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REVIEW 2 major objections 6 minor 1 cited by

At 64 GBaud, a coherent transceiver's ~25 dB back-to-back ceiling makes 1024-QAM infeasible on standard and hollow-core fiber alike.

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2026-08-02 10:24 UTC pith:HESOSBA3

load-bearing objection Useful integrated budget for HCF system design, but the '1024-QAM infeasible at 64 GBaud' headline rests on a hand-calibrated transceiver curve; the qualitative bottleneck shift is robust, the exact boundary is not. the 2 major comments →

arxiv 2606.23527 v4 pith:HESOSBA3 submitted 2026-06-22 physics.optics

System-Level Limits of Higher-Order QAM in Hollow-Core Fiber Systems

Md Ghulam Saber , Zhiping Jiang This is my paper
classification physics.optics
keywords hollow-core fibercoherent optical transmissionhigher-order QAMtransceiver SNR ceilingeffective SNR budgetinter-modal interferenceCO2 absorptionquadrature amplitude modulation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tries to establish that the practical ceiling on modulation order in coherent optical systems is set by the transceiver's own back-to-back SNR, not by the fiber, once hollow-core fiber removes fiber nonlinearity. It builds a per-channel effective-SNR budget that combines optical-link noise, a symbol-rate-dependent transceiver ceiling, and secondary penalties in reciprocal form, then applies it at a deployment-realistic 64 GBaud, 75 GHz-spaced, 6 THz WDM system. The headline result: 1024-QAM needs about 29.6 dB Es/N0, but a best-in-class transceiver delivers only about 25.3 dB back-to-back at that baud, so 1024-QAM and above are infeasible on either fiber. Hollow-core fiber still wins on reach: 256-QAM reach improves from about 45 to about 170 km and 64-QAM from about 415 to about 2275 km at an inter-modal interference coefficient of -55 dB/km. CO2 gas lines matter mainly in the L-band, where a channel on a line loses one to two QAM orders, while line-avoiding C-band channels follow the gas-free baseline.

Core claim

The central discovery is that a real coherent transceiver has a finite, symbol-rate-dependent back-to-back SNR ceiling—set by converter ENOB at the operating rate, analog bandwidth, and Tx/Rx nonlinearity—and that at 64 GBaud this ceiling (~25.3 dB for the high-performance class) sits below the 29.6 dB Es/N0 requirement for 1024-QAM. Because the total SNR combines the link SNR and the transceiver ceiling in parallel (reciprocally), no fiber improvement can lift the delivered SNR above the ceiling. The paper concludes that hollow-core fiber's near-vacuum Kerr nonlinearity does not enable ultra-high QAM at deployable baud rates; it enables longer reach and higher baud at a given modulation ord

What carries the argument

The key object is the effective-SNR budget: 1/SNR_total = 1/SNR_link + 1/SNR_TRx(Rs) + sum_i 1/SNR_i, where SNR_link collects true optical noise powers (ASE, Kerr NLI, inter-modal interference, pigtail NLI), SNR_TRx is a parametrized transceiver back-to-back ceiling from ENOB-at-rate, analog bandwidth, and Tx/Rx nonlinearity, and the remaining impairments (phase noise, equalization-enhanced phase noise, timing jitter, PDL, line-system penalties, CO2 gas-notch ISI) enter as equivalent SNR floors. The reciprocal form is what makes the ceiling binding: the achievable SNR can never exceed the transceiver ceiling no matter how clean the link is.

Load-bearing premise

The load-bearing premise is that the parameterized back-to-back transceiver SNR ceiling—ENOB0 of 5.5 at 32 GBaud, a 0.6 bit/octave roll-off, a 38 dB analog floor, and a 42 dB nonlinearity floor—accurately represents real 64-GBaud coherent transceivers; it is calibrated to published trends rather than measured, and its absolute level shifts the exact baud at which 1024-QAM becomes infeasible.

What would settle it

Measure the back-to-back SNR of a state-of-the-art 64-GBaud coherent transceiver into an ideal link. If it exceeds about 29.6 dB (the 1024-QAM requirement with shaping credit and margin), the 64-GBaud infeasibility claim collapses on hollow-core fiber, since the corresponding link SNR there is about 35 dB. Alternatively, an end-to-end 64-GBaud 1024-QAM transmission over a few kilometers of hollow-core fiber with standard external-cavity lasers would directly refute the ceiling claim if successful.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Ultra-high QAM (1024-QAM and above) is feasible only at low baud rates, roughly below 24 GBaud, even with a high-performance transceiver; at 64 GBaud the maximum feasible order is 256-QAM on either fiber.
  • Hollow-core fiber's practical value is reach and baud at a given order rather than raw modulation order: about 3.8x more reach for 256-QAM and 5.5x more for 64-QAM at the baseline IMI coefficient.
  • Improving the distributed inter-modal interference coefficient is the highest-leverage fiber-side lever: moving from -55 to -73 dB/km extends 256-QAM reach from about 170 km to about 975 km, though the paper flags this as a laboratory bound.
  • CO2 absorption forces spectral planning: line-avoiding C-band channels follow the gas-free baseline, while L-band channels on strong lines lose one to two QAM orders unless the core is sealed or mitigation is used.
  • Any future move beyond 256-QAM at deployable baud rates requires transceiver improvements—higher ENOB at rate, wider analog bandwidth, and lower Tx/Rx nonlinearity—rather than fiber improvements.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the parameterized transceiver ceiling is optimistic—for example, if a real 64-GBaud transceiver delivers more than about 30 dB back-to-back SNR—1024-QAM could become feasible on hollow-core fiber at 64 GBaud, so the exact crossover baud is uncertain even though the transceiver-limited picture likely survives.
  • The same reciprocal budget could be reused for future converter generations or other fiber types by swapping in a different ENOB-at-rate curve; the framework predicts a baud-versus-order design rule in which higher baud forces moderate order.
  • The CO2 notch-ISI result suggests a testable mitigation prediction: spectral pre-emphasis or digital-subcarrier avoidance should recover most of the C-band worst-channel reach penalty at modest spectral cost, while L-band avoidance remains spectrally expensive because the strong lines are denser than the channel bandwidth.
  • The IMI-reach prediction could be tested directly by measuring the cabled inter-modal interference coefficient on deployed hollow-core fiber; the paper itself identifies cabled-IMI characterization as the key open measurement for this class of result.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. This paper develops a per-channel effective-SNR budget for coherent WDM transmission over hollow-core fiber (HCF) and standard SMF, combining ASE, Kerr NLI, inter-modal interference (IMI), pigtail NLI, CO2 gas absorption, a parameterized transceiver back-to-back (B2B) SNR ceiling, and SNR-equivalent penalties for phase noise, EEPN, jitter, PDL, and line-system effects. The central quantitative claim is that at 64 GBaud with 75 GHz spacing, the modeled transceiver B2B ceiling (~25.3 dB for the 'high-performance' class) falls below the net requirement for 1024-QAM (~29.0 dB), making 1024-QAM and higher infeasible on either fiber regardless of fiber quality. HCF's advantage is consequently stated to be reach and baud at a given modulation order (e.g., 256-QAM reach ~170 km vs ~45 km at κ=-55 dB/km), with additional analysis of CO2 absorption, launch power, and IMI sensitivity. The model is a synthesis of published formulas and parametrized/calibrated components, with explicit caveats about unmeasured quantities.

Significance. If the transceiver B2B ceiling were anchored to direct measurement, this would be an important reframing of the HCF roadmap: it would show that HCF's near-vacuum nonlinearity does not automatically translate into ultra-high QAM at deployment baud rates, and that converter ENOB and analog bandwidth are the system bottleneck. The paper's transparency about its parameters and its external consistency checks (20 GBaud PS-1024-QAM and 60 GBaud PS-256-QAM demonstrations) are strengths, and the qualitative conclusion that the transceiver becomes the limiting factor at high baud is plausible. However, the absolute '1024-QAM infeasible at 64 GBaud' boundary is not yet anchored to a measured B2B curve; a ~1-bit ENOB shift at 64 GBaud would change the feasibility conclusion. The framework is valuable, but the headline quantitative claim needs additional support.

major comments (2)
  1. [Section III-B, Eq. (8), Table II; Section IV-A; Abstract] The central '1024-QAM infeasible at 64 GBaud' claim rests on the unmeasured, hand-calibrated transceiver B2B ceiling. The model uses ENOB0=5.5 at 32 GBaud, 0.6 bit/octave roll-off, S_afe=38 dB, and S_nl=42 dB. At 64 GBaud this gives ENOB≈4.9 and SNR_TRx≈25.3 dB, while the net 1024-QAM requirement from Eq. (3) is 29.57-1.53+1.0≈29.0 dB—a gap of about 3.7 dB. A ~1-bit increase in ENOB at 64 GBaud (ENOB≈6.0 instead of 4.9) raises the quantization floor by about 6 dB and, even with the parallel floors, brings the ceiling near or above 29 dB, making 1024-QAM feasible on HCF at short reach. The external anchors (Fan 20 GBaud, Wang 60 GBaud) exercise lower orders or lower baud rates, and the Varughese anchor near 100 GBaud is itself model-based; none pins the 64-GBaud high-order crossover to ±1 bit. Since the abstract presents the boundary as a physical result, the paper should either include a
  2. [Section III-F, Eq. (19)] The closed form for the all-pairs splice-MPI sum appears incorrect as printed. For N_s=2, Eq. (18) gives S(2,ζ)=ζ, but the numerator shown in Eq. (19), if read as ζ^{N_s-1}-N_sζ+ζ^{N_s}, gives (ζ-2ζ+ζ^2)/(1-ζ)^2=(ζ^2-ζ)/(1-ζ)^2<0 for 0<ζ<1. The correct closed form should be [(N_s-1)ζ - N_sζ^2 + ζ^{N_s+1}]/(1-ζ)^2. If this is a typographical error, it should be corrected; if not, the numerical discrete-MPI results in Section IV-D and the conclusion that splice MPI is below the distributed-IMI floor are unreliable. This is a load-bearing point for the paper's 'distributed κ dominates; discrete splice MPI is small' message.
minor comments (6)
  1. [Section III-D] The text says EEPN 'enters the transceiver ceiling of Eq. (8),' but Eq. (8) is the pure B2B ceiling and Section II-A explicitly excludes EEPN from that ceiling. EEPN should enter Eq. (2) as a separate SNR-equivalent penalty.
  2. [Section III-B] The analog-bandwidth floor S_afe(R_s) depends on an unspecified R_bw. 'Calibrated so the bandwidth penalty approaches ~10 dB near 100 GBaud' is not sufficient to reproduce Table II; please state R_bw or the explicit calibration formula.
  3. [Section III-F] The symbol κ is used both for the distributed IMI coefficient (dB/km) and for the linear splice coupling coefficients κ_in, κ_out. This is confusing; use different symbols (e.g., η for coupling).
  4. [Section IV-A] The text says the ceiling 'crosses the 1024-QAM requirement near 24 GBaud.' Using the stated parameters and the net requirement of Eq. (3) (~29.0 dB), the crossover appears to be closer to 27–29 GBaud. Please clarify whether the comparison uses the raw threshold 29.57 dB or the net requirement, and derive the crossover from the formulas.
  5. [Figure 1 and Eq. (3)] The 'required-SNR lines' in Fig. 1 should state explicitly whether they include G_PCS and the 1.0 dB margin; the text uses both 'threshold' and 'net requirement' at different points.
  6. [Eq. (9)] The phase-noise penalty δ_PN=(ΔνT_s/τ_1dB)^2 is not derived. The small-signal BPS variance analysis cited from Pfau scales linearly in ΔνT_s for the phase-error variance; a quadratic scaling should be justified or replaced with a linear form calibrated at the same 1 dB point.

Circularity Check

1 steps flagged

Low-baud 'external check' is a calibration loop: Fan/Wang demonstrations are used to inform the transceiver ceiling and then returned as confirmation; the 64 GBaud central claim still rests on independent converter/ENOB anchors.

specific steps
  1. fitted input called prediction [Section I (Introduction); Section III-B (Transceiver Back-to-Back SNR Ceiling); Section IV-A; Section V-E]
    "The resulting estimates are consistent with, and informed by, the PDM-PS-256-QAM NANF demonstration of Wang et al. [27] and the PDM-PS-1024-QAM DNANF demonstration of Fan et al. [28]. ... remains consistent with the back-to-back SNRs realized in published high-order-QAM experiments ... Extending the same model to low baud provides an external check on its calibration: ... indeed returns 1024-QAM as the maximum feasible order at 20 GBaud over 5 km—matching the DNANF demonstration of Fan et al. [28]."

    The Fan/Wang demonstrations are first used to inform or calibrate the transceiver ceiling: the unmeasured calibration constants S_afe and S_nl in Eq. (8) were set so the ceiling 'remains consistent with the back-to-back SNRs realized in published high-order-QAM experiments,' and the Introduction says the resulting estimates are 'informed by' Wang [27] and Fan [28]. The same Fan 20 GBaud PS-1024-QAM point is then re-used as an 'external check' and reported as 'matching' the model's returned maximum feasible order. Because the Fan operating point is inside the calibration set used to choose the parameters, its agreement with the model is enforced by construction rather than independently confirmed. This is a fitted-input-called-prediction loop in the validation argument; it does not by itsel

full rationale

The core SNR budget (Eqs. (1)-(8)) is a forward model assembled from independent literature anchors: BER thresholds from standard QAM formulas, Kerr NLI from the eGN model, IMI/MPI from Poggiolini-Poletti and Mlejnek/Downie, EEPN from Shieh-Ho, and ENOB trends from Walden/Murmann. The 64 GBaud headliner (SNR_TRx ~25.3 dB, making 1024-QAM infeasible) is not fitted to that conclusion; the paper explicitly states the ceiling is a parametrized, unmeasured model and that its absolute calibration shifts the crossover baud. Thus the central transceiver-limited claim is not circular by construction. However, the low-baud 'external check' is circular: the Fan [28] and Wang [27] demonstrations are described as informing/calibrating the same ceiling and then returned as confirming 'boundaries' and a 'matching' 20 GBaud result. That agreement is a calibration-consistency loop, not independent prediction. The self-citations in the reference list are contextual and not load-bearing. Overall this is partial validation circularity, not a definitional collapse of the main derivation, so a score of 4 is appropriate.

Axiom & Free-Parameter Ledger

11 free parameters · 10 axioms · 0 invented entities

The central claim depends on the calibration of the unmeasured transceiver B2B ceiling (ENOB0, roll-off, Saf, Snl), on the order-dependent PCS gain interpolation, and on the gas-ISI saturation constants; all other terms are literature models or standard formulas. No new physical entities are introduced.

free parameters (11)
  • ENOB0 reference at 32 GBaud = 5.5 (high-performance); deployable ~2.5–3 dB lower
    Converter ENOB anchor from surveys [37],[38]; sets level of B2B ceiling.
  • ENOB roll-off slope sb = 0.6 bit/octave
    Chosen milder than ~1 bit/octave constant-FOM survey trend; directly controls ceiling at 64 GBaud.
  • Analog front-end floor Saf = 38 dB
    Calibration parameter set to reproduce Varughese's ~10 dB bandwidth penalty near 100 GBaud.
  • Tx/Rx nonlinearity floor Snl = 42 dB
    Calibration parameter for PAPR-dependent floor in Eq. (8).
  • PCS shaping credit GPCS(M) = 0.4 (16Q), 0.8 (64Q), 1.20 (256Q), 1.53 (≥1024Q) dB
    Order-dependent interpolation anchored to Fehenberger and Cho/Winzer; directly affects feasibility threshold.
  • BPS 1-dB tolerance for 1024-QAM = 1.5e-6
    Extrapolated from Pfau scaling; authors flag as model value, not measured.
  • Gmod scaling coefficient = 0.88 in Eq. (10)
    Pilot-aided CPE improvement interpolation; author-stated model assumption.
  • Grcm scaling coefficient = 7.6 in Eq. (11)
    Residual-carrier CPE improvement interpolation anchored to [50] at 256-QAM; 1024-QAM purely interpolated.
  • Gas-notch ISI saturation constants = δmax≈5.5 dB, A0≈6 dB
    Calibrated to Sillekens/Sohanpal [56] and Wang [39]; govern L-band channel-on-line penalty.
  • MFA taper NLI coefficient = estimated, sub-dB at operating launch
    Acknowledged as estimated not measured; enters pigtail NLI at high launch.
  • Baseline distributed IMI coefficient κ = −55 dB/km
    Input from literature, used as headline scenario; also swept in sensitivity.
axioms (10)
  • domain assumption GN/eGN model gives Kerr NLI power ∝ γ²·L_eff per span (Eq. 14)
    Adopted from Poggiolini [16],[17]; assumes Gaussian signal statistics and partial coherence exponent ε≈0.05.
  • standard math Independent additive noise powers add reciprocally in SNR (Eq. 2)
    Parallel-noise combination per Klaus-Winzer; assumes impairments independent or representable as equivalent noise floors.
  • standard math Gray-coded square M-QAM BER at pre-FEC 2e-2 sets SNR_th(M) (Eq. 4)
    Standard AWGN BER formula; ignores implementation penalties and non-Gaussian NLI.
  • domain assumption Phase noise equivalent linewidth is Δν_TX+Δν_LO and residual penalty is quadratic in Δν·T_s (Eq. 9)
    Follows Pfau/Savory Wiener-phase analysis; CPE block-length and decision-feedback details are collapsed.
  • standard math SQNR = 6.02·ENOB + 1.76 dB with PAPR back-off (Eq. 7)
    Bennett quantization model for full-scale sinusoid.
  • domain assumption EEPN variance per Shieh-Ho with Rs→Rs/Nsc for DSCM (Eq. 13)
    First-order scaling; authors note no full DSCM DSP simulation.
  • domain assumption IMI is an additive noise power linear in P_ch and L (Eq. 16)
    Follows Poggiolini/Poletti [18]; neglects possible non-stationarity of modal coupling.
  • ad hoc to paper Transceiver B2B ceiling = parallel combination of quantization, analog-bandwidth, nonlinearity floors (Eq. 8)
    This paper's parameterized model; not a measured B2B curve and calibration shifts crossover baud.
  • ad hoc to paper Gas-notch ISI penalty saturates per Eq. (22) with δmax≈5.5 dB, A0≈6 dB
    Phenomenological calibration anchored to Sillekens/Sohanpal [56] and Wang [39].
  • domain assumption CO2 line comb: Lorentzian P/R branches, spacing ~23 GHz, FWHM ~1.5 GHz, anchored to 0.5 dB/km line-center loss
    Based on Wang et al. [39] spectroscopy; channel-averaging approximation.

pith-pipeline@v1.3.0-alltime-deepseek · 24961 in / 20415 out tokens · 188848 ms · 2026-08-02T10:24:52.619056+00:00 · methodology

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read the original abstract

Hollow-core fiber (HCF) is widely expected to enable higher-order quadrature amplitude modulation (QAM) because of its near-vacuum Kerr nonlinearity and higher launch power. We develop a per-channel effective signal-to-noise ratio (SNR) budget that combines, in reciprocal form, optical-link impairments including amplified spontaneous emission, Kerr nonlinear interference (NLI), inter-modal interference (IMI), pigtail NLI, and CO2 gas absorption; a parameterized, symbol-rate-dependent transceiver back-to-back SNR ceiling determined by effective-number-of-bits at rate, analog bandwidth, and Tx/Rx nonlinearity; and the remaining transceiver and line impairments, including laser phase noise, equalization-enhanced phase noise, timing jitter, polarization-dependent loss, and amplifier gain ripple with filter narrowing, each expressed as an equivalent SNR floor. The central result, at a representative 64GBaud system with 75GHz channel spacing over 6THz, is that once HCF removes the fiber limits, the transceiver ceiling rather than the fiber sets the achievable modulation order: a roughly 25dB ceiling at 64GBaud makes 1024-QAM and above infeasible on either fiber, confining ultra-high-order QAM to low baud rates. HCF therefore provides its main advantage in reach and achievable baud rate at a given modulation order: at an IMI coefficient of kappa=-55dB/km, 256-QAM reach increases from about 45km to about 170km and 64-QAM reach from about 415km to about 2275km when moving from single-mode fiber to HCF. In the C-band, CO2 absorption lines are weak and sparse, so channels placed away from the lines follow the gas-free baseline, while only worst-case placements lose reach at long distances. In the L-band, the stronger absorption bands are denser than the channel bandwidth, making line avoidance spectrally costly, and a channel placed on a line loses one to two QAM orders.

Figures

Figures reproduced from arXiv: 2606.23527 by Md Ghulam Saber, Zhiping Jiang.

Figure 1
Figure 1. Figure 1: EEPN penalty versus distance for SMF and HCF across QAM orders. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: Transceiver back-to-back SNR ceiling SNR [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Phase-noise tolerance under the three CPE classes: (a) maximum per-laser linewidth for 1 dB penalty versus QAM order; (b) phase-noise penalty [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: EEPN penalty versus distance for SMF and HCF across QAM orders. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Distributed versus discrete inter-modal interference: (a) effective splice MPI versus HCF–HCF splice LP [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 3
Figure 3. Figure 3: Phase-noise tolerance under the three CPE classes: (a) maximum per-laser linewidth for 1 dB penalty versus QAM order; (b) phase-noise penalty [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: SMF-pigtail NLI in HCF coherent links: (a) pigtail NLI penalty versus one-sided pigtail length; (b) pigtail-aware optimum total WDM launch power [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 4
Figure 4. Figure 4: Distributed versus discrete inter-modal interference: (a) effective splice MPI versus HCF–HCF splice LP [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: SNR penalty breakdown by QAM order at 100 km for (a) SMF and (b) HCF. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 5
Figure 5. Figure 5: SMF-pigtail NLI in HCF coherent links: (a) pigtail NLI penalty versus one-sided pigtail length; (b) pigtail-aware optimum total WDM launch power [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Maximum feasible QAM order versus distance for SMF and HCF at [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 6
Figure 6. Figure 6: SNR penalty breakdown by QAM order at 100 km for (a) SMF and (b) HCF. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Maximum feasible QAM order as a function of symbol rate and link distance for SMF (left) and HCF baseline (right). [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 7
Figure 7. Figure 7: Maximum feasible QAM order versus distance for SMF and HCF at [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) Combined pigtail × distributed-IMI design space at 100 km; (b) spectral efficiency versus distance for representative HCF operating points, with SMF as reference. short reach (≲ 5 km at 32 GBaud, extending to ≲ 1 km at 20 GBaud and below), confined by the modern-pilot CPE budget at 50 kHz ECL lasers; 4096-QAM is not reached on SMF anywhere in the swept space. This is consistent with the published ≥ 204… view at source ↗
Figure 8
Figure 8. Figure 8: Maximum feasible QAM order as a function of symbol rate (16–128 GBaud) and link distance for SMF (left) and HCF baseline (right), on a [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: (a) Combined pigtail × distributed-IMI design space at 100 km; (b) spectral efficiency versus distance for representative HCF operating points, with SMF as reference. 0.0 0.1 0.2 0.3 0.4 0.5 Excess loss (dB/km) (a) Modeled CO2 line spectrum CO2 line spectrum 0.50 dB/km (Wang 2025) 1520 1540 1560 1580 1600 1620 Wavelength (nm) 0.00 0.02 0.04 0.06 0.08 0.10 Excess loss (dB/km) (b) Channel-averaged loss and W… view at source ↗
Figure 10
Figure 10. Figure 10: CO2 gas-line absorption. (a) Modeled CO2 line spectrum (line-center excess loss). (b) 64 GHz channel-averaged excess loss with the C-band and L-band WDM grids overlaid, on a ∼5× finer vertical scale than (a). (c) Max feasible QAM order versus distance (HCF, κ = −55 dB/km, 64 GBaud) for a clean C-band channel, the worst C-band channel, and a worst-case L-band channel-on-line [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figure 11
Figure 11. Figure 11: 256-QAM reach versus distributed IMI coefficient [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗

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Reference graph

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