{"id":"14329028-8172-47cc-b741-6e45c0aa085e","arxiv_id":"2512.07494","paper_version":3,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"Tuning an excitation phase in coupled-mode theory is claimed to merge an exceptional point with a quasi-bound state in the continuum, producing narrow resonances in stacked nanorod cavities.","lead":"This paper claims that adding a phase delay to the excitation of one of two coupled optical modes lets an exceptional point and a quasi-bound state in the continuum merge at the same wavelength in nanophotonic cavities. It reports numerical simulations of stacked gold–silicon and gold–gold nanorod dimers supporting this mechanism.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Excitation phase θ does not enter the Hamiltonian; the single-peak response at fixed φ is a dark-mode Fano effect, not an exceptional point.","rationale":"The reader's weakest assumption identifies precisely the load-bearing flaw: θ does not enter the Hamiltonian, so it cannot create an eigenvalue degeneracy. My read of the paper confirms this. The text repeatedly emphasizes that the excitation phase reshapes interference 'without modifying the intrinsic eigenmodes,' which is exactly why the single-peak response at θ=π/2 in Fig. 1(c) is a dark-mode Fano effect rather than an EP. The paper's own Fig. 2 only obtains an EP by simultaneously changing φ (φ=θ), which is a change to the Hamiltonian and not a pure excitation-phase effect. The additional issue of the QBIC criterion using the broad low-frequency mode as γ_L further weakens the claim by making the QBIC classification trivial. The FDTD simulations may indeed show line narrowing, but that is consistent with conventional Fano dark-mode physics and does not validate the exceptional-point interpretation. Therefore the central claim is unsupported, and the reader's REJECT verdict remains appropriate. No ad hominem is intended; the concern is strictly about the argument's logical consistency and adherence to standard definitions of exceptional points.","tokens_in":14172,"tokens_out":7231,"duration_ms":62050,"concrete_test":"For the parameters of Fig. 1(c) (φ=π/4, κ=0.94γ_L, and the original mode parameters used to generate Fig. 1(b)), compute the eigenvalues of H in Eq. (3) as θ is varied from 0 to 2π/4. If the eigenvalues are unchanged and non-degenerate, the observed single-peak spectrum at θ=π/2 is not an EP. Then compute the excitation coefficient of the broad eigenmode: show it vanishes at θ=π/2, confirming a dark-mode Fano effect. This can be done analytically from Eqs. (4)–(6).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that tuning the excitation phase θ merges an EP and a QBIC at one spectral position. But θ appears only in the source vector on the RHS of Eq. (1); the Hamiltonian H in Eq. (3) is independent of θ. Consequently the eigenfrequencies and eigenmodes are fixed for given ω1, ω2, γ1, γ2, κ, φ. The spectrum in Fig. 1(c) is obtained with φ and κ fixed, so the single narrow peak at θ=π/2 cannot arise from eigenvalue coalescence; it arises because the excitation vector [γ_C1, γ_C2 e^{iθ}]^T becomes orthogonal to one of the two eigenmodes, leaving only one Lorentzian in the extinction (Eq. 6). This is a standard Fano dark-mode configuration, not an exceptional point. In Fig. 2, the authors set φ=θ, so θ indirectly changes H via the coupling phase; that is a parameter tuning of H, and it contradicts the abstract's claim that the limitation of the eigenvalue framework is overcome by adding an excitation phase without modifying intrinsic eigenmodes. Moreover, the QBIC classification in Fig. 2 uses γ_L as the linewidth of the low-frequency (broad) mode, so the condition γ_-<γ_L is almost always satisfied; the EP region trivially falls inside this 'QBIC' region. Thus the paper's central EP–QBIC merging is not established by the model as written.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper claims that introducing an excitation-phase degree of freedom in a two-mode non-Hermitian nanophotonic cavity allows an exceptional point (EP) and a quasi-bound state in the continuum (QBIC) to merge at the same spectral position, even though conventional eigenvalue analyses supposedly forbid such coexistence. The authors develop a coupled-mode theory (CMT) with a source term containing an excitation phase θ, show that a single narrow extinction peak appears for θ=π/2 at fixed coupling phase and strength, label this as an EP–QBIC state, and support the claim with FDTD simulations of Au–Si and Au–Au stacked nanorod dimers. They also report Q-factor enhancements of over an order of magnitude and a plasmonic case exceeding the material-loss limit.","tokens_in":14583,"tokens_out":5528,"duration_ms":52090,"significance":"If the central claim were correct, it would offer a conceptually new route to high-Q resonances at eigenvalue degeneracies, with potential impact in sensing, lasing, and nonlinear photonics. The manuscript includes both CMT analytics and FDTD simulations, and the numerical effort is substantial. However, the claim rests on a misidentification: the excitation phase θ does not enter the Hamiltonian, so it cannot create an exceptional point. The observed single-peak response at θ=π/2 is a standard dark-mode/Fano excitation effect, not eigenvalue coalescence. The QBIC classification is also weakened by an inconsistent definition of γ_L. These issues are load-bearing and render the central result unsupported.","major_comments":[{"comment":"The excitation phase θ appears only in the source vector on the right-hand side of Eq. (1), while the Hamiltonian H in Eq. (3) is independent of θ. Consequently, the eigenfrequencies and eigenmodes are fixed for given ω1,ω2,γ1,γ2,κ,φ. The spectral change from a Fano doublet at θ=0 to a single narrow peak at θ=π/2 in Fig. 1(c) is therefore a change in the excitation overlap—one eigenmode becomes dark—not a coalescence of eigenvalues. The single narrow peak at θ=π/2 is the same high-Q eigenmode present at θ=0. Calling this an EP requires either an unstated change in φ (as in Fig. 2, where φ=θ) or a nonstandard definition of EP. The abstract's claim that the mechanism works 'without modifying the intrinsic eigenmodes' is inconsistent with the Fig. 2 procedure, which tunes φ=θ and thus changes H. The central identification of an EP–QBIC state is not established by the CMT as presented.","section":"Methods, Eqs. (1)–(3) and Fig. 1(c)"},{"comment":"The QBIC criterion is defined as γ− ≤ γ_L, where γ_L is stated to be the linewidth of the original low-frequency mode. In the example of Fig. 1, the low-frequency mode is the broad, high-loss mode (γ≈0.556 eV), while the high-frequency mode is the narrow, low-loss mode (γ≈0.0102 eV). The text nevertheless refers to γ_L as the 'original low-loss one.' With γ_L taken as the broad-mode linewidth, the condition γ− < γ_L is satisfied whenever the coupled low-frequency mode is narrower than the original broad mode, which is nearly always true and trivially includes the EP region, whose linewidth is (γ_H+γ_L)/2 ≈ 0.28 eV < 0.556 eV. The EP–QBIC 'merging' shown in Fig. 2(c,f) is therefore an artifact of an overly permissive and inconsistently defined QBIC criterion, not a nontrivial coincidence.","section":"Results, Fig. 2(c) and surrounding text"},{"comment":"The FDTD validation is partly circular. All CMT parameters except the coupling strength κ are extracted from isolated-rod simulations, and κ is the only free parameter. The simulated single peak in the hybrid dimer is then labeled EP–QBIC using the same CMT criteria whose validity is under question. Since a single narrow peak can arise from a dark-mode Fano configuration without any eigenvalue degeneracy, the FDTD spectra of Fig. 3(b,c) do not independently confirm the existence of an EP. The agreement shown in Fig. 3(d) is a trend in linewidth versus gap, not a test of eigenmode coalescence. A direct eigenvalue analysis or an unambiguous signature of the EP (e.g., eigenvalue Riemann-surface topology or eigenvector coalescence) is lacking.","section":"Fig. 3(d) and 'Simulated and analytical extinction spectra'"},{"comment":"The paper asserts that the impossibility of EP–QBIC coexistence is a limitation of the eigenvalue framework and that an excitation-phase degree of freedom overcomes it. However, when φ=θ is used (as in Fig. 2), θ does enter the Hamiltonian through the coupling phase and hence modifies the eigenvalues. The eigenvalue framework is fully capable of describing the resulting EP; the source phase is not needed for the eigenvalue degeneracy. The philosophical claim that the eigenvalue framework itself is the obstacle is therefore not supported by the model.","section":"Abstract and Introduction, 'eigenvalue framework' claim"}],"minor_comments":[{"comment":"The affiliation line repeats 'University, Changsha 410083, China' twice; this should be corrected.","section":"Affiliations"},{"comment":"The statement that 'the phase delay θ induced by plane wave excitation cannot exceed the spatial phase delay φ between two modes' is asserted without justification or a formal definition of the phase relationship. Clarify the physical origin of this inequality.","section":"Fig. 1(d) and text"},{"comment":"The 'volcanic eruption' line shape and its interpretation in terms of a diabolic-point-like state need a more precise definition. Is the frequency degeneracy with unequal linewidths a diabolic point in the usual sense, and what is its relation to the EP–QBIC discussion?","section":"Fig. 4(c)"},{"comment":"The claim that the Q factor 'surpasses the theoretical limit imposed by intrinsic material loss' should be clarified: for a single plasmon resonance the maximum Q is limited by Im(ε)/Re(ε), but a coupled-mode scenario can produce a narrower dark mode because radiative loss is suppressed while material loss remains. Specify the precise reference limit and how it is computed.","section":"Fig. 4(b) and associated text"},{"comment":"The lower panel is said to show 'EP-QBIC gradually approaching EP-BIC,' but the text at the end of the Results section states that approaching BIC in practical systems is challenging. This is consistent, but the Supplementary caption should be checked for a typo: 'EP–QBIC' appears twice in the lower panel description.","section":"Supplementary Fig. S2"}],"recommendation":"reject","confidential_remarks":"The manuscript has a substantial numerical component and an interesting observation of a phase-controlled narrow resonance, but the central claim that this constitutes an exceptional point is not supported by the authors' own equations. The excitation phase is a source-term parameter, not a Hamiltonian parameter; the single-peak response is a dark-mode Fano effect. This is not a minor fix—it undermines the entire EP–QBIC narrative. The QBIC criterion is also defined in a way that makes the claimed merging trivial. I do not see a viable path to revision within the scope of the current claim, though the underlying FDTD results could support a more modest paper about excitation-phase-controlled Fano resonances and Q enhancement."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the central claim—that tuning an excitation phase θ merges an exceptional point and a quasi-BIC—does not survive contact with its own equations. θ appears only in the source vector of Eq. (1); the Hamiltonian in Eq. (3) is θ-independent. The single-peak, high-Q spectrum at θ=π/2 is just the Fano dark-mode case where the broad eigenmode is not excited. That is a useful trick, but it is not an EP.\n\nWhat is genuinely new: the parameter maps in Fig. 1d and Fig. 2 connecting coupling strength, coupling phase, and excitation phase to QBIC conditions, plus the FDTD demonstration on stacked Au-Si nanorods where the gap controls coupling and the linewidth narrows. The CMT-to-FDTD comparison in Fig. 3d, with all parameters except coupling taken from the individual-mode simulations, is a reasonable validation and shows an honest discrepancy at small gaps.\n\nThe soft spots are load-bearing. First, the EP-QBIC label. In Fig. 1c, φ and κ are fixed, so the eigenmodes of H are fixed; θ only changes the weights of the two Lorentzians in the extinction. That is textbook Fano interference, not coalescence. In Fig. 2, the authors set φ=θ, which does make θ enter H, but then the abstract's claim that the intrinsic eigenmodes are \"not modified\" is wrong—they are modifying the coupling phase. Second, the QBIC region in Fig. 2c is defined as γ₋ < γ_L where γ_L is the linewidth of the low-frequency original mode. In their example (Au and Si), that is the high-loss mode, so the inequality is easy to satisfy; the EP region landing inside this 'QBIC' region is trivial. Third, the pure-plasmonic claim of exceeding the material-loss limit is not rigorously supported; the 15× Q enhancement and the comparison to a 'limit' would need a careful derivation of what that limit is for a coupled dimer.\n\nThe paper is worth a serious referee because the engineering demonstration is plausible and the CMT machinery is mostly sound, but the interpretation is wrong. A referee should ask for a rewrite that either drops the EP language or clearly separates the Hamiltonian-level EP (which exists when φ, κ are tuned) from the excitation-phase effect. In its current form, I would not cite it for the EP-QBIC claim, but I would be interested in the phase-controlled line-narrowing data. Recommendation: send to peer review, expect major revision or rejection.","headline":"Theta never enters the Hamiltonian, so the EP-QBIC claim is unsubstantiated; the real content is a solid, useful demonstration of phase-controlled Fano line narrowing in stacked nanorods.","tokens_in":15065,"tokens_out":4583,"would_cite":false,"duration_ms":39416,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A single excitation-phase choice can merge an exceptional point and a quasi-bound state in the continuum at the same frequency in two-mode nanophotonic cavities.","keywords":["exceptional point","bound state in the continuum","quasi-BIC","excitation phase","coupled mode theory","nanophotonic cavity","Fano resonance","plasmonic nanorod dimer"],"falsifier":"Measure the extinction spectrum of the stacked dimer while sweeping the excitation phase from θ=0 to θ=π/2 with the coupling phase fixed. If the narrow peak keeps the same frequency and linewidth while the broad peak disappears, the phase is only deselecting a mode rather than creating a degeneracy. A second check: at the claimed EP, a small detuning of φ or κ should split the resonance with a square-root dependence, the signature of an exceptional point.","tokens_in":14063,"feed_emoji":"🔬","tokens_out":7430,"duration_ms":71408,"temperature":0.7,"pith_summary":"This paper tries to establish that the usual impossibility of placing an exceptional point and a quasi-bound state in the continuum at the same spectral position in a two-mode non-Hermitian cavity is a limitation of the eigenvalue framework, not of the underlying physics. Adding an excitation-phase delay between the driving of the two modes reshapes the interference between their radiation channels without altering the intrinsic eigenmodes, and this extra knob permits the exceptional-point condition and the quasi-BIC condition to be met simultaneously. Using coupled-mode theory and full-wave simulations of stacked gold-silicon nanorod dimers, the authors demonstrate a single narrow resonance with Q around 125 and an order-of-magnitude quality-factor enhancement, and they report a purely plasmonic case whose Q exceeds the intrinsic material-loss limit. If the claim holds, the excitation phase becomes a practical control for high-Q resonances at eigenmode degeneracies.","feed_headline":"One phase setting merges exceptional point and quasi-BIC","feed_subtitle":"In stacked nanorod cavities, that phase choice yields Q≈125 and an order-of-magnitude Q increase.","key_machinery":"The central object is the excitation phase θ in the source vector of the coupled-mode equations, working together with the non-Hermitian 2×2 Hamiltonian whose eigenvalues define the exceptional point (a degeneracy where two eigenvalues and their eigenvectors coalesce). Because θ does not appear in the Hamiltonian, it cannot change eigenmode frequencies or linewidths; instead it controls the relative phase with which the two coupled modes are driven, i.e., the interference between radiation channels. This lets the extinction spectrum be tuned from a Fano double-peak (conventional QBIC) to a single-peak EP-QBIC while the intrinsic mode structure stays fixed, and it provides a direct mapping be","core_discovery":"The paper claims that in a two-mode non-Hermitian cavity, the failure to merge an exceptional point and a quasi-BIC at one frequency is not fundamental but stems from leaving the driving field out of the picture. In the coupled-mode equations, the excitation phase enters only the source term and not the Hamiltonian, so it can be varied to change which superposition of the two eigenmodes the incident field excites, without moving the eigenfrequencies or linewidths. With a suitable coupling strength and coupling phase, the right excitation phase produces a single-peak, narrow-linewidth response (Q≈125) in which the two new modes share both frequency and linewidth — the exceptional point — and","pith_inferences":["A practical next step would be to make the excitation phase dynamically adjustable with a shaped or tilted wavefront; the same cavity could then toggle between a broad Fano response and a narrow high-Q resonance at fixed geometry.","Because θ is absent from the Hamiltonian, the merged resonance is the selected excitation of an existing degenerate eigenmode rather than a newly created mode — this suggests the phase-control strategy should transfer to any two-mode non-Hermitian radiator, including metasurfaces, waveguide-coupled rings, or acoustic analogs, wherever a relative drive phase can be imposed.","A direct experimental falsification of the 'merging' interpretation is to perturb φ or κ slightly around the claimed EP point and look for the characteristic square-root splitting of the resonance; observing linear splitting would indicate a diabolic-point-like degeneracy instead."],"forward_implications":["At the EP-QBIC condition, the cavity response is a single narrow resonance with Q≈125, more than an order of magnitude above the uncoupled nanorod modes.","The excitation phase is a necessary control: at θ=0 no choice of coupling strength or coupling phase produces an EP-QBIC, and tuning θ sweeps the spectrum between conventional QBIC and EP-QBIC.","Because the EP region lies wholly inside the QBIC region in the θ-κ plane, the merging is a systematic feature of the two-mode model rather than an accidental crossing.","Increasing the coupling strength drives both conventional QBIC and EP-QBIC toward ideal BICs, so the model supports an EP-BIC as a limiting case.","In a purely plasmonic dimer, the phase-controlled QBIC raises Q by over 15 times, exceeding the intrinsic material-loss limit of roughly 12."],"fun_headline_variants":["Excitation phase merges exceptional point and quasi-BIC","One phase unites exceptional point and quasi-BIC","Phase control fuses exceptional point with quasi-BIC","Phase degree frees exceptional point–BIC merge"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is that the single narrow peak obtained at the chosen excitation phase is genuinely an exceptional point of the two-mode Hamiltonian, and not a conventional Fano dark-mode line in which the broad mode is simply not excited; if that identification is wrong, the central claim collapses.","fun_headline_variants_meta":{"raw":{"variants":["Excitation phase merges exceptional point and quasi-BIC","One phase unites exceptional point and quasi-BIC","Phase control fuses exceptional point with quasi-BIC","Phase degree frees exceptional point–BIC merge"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000186,"raw_usage":{"total_tokens":1159,"prompt_tokens":738,"completion_tokens":421,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":482,"completion_tokens_details":{"reasoning_tokens":357}},"tokens_in":482,"tokens_out":421,"duration_ms":4985,"temperature":1.0,"reasoning_tokens":357,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T17:56:13.025085+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the extinction spectrum of the stacked dimer while sweeping the excitation phase from θ=0 to θ=π/2 with the coupling phase fixed. If the narrow peak keeps the same frequency and linewidth while the broad peak disappears, the phase is only deselecting a mode rather than creating a degeneracy. A second check: at the claimed EP, a small detuning of φ or κ should split the resonance with a square-root dependence, the signature of an exceptional point.","supporting_citations":[],"review_version":1}