{"id":"ad8007ce-bdf3-47cf-9b5e-1cd5ac8e36dc","arxiv_id":"2606.03999","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Derives closed-form Airy beam trajectory dispersion across THz subcarriers via Fresnel integral and introduces TTD-assisted beamforming to control it for sensing or communication.","lead":"The paper examines frequency-dependent dispersion in Airy beams for near-field wideband terahertz links, deriving a closed-form trajectory and proposing a true-time-delay beamforming structure to either enable curved scanning or suppress drift. A smart generalist might read it to see how specialized beam shapes could be managed in future high-frequency wireless systems for sensing or reliable links.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Fresnel integral derivation assumes paraxial near-field propagation holds uniformly across wide THz bandwidth without dominant frequency-dependent losses or non-paraxial effects","rationale":"The reader's weakest assumption correctly isolates the modeling step that must hold for both the derivation and the TTD design to be reliable. Because the full text is now accessible, the concern can be tested directly rather than left unverified; this moves the verdict from UNVERDICTED to CONDITIONAL pending the check.","tokens_in":1630,"tokens_out":355,"duration_ms":22671,"concrete_test":"Recompute the trajectory expression (Eq. derived from Fresnel integral) at the band edges using the exact Rayleigh-Sommerfeld diffraction integral with the same aperture and frequency range; if the main-lobe shift deviates by >15% from the closed-form prediction at any subcarrier, the Fresnel-based claim requires qualification.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim rests on deriving a closed-form trajectory expression directly from the Fresnel diffraction integral for Airy beams. This integral is itself a paraxial approximation valid only when the observation distance satisfies specific Fresnel number conditions and when propagation can be treated as frequency-independent in phase and amplitude. In the THz near-field wideband regime, atmospheric absorption, dielectric dispersion, and array element frequency response introduce amplitude and phase variations across subcarriers that are not captured by the standard Fresnel kernel. If these effects alter the effective trajectory by more than the predicted dispersion, the closed-form expression and the subsequent TTD control scheme lose predictive power. The paper provides no explicit error bound or comparison against the full Rayleigh-Sommerfeld integral or full-wave simulation to confirm the approximation remains dominant.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"This letter investigates Airy beam dispersion in near-field wideband terahertz communications. Unlike conventional beams, Airy beams exhibit frequency-dependent shifts in both the reference focusing point and the self-bending main-lobe trajectory. Based on the Fresnel diffraction integral, a closed-form trajectory expression is derived to characterize dispersion across subcarriers. A true-time-delay (TTD)-assisted Airy beamforming structure is proposed to control the dispersion, enabling either frequency-dependent curved trajectory clusters for sensing or suppression of drift for communication.","tokens_in":1785,"tokens_out":414,"duration_ms":31688,"significance":"If the closed-form derivation holds and the TTD structure provides effective control without unmodeled effects dominating, the work would offer a useful analytical tool and practical beamforming approach for managing dispersion in wideband near-field THz systems, which is relevant for both reliable links and sensing applications. The explicit derivation from the Fresnel integral is a positive feature when it avoids fitted parameters.","major_comments":[{"comment":"The central claim rests on deriving a closed-form trajectory expression directly from the Fresnel diffraction integral. The manuscript provides no explicit error bound, comparison against the Rayleigh-Sommerfeld integral, or full-wave simulation results to confirm that paraxial and frequency-independent assumptions remain dominant across the THz bandwidth, where atmospheric absorption, dielectric dispersion, and array frequency response could alter the effective trajectory (see skeptic note on weakest assumption).","section":"Derivation of closed-form trajectory expression (abstract and associated section)"}],"minor_comments":[{"comment":"The abstract would benefit from specifying the considered frequency range, array aperture, and propagation distances to allow readers to assess the regime of validity.","section":"Abstract"},{"comment":"Notation for the trajectory expression and TTD parameters should be defined consistently when first introduced to improve readability.","section":"Main text"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive comment on validating the closed-form derivation. We address the concern point-by-point below and outline planned revisions.","responses":[{"response":"We agree that explicit validation strengthens the central claim. The Fresnel integral is the standard starting point for obtaining a tractable closed-form trajectory under the paraxial near-field regime; the frequency-independent array response is justified because each subcarrier is narrowband in typical THz OFDM. In revision we will add a dedicated subsection that (i) numerically compares the closed-form trajectory against direct quadrature of the Fresnel integral across the full bandwidth and reports explicit L2 error bounds for the considered array sizes and distances, and (ii) discusses the expected influence of atmospheric absorption and dielectric dispersion, showing that for the short-range scenarios targeted these effects shift the absolute path loss but do not materially alter the normalized trajectory shape derived from the phase term. Full-wave (Rayleigh-Sommerfeld or FDTD) validation lies outside the letter’s analytical scope and would require resources disproportionate to the contribution; we will note this limitation and cite relevant full-wave studies on THz near-field beams for readers interested in quantitative deviation estimates.","revision_made":"partial","referee_comment":"[Derivation of closed-form trajectory expression (abstract and associated section)] The central claim rests on deriving a closed-form trajectory expression directly from the Fresnel diffraction integral. The manuscript provides no explicit error bound, comparison against the Rayleigh-Sommerfeld integral, or full-wave simulation results to confirm that paraxial and frequency-independent assumptions remain dominant across the THz bandwidth, where atmospheric absorption, dielectric dispersion, and array frequency response could alter the effective trajectory (see skeptic note on weakest assumption)."}],"tokens_in":1224,"tokens_out":366,"duration_ms":27836,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper derives a closed-form expression for how the main-lobe trajectory of an Airy beam shifts across subcarriers in the near-field THz regime and then gives a TTD beamforming structure that can either cluster those trajectories for scanning or hold them steady for communication.\n\nThe derivation starts from the Fresnel diffraction integral and produces an explicit trajectory formula that captures both focal-point migration and the self-bending path. The TTD design is concrete: choose the delay values to produce the desired dispersion behavior. That matches the two use cases laid out in the abstract and gives a practical handle on something that ordinary phase-only beamformers cannot fix.\n\nThe math is traceable and the control idea is new in this setting. The work stays within the standard Fresnel framework rather than inventing new entities, which keeps the contribution focused.\n\nThe main limitation is the model itself. The Fresnel kernel assumes paraxial propagation and treats amplitude and phase as frequency-independent inside the integral. In wideband THz, atmospheric absorption, material dispersion, and element responses vary across the band; if those effects shift the trajectory by more than the predicted dispersion, the closed-form expression and the TTD solution lose accuracy. The abstract does not report error bounds or comparisons to the Rayleigh-Sommerfeld integral or full-wave results, so the size of this gap is not yet clear.\n\nThis is for people already working on near-field THz beamforming or self-accelerating beams. A reader who needs an explicit trajectory formula or a TTD architecture for dispersion management will get direct value. It is narrow but grounded enough to deserve a serious referee.","headline":"Closed-form Airy trajectory from Fresnel plus TTD control is the actual addition, but the paraxial wideband assumption needs direct checks against frequency-dependent losses.","tokens_in":2249,"tokens_out":405,"would_cite":false,"duration_ms":36369,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Airy beams in near-field wideband THz show frequency-dependent shifts of both focal point and self-bending trajectory that a closed-form expression and TTD structure can characterize and control.","keywords":["Airy beam","dispersion","terahertz communications","near-field","true-time-delay","beamforming","trajectory","wideband"],"falsifier":"A laboratory measurement of actual main-lobe positions at several subcarrier frequencies in a near-field THz testbed, compared directly against the positions predicted by the closed-form trajectory formula; systematic mismatch would show the model does not capture the dispersion.","tokens_in":2525,"feed_emoji":"📡","tokens_out":717,"duration_ms":31587,"temperature":0.7,"pith_summary":"The paper examines dispersion in Airy beams used for near-field terahertz communications across wide bandwidths. Unlike ordinary beams whose main effect is focal-point migration, Airy beams move both their reference focus and the path of their curved main lobe as frequency changes. From the Fresnel diffraction integral the authors obtain an explicit formula for the trajectory at each subcarrier. They then introduce a true-time-delay beamforming architecture whose delay values can be set either to produce clusters of curved trajectories suited to sensing scans or to cancel the drift for steady communication links.","feed_headline":"Closed-form formula tracks Airy beam dispersion in THz","feed_subtitle":"TTD beamforming lets designers create curved scanning paths or suppress drift for stable links.","key_machinery":"The closed-form trajectory expression obtained from the Fresnel diffraction integral, which tracks the frequency-dependent location of the self-bending main lobe, together with the TTD-assisted beamforming structure that adjusts per-element time delays to steer or stabilize that location.","core_discovery":"Based on the Fresnel diffraction integral, a closed-form trajectory expression is derived to characterize the dispersion behavior across subcarriers. Furthermore, a true-time-delay (TTD)-assisted Airy beamforming structure is developed to actively control the trajectory dispersion. By properly designing the time delay parameters, the proposed scheme can either generate frequency-dependent curved trajectory clusters for sensing-oriented scanning or suppress trajectory drift for reliable communication.","pith_inferences":["The derived trajectory formula could be used to set bandwidth limits beyond which Airy beams become unsuitable for wideband THz links without compensation.","Hardware realization would require calibration of the time delays to match the exact array geometry and frequency range.","Similar dispersion control might be explored for other accelerating beams in optical or millimeter-wave regimes.","Full-wave electromagnetic simulations could be compared with the Fresnel-based formula to identify the distance or bandwidth at which higher-order effects appear."],"forward_implications":["Trajectory dispersion can be harnessed to produce multiple curved paths at different frequencies for sensing-oriented scanning.","Time delay parameters can be chosen to eliminate trajectory drift, supporting reliable wideband communication.","The reference focusing point shift can be treated separately from control of the main-lobe bending path.","The same structure applies to both sensing and communication use cases by simple choice of the delay values."],"fun_headline_variants":["Closed-form Airy trajectory expression for THz dispersion","TTD structure manages Airy beam dispersion in wideband THz","Derived Airy path formula tracks dispersion across THz subcarriers","Airy beamforming with time delays controls THz trajectory shifts","Fresnel integral yields Airy self-bending locus in THz"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The Fresnel diffraction integral provides a sufficiently accurate model for Airy beam propagation in the near-field THz regime across the considered bandwidth, without dominant unmodeled effects such as frequency-dependent material losses or array imperfections.","fun_headline_variants_meta":{"raw":{"variants":["Closed-form Airy trajectory expression for THz dispersion","TTD structure manages Airy beam dispersion in wideband THz","Derived Airy path formula tracks dispersion across THz subcarriers","Airy beamforming with time delays controls THz trajectory shifts","Fresnel integral yields Airy self-bending locus in THz"]},"model":"grok-4.3","cost_usd":0.00475,"raw_usage":{"total_tokens":2287,"prompt_tokens":559,"num_sources_used":0,"completion_tokens":71,"cost_in_usd_ticks":47499500,"prompt_tokens_details":{"text_tokens":559,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1657,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":559,"tokens_out":71,"duration_ms":19484,"temperature":1.0,"reasoning_tokens":1657,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-30T13:37:56.190836+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A laboratory measurement of actual main-lobe positions at several subcarrier frequencies in a near-field THz testbed, compared directly against the positions predicted by the closed-form trajectory formula; systematic mismatch would show the model does not capture the dispersion.","supporting_citations":[],"review_version":1}