet map should break down, and the predicted discrete sidebands would be expected to shift or merge as inter-pass nonlinear interactions at the crossing turn on; this regime is testable by varying pulse duration at fixed cavity geometry.","The same machinery should carry over to solid-state MPCs with different dispersion and Kerr coefficients, so the sideband detuning formula suggests a design rule: choose $R_0$, $L_{\\mathrm{cav}}$, and gas pressure to place sidebands at target frequencies.","The pump-depleted model's coherent back-conversion hints at an all-optical switch or frequency shifter: seeding a strong sideband pair could convert power back toward the pump or to another radial channel, though the paper does not develop this application.","The orbital-angular-momentum selection rule implies a Gaussian pump can generate counter-rotating vortex sidebands without bulk vortex optics; simulating or measuring those vortex channels is a natural extension the paper leaves open."],"forward_implications":["A mode-matched MPC becomes a discrete parametric amplifier whose sideband spectrum is fixed by cavity geometry and gas pressure, instead of by fiber design.","In a normally dispersive gas the theory predicts multiple sideband pairs from different Floquet orders and radial indices; for the $p_s=1$, $h=0$ branch at 5 bar the detuning shifts from roughly 96 to 46 THz as $C$ goes from 0.05 to 1.95.","Pump depletion sets a hard conversion ceiling: a single signal-idler pair can convert at most $1-|D_h|/2$ of the pump, and no exponential growth occurs once $|D_h|\\ge 2$.","GPI can degrade spatial beam quality in nonlinear pulse compression by populating higher-order radial modes, while also enabling tunable multicolor generation, with angular-momentum conservation allowing counter-rotating vortex sidebands from a Gaussian pump."],"supporting_citations":[{"why":"Reports the first observation of geometric parametric instability in graded-index multimode fibers; supplies the phenomenon this paper transposes to multipass cells.","marker":"[5]"},{"why":"Gives the single-pass Gouy phase of Laguerre-Gauss modes in multipass cells, the uniform mode spacing that the Floquet lattice relies on.","marker":"[18]"},{"why":"Prior hybrid model of quasi-phase-matched four-wave mixing in multipass cells; the paper extends this to transverse-mode GPI.","marker":"[19]"},{"why":"Demonstrates vector modulation instability in gas-filled multipass cells, a neighboring instability the theory must not conflict with.","marker":"[20]"},{"why":"Provides the orbital-angular-momentum selection rule for four-wave mixing between Laguerre-Gauss modes, used to fix which sideband pairs couple.","marker":"[24]"},{"why":"Defines the symmetric two-mirror multipass geometry whose equivalent-waveguide collinear model is the basis of the Floquet map.","marker":"[25]"},{"why":"Standard coupled-mode and modulation-instability formalism from nonlinear fiber optics, the basis of the small-signal gain and bandwidth derivation.","marker":"[34]"},{"why":"Textbook coupled-amplitude equations for degenerate four-wave mixing, from which the pump-depleted coupled-mode model is derived.","marker":"[35]"},{"why":"Supplies the multimode generalized nonlinear Schrödinger equation model and numerical solver used in the simulations.","marker":"[36, 37]"}],"fun_headline_variants":["Geometric parametric instability found in gas-filled multipass cells","Multipass cells shake out discrete sidebands via geometric phase","Tunable sideband generation from nonlinear multipass cells","Floquet condition tunes sidebands in gas-filled multipass cells"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The model assumes successive mirror-to-mirror passages through the cell interior do not interact nonlinearly with each other--the pulse is much shorter than the temporal separation between crossings--so the single-pass Floquet map is the correct evolution operator.","fun_headline_variants_meta":{"raw":{"variants":["Geometric parametric instability found in gas-filled multipass cells","Multipass cells shake out discrete sidebands via geometric phase","Tunable sideband generation from nonlinear multipass cells","Floquet condition tunes sidebands in gas-filled multipass cells"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00021,"raw_usage":{"total_tokens":1484,"prompt_tokens":1091,"completion_tokens":393,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":707,"completion_tokens_details":{"reasoning_tokens":323}},"tokens_in":707,"tokens_out":393,"duration_ms":4441,"temperature":1.0,"reasoning_tokens":323,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:31:11.750323+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the first $p_s=1$, $h=0$ sideband pair in an argon-filled MPC at 5 bar, pumped at 1030 nm, for $C=0.05$ and $C=1.95$; Eq. (14) predicts detunings near 96 THz and 46 THz, respectively. If no sidebands emerge at the predicted detunings, or their dependence on $C$ and pressure deviates from $\\sqrt{(4\\Phi_0+2\\pi h)/(\\beta_2 L_{\\mathrm{cav}})}$ scaling, the Floquet quasi-phase-matching picture fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports the first observation of geometric parametric instability in graded-index multimode fibers; supplies the phenomenon this paper transposes to multipass cells."},{"cited_title":"Daher, F","cited_arxiv_id":null,"evidence_quote":"Gives the single-pass Gouy phase of Laguerre-Gauss modes in multipass cells, the uniform mode spacing that the Floquet lattice relies on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior hybrid model of quasi-phase-matched four-wave mixing in multipass cells; the paper extends this to transverse-mode GPI."},{"cited_title":"Hanna, M","cited_arxiv_id":null,"evidence_quote":"Demonstrates vector modulation instability in gas-filled multipass cells, a neighboring instability the theory must not conflict with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the orbital-angular-momentum selection rule for four-wave mixing between Laguerre-Gauss modes, used to fix which sideband pairs couple."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the symmetric two-mirror multipass geometry whose equivalent-waveguide collinear model is the basis of the Floquet map."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Standard coupled-mode and modulation-instability formalism from nonlinear fiber optics, the basis of the small-signal gain and bandwidth derivation."},{"cited_title":"B¨ orzs¨ onyi, Z","cited_arxiv_id":null,"evidence_quote":"Textbook coupled-amplitude equations for degenerate four-wave mixing, from which the pump-depleted coupled-mode model is derived."}],"review_version":1}