Dual slow-light enhanced photothermal gas spectroscopy on a silicon chip

Domain: physics
Published: 2025-11-26
Editorial outcome: major_revision

Abstract
Integrated photonics sensors have attracted significant attention recently for their potential for high-density integration. However, they face challenges in sensing gases with high sensitivity due to weak light-gas interaction. Slow light, which dramatically intensifies light-matter interaction through spatial compression of optical energy, provides a promising solution. Herein, we demonstrate a dual slow-light scheme for enhancing the sensitivity of photothermal spectroscopy (PTS) with a suspended photonic crystal waveguide (PhCW) on a CMOS-compatible silicon platform. By tailoring the dispersion of the PhCW to generate structural slow light to enhance pump absorption and probe phase modulation, we achieve a photothermal efficiency of 3.6×10−4 rad·cm·ppm−1·mW−1·m−1, over 1−3 orders of magnitude higher than the strip waveguides and optical fibers. With a 1-mm-long sensing PhCW incorporated in a stabilized on-chip Mach-Zehnder interferometer with a footprint of 0.6 mm2, we demonstrate acetylene detection with a sensitivity of 1.4×10−6 in terms of noise-equivalent absorption and length product (NEA·L), the best among the reported photonic waveguide gas sensors to our knowledge. The dual slow-light enhanced PTS paves the way for integrated photonic gas sensors with high sensitivity, miniaturization, and cost-effective mass production.

Introduction
Integrated photonics has the potential for widespread applications in communications, sensing, metrology, and information processing1,2. Silicon-based on-chip gas sensing is an emerging field of integrated photonics, which has attracted increasing attention due to its unique advantages in size, weight, power efficiency, and cost, but faces a challenge in detection sensitivity due to inherently weak light-matter interaction3,4. Slow light offers an effective means for improving light-matter interaction on the photonic chip, which arises from strong interference between the forward-propagating and back-scattered waves in a photonic crystal5–8, leading to enhanced electromagnetic field intensity9–12.

Photothermal spectroscopy (PTS) is a sensitive gas detection method. It detects the phase change of a probe beam due to the reflective index (RI) change of the gas medium, originating from the gas absorption of a modulated pump beam13–15. The sensitivity performance of PTS gas sensors may be quantified by defining the normalized photothermal (PT) efficiency in the unit of rad·cm·ppm−1·mW−1·m−1, indicating the magnitude of probe phase modulation per unit gas concentration (ppm), absorption coefficient (cm−1), absorption distance (m), and pump power (mW)16,17. Early works on free-space-based PTS have demonstrated PT efficiency of ~10−10 rad·cm·ppm−1·mW−1·m−1 level18,19. Optical fibers and waveguides provide much tighter light confinement than free space, which enhances the optical field intensity for light-gas interaction and hence the PT efficiency20. Silica hollow-core fibers (HCFs) with a core diameter of a few tens of micrometers have demonstrated PT efficiency of ~10−6 rad·cm·ppm−1·mW−1·m−121,22, and an on-chip chalcogenide waveguide with a core-thickness of ~200 nm demonstrated PT efficiency of ~10−5 rad·cm·ppm−1·mW−1·m−123.

In this work, we propose a dual slow-light enhanced PTS on a suspended silicon photonic crystal waveguide (PhCW) to dramatically improve the on-chip PT efficiency. We leverage the PhCW to generate a strong slow-light effect by tailoring the structural dispersion24. The dual slow-light region is designed to cover both the pump and probe wavelengths, where the pump slow light enhances the optical field intensity for gas absorption, and the probe slow light amplifies the PT-induced phase modulation. A suspended structure is designed to achieve higher light-gas overlap as well as better heat accumulation by using low-thermal-conductivity air as the top and bottom claddings. A silicon-integrated PTS gas sensor with dual slow-light enhancement demonstrates on-chip PT efficiency of 3.6×10−4 rad·cm·ppm−1·mW−1·m−1, over 1−3 orders of magnitude higher than the strip waveguides and optical fibers. The PT efficiency is proportional to the product of group indices of the pump and probe, which can be further enhanced by dispersion optimization.

Results
Theory
Figure 1a illustrates the basics of the dual slow-light enhanced PTS on a suspended silicon two-dimensional (2D)-PhCW. The PhCW is composed of air holes etched into hexagonal lattices of silicon, and the suspended structure is formed by removing the silica bottom cladding layer. The slow-light modes, generated by a line defect, propagate along the z-direction. These modes are confined in the silicon layer by total internal reflection in the x-direction and localized in the defect by the photonic bandgap in the y-direction. A pump and a probe slow-light modes co-propagate along the PhCW, where the modulated pump absorption by gas molecules induce a heat source that changes the temperature distribution and hence modulates the phase of the probe beam. The optical intensities of both beams are compressed spatially by the slow-light effect in the PhCW, leading to enhanced efficiency of the pump absorption and probe phase modulation. The heat-source (Q) over the waveguide cross-section (x-y) at propagation distance z equals to the absorbed pump intensity through Beer-Lambert law and is given by

Q e(x,y)= e I (0) [1−exp (− n gpαCγz )/ n gpαCγP (1)
n (0) n (0) p
gas gas

where n (0) and e I (0) are the gas RI and modulated optical intensity of the pump beam with superscript (0) denotes the values in the absence of gas absorption, α the gas absorption coefficient, C the gas concentration. The “~” denotes the frequency-domain amplitude of the modulated variables. n is the group index directly related to the energy transport velocity, i.e., the group velocity in the absence of loss25. n represents the group index at pump wavelength λ , which enhance g via the slow-light effect. As shown in Fig. 1b, the heat source also depends on the fractional power of the pump mode in gas, quantified as γP . Here, the spatial confinement factor γ represents the fraction of energy that interacts with the surrounding gas (~13%)26, and P is the incident pump power.

The heat source alters the temperature distribution (T) through heat conduction. For an intensity-modulated pump beam, the amplitude of the temperature oscillation may be approximated as T /Q =κ, with κ the thermal conductivity of the waveguide20. The profile of the temperature change is shown in Fig. 1c. Due to the low-thermal conductivity of the gas medium (~0.02 W/m/K), the suspended structure lowers the heat conduction in the x-direction and facilitates the heat accumulation. Due to significant overlap with the probe field, as shown in Fig. 1d, the modulated T changes the phase of the probe beam via the PT-induced RI variation. The slow-light enhanced PT phase modulation amplitude (Δϕ ) is approximated as:

Δϕ~ (cid:4) 2πn gb L eTOhψ jT ~jψ i (2)
λ n Si b b Si
b Si

where n is the group index at the probe wavelength λ , L the PhCW length, ψ the normalized probe mode distribution, eTO the thermo-optic (TO) coefficient of silicon (~1.8×10−4 K−1). We neglect the contribution of gas-induced TO effect due to its very small TO coefficient (−0.91×10−6 K−1) as compared to that of silicon with relative error <1% (Fig. S1). The probe phase modulation is primarily decided by the spatial integration of ψ and T in the silicon region. From Eq. (1) and (2), the phase modulation is related to the product of n and n , given by:

Δϕe =k*αCLP / 2πn gp n gb L eTOαCγP (3)
p λ κ Si p
b Si

here k* is defined as the normalized PT efficiency in the unit of rad·cm·ppm−1·mW−1·m−1, representing the phase modulation (in rad) of the probe beam normalized by αCP L (in cm−1·ppm·mW·m). As shown in Eq. (3), the slow-light effect of PhCW greatly improves the PT phase modulation, which is attributed to the enhanced n that amplifies the heat generation and n that amplifies the probe phase modulation. Detailed theory refers to Supplementary S1.

Simulation of PhCWPTS
The PhCW is on a silicon-on-insulator (SOI) wafer with a 220-nm-thick top-silicon layer and three rows of defect holes. The lattice constant (a) and radius of the defect holes (R, r , r) are optimized using the RSoft band-solver (Supplementary S2). The dispersion diagram of the PhCW is depicted in Fig. 2a with optimal parameters of a=500 nm, R=0.38a, r =0.6R, and r =0.7R. There is an even mode and an odd mode in the photonic bandgap. The even mode, easily excited by the fundamental TE mode of the input strip waveguide, is used for gas sensing. The slow-light wavelength band includes pump and probe regions. The pump region covers the C H vibrational-rotational absorption band (1515−1543 nm), and the probe region is in the non-absorption band (1543−1572 nm). The group index of the slow-light mode can be expressed as n =c·dk/dω, with k representing the wave vector, ω the angular frequency, and c the speed of light in vacuum. The n value is calculated from the reciprocal of the slope of the guided even mode curve, and n in the probe region is larger than in the pump region due to flatter dispersion. Since a high n may lead to a large propagation loss, the pump wavelength should be selected in a region with a moderate n to balance the loss and slow-light enhancement. In contrast, phase modulation is independent of the probe power; therefore, the probe wavelength can be chosen in a region where a larger n is preferable.

Figure 2b depicts the calculated heat source Q , phase modulation Δϕ , n and n values as functions of wavelength. The n varies from 5 to 24 in the pump region, while the n varies from 24 to 270 in the probe region. The change in Q results from the combined effect of gas absorption coefficient and n -enhanced heating power. Δϕ increases with rising wavelength, which is highly consistent with the trends of n change against the wavelength, suggesting that higher n enhances the PT-induced phase modulation. Figure 2c shows the calculated change of temperature for three different absorption (pump) wavelength λ , corresponding to n of 5, 10, and 24, respectively. The peak temperature variation (T) increases linearly with rising n values. Figure 2d shows the frequency-domain Δϕ for three different probe wavelength λ , corresponding to n of 27, 58, and 106, respectively. Δϕ also increases linearly with rising n values. Owing to the suspended design, the modulation bandwidth extends to ~1 MHz, which is beneficial for phase-sensitive detection at higher frequencies with lower 1/f noise27.

The PTS chip
The silicon-integrated PTS chip is fabricated with a CMOS-compatible process (Details in “Methods” and Supplementary S3). As shown in Fig. 3a, the device consists of an input/output subwavelength grating coupler (SWGC) and a Mach-Zehnder interferometer (MZI) with an ultracompact footprint of ~0.6 mm2 (4.5L×0.13W mm2). The strip waveguide after the input SWGC is narrowed down to a width of 0.5 μm over a length of 100 μm to ensure fundamental TE transmission in the MZI (Fig. S4). The waveguide width is then expanded to ~2 μm before the Y-splitter of the MZI. The suspended 2D-PhCW with a length of 1 mm forms part of the sensing arm. The reference arm consists of a single-mode strip waveguide with a width of 0.5 μm. As shown in Fig. 3b, the Y-splitter features a waveguide width ratio of 3:1 (i.e., power splitting ratio of 9:1) to compensate for the relatively larger loss of the PhCW and ensure approximately equal optical power in the two arms28. A Y-combiner is used to combine the fields from the two arms into the output SWGC for interferometric measurement. The corresponding SEM images of the 2D-PhCW and the suspended structure are shown in Fig. 3c, d, respectively. A 100-μm-long tapered strip waveguide is fabricated before the PhCW to ensure precise excitation of the TE mode, thereby selectively exciting TE even mode in the 2D-PhCW12,29,30. Figure 3e shows more details of the transition region, showing the gradual variation of hole size along the central line defect, which is used to reduce the coupling loss between the strip waveguide and the PhCW.

Experimental characterization
The PhCW for slow-light enhancement is characterized by its n values, which can be determined from the wavelength difference (Δλ) between adjacent peaks of the on-chip MZI transmission (Details in “Methods”)31. As shown in Fig. 4a, in the spectral range of interest (1480−1575 nm), Δλ reduces significantly from ~4.6 nm at 1480 nm to around ~0.02 nm at 1573 nm, and becomes small beyond 1573 nm, making it hard to determine the n value accurately due to the background noise and the resolution of the optical spectrum analyzer (0.02 nm). Figure 4b highlights the n values deduced from the averaged transmission spectrum of the adjacent two interference fringes. For wavelengths below 1572 nm (n ≈81), the measurement is considered reasonably accurate as Δλ is larger than the spectral resolution. For wavelengths at 1573.5 nm (n ≈107) and beyond, the measurement error may increase considerably due to the limited spectral resolution. Therefore, we chose a probe wavelength at 1572 nm in our gas detection experiments, instead of a longer wavelength (corresponding to larger n ), to enhance more of the PTS signal.

We then examine the slow-light enhanced pump absorption with a fixed probe wavelength (Detailed set-up in the next section). Figure 4c shows the measured PTS signal (S) of 5% C H for 14 different wavelengths from ~1512 to ~1542 nm, corresponding to peaks of the C H absorption lines. Here, S represents the first-harmonic (1f) amplitude demodulated from the MZI output. We compare the PTS performance with pump wavelengths set at points A and B. Although the absorption coefficient at point B (1.05 cm⁻¹ at 1531.58 nm) is ~90% that at point A (1.17 cm⁻¹ at 1520.08 nm), the PTS signal at point B is 1.74 times larger due to a higher value of n (1.95), which is highly consistent with the product (1.75) of the absorption coefficient and n , indicating the slow-light enhanced pump absorption.

The slow-light enhancement on probe phase modulation is further investigated with the pump wavelength fixed at B with 1% C H filled into the gas cell. Figure 4d shows the measured S, fringe contrast (ν), and resultant Δϕ at different probe wavelengths. The solid lines are the corresponding calculated values (Details in Supplementary S4). As the probe wavelength increases, Δϕ also rises due to the increment of n , indicating that the slow-light effect can indeed enhance the probe phase modulation. However, with increasing n , the slow-light-induced propagation loss in PhCW-based sensing arm increases correspondingly (Supplementary S9), which leads to a decreasing ν due to the unbalanced power of the two MZI arms31. Using a variable on-chip attenuator in the reference arm could rebalance the power distribution to further enlarge the MZI contrast and the PTS signal32. Overall, the dual slow-light enhancement is determined by both n and n values. Figure 4e delves into the linear relationship between Δϕ and the product of n and n (R2=0.96), unveiling the dual slow-light enhancement in the pump-probe PTS scheme (Details in Supplementary S5).

On-chip gas sensing
The performance of dual slow-light enhanced PTS for gas sensing is evaluated by utilizing the setup shown in Fig. 5a. The pump is from a distributed feedback (DFB) laser, with its wavelength fixed at the center of the P(11) absorption line of C H at 1531.58 nm. The pump intensity is modulated by an acousto-optic modulator (AOM) and amplified by an Er-doped fiber amplifier (EDFA). The probe beam, from an external cavity diode laser (ECDL) with a 100 kHz linewidth, is co-coupled with the pump beam into the on-chip MZI via a wavelength-division multiplexer (WDM). Two polarization controllers (PC) are used to adjust the polarization state of the pump and probe to maximize the fiber-SWGC coupling efficiency. The MZI output is filtered by a narrowband filter (<1 nm) to block the residual pump beam, and the transmitted probe beam is focused onto a photodiode (PD). The PD signal is sent to a lock-in amplifier (LIA) for 1f demodulation. A sinusoidal signal from a function generator (FG) drives the AOM, which also serves as a reference for the LIA. The silicon-integrated on-chip MZI with the sensing PhCW is packaged inside a compact gas cell with a dimension of 5×2×1 cm3 and a volume of <10 mL (Supplementary S6). Gas sensing experiments are conducted by filling different C H :N mixtures into the packaged gas cell.

Figure 5b shows the 1f-PTS signal and the 1σ noise level as functions of the pump power coupled into the PhCW. We examined the PTS signal and noise with two pairs of pump-probe wavelengths. The first pair has a pump wavelength of 1531.58 nm and a probe wavelength of 1572 nm, corresponding to a large n ×n value of 1458. In contrast, the second pair utilizes a pump wavelength of 1520.08 nm and a probe wavelength of 1542 nm with a relatively small n ×n value of 176. The PTS signals for both pairs show approximately linear relationships with the pump power, while the amplitude in the first pair is ~8 times larger than the latter, which is close to the proportion of their n ×n values. There is no significant increase in noise levels with increasing n ×n values, indicating the signal-to-noise ratio (SNR) can be enhanced by operating at the slow-light regime (Supplementary S7). Figure 5c shows the measured PT efficiency with varying pump modulation frequency, which exhibits no significant change at low frequencies (<100 kHz) and decreases relatively rapidly beyond 500 kHz. The k* value at 50 kHz is 3.6×10−4 rad·cm·ppm−1·mW−1·m−1, and the 3−dB modulation bandwidth is ~500 kHz (Details in “Methods”). Figure 5d shows the linear relationship of the 1f-PTS signal with increasing C H concentration from 0 to 30%, giving a linear dynamic range of >2.5×104. While the PTS signal scales linearly with concentration, the noise level remains stable, leading to a proportional increase in SNR across the entire dynamic range. As a result, the precision remains approximately unchanged across different concentration levels.

Figure 5e shows the Allan-Werle analysis based on the measured noise level over a 2-h period with pump wavelength tuned away from the absorption line at 1531.27 nm. As shown in Figs. S15a, b, two more long-term noise measurements with pure N were conducted under different conditions: when the pump was aligned to the absorption line at 1531.58 nm and away from absorption at 1531.27 nm, respectively. The n value at these two wavelengths remains essentially the same. The Allan deviation results indicate that at an averaging time of ~200 s, the 1σ minimum detection limit (MDL) reaches its minimum in both cases: 15 ppm (at 1531.58 nm) and 12 ppm (at 1531.27 nm), corresponding to a minimal noise-equivalent absorption (NEA) coefficient of 1.4×10⁻5 cm−1. We further evaluated the signal fluctuation at the C₂H₂ concentration of 1000 ppm, as shown in Fig. S15(c). The 1σ fluctuation is estimated to be 18 ppm at an averaging time of 100 s, slightly larger than the 1σ MDL value obtained with pure N (Supplementary S10). With respect to the sources of noise and drift over extended measurement times, at short integration times within 200 s, the noise mainly emanates from the relative intensity noise of the probe laser and electronic noise of the electrical circuits. At longer times over 200 s, the system drift dominates, which is mainly due to external temperature variation and pump/probe light power fluctuations that vary slowly over time.

Methods
Numerical simulation
The photonic band structure and dispersion relation of the PhCW are tailored and simulated using the RSoft band-solver. The group index is extracted from the dispersion diagram. Each band is fitted based on 100 points in the lattice along the Γ-K direction. The slow-light parameter optimizations and transmission modes of the PhCW are simulated using Ansys Lumerical FDTD. The optical mode and thermal field, as well as time- and frequency-domain profiles, are simulated using a three-dimensional finite-element method (3D-FEM) with COMSOL Multiphysics. For the optical mode calculation, the pump and probe modes are calculated using an eigensolver in COMSOL with the Floquet boundary condition applied to the front and back surfaces. For the thermal field, a symmetry boundary is applied to the front and back surfaces to simulate a scenario where the structure is infinitely periodic along the z-axis. The other boundaries surrounding the PhCW are allowed to transfer the heat to the air via natural convective heat flux. The phase modulation Δϕ~ is calculated by integrating the mode overlapping between the probe and the thermal fields over the entire PhCW structure.

Silicon chip fabrication
The silicon-based photonic crystal patterns of the 2D-PhCW, input/output SWGCs, and other strip waveguides in the MZI are fabricated on the same SOI wafer using electron beam lithography (EBL) and inductively coupled plasma (ICP) dry-etching. The silica bottom cladding of the photonic crystal region is wet-etched subsequently using buffer oxide etching solution. Before wet-etching, ultraviolet (UV) photoresist is used to protect the strip waveguide and SWGC areas, preventing collapse due to excessive etching. A suspended 2D-PhCW is obtained after removing the UV photoresist.

Group index determination
To determine the n values of the slow-light PhCW, the on-chip integrated MZI is connected with a broadband light source and an optical spectrum analyzer (OSA). The broadband source encompasses a wavelength range of 1450–1640 nm, facilitated by an OSA with a spectral resolution of 20 pm. The n values of the PhCW can be derived from the interference spectrum using the following formula n (λ)=λ×λ /(Δλ×L)+n ref(λ), where λ and λ represent the wavelengths of the fringe peaks, Δλ=|λ -λ | the wavelength difference between adjacent peaks, L the PhCW length, and n ref(λ) is the group index of the reference arm5.

PT efficiency determination
The PT efficiency k* value of the dual slow-light enhanced PTS on PhCW is determined based on the experimental result using the formula k*=Δϕ~=αCP L17. Here, Δϕ~ is obtained by comparing the experimental 1f-LIA output with fringe contrast. α is the absorption coefficient of the P(11) rovibrational transition, which is taken from the high-resolution transmission (HITRAN) molecular absorption database. C is the gas concentration, P is the input pump power, and L is the PhCW length. Under 5% C H concentration and 1-mm-length PhCW, a k* value of 3.6×10−4 rad·cm·ppm−1·mW−1·m−1 is obtained at the modulation frequency of 50 kHz.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript of interest for several reasons: a) it shows that on-chip NIR gas sensing with a fairly low detection limit is achievable, b) it effectively and convincingly utilizes slow light in a photonic crystal waveguide with tangible advantages, and c) it is accomplished with a compact, at least partially packaged device. The use of photo-thermal spectroscopy appears to be indeed a promising approach to addressing the challenge of fringes that have historically limited the performance of integrated circuits for spectroscopy. The paper is well-written, featuring a thorough theoretical analysis and detailed descriptions of both simulations and theoretical components. However, there are some inconsistencies highlighted below that must be addressed before I can recommend this work for publication:\n-Fig. 2b: It is unclear if the absorption coefficient for C₂H₂ was used in the calculation of the heat source Q, as the wavelength dependence of Q appears to increase monotonously even in the spectral region with the weakest lines. On the other hand, the scattered phase modulation data for low ngb are surprising. How do the authors explain the shape resembling the absorption band?\n-Line 181: Reference 28 appears irrelevant.\n-Fig. 3d: The authors' description of non-suspended Si evidently points to a suspended part of the access waveguide. Please explain or correct.\n-Fig. 4b and Line 206: The method of experimental determination of the waveguide group index, which uses the peak values of likely under-sampled interference fringes (authors admit their spectrometer resolution is comparable with the fringe period), introduces large errors in the data. Therefore, the fringes should either be fitted to recover the peak values, or several adjacent group index values should be averaged. In this line of argumentation, considering Fig. 4b and its inset, it is unlikely that a group index of 100 is achieved, but rather an index around 50. Also, I would like the authors to comment on their statement regarding the origin of fluctuations associated with Bloch-Floquet mode fluctuations, as opposed to fluctuations due to under-sampling and possible fringes caused by reflections in the PIC, which I consider likely.\n-Line 214, Fig. 4c: The authors claim that the PTS signal is “nearly twice as large” at point B; however, absorptions are nearly equal, and the pump group index appears to be much more than twice as large at point B than at point A. Do the experimental data really show linear dependence of PTS on n_gp, and could you provide a clear, quantitative evidence? Also, why do the authors prefer to present the normalized n_gp as opposed to the absolute value, which is, in my opinion, more informative?\n-Fig. 4e: The claim that the figure demonstrates linear dependence on n_gp x n_gb is wrong, as only n_gb was varied in the experiment. So it only shows linear dependence on n_gb. This also refers back to my previous question: can your data indeed demonstrate the linear dependence on n_gp? Also, it seems that not all data reported in Fig. 4b were used in Fig. 4d and Fig. 4e, which makes me wonder how the plotted points were selected and if the spread of results is actually much larger than reported in the plots of Figs. 4d and 4e.\n-Line 283: The authors write that the Allan deviation in Fig. 5e was measured with the pump tuned away from the absorption lines. How far away was the pump tuned, and did it have a comparable group index? If not, the noise analysis is not credible. A more rigorous approach would be to measure with N₂ in the same configuration as during the C₂H₂ experiment, or at a very low C₂H₂ concentration. Demonstrating the measurement precision at a certain concentration may be of equal, or even greater value than measuring the minimal detection limit, and the comparison of precision and MDL would be desirable.\n-Linked to the previous point, in section S8: Regarding the noise level evaluation, noise levels with N₂ and C₂H₂ are shown. The Allan deviation in Fig. 5e starts at a comparable value to the noise level with N₂, which is expected. However, since noise with C₂H₂ is 100x higher than with N₂, is the expected precision 800 ppm instead of 8 ppm? Please comment. Also, the sentence in S8, line 364, “When pump turns on…” is confusing; could you be more specific/descriptive?\n-How do you ensure that the device operates at the quadrature point of the MZI? Is the chip thermally stabilized, and if so, how precise must the temperature stabilization be to achieve the reported performance?\n-In Table 1: Some more recent works on photonic trace gas sensing were not mentioned, and I recommend adding https://doi.org/10.1021/acsphotonics.3c01085, https://pubs.acs.org/doi/10.1021/acs.nanolett.2c01198, and https://doi.org/10.1364/OPTICA.533710. The MDL of 8 ppm is still rather high compared to the state-of-the-art result of 0.02 ppm for CO₂ reported in the last work in the mid-infrared, and this should be made clear. Nevertheless, the NEAL is impressive, and the fact that this is achieved in the NIR, where photonics is mature and relatively easy to integrate with both light sources and detectors, is of undeniable value.\n-In addition, I recommend removing reference 43, as this paper, in agreement with https://doi.org/10.1021/acsnano.4c01856, is not credible and should have been retracted.\n-For completeness, the authors can mention any drawbacks of the device and provide an outlook for possible further optimization.\n-a more detailed explanation/analysis on why PTS is less sensitive to fringing could be of interest, as some sensitivity would certainly exist, particularly in a complex PIC as reported here.\nSupplementary Information:\n-Line 84: Possible typo; S9 should be S12.\n-Fig. S2: The figure is ambiguous. It states that S2c) was done with r1=0 and shows spatial confinement of 0.1 at the selected r0, while Fig. S2d shows spatial confinement of 0.05 at r1=0. Please check and correct.\n-Line 258: With only a 2 µm oxide layer, SOI PICs show, to my knowledge, some substrate leakage. For mm-long samples, this may be negligible, but using wafers with at least a 3 µm oxide layer can be recommended.", "reviewer_2": "In this study, the authors harnessed slow-light effects in a photonic crystal waveguide to enhance photothermal gas spectroscopy. The pump laser induces localized heating in the waveguide due to gas absorption, while the non-absorbing probe laser experiences a temperature-dependent phase shift. Numerical simulations and experimental validations were conducted.\n• How does this approach compare to non-photothermal spectroscopy (PTS) methods?\n• Some figure captions are overly long and should be shortened.\n• The lowest measured C₂H₂ concentration was 5%. On page 9, the authors state: \"Fig. 5(e) presents the Allan-Werle analysis based on measured noise levels over a 2-hour period with the pump wavelength detuned from absorption lines. The Allan deviation indicates a minimum detection limit (MDL) of 8 ppm C₂H₂ and a noise-equivalent absorption (NEA) coefficient of 9.2 × 10⁻⁶ cm⁻¹ at 200 s.\"—Is this sensitivity sufficient?\n• When compared to state-of-the-art gas sensors, the noise-equivalent absorption-length product (NEA∙L) of 9.2×10⁻⁷ represents the highest sensitivity reported for a photonic waveguide-based sensor. This performance is competitive with the best photothermal and optical gas sensors, approaching the sensitivity levels of advanced cavity-enhanced techniques while maintaining a compact (0.6 mm² footprint), CMOS-compatible, and scalable design. Therefore, I do not see clear evidence of the benefit of the reported device.", "reviewer_3": "The manuscript describes an integrated photonic sensor for gas detection based on a dual slow-light-enhanced photothermal spectroscopy strategy. The authors combine slow-light effects at both the pump and probe wavelengths in a suspended silicon photonic crystal waveguide, aiming to increase photothermal efficiency for acetylene sensing. While the methodological details and experimental procedures are presented clearly, several concerns lessen the impact and novelty of the work.\nFirst, although slow-light phenomena in photonic crystals have long been recognized for boosting light–matter interactions, the fundamental concept here—using a slow-light waveguide for enhanced sensitivity—does not appear to offer a disruptive advance over existing techniques. Multiple research groups have employed similar strategies to harness slow-light in photonic crystal sensors, and the incremental improvement presented does not substantially exceed what is typically achievable with established platforms.\nSecond, the stated minimum detection limit of around 8 ppm for acetylene is not convincingly benchmarked against the broad landscape of state-of-the-art technologies. The discussion focuses primarily on a qualitative comparison to previously reported photonic methods, but many other on-chip and fiber-based solutions currently achieve significantly lower detection thresholds (orders of magnitude). Without a comprehensive performance comparison, it remains unclear whether this device represents a significant leap or merely an incremental step.\nThird, the manuscript would benefit from a more in-depth assessment of technical limitations. While the authors emphasize the slow-light effect and suspended design as key enhancements, it would be informative to explore potential drawbacks, such as increased propagation loss at higher group indices or the trade-offs in device robustness and fabrication complexity. The authors do provide a theoretical derivation of the photothermal phase modulation and refer to numerical simulations that confirm certain findings, but the discussion of sources of noise and drift over extended measurement times is somewhat limited.\nFourth, from a methodological standpoint, the fabrication details are explicit, and the basic experimental arrangement is standard for photothermal measurements. The data on waveguide characterization, group index determination, and photothermal signal scaling with pump power all suggest competent execution. Nevertheless, the manuscript does not sufficiently highlight how these technical steps move beyond work already available in the literature on integrated photonic crystal sensors.\nOverall, the article offers an incremental contribution that confirms some expected advantages of dual slow-light enhancement in a photonic crystal waveguide. However, the claimed improvements do not convincingly surpass what other research groups have demonstrated, nor does the manuscript provide a strong argument for a fundamentally new approach. Consequently, although the work is carefully executed, it does not appear to meet the high novelty and impact standards expected by a top-tier journal.\nIn light of these considerations, the recommendation is to reject the paper. The demonstrated device achieves moderate performance gains that do not clearly outpace existing sensor architectures, and the authors’ discussion does not sufficiently establish the broader significance of these findings for integrated photonic gas sensing."}, "author_response": "Point-by-point response to referees\nReviewers' comments:\nReviewer #1 (Remarks to the Author):\nComment 1.1: The manuscript of interest for several reasons: a) it shows that on-chip NIR gas sensing with a fairly low detection limit is achievable, b) it effectively and convincingly utilizes slow light in a photonic crystal waveguide with tangible advantages, and c) it is accomplished with a compact, at least partially packaged device. The use of photo-thermal spectroscopy appears to be indeed a promising approach to addressing the challenge of fringes that have historically limited the performance of integrated circuits for spectroscopy. The paper is well-written, featuring a thorough theoretical analysis and detailed descriptions of both simulations and theoretical components. However, there are some inconsistencies highlighted below that must be addressed before I can recommend this work for publication:\nResponse: We sincerely thank the reviewer for the thoughtful evaluation and acknowledging the importance of our work. In the following, we provide detailed responses to the concerns raised by the reviewer, and highlight the corresponding revisions in yellow in the manuscript and supplementary information. We believe that addressing these points will further clarify the strength and impact of our results.\nComment 1.2: -Fig. 2b: It is unclear if the absorption coefficient for C₂H₂ was used in the calculation of the heat source Q, as the wavelength dependence of Q appears to increase monotonously even in the spectral region with the weakest lines. On the other hand, the scattered phase modulation data for low ngb are surprising. How do the authors explain the shape resembling the absorption band?\nResponse: In Fig. 2(b), the heat source Q for the 9 different wavelengths was calculated assuming a fixed absorption coefficient of 1.05 cm⁻¹, which equals to the absorption of C₂H₂ at 1531.58 nm, rather than applying the actual wavelength-dependent absorption profile of C₂H₂ which varies with wavelength. This was done to explicitly examine the effect of the pump group index ( ) on heat source power Q to enable a clearer interpretation of the trend. In fact, the heat source always depends on the wavelength of the pump via the wavelength-dependent absorption coefficient, which must be taken into account for practical applications. To avoid confusion, we have now added the calculated Q values by using the actual absorption spectrum of C₂H₂, as shown in Fig. R1(a) below. As expected, when actual absorption coefficients are considered, the spectral profile of Q follows the C₂H₂ lineshape. In contrast, under the fixed-absorption coefficient, Q value increase with rising wavelength, which is consistent with the trend of value and the wavelength, indicating that higher indeed enhances the absorption-induced heat source power Q.\nAs for the fluctuation of the phase modulation at low values, these data are calculated by using our pervious \"wavelength-domain\" solver based on 20-period PhCW. For such a finite-length PhCW, the calculated exhibits fluctuations and has been observed and explained by other research (also see Comment 1.5).1 The observed fluctuation here does not correspond to C₂H₂ absorption band since the corresponding wavelengths fall outside the C₂H₂ absorption band. As suggested by the reviewer, this fluctuation might be confusing for understanding the -enhanced phase modulation. We have changed our numerical model to an infinitely long PhCW employing Floquet boundary condition, and the calculated by \"eigen mode\" solver now changes smoothly with the wavelength, as shown in Fig. R1(b). The revised simulation results show that the fluctuations are significantly suppressed, and the spectral response becomes consistent with expectations. The updated data is also shown in Fig. 2(b) of the revised manuscript accordingly.\nFig. R1 (a) Dependence of on pump wavelength assuming constant absorption coefficient of 1.05 cm⁻¹ (purple square) and using the actual absorption coefficients of C₂H₂ (orange square). The blue line denotes values and purple line denotes actual absorption coefficients. (b)Phase modulation amplitude as a function of the wavelength (green square) for constant absorption of 1.05 cm⁻¹. The blue line denotes values.\nWe now include a brief explanation in the manuscript and Methods to clarify this point:\n\"Fig. 2(b) depicts the calculated heat source , phase modulation as functions of wavelength. The blue curves show the n and n values calculated from the reciprocal of the slope of the even mode dispersion curve in Fig. 2(a). The n varies from 5 to 24 in the pump region (1515−1543 nm) while the n from 24 to 270 in the probe region (1543−1572 nm). Both and increase with rising wavelength, which are highly consistent with the trends of n change against the wavelength, suggesting that higher n enhances both the absorption-induced heating power and the PT-induced phase modulation. It should be stated that, in the calculation of and , we have assumed a constant absorption coefficient of 1.05 cm−1, which equals to the value of C H absorptionat 1531.58 nm. In fact, the absorption coefficients are different from different absorption lines, which should be taken into consideration for real applications.\"\n\"Numerical simulation. The optical mode and thermal field as well as time- and frequency-domain profile are simulated using a three-dimensional finite-element-method (3D-FEM) with COMSOL Multiphysics. For the optical mode calculation, the pump and probe modes are calculated using eigen solver in COMSOL with the Floquet boundary condition applied to the front and back surface. For thermal field, a symmetry boundary is applied to the front and back surfaces to simulate a scenario where the structure is infinitely periodic along the z-axis. The other boundaries surrounding the PhCW are allowed to transfer the heat to the air via natural convective heat flux. The phase modulation is calculated by integrating the mode overlapping between the probe and the thermal fields over the entire PhCW structure. Since the optical mode is solved using eigen solver, the calculated result assumes infinite periodicity of PhCW. For the fabricated PhCW used for the real experiment, the finite-period PhCW may lead to fluctuations.\"\nComment 1.3: -Line 181: Reference 28 appears irrelevant.\nResponse:We now replaced Ref. 28 with a more relevant paper as follows:\n[28] Xie, S., Veilleux, S., & Dagenais, M. On-chip high extinction ratio single-stage Mach-Zehnder interferometer based on multimode interferometer. IEEE Photonics Journal, 14(4), 1-6 (2022).\nComment 1.4: -Fig. 3d: The authors' description of non-suspended Si evidently points to a suspended part of the access waveguide. Please explain or correct.\nResponse: The description of the non-suspended silicon in Fig. 3(d) has been removed to avoid confusion, as shown in the revised Fig. R2. It is worthy clarifying that, while the prepared strip waveguide is intended to remain non-suspended in order to facilitate coupling of the pump/probe beams into the suspended PhCW and to enhance mechanical stability, a small section of the strip waveguide near the PhCW inlet is also subjected to wet etching and thus becomes suspended, while most of the strip waveguide are non-suspended. The suspended zone is within 20 μm and does not compromise the mechanical stability of the overall structure.\nFig. R2 Suspended structure of the 2D-PhCW with air serving as the top and bottom claddings, while silicon serving as the core layer. The non-suspended strip waveguide (not shown in this figure) is located away from the light inlet to the PhCW.\nComment 1.5: -Fig. 4b and Line 206: The method of experimental determination of the waveguide group index, which uses the peak values of likely under-sampled interference fringes (authors admit their spectrometer resolution is comparable with the fringe period), introduces large errors in the data. Therefore, the fringes should either be fitted to recover the peak values, or several adjacent group index values should be averaged. In this line of argumentation, considering Fig. 4b and its inset, it is unlikely that a group index of 100 is achieved, but rather an index around 50. Also, I would like the authors to comment on their statement regarding the origin of fluctuations associated with Bloch-Floquet mode fluctuations, as opposed to fluctuations due to under-sampling and possible fringes caused by reflections in the PIC, which I consider likely.\nResponse: We thank the reviewer for this insightful comment. We agree that using only the peak values of potentially under-sampled interference fringes could introduce errors in the determination of the group index. In this revised analysis, we averaged the calculated values of adjacent two interference fringes to improve the estimation precision. The updated inset in Fig. 4(b) (now Fig. R3) shows a smoother curve, which exceed 100beyond ~1573.5 nm.\nFig. R3 The measured values deduced from the averaged spectrum. λ : pump region, λ : probe region.\nAs for the origin of fluctuations, we agree that the spectral under sampling and the possible fringes caused by reflections within the PIC are very likely contributors to the observed fluctuations, particularly in the high region. The fringe period in this regime can be ~0.02 nm or even smaller, which approaches the resolution of the optical spectrum analyzer (OSA) and therefore cannot be fully resolved. Even though we have employed averaging method, it still leads to systematic errors and hence fluctuations in the measured . Furthermore, fringes due to PIC internal reflections, which are also referred to as Fabry-Perot (F-P) fringe, make it more difficult to separate the actual response. As shown in Fig. R3, in the high region, the fringe period becomes comparable to or even smaller than that of the F-P fringe, contributing to the measured fluctuations. However, we initially attributed the fluctuations to Bloch-Floquet mode fluctuations, rather than these measurement artifacts, was based on the observation that similar fluctuations also occur in the low region. In this region, since the spectral resolution is adequate and F-P fringes can be well-separated from the transmission spectrum signal, neither can be fully accounted for the observed fluctuation behavior.\nIn the previous manuscript, we proposed that the fluctuation may be inherent to the physical structure of the finite-length PhCW.1 The term Bloch-Floquet modes refers to optical modes propagating in the PhCW that are periodic both in space (Bloch theory) and in time (Floquet theory).2 However, since the PhCW in our experiment has a finite length, this periodicity is not infinite, and the properties of the Bloch–Floquet modes are different from the idealized infinite-length PhCW: there are isolated instead of a continuum of Bloch-Floquet modes around the band edge.3 This modal discreteness leads to fluctuations in the value against excitation wavelength, even in the absence of measurement-related artifacts.\nFollowing your comment, we now include a brief explanation in the manuscript and explicitly distinguished between measurement-related and physical origins of the fluctuations: \"Some fluctuations are observed, which we believe are primarily due to the intrinsic nature of Bloch-Floquet mode behavior in the finite-length PhCW.3,4 In the high region near the band gap, the limited spectral resolution and possible Fabry-Perot fringe also contributes to the deviations in the measured values.\"\nComment 1.6: -Line 214, Fig. 4c: The authors claim that the PTS signal is “nearly twice as large” at point B; however, absorptions are nearly equal, and the pump group index appears to be much more than twice as large at point B than at point A. Do the experimental data really show linear dependence of PTS on n_gp, and could you provide a clear, quantitative evidence? Also, why do the authors prefer to present the normalized n_gp as opposed to the absolute value, which is, in my opinion, more informative?\nResponse: Thanks for the reviewer’s comment. The normalized values against its maxima are previously used to better present the variation trend and parameter comparison. In line with the comment, we have updated Fig. 4(c) to show the absolute values of the PTS signal S and pump group index ( ) instead of normalized values. The updated version is also included in following Fig. R4(a).\nFor comparison, although the C₂H₂ absorption coefficient at point B (1531.58 nm, 1.05 cm⁻¹) is 0.9× lower (i.e., 1.05/1.17=0.9)that at point A (1520.08 nm, 1.17 cm⁻¹), the corresponding at point B is 1.95× higher (i.e., 14.5/7.4= 1.95) than at point A. Meanwhile, the measured PTS signal at point B is 1.74× higher (i.e., 0.204/0.117=1.74) than at point A , which is highly consistent (1.75) with the product of the absorption coefficient and (i.e., 1.95×0.9= 1.75).\nTo quantify the slow-light enhancement to absorption strength, we analyzed the ratio of the PTS signal to the maximum absorption, which is independent of the absorption coefficient of the absorption line. As shown in Fig. R4(b), plotting this ratio against the absolute values of yields a linear relationship with R² = 0.94. This confirms that slow-light effects enhance light-gas interaction scaling linearly with .\nFig. R4 (a) Measured PTS signal S (blue circles) and C H absorption coefficient (purple circles) as functions of pump wavelength. The orange square represents the measured values. (b) Linear dependence of the ratio of PTS signal over maximum absorption coefficient on .\nComment 1.7: -Fig. 4e: The claim that the figure demonstrates linear dependence on n_gp x n_gb is wrong, as only n_gb was varied in the experiment. So it only shows linear dependence on n_gb. This also refers back to my previous question: can your data indeed demonstrate the linear dependence on n_gp? Also, it seems that not all data reported in Fig. 4b were used in Fig. 4d and Fig. 4e, which makes me wonder how the plotted points were selected and if the spread of results is actually much larger than reported in the plots of Figs. 4d and 4e.\nResponse: We appreciate the reviewer’s insightful comments. In our original manuscript, both n and n were varied in the experiment, and the result in Fig. 4(e) was obtained from the measured n ×n . Following your comment, we have revised Supplement S5 and added Fig. R5 to further clarify this point.\nIn this work, we conducted two separate experimental series to examine the relationship between phase modulation and the product of n and n . In the first series, we measured the PTS signals with a fixed pump wavelength (1531.58 nm, n =15) and varied probe wavelengths from 1540 nm to 1573 nm. In the second series, we measured the PTS signals with a fixed probe wavelength (1572 nm, n =81) and varied pump wavelengths to align to the C H absorption lines in the range from 1520 nm to 1540 nm.\nWe wish to clarify that we did not artificially select the data point to draw our conclusion. Fig. 4(b) in the manuscript is used to present the measured group indices across the full range of wavelengths (including the pump and the probe wavelength bands) based on measured interference spectra. Since the C H only exhibits absorption in discrete wavelengths, the pump wavelength and hence n could only be chosen at separate absorption lines (we select 14 pump wavelengths aligned to 14 absorption lines of C H ). As for the probe wavelength, it needs to be chosen outside the absorption band to characterize the relationship between phase modulation and n (we choose 22 probe wavelengths). The result of n ×n is based on two experiment series: varying n with fixed n , and varying n with fixed n . For clarity, here we show the relationships of the two series separately in the following Figs. R5(a) and (b). The overall relationship between the phase modulation and n ×n value is shown in Fig. R5(c), which is also plotted in Fig. 4(e) of the manuscript. The three linear relationships of phase modulation with n , n , and n ×n are obtained with R2>0.94.\nFig. R5 Measured (normalized against its maxima) as functions of n , n and n ×n . (a) Varying n with fixedn . (b) Varying n with fixed n . (c) Varying n ×n .\nComment 1.8: -Line 283: The authors write that the Allan deviation in Fig. 5e was measured with the pump tuned away from the absorption lines. How far away was the pump tuned, and did it have a comparable group index? If not, the noise analysis is not credible. A more rigorous approach would be to measure with N₂ in the same configuration as during the C₂H₂ experiment, or at a very low C₂H₂ concentration. Demonstrating the measurement precision at a certain concentration may be of equal, or even greater value than measuring the minimal detection limit, and the comparison of precision and MDL would be desirable.\nResponse: Thank you for your valuable comment. We have added a new Supplement S11 to clarify this point.\nIn this experiment, the pump wavelength for PTS sensing was set to 1531.58 nm, corresponding to the P(11) C₂H₂ absorption line. For the Allan deviation characterization, we tuned the pump wavelength slightly away (~0.3 nm) from the absorption line to 1531.27 nm, where the absorption of C₂H₂ is negligible. The group indexes at these two wavelengths are essentially the same.\nWe further conducted two long-term noise measurements under different conditions to clarify this point. As shown in Fig. R6(a), the blue line represents the noise in pure N₂ when the pump was adjusted to 1531.58 nm (on the absorption line), and the red line represents the noise in pure N₂ when the pump was adjusted to 1531.27 nm (off the absorption line). As shown in Fig. R6(b), Allan-Werle analysis was conducted to determine the optimal integration time and minimum detection limit (MDL) for these two conditions. The results show that at ~200 s integration time, the Allan deviation reaches its 1σ MDL in both cases: 9 ppm (at 1531.58 nm) and 8 ppm (at 1531.27 nm), indicating minimal differences and confirming the reliability of the off-absorption line noise characterization.\nTo further demonstrate the measurement precision, we fixed a lower C₂H₂ concentration at 1000 ppm and measured the 30-min stability with 1-s time constant using lock-in amplifier. As shown in Fig. R6(c), 1σ precision of ~42 ppm was estimated from the standard deviation analysis, and a 200 s-moving average of the time-trace raw data shows a 1σ precision of 10 ppm, slightly larger than the MDL obtained with pure N .\nFig. R6 (a) Long-term noise measurement in N environment with the pump wavelength tuned on (blue lines) and off (red lines) the absorption line and (b) corresponding Allan-Werle analysis. (c) Precision estimation with a fixed C₂H₂ concentration of 1000 ppm. The blue lines represent the raw data, while the 200 s moving average is displayed by red lines.\nComment 1.9: -Linked to the previous point, in section S8: Regarding the noise level evaluation, noise levels with N₂ and C₂H₂ are shown. The Allan deviation in Fig. 5e starts at a comparable value to the noise level with N₂, which is expected. However, since noise with C₂H₂ is 100x higher than with N₂, is the expected precision 800 ppm instead of 8 ppm? Please comment. Also, the sentence in S8, line 364, “When pump turns on…” is confusing; could you be more specific/descriptive?\nResponse: Thank you for your valuable comment. We would like to clarify that the observed power spectral density (PSD) values in section S8 (now Supplement S7) are not the noise levels. The background traces correspond to the noise levels. We now revised the Supplement S7 to further clarify this point.\nAs shown in Fig. R7(a), we initially tested the scenario with no pump beam and the probe beam bypassed the MZI and directly entered the photodetector (PD), and we monitored its PSD using an electrical spectrum analyzer (ESA), which is represented by the red line in Fig. R7(b). Subsequently, when both pump and probe beams were coupled into the MZI in a 1% C₂H₂ environment, a PTS signal at 50 kHz was observed (blue line in Fig. R7(b)). For comparison, the PTS signal in pure N₂ environment is shown as the purple line in Fig. R7(b). It is important to note that the purple curve obtained under the N₂ environment serves as a baseline, which is constant under fixed pump power and is independent of gas concentrations. This phenomenon, as reported in prior studies,5,6 is attributed to the Kerr effect in silicon. The 100× signal increase in the presence of C₂H₂ compared to N₂ indicates that the PTS signal for 1% C₂H₂ is 100 times larger than the Kerr-induced signal under pure N environment. The Kerr signal is wavelength independent and could be removed by simply scanning the pump wavelength across the absorption line. Fig. R7(c) shows the signal detected by scanning the pump laser wavelength (via temperature tuning) across the absorption under 1% C H and pure N environments.\n\"When pump turns on\" refers to the case 2 where both the pump and probe are coupled into the MZI in the 1% C₂H₂ environment. The background traces around these signals correspond to the noise levels, which, for the above three scenarios, are close to the probe relative intensity noise of 3×10–7 V/√Hz at 50 kHz, indicating that the on-chip MZI and the pump laser contribute minimally to the overall system noise.\nFig. R7 (a) Schematic of the three PSD measurement set-ups. (b) The measured PSD without using the pump and with probe beam directly detected by PD (red line, case 1); pump and probe beams are coupled into the MZI placed in 1% C₂H₂ environment (blue line, case 2); pump and probe are coupled into the MZI in N environment (purple line, case 3). (c) The detected 1f signal for 1% C₂H₂ (blue line, case 2) and for pure N (purple line, case 3) at 50 kHz when the pump wavelength is scanned across a C H absorption line.\nComment 1.10: -How do you ensure that the device operates at the quadrature point of the MZI? Is the chip thermally stabilized, and if so, how precise must the temperature stabilization be to achieve the reported performance?\nResponse: We appreciate the reviewer’s insightful comment. We now revised the Supplement S6 and added a new Fig. R8 to clarify this point. To operate the device at the quadrature point (Q-point) of the on-chip MZI, we select the mid-point of the wavelength-swept probe cycle, which corresponds to the average transmission level (~0.401 V) of the MZI fringe, as shown in Fig. R8(a). To maintain stable quadrature operation, we implemented thermal stabilization of the entire gas cell, including the MZI and other waveguide structures within it. As shown in Fig. R8(b), we performed an experiment in which the temperature of the thermal controller was adjusted from 24.97 ℃ to 25.02 ℃ in increments of 10 mK. We then recorded the variation in the Q-point (i.e. phase) change, which enables us to obtain the temperature-to-phase conversion coefficient of 191°/K. In this work, we control the temperature of the gas cell to ±2.6 mK, which ensures the stable operation (standard deviation of 0.5°) around the Q-point.\nFig. R8 (a) Sweeping the probe wavelength around Q-point. (b) Relationship between the phase variation and temperature change using thermal controller.\nComment 1.11: -In Table 1: Some more recent works on photonic trace gas sensing were not mentioned, and I recommend adding https://doi.org/10.1021/acsphotonics.3c01085, https://pubs.acs.org/doi/10.1021/acs.nanolett.2c01198, and https://doi.org/10.1364/OPTICA.533710. The MDL of 8 ppm is still rather high compared to the state-of-the-art result of 0.02 ppm for CO₂ reported in the last work in the mid-infrared, and this should be made clear. Nevertheless, the NEAL is impressive, and the fact that this is achieved in the NIR, where photonics is mature and relatively easy to integrate with both light sources and detectors, is of undeniable value.\nResponse: We thank the reviewer for highlighting these important and up-to-date contributions in the field of photonic trace gas sensing. We have added the suggested references to the revised Table 1 and updated the bibliography of Refs. 37, 38, 50 accordingly.\nWe now revised the Discussion to clarify this point: \"We note that the MDL for C H detection remains relatively higher than that of mid-infrared photonic sensors.7-9 However, the achieved NEA∙L sensitivity is highly impressive, and the fact that this is achieved in the near-infrared band, where photonics is mature and easy integrated with both light sources and detectors, is of undeniable value.\"\nComment 1.12: -In addition, I recommend removing reference 43, as this paper, in agreement with https://doi.org/10.1021/acsnano.4c01856, is not credible and should have been retracted.\nResponse: In accordance with reviewer’s suggestion, we have removed Ref. 43 from the manuscript.\nComment 1.13: -For completeness, the authors can mention any drawbacks of the device and provide an outlook for possible further optimization.\nResponse: We have revised the Discussion in the revised manuscript to clarify this point. The main limitations of the current PTS device stem from its optical losses, which include several aspects: (1) The slow-light-induced propagation loss increases as the group index increases, which is an intrinsic property in PhCW-PTS devices. For the pump beam, this can be overcome by increasing the laser power. For the probe beam, as long as the light level is sufficient at the PD, it would be not a problem. Also to further enlarge the fringe contrast of the MZI, on-chip attenuator could be used to better balance the power distribution between the MZI arms. (2) The waveguide-based propagation loss is mainly due to the sidewall roughness and could be minimized by optimizing the lithography and etching fabrication process. (3) The coupling loss primarily occurs at the coupling interface between the input/output fiber and the subwavelength grating, which is relatively large of ~9 dB/facet. Further optimization of the subwavelength grating design could reduce it to below ~1 dB.10 (4) To reduce the possible substrate leakage at the working wavelengths, using a SOI wafer with a thicker buried oxide layer, such as 3 μm, would benefit a lot.\nComment 1.14: -a more detailed explanation/analysis on why PTS is less sensitive to fringing could be of interest, as some sensitivity would certainly exist, particularly in a complex PIC as reported here.\nResponse: We appreciate the reviewer’s insightful comment. We now include a brief clarification in the Supplement S9 to clarify this point. As noted, fringing effect (i.e., etalon noise) is indeed a concern in integrated photonic systems due to reflections at material interfaces (e.g., Si/SiO₂ or Si/air) and waveguide line-edge roughness imperfections. In direct absorption spectroscopy (DAS), such fringes often dominate the noise baseline, particularly in low-concentration regimes where weak absorption signals can be obscured by periodic interference patterns. DAS typically uses a single laser for both excitation and detection, so any baseline fluctuation or fringing directly affects the signal. Moreover, increasing pump power in DAS amplifies both signal and fringe-induced noise, limiting the achievable signal-to-noise ratio (SNR).\nIn contrast, PTS employs separate pump and probe beams, thus offers two inherent advantages that reduce sensitivity to fringing: (1) For the pump fringing, the pump excites the gas-induced local heating and a refractive index change; the resulting thermal perturbation is detected by the probe via interferometric phase modulations (e.g., through an MZI). Increasing pump power in PTS amplifies the signal without significantly increasing the noise baseline, since the noise is dominated by the probe beam. Only when the pump power becomes high enough that pump-intensity noise takes over, does the signal-to-noise ratio (SNR) cease to improve and fringe drift become problematic. In our experiments, even at pump powers of several hundred milliwatts, increasing the pump power continued to enhance the SNR, confirming that the noise is governed by the probe and that the system remains essentially insensitive to pump fringing. (2) As for the probe fringing, the probe is fixed in wavelength, which detects the modulated thermal signal due to absorption of intensity or wavelength modulated pump using with lock-in harmonic detection. This synchronous demodulation isolates the dynamic modulated signal from static and broadband background noise, including fringing. Any residual etalon effects in the probe path manifest as static patterns and are inherently filtered out by the lock-in amplifier.\nTo further mitigate the fringing effect in the PIC, we have implemented several designs in this work: (i) Input/output sub-wavelength grating couplers were optimized for polarization control and reducing coupling-related noise (Fig. S3). (ii) A taper waveguide before the MZI ensures single TE₀ mode operation, avoiding high-order mode interference noise (Fig. S4). (iii) Transition structures near two ends of the PhCW are introduced to reduce the coupling loss from the strip waveguide to the PhCW (Fig. S5). We also acknowledge that residual phase fluctuations may still arise from unavoidable optical interference within the PIC. This will be further minimized through fabrication improvements and integrated packaging techniques.\nSupplementary Information:\nComment 1.15: -Line 84: Possible typo; S9 should be S12.\nResponse: We have corrected the number from “S9” to “S12” in the revised Supplement S1.\nComment 1.16: -Fig. S2: The figure is ambiguous. It states that S2c) was done with r1=0 and shows spatial confinement of 0.1 at the selected r0, while Fig. S2d shows spatial confinement of 0.05 at r1=0. Please check and correct.\nResponse: We thank the reviewer for identifying this inconsistency. After a thorough review, we have revised Fig. S2 (here Fig. R9) as follows.\nFig. R9 (a) Structure of the suspended 2D-PhCW and corresponding dimensional parameters. Right inset shows the y-z plane with parameters oflattice constant(a), the radius of three kinds of defect holes(R, r , and 0 r ), and the height of the air-based bottom cladding (h). (b) Photonic band gap versus R/a. The spatial 1 confinement of the energy density and guided mode bandwidth (B ) versus(c) r /R for r =0, and (d) r /R for w 0 1 1 r = 0.6R.\nResponse: Thank you for the valuable suggestion. In the current PhCW design, we primarily excite the transverse electric (TE) mode, whose mode field energy is largely confined within the core layer of the waveguide. This differs from transverse magnetic (TM) modes, which typically exhibit dual-layer field distribution and higher susceptibility to substrate leakage. Additionally, the 1-mm-long PhCW operates in the near-infrared band, with a mode field diameter below 1 μm. Given this confinement, the 2-μm-thick buried oxide (BOX) used in our current wafer platform is sufficient to prevent significant leakage into the substrate at the working wavelengths. In further work, we will consider reviewer's suggestion and replace the wafer with a thicker BOX (e.g., 3 μm) to reduce the possible substrate leakage. Following your suggestion, we have included a brief clarification in the Discussion merged with Comment 1.13.\nReviewer #2 (Remarks to the Author):\nComment 2.1: In this study, the authors harnessed slow-light effects in a photonic crystal waveguide to enhance photothermal gas spectroscopy. The pump laser induces localized heating in the waveguide due to gas absorption, while the non-absorbing probe laser experiences a temperature-dependent phase shift. Numerical simulations and experimental validations were conducted.\nResponse: We thank the reviewer for the accurate comment of our study.\nComment 2.2: How does this approach compare to non-photothermal spectroscopy (PTS) methods?\nResponse: Waveguide absorption spectroscopic gas sensors reported so far include direct absorption spectroscopy (DAS), and photothermal spectroscopy (PTS). Compared to DAS, PTS-based approach offers several critical advantages: (1) DAS relies on detecting small absorption-induced intensity changes, which are highly susceptible to background fluctuations and fringing noise, particularly in low-concentration detection. In contrast, PTS measures thermally induced phase shifts via a modulated pump-probe scheme. This inherently rejects static background noise and enables ultralow-noise detection, significantly improving the signal-to-noise ratio (SNR). (2) The sensitivity of PTS scales inversely with the optical mode area. Our integrated photonic platform features tight optical confinement and strong light–matter interaction, resulting in much higher sensitivity than traditional fiber or free-space optical systems. (3) PTS is well-suited to on-chip integration, allowing for compact, scalable, and robust sensor systems that outperform the bulky setups required for most DAS-based free-space/fiber approaches.\nFollowing your comment, we added Table S1 (here R1) in Supplement S11. In Table R1, we provide a detailed comparison of our PTS sensor with state-of-the-art DAS sensors, demonstrating a 1–3 orders of magnitude improvement both in sensitivity and dynamic range, achieving the best reported NEA∙L to date among photonic waveguide gas sensors. The demonstrated dual slow-light enhanced PTS sensor with high sensitivity, high integration and large dynamic range shows comprehensive advantages over other DAS sensors and presents a significant leap for developing next-gen integrated photonic gas sensors.\nTable R1 Comparison of the dual slow-light enhanced PTS sensor and other waveguide gas sensors\nYear Method Gas Waveguide Γ Loss L MDL NEA NEA∙L Dynamic\nλ(nm) type (%) (dB/cm) (cm) (time) (cm-1) range\nCH\n2566 2 5\nCH\n2023 2 2 ChG-strip 10.5 2.5 2\nDAS 1531 65 ppm (100s) 7.5×10-5 1.5×10-4 1.5×103\nCO\nPTS 2 2 Si-2D PhCW 234 50 0.1 8 ppm (200s) 9.2×10-6 9.2×10-7 >3.75×104\nwork 1531\n: effective confinement factor, defined as the product of n and spatial confinement of the energy density γ, MDL: Minimum detection limit, NEA: Noise equivalent absorption, NEA∙L: Product of the noise equivalent absorption coefficient and the interaction length. Si: Silicon, Ta O : Tantalum pentoxide, Ge: Germanium, ChG: Chalcogenide 2 5 glass, LN: Lithium niobate, CH : Methane, CO :Carbon dioxide.\n4 2\nComment 2.3: Some figure captions are overly long and should be shortened.\nResponse: We have modified several long captions of Figs. 2 and 4, as follows:\n\"Fig. 2 Numerical simulation of PTS based on PhCW. (a) Dispersion diagram of the 2D-PhCW with optimized parameters. The slow-light wavelength band includes pump and probe regions. (b) The heat source , phase modulation amplitude , n and n as functions of the wavelength. In the pump region, the values gp gb of at the C H absorption line centers are shown as the purple squares while n as a function of λ is shown Q 2 2 Δϕ gp p as the left blue line. In the probe region, (green squares, normalized values against their maxima) and n Q gb (right blue line) as functions of λ are shown. (c) Time-domain temperature response for three different λ of b p 1520.08, 1531.58, and 1542.24 nm, corresponding to n of 5, 10 and 24, respectively, at the pump modulation gp frequency of 50 kHz (upper panel). The peak temperature variation shows a linear relationship to n (lower gp panel). (d) Frequency-domain phase modulation for three different λ of 1556, 1568 and 1570 nm, b corresponding to n of 27, 58 and 106, respectively (upper panel). The increases linearly with rising n gb Δϕ gb for a fixed n of 10 (lower panel).\"\nΔϕ gp\n\"Fig. 4 Experimental characterization of the dual slow-light PhCW PTS. (a) Transmission spectrum of the on-chip MZI. The n value is determined from the ∆λ between adjacent peaks. The insets show the enlargements g within the wavelength ranges of 1560−1575 nm and 1570−1573 nm, respectively. (b)The n values deduced g from the averaged transmission spectrum of adjacent two interference fringes. The purple-shaded area with modest n values is the pump wavelength band covering the C H absorption lines. The blue-shaded area gp 2 2 has large n values, which is away from C H absorption and serves as the probe wavelength band. (c) gb 2 2 Measured PTS signal S (blue circles) and C H absorption coefficient (purple lines) as functions of pump 2 2 wavelength. The probe wavelength is fixed at 1572 nm. The local absorption coefficient maxima at A (1520.08 nm) and B (1531.58 nm) are selected for comparison. The orange square denotes n values. (d) Measured gp PTS signal S (blue circles), fringe contrast ν (black squares), and deduced phase modulation amplitude (red triangles) as functions of probe wavelength with the pump wavelength fixed at 1531.58 nm. (e) The Δϕ measured as a function of n ×n normalized against its maxima. The red line is the linear fitting with R2 gp gb value of 0.96.\"\nΔϕ\nComment 2.4: The lowest measured C₂H₂ concentration was 5%. On page 9, the authors state: \"Fig. 5(e) presents the Allan-Werle analysis based on measured noise levels over a 2-hour period with the pump wavelength detuned from absorption lines. The Allan deviation indicates a minimum detection limit (MDL) of 8 ppm C₂H₂ and a noise-equivalent absorption (NEA) coefficient of 9.2 × 10⁻⁶ cm⁻¹ at 200 s.\"—Is this sensitivity sufficient?\nResponse: We appreciate the reviewer’s comment. To further validate the sensitivity of our PhCW-PTS sensor, we conducted additional experiments using a much lower C₂H₂ concentration of 1000 ppm, the results are shown in the newly added Fig. R10(a). We observed that the 1σ precision remains 42 ppm without averaging, and an improved precision of 10 ppm is obtained after 200 s moving averaging, which is consistent with the 8 ppm MDL obtained from the Allan-Werle analysis at 200 s in N₂ atmosphere.\nWe also evaluated the sensor's performance across a range of C₂H₂ concentrations from 0 to 30%, as shown in Fig. R10(b). While the photothermal signal scales linearly with concentration, the noise level remains unchanged. As a result, the precision for 5% and 30% C₂H₂ are estimated to be ~39 and ~45 ppm, respectively, which is close to the precision estimated under 1000 ppm C H . Hence, the precision remains nearly unchanged 2 2 across different concentration levels, confirming that our sensor offers sufficient sensitivity for detecting low gas concentration levels.\nFig. R10 (a) Precision estimation with a fixed C₂H₂ concentration of 1000 ppm. The blue lines represent the raw data, while the 200 s moving average is displayed by red lines. (b) The signal and noise level of 1f output with different concentrations. The purple points show the standard deviation of the noise level.\nWe have clarified this point in Fig. 5(d) and include a brief clarification in the manuscript: \"Fig. 5(d) shows the linear relationship of the 1f-PTS signal with increasing C H concentration from 0 to 30%, giving a linear 2 2 dynamic range of >3.75×104. While the PTS signal scales linearly with concentration, the noise level remains stable, leading to a proportional increase in SNR across the entire dynamic range. As a result, the 1σ precision remains approximately unchanged across different concentration levels.\"\nComment 2.5: When compared to state-of-the-art gas sensors, the noise-equivalent absorption-length product (NEA∙L) of 9.2×10⁻⁷ represents the highest sensitivity reported for a photonic waveguide-based sensor. This performance is competitive with the best photothermal and optical gas sensors, approaching the sensitivity levels of advanced cavity-enhanced techniques while maintaining a compact (0.6 mm² footprint), CMOS-compatible, and scalable design. Therefore, I do not see clear evidence of the benefit of the reported device.\nResponse: We appreciate the reviewer’s valuable suggestion. We have compiled another Table R2 benchmarking our device against representative free-space/fiber-based optical gas sensor, including advanced cavity-enhanced techniques. We think now the strong points of our result are clearer.\nOur on-chip PhCW-PTS sensor achieves an NEA·L of 9.2×10⁻⁷, represents the highest sensitivity (in terms of NEA·L) reported for a photonic waveguide-based sensor, and also approaches the most advanced free-space/fiber sensors, which typically require large, complex, and non-integrated setups. Importantly, our sensor offers several distinct advantages beyond sensitivity: (1) The entire sensing device occupies only 0.6 mm², which is many orders of magnitude smaller than most free-space or fiber-based setups. (2) The silicon-based PhCW is fabricated using standard CMOS-compatible process, enabling low-cost mass production and seamless integration with electronic and photonic components. (3) Scalability for potential dense on-chip sensor arrays or deployment in portable, distributed, or wearable platforms where size, power and price are critical. (4) A compact, partly integrated architecture, including waveguide, interferometer, and gas cell, setting the stage for future inclusion of on-chip light sources and detectors.\nWe have updated the Discussion of the manuscript and Supplement S11 to better highlight these advantages with the following revised statement: \"When compared to state-of-the-art free-space and fiber-based gas sensors, as listed in Table S3, the NEA·L sensitivity of our sensor approaches that of the most advanced free-space/fiber sensors, while offering distinct benefits in terms of compactness, CMOS compatibility, and scalable integration, which are key features for next-gen, miniaturized, and distributed gas sensing platforms.\"\nTable R2 Performance comparison of the on-chip sensor with other free-space/fiber optical sensors\nSensor Year Method Gas& Physical length Effective path Dynamic NEA NEA∙L\ntype λ(nm) & gas cell length (m) range (cm-1)\nCH\nCH\nspace 2019 OA-ICOS 4 28 cm cavity 27000 >2.6×102 7.3×10-10 (30s) 1.9×10-3\n1654\nsensors\nNH\nOptical 2021 PTS-FPI 2 2 5 cm HC-ARF 0.05 6.2×104 2.3×10-9 (670s) 1.1×10-8\n1530\nfiber\nCH\nsensors 2015 PTS-MZI 2 2 10 m HC-PBF 10 5.3×105 2.3×10-9 (1s) 2.3×10-6\n2 2 0.1 cm PhCW 0.001 >3.75×104 9.2×10-6 (200s) 9.2×10-7\nsensor work chip MZI 1531\nTDLAS: Tunable diode laser absorption spectroscopy, OF-CEAS: Optical feedback cavity-enhanced spectroscopy, OA-ICOS: Off-axis integrated cavity output spectroscopy, CRDS: Cavity ringdown spectroscopy, LITES: Light-induced thermoelectric spectroscopy. MPC: multi-pass cell, HC-PBF: hollow-core photonic bandgap fiber, HC-ARF: hollow-core anti-resonant fiber, MZI: Mach-Zehnder interferometer, FPI: Fabry-Pérot interferometer.\nReviewer #3 (Remarks to the Author):\nComment 3.1: The manuscript describes an integrated photonic sensor for gas detection based on a dual slow-light-enhanced photothermal spectroscopy strategy. The authors combine slow-light effects at both the pump and probe wavelengths in a suspended silicon photonic crystal waveguide, aiming to increase photothermal efficiency for acetylene sensing. While the methodological details and experimental procedures are presented clearly, several concerns lessen the impact and novelty of the work.\nResponse: Thanks for the reviewer’s accurate description. In the following, together with detailed responses to the reviewer’s comments, we indicate what we have added in the manuscript to improve the statement of impact and novelty of the work. We think now the strong points of our results are clearer.\nComment 3.2: First, although slow-light phenomena in photonic crystals have long been recognized for boosting light–matter interactions, the fundamental concept here—using a slow-light waveguide for enhanced sensitivity—does not appear to offer a disruptive advance over existing techniques. Multiple research groups have employed similar strategies to harness slow-light in photonic crystal sensors, and the incremental improvement presented does not substantially exceed what is typically achievable with established platforms.\nResponse: Thank you for your thoughtful comment. We have updated the Discussion of the manuscript and Supplement S11 to better highlight some innovative points with the following revised statement:\n(1) While previous research on slow-light-based gas sensors has primarily focused on enhancing light-matter interactions through a single slow-light effect, in combination with direct absorption spectroscopy (DAS), the absorption is linearly proportional to the enhancement of group index . Our work introduces a significant departure from this approach. We present a new scheme of dual slow-light effect. Our results confirm for the first time that the on-chip photothermal efficiency is proportional to the product of group indices of the pump and probe, which is attributed to the amplified perturbation on both the real and imaginary part ofthe eigen values. We believe the innovative dual slow-light scheme is also applicable to a wide range of photonic sensing systems, including liquid analyte detection, mid-IR integrated sensors, and other dual-light systems for the study of light-matter interactions, opening avenues for compact devices for smart-home monitoring, point-of-care diagnostics, environmental surveillance, and wearable technology.\n(2) For the field of gas detection, for the first time, we demonstrate the use of photothermal spectroscopy (PTS) in a slow-light on-chip sensor, marking a shift to an indirect sensing technique that fundamentally differs from DAS. PTS is recognized as a high-sensitivity, background-free and low-noise spectroscopic method for gas sensing. More significantly, we introduce a dual slow-light enhanced PTS approach with detailed theoretical formulation and experimental investigations. For the pump beam, the slow light enhancement on absorption corresponds to the real-valued perturbation on permittivity. For the probe beam, the slow light enhancement on phase modulation corresponds to the imaginary-valued perturbation on permittivity. The combination of the two effects significantly improves the PTS sensitivity.\n(3) For the field of on-chip sensing, our method provides excellent examples for improving the performance of dual slow-light enhanced spectroscopic method. For the dual-slow light enhancement factor, our dispersion engineering creates dual-wavelength photonic crystal bandgaps, which also inspires further investigation on higher order bandgaps (i.e. pump and probe travels in independently engineered slow-light bands) for even higher dual slow-light enhancement factor. For the PTS, the photothermal process was optimized by the suspended design for better pump-gas overlapping and heat accumulation for higher sensitivity. For the fabricated sensors, we incorporated the PhCW with a high-contrast Mach-Zehnder interferometer (MZI) in a compact and scalable platform for portable gas sensing applications, which has not been achieved in traditional fiber- or waveguide-based sensors.\n(4) To further clarify the novelty and impact of our work, we provide a comprehensive comparison in Table R3, highlighting the substantial advantages of our dual slow-light PTS sensor over existing single slow-light sensors (including PhCWs and subwavelength grating waveguides). Our sensor outperforms the previous sensors by 1–3 orders of magnitude in terms of NEA·L sensitivity and dynamic range. Furthermore, most previously reported PhCW/SWG-based systems operated in the mid-infrared (MIR) range to access stronger absorption lines. However, this typically required the use of MIR photodetector (PD), which are expensive, bulky, and not easily compatible with fiber-optic systems. In contrast, this PhCW-PTS device utilizes only a near-infrared (NIR) PD, which is mature, cost-effective, and easy integrated with telecom optical fibers. Also, it is possible to extend the system to MIR-PTS by simply replacing the MIR pump source, without using the MIR-PD. The existing NIR PD would still be sufficient for the operation, offering a significant advantage in terms of both cost and integration.\nTable R3Comparison of the dual slow-light PhCW-PTS sensor and other PhCW/SWG gas sensors\nYear Method Gas Waveguide Γ n Loss L MDL NEA NEA∙L Dynamic\ng\nλ(nm) type (%) (dB/cm) (cm) @time (cm-1) range\nCH\n4345 20 ppb 13CO (60s)\n3400\nCH\nPTS 2 2 Si-2D PhCW 234 18/81 50 0.1 8 ppm (200s) 9.2×10-6 9.2×10-7 >3.75×104\nwork 1531\nIMS: Intensity modulation spectroscopy. Single slow-light effect is used in other PhCW sensors. SWG: Sub-wavelength grating waveguide, SiN: Silicon nitride, Ge: Germanium, C H : Toluene, C H O: Acetone.C H O: 7 8 3 6 2 6 Alcohol. #In our previous work, the non-suspended single-slow-light PhCW is used for pump beam for DAS measurement. In this suspended PhCW, dual slow-light is used for both pump and probe beam for PTS measurement.\nComment 3.3: Second, the stated minimum detection limit of around 8 ppm for acetylene is not convincingly benchmarked against the broad landscape of state-of-the-art technologies. The discussion focuses primarily on a qualitative comparison to previously reported photonic methods, but many other on-chip and fiber-based solutions currently achieve significantly lower detection thresholds (orders of magnitude). Without a comprehensive performance comparison, it remains unclear whether this device represents a significant leap or merely an incremental step.\nResponse: We have added Tables R1 and R2 to give a comprehensive performance comparison between free-space, fiber, and waveguide-based sensors. We have also updated the Discussion of the manuscript and Supplement S11 to better highlight these advantages with the following revised statement:\n(1) Free-space sensors, such as cavity-enhanced techniques with path lengths on the order of hundreds of kilometers, do indeed offer high sensitivity. However, their experimental setups are typically bulky, difficult to align, and unsuitable for portable, wearable, weight-limited applications. In contrast, on-chip waveguide sensors offer compactness, confining light to millimeter- or centimeter-scale waveguide paths. Despite the inherent challenge in high sensitivity due to short optical paths on-chip, our work significantly enhances the sensitivity of waveguide sensors by employing a dual slow-light mechanism with millimeter-scaled path length. Even compared with free-space optical sensors, our device demonstrates an impressive noise-equivalent absorption-length (NEA·L) of 9.2×10⁻⁷, which even approaches that of the most advanced free-space/fiber sensors, while maintaining a compact (0.6 mm² footprint of the sensing device), CMOS-compatible, scalable on-chip design, and ultra-short length of only 1 mm.\n(2) Compared to existing optical fiber-based PTS sensors, our dual slow-light PhCW enhances both pump absorption and probe phase modulation simultaneously, achieving an unprecedented photothermal efficiency of 3.6×10⁻⁴ rad·cm·ppm⁻¹·mW⁻¹·m⁻¹. This is more than 3 orders of magnitude higher than conventional optical fibers, such as hollow-core fibers. Due to this enhanced photothermal efficiency, our sensor outperforms fiber-PTS sensors (which typically require >100 mW of pump power and fiber lengths at the level of 10 cm to meters) even at a pump power of only 10 mW and a 1-mm path length.\n(3) Compared to other optical waveguide gas sensors, our sensor, through optimal design of the PhCW, the optimization of the bandgap and slow-light parameters, achieves NEA∙L performance that is 1-4 orders of magnitude higher than the other reported waveguide sensors to our knowledge. Moreover, integrated photonic sensors have attracted significant attention due to their potential for high-density integration. For on-chip integration of this PTS sensor, we have integrated the sensing PhCW into the on-chip MZI for interferometric measurement. We also encapsulated the gas chamber for portable sensing applications. Such a level of integration has not been achieved before in fiber or waveguide-based sensors.The demonstrated slow-light enhanced PTS sensor offers a superior sensitivity, integration, scalability, and dynamic range compared to existing free-space, fiber, and waveguide-based sensors. This work represents a notable advancement in the development of next-generation integrated photonic gas sensors.\nTable R1 Comparison of the dual slow-light enhanced PTS sensor and other waveguide gas sensors\nYear Method Gas Waveguide Γ Loss L MDL NEA NEA∙L Dynamic\nλ(nm) type (%) (dB/cm) (cm) (time) (cm-1) range\nCH\n2566 2 5 strip#\nCH\n2023 2 2 ChG-strip 10.5 2.5 2\nDAS 1531 65 ppm (100s) 7.5×10-5 1.5×10-4 1.5×103\nCO\nPTS 2 2 234 50 0.1 8 ppm (200s) 9.2×10-6 9.2×10-7 >3.75×104\nwork 1531 PhCW\n: effective confinement factor, defined as the product of n and spatial confinement of the energy density γ, MDL: Minimum detection limit, NEA: Noise equivalent absorption, NEA∙L: Product of the noise equivalent absorption coefficient and the interaction length. Si: Silicon, Ta O : Tantalum pentoxide, Ge: Germanium, ChG: Chalcogenide 2 5 glass, LN: Lithium niobate, CH : Methane, CO :Carbon dioxide.\n4 2\nTable R2 Performance comparison to other free-space/fiber spectroscopic sensors\nSensor Year Method Gas& Physical length Effective path Dynamic NEA NEA∙L\ntype λ(nm) & gas cell length (m) range (cm-1)\nCH\nCH\nspace 2019 OA-ICOS 4 28 cm cavity 27000 >2.6×102 7.3×10-10 (30s) 1.9×10-3\n1654\nsensors\nNH\nOptical 2021 PTS-FPI 2 2 5 cm HC-ARF 0.05 6.2×104 2.3×10-9 (670s) 1.1×10-8\n1530\nfiber\nCH\nsensors 2015 PTS-MZI 2 2 10 m HC-PBF 10 5.3×105 2.3×10-9 (1s) 2.3×10-6\n2 2 0.1 cm PhCW 0.001 >3.75×104 9.2×10-6 (200s) 9.2×10-7\nsensor work chip MZI 1531\nTDLAS: Tunable diode laser absorption spectroscopy, OF-CEAS: Optical feedback cavity-enhanced spectroscopy, OA-ICOS: Off-axis integrated cavity output spectroscopy, CRDS: Cavity ringdown spectroscopy, LITES: Light-induced thermoelectric spectroscopy. MPC: multi-pass cell, HC-PBF: hollow-core photonic bandgap fiber, HC-ARF: hollow-core anti-resonant fiber, MZI: Mach-Zehnder interferometer, FPI: Fabry-Pérot interferometer.\nComment 3.4: Third, the manuscript would benefit from a more in-depth assessment of technical limitations. While the authors emphasize the slow-light effect and suspended design as key enhancements, it would be informative to explore potential drawbacks, such as increased propagation loss at higher group indices or the trade-offs in device robustness and fabrication complexity. The authors do provide a theoretical derivation of the photothermal phase modulation and refer to numerical simulations that confirm certain findings, but the discussion of sources of noise and drift over extended measurement times is somewhat limited.\nResponse: Following your constructive suggestion, we now include a brief explanation in the Discussion of the manuscript to clarify this point.\nThe main limitations of the current PTS device stem from its optical losses, which include several aspects:\n(1) The slow-light-induced propagation loss increases as the group index increases, which is an intrinsic property in PhCW-PTS devices. For the pump beam, this can be overcome by increasing the laser power. For the probe beam, as long as the light level is sufficient at the PD, it would be not a problem. Also to further enlarge the fringe contrast of the MZI, on-chip attenuator could be used to better balance the power distribution between the MZI arms. (2) The waveguide-based propagation loss is mainly due to the sidewall roughness and could be minimized by optimizing the lithography and etching fabrication process. (3) The coupling loss primarily occurs at the coupling interface between the input/output fiber and the subwavelength grating, which is relatively large of ~9 dB/facet. Further optimization of the subwavelength grating design could reduce it to below ~1 dB.10 (4) To reduce the possible substrate leakage at the working wavelengths, using a SOI wafer with a thicker buried oxide layer, such as 3 μm, would benefit a lot.\nAs shown in Fig. R11, we employed the Allan deviation plot to analyze the system's noise and drift behavior over extended measurement times. At short integration time within 200 s, the Allan deviation decreases as the integration time increases with a fitted slope of approximately −0.59, indicating that white noise dominants, which mainly emanates from relative intensity noise of the probe laser and electronic noise of the electrical circuits. At longer time over 200 s, the Allan deviation decreases with fluctuations, which is a signature of system drift. Major drift sources include external temperature variation and pump/probe light power fluctuations that vary slowly over time.\n10-6\n10-7\n10-8\n200 s\n10-9\n1 10 100 1000\nFig. R11 Allan-deviation analysis of the noise and drift over extended measurement times.\nComment 3.5: Fourth, from a methodological standpoint, the fabrication details are explicit, and the basic experimental arrangement is standard for photothermal measurements. The data on waveguide characterization, group index determination, and photothermal signal scaling with pump power all suggest competent execution. Nevertheless, the manuscript does not sufficiently highlight how these technical steps move beyond work already available in the literature on integrated photonic crystal sensors.\nResponse: We thank the reviewer for this valuable comment. In this work, we present a fundamentally new scheme of dual slow-light enhanced PTS with detailed theoretical formulation and experimental investigations. Therefore, our methodology aims to optimize the performance of the dual slow-light enhanced PTS, which has not been reported in previous literatures. Following your comment, we have updated the Discussion of the revised manuscript to highlight the advantages of our work clearly.\n(1) We report a new theoretical framework as a guideline for PhCW design. Our perturbation theory on guided modes, along with the approximate solution of the heat transfer, provides a quantitative relationship between the dual slow-light PTS and the PhCW structures, such as the material properties, dimensions, and the suspended design. We also provide numerical simulations on a 3D Multiphysics model for separately analyze the optical and thermal dynamics. We include a detailed oscillation phenomenon analysis that explains how the group index influences the behavior of slow-light effect, particularly in the context of photothermal, thermo-optic, and interference effects. The PhCW optimization dramatically affects the pump absorption and probe photothermal effect, hence decides the dual slow-light PTS performance.\n(2) We report the first experimental verification that the on-chip PTS sensitivity (i.e., photothermal efficiency) is proportional to the product of and , which is highly consistent with our theoretical formulation. Through photothermal characterization experiments, we detailed how this relationship is observed experimentally, emphasizing the linear scaling of the photothermal signal with the combined and across multiple device designs. This approach introduces a new method of quantifying and harnessing dual slow-light enhancement for gas sensing and other light-matter interactions.\nComment 3.6: Overall, the article offers an incremental contribution that confirms some expected advantages of dual slow-light enhancement in a photonic crystal waveguide. However, the claimed improvements do not convincingly surpass what other research groupshave demonstrated, nor does the manuscript provide a strong argument for a fundamentally new approach. Consequently, although the work is carefully executed, it does not appear to meet the high novelty and impact standards expected by a top-tier journal. In light of these considerations, the recommendation is to reject the paper. The demonstrated device achieves moderate performance gains that do not clearly outpace existing sensor architectures, and the authors’ discussion does not sufficiently establish the broader significance of these findings for integrated photonic gas sensing.\nResponse: We appreciate the reviewer’s constructive comment. We have updated the Discussion of the revised manuscript to highlight the advantages of our work clearly.\n(1) In this work, we present a fundamentally new scheme of dual slow-light effect for the first time, and perform the first dual slow-light-based sensing enhancement with detailed theoretical formulation and experimental investigations.\n(2) We present the first realization of dual slow-light enhanced on-chip PTS, which has not been reported for waveguide, for fiber and for free space. Our results demonstrate that the photothermal efficiency is proportional to the product of group indices of the pump and probe, which simultaneously enhances both the pump absorption and the probe phase modulation in a dispersion-engineered PhCW. This dual slow-light scheme amplifies the photothermal efficiency to 3.6×10⁻⁴ rad·cm·ppm⁻¹·mW⁻¹·m⁻¹, which surpass traditional free-space/fiber sensors by more than 3 orders of magnitude, and is over an order of magnitude higher than that of reported waveguide sensors.\n(3) With a 1-mm-long sensing PhCW incorporated in a stabilized on-chip MZI with a footprint of 0.6 mm2, we demonstrate C H detection with a NEA·L sensitivity of 9.2×10⁻⁷, which surpasses previously reported waveguide gas sensors by 1-3 orders of magnitude. This sensor even approaches that of the most advanced free-space/fiber sensors, while offering distinct benefits in terms of compactness, CMOS compatibility, and scalable integration, which are key features for next-gen, miniaturized, and distributed gas sensing platforms.\n(4) We demonstrate a compactintegration of a sensing device with suspended PhCW, on-chip MZI, and gas chamber. Such a miniaturization and integration level are not achievable with traditional fiber and waveguide systems, positioning our platform for future chip-scale sensing systems that could integrate light source and detector on a single chip.\n(5) The demonstrated novel dual slow-light scheme is not limited to gas sensing. It is extendable to a broad range of photonic platforms, including liquid analyte detection, mid-IR integrated sensors, and other dual-light systems for studying light-matter interactions. The potential applications of this work span areas such as smart homes, point-of-care diagnostics, environmental monitoring, and wearable devices, etc.\nReferences"}, {"round": 2, "reviewer_comments": {"reviewer_1": "While I agree with the other reviewers that this work does not represent a transformative leap in the state of the art, I continue to believe that the novelty of combining dual slow light with PTS in a packaged on-chip device, along with a reasonable detection limit, justifies publication in Nature Communications. The reported low NEA.L value sets a new benchmark for on-chip gas sensing and will likely be of interest to the broader research community.\nIn their revised manuscript, the authors have largely addressed my questions and comments. However, I outline below a few areas where I remain unconvinced and encourage the authors to revisit their arguments. In particular, I suggest they take a more conservative stance on the reported detection limit, as the Allan deviation data suggest a value approximately twice as large as claimed (see comment 1.8).\nComment 1.2\n- I feel there is no sense calculating with a constant absorption coefficient to simulate the heat source, if this varies as a function of the wavelength I reality. I suggest removing these Data from R1a), as this is confusing. Assuming a constant absorption coefficient of course makes sense for R1b) reflecting the choice of the pump wavelength.\nComment 1.5\n- I am still not convinced about the Bloch-Floquet mode fluctuations argument in your structure, which is much longer than structures where the phenomenon was studied. Especially in the low ng region this phenomenon should not be observable, as modes are predominantly index guided and energy is carried by one mode component. Unless you provide an evidence for observation of such mode in a structure close to your length, I suggest to remove this hypothesis.\nComment 1.8\n- The plots you provided are convincing. However, the determination of the LOD from R6b is not correct, as you cannot take a minimum of your trace with random fluctuations, but the average for the given averaging time instead. The difference in LOD is not dramatic, but by about a factor 2 worse (around 20 ppm). Instead of taking a moving average of the trace in R6c, you better provide an Allan plot that may explain the discrepancy with R6b (I expect a slightly worse value from R6b than LOD measured with N2).", "reviewer_2": "After a thorough review of the manuscript titled “Dual slow-light enhanced photothermal gas spectroscopy on a silicon chip” and the associated point-by-point rebuttal, I believe the authors have satisfactorily addressed all reviewer concerns, and the manuscript can be recommended for publication.", "reviewer_3": "While the manuscript is technically sound, it falls short of the breakthrough standard expected for Nature Communications.\nIncremental novelty – The “dual slow‑light” concept is a straightforward extension of single slow‑light photonic‑crystal schemes already reported for on‑chip gas sensing. The work does not introduce new physics or device architecture, merely cascading two well‑known effects.\nModest performance gains – The reported minimum detection limit (8 ppm C₂H₂) and NEA·L of 9.2 × 10⁻⁷ cm⁻¹·m are respectable for specialist journals, but remain one‑to‑two orders of magnitude above state‑of‑the‑art waveguide or cavity‑enhanced sensors (see Table 1 of the manuscript). The claimed “unprecedented” photothermal efficiency relies on a 1‑mm path; absolute sensitivity is still limited.\nMethodological concerns – Group‑index values above 100 are inferred from under‑sampled interferometric fringes, casting doubt on the linear ngp × ngb scaling. Thermal drifts are discussed qualitatively but not quantified under realistic field conditions, and Kerr‑induced background signals remain significant.\nEditorial fit – The manuscript would suit a specialized photonics or sensor journal. It does not deliver the conceptual advance or broad impact required by Nature Communications.\nFor these reasons, I recommend rejection."}, "author_response": "Point-by-point response to referees\nReviewers' comments:\nReviewer #1 (Remarks to the Author):\nComment 1.1: While I agree with the other reviewers that this work does not represent a transformative leap in the state of the art, I continue to believe that the novelty of combining dual slow light with PTS in a packaged on-chip device, along with a reasonable detection limit, justifies publication in Nature Communications. The reported low NEA.L value sets a new benchmark for on-chip gas sensing and will likely be of interest to the broader research community.\nResponse: We sincerely thank the reviewer for the professional evaluation and acknowledging the importance of our work. In the following, we provide detailed responses to the concerns raised by the reviewer, and highlight the corresponding revisions in yellow in the main manuscript and supplementary information.\nComment 1.2: In their revised manuscript, the authors have largely addressed my questions and comments. However, I outline below a few areas where I remain unconvinced and encourage the authors to revisit their arguments. In particular, I suggest they take a more conservative stance on the reported detection limit, as the Allan deviation data suggest a value approximately twice as large as claimed (see comment 1.8).\nResponse: Following your comment, we have re-evaluated and revised the reported detection limit. Please refer to the Response to Comment 1.5 of this document.\nComment 1.3: Comment 1.2- I feel there is no sense calculating with a constant absorption coefficient to simulate the heat source, if this varies as a function of the wavelength I reality. I suggest removing these Data from R1a), as this is confusing. Assuming a constant absorption coefficient of course makes sense for R1b) reflecting the choice of the pump wavelength.\nResponse: We appreciate the reviewer’s insightful comment. To avoid confusing, we have removed the data for the constant absorption coefficient and redraw the Fig. R1(a) and Fig. 2(b) in the manuscript as follows:\n25\n20\n15\n10\n5\n0\n1515 1520 1525 1530 1535 1540\nFig. R1 Dependence of on pump wavelength using the actual absorption coefficients of C₂H₂ (orange square). The blue line denotes values and purple line denotes the absorption coefficients of C₂H₂.\nComment 1.4: Comment 1.5- I am still not convinced about the Bloch-Floquet mode fluctuations argument in your structure, which is much longer than structures where the phenomenon was studied. Especially in the low ng region this phenomenon should not be observable, as modes are predominantly index guided and energy is carried by one mode component. Unless you provide an evidence for observation of such mode in a structure close to your length, I suggest to remove this hypothesis.\nResponse: We appreciate the reviewer’s professional comment. To address the concern about the origin of the observed oscillations, we have numerically calculated the curve of our PhCW structure for different number of periods in full 3D COMSOL simulation, for N = 5, 15, 25, ∞, the results are shown in Fig. R2. The results indicate that as the PhCW length increases, there are more fluctuations in over the wavelength range of 1480 to 1580 nm, and the amplitude of fluctuation increases when value becomes large. In the limit of an infinitely long PhCW, the curve becomes a perfectly smooth curve as theoretically expected. This behavior is consistent with what has been reported in PhCWs and it was referred to as Bloch-Floquet mode fluctuations in Ref. [1] (In Ref. [1]’s experiment, the N value is about 572). However, a direct simulation for N = 2000, corresponding to our experimental structure, is required but currently beyond our computational capacity, as a full 3D COMSOL calculation would demand extremely large running memory. Therefore, we agree that further research will be necessary to validate the origin of the observed oscillations.\nWe thank the reviewer again for careful consideration on the fluctuations. We have revised our discussion to: \"Some fluctuations are observed particularly in the high region. Such a behavior has been observed previously and could be attributed to Bloch–Floquet modes in the finite-length PhCW[1], which could also be due to measurement uncertainties caused by the limited spectral resolution.\"\n[1] Vlasov, Y. A., O'Boyle, M., Hamann, H. F. & McNab, S. J. Active control of slow light on a chip with photonic crystal waveguides. Nature 438, 65-69 (2005).\nFig. R2 Group index estimation in a N-period PhCW. (a) Full 3D model of finite length suspended PhCW structure with N = 5, 15, 25. For N = ∞ case, we employed the infinite period boundary condition to the front and back surfaces of the N = 1 PhCW structure to calculate . (b) Simulated curve as a function of incident wavelength for N = 5, 15, 25 and ∞.\nComment 1.5: Comment 1.8- The plots you provided are convincing. However, the determination of the LOD from R6b is not correct, as you cannot take a minimum of your trace with random fluctuations, but the average for the given averaging time instead. The difference in LOD is not dramatic, but by about a factor 2 worse (around 20 ppm). Instead of taking a moving average of the trace in R6c, you better provide an Allan plot that may explain the discrepancy with R6b (I expect a slightly worse value from R6b than LOD measured with N2).\nResponse: We appreciate the reviewer’s insightful comment. To accurately estimate the minimum detection limit (MDL, i.e. LOD) of our PhCW-PTS sensor, we recalculated the Allan deviation plot by averaging the data through a 1000-point window smoothing. As shown in Fig. R3, under the pure N environment, when the pump wavelength is tuned to the absorption line, the MDL is averaged to be 15 ppm, while off the absorption line, it is 12 ppm. We further evaluated the signal fluctuation by measuring the C₂H₂ concentration at 1000 ppm. The 1σ fluctuation is estimated to be 18 ppm at 100 s, slightly larger than the 1σ MDL value obtained with pure N . The three values are all below 20 ppm.\nFig. R3 Allan deviation analysis for PTS measurement. (a) Noise measurement in N environment with the pump wavelength tuned on (blue lines) and off (red lines) the absorption line and (b) corresponding Allan-deviation analysis.(c) Signal fluctuation with a fixed C₂H₂ concentration of 1000 ppm and (d) corresponding Allan-deviation analysis.\nReviewer #2 (Remarks to the Author):\nComment: After a thorough review of the manuscript titled “Dual slow-light enhanced photothermal gas spectroscopy on a silicon chip” and the associated point-by-point rebuttal, I believe the authors have satisfactorily addressed all reviewer concerns, and the manuscript can be recommended for publication.\nResponse: We sincerely appreciate the reviewer’s positive comment.\nReviewer #3 (Remarks to the Author):\nComment 3.1: While the manuscript is technically sound, it falls short of the breakthrough standard expected for Nature Communications. Incremental novelty – The “dual slow light” concept is a straightforward extension of single slow light photonic crystal schemes already reported for on chip gas sensing. The work does not introduce new physics or device architecture, merely cascading two well known effects.\nResponse: We appreciate the reviewer’s constructive comment. We believe our dual slow-light effect in on-chip photothermal spectroscopy (PTS) is a novel concept for gas sensing. Previous single slow-light effect is mainly used in direct absorption spectroscopy that only uses one light beam to detect intensity changes induced by absorption. On-chip PTS is a completely different technology that utilizes the interaction between two light beams and the heat generated due to gas absorption to detect photothermal phase modulation signal, following the laws of optical-thermal-optical process rather than a purely optical absorption process. Using the dual slow-light enhanced on-chip PTS, the NEA∙L sensitivity for acetylene detection is improved to 1.4×10⁻6, which is the highest sensitivity reported for photonic waveguide gas sensors to our knowledge.\nTo realize the dual slow-light enhanced PTS concept, we also need to innovatively design and fabricate the device. We have fabricateda highly integrated PTS chipwith a compact footprint of ~0.6 mm2. To be more specific, the defect holes in the PhCW were optimized to achieve enhanced dual-wavelength slow-light effect. Subwavelength grating couplers were optimized for polarization control (Supplementary Fig. S3). Multi-taper waveguides were designed on the chip to ensure single mode transmission (Supplementary Fig. S4). Transition structures near two ends of the PhCW were fabricated to reduce the coupling loss from the strip waveguide to the PhCW (Supplementary Fig. S5). We also incorporated the PhCW with a high-contrast on-chip MZI, and further packaged the PTS chip into a miniature gas chamber for portable gas sensing applications.\nComment 3.2: Modest performance gains – The reported minimum detection limit (8 ppm C₂H₂) and NEA·L of 9.2 × 10 ⁷ cm ¹·m are respectable for specialist journals, but remain one to two orders of magnitude above state of the art waveguide or cavity enhanced sensors (see Table 1 of the manuscript). The claimed “unprecedented” photothermal efficiency relies on a 1 mm path; absolute sensitivity is still limited.\nResponse: We appreciate the reviewer’s constructive comment. The free-space cavity-enhanced sensors, which can achieve effective optical path lengths of hundreds of meters to tens of kilometers, indeed offer higher absolute sensitivity of ppb-ppt regime. However, their experimental setups are complex, bulky and impractical for portable on-chip applications. By contrast, on-chip waveguide sensors offer ultra-compact integration with millimeter–centimeter light paths. The fundamental challenge lies in how to improve the on-chip sensitivity under such a short waveguide length. To address this limitation, prior works have often shifted to the mid-infrared (MIR) spectral range, where stronger molecular absorption lines enable improved absolute sensitivity. Nevertheless, such MIR approaches, which requires MIR sources and photodetectors, remain costly, bulky, and difficult to be integrated into a compact form.\nHere we presented a PhCW-PTS sensor operating entirely in the NIR using only a telecom-compatible source and photodetector. Despite the intrinsically weaker NIR absorption than MIR (weaker 1–3 orders of magnitude) and short chip length (1 mm), our device achieves the highest NEA·L sensitivity reported for a waveguide sensor, and even approaching state-of-the-art cavity-enhanced free-space systems. Such a sensitivity mainly benefits from the dual slow-light effect of a nanoscale PhCW and the high photothermal efficiency of on-chip PTS. Further improvements in absolute sensitivity are possible. By optimizing the PhCW structure, including its bandgap and slow-light parameters, the n in the C₂H₂ absorption region could be increased from ~10 to 100 and beyond, enabling nearly 10× enhancement in pump light-gas interaction. Additionally, optimizing light coupling into the chip from ~9 dB to below 1 dB/facet would be possible, which could allow another 10× increase in launched pump power and thus improving the on-chip absolute sensitivity.\nIt is also worth clarifying that photothermal efficiency k* is independent of the path length but depends on the waveguide structure. It serves as a reasonable indicator for comparing photothermal efficiencies, as it normalizes the parameters of light power, path length, gas concentration, and absorption coefficient. As shown in Supplementary Fig. S12, the PhCW achieves k* of 5.8×10⁻⁴ rad·cm·ppm⁻¹·mW⁻¹·m⁻¹, which exceeds the performance of hollow-core fibers (HCFs, ~10⁻⁶) by 2–3 orders of magnitude, and surpasses conventional strip waveguides (~10⁻⁵) by 1–2 orders of magnitude. This remarkable enhancement arises from three key factors: the small mode field area in PhCWs, the high thermo-optic coefficient of silicon, and most importantly, the dual slow-light enhancement effect of the PhCW.\nComment 3.3: Methodological concerns – Group index values above 100 are inferred from under sampled interferometric fringes, casting doubt on the linear ngp × ngb scaling. Thermal drifts are discussed qualitatively but not quantified under realistic field conditions, and Kerr induced background signals remain significant.\nResponse: We thank the reviewer for this insightful comment. The accuracy of calculation is mainly affected by the spectral resolution of the optical spectrum analyzer. We have averaged the calculated values of adjacent two interference fringes to improve the estimation precision. For wavelengths below 1572 nm ( ≈ 81@1572 nm), the measurement is considered as reasonably accurate as the fringe interval is larger than the spectral resolution of the optical spectral analyzer (0.02 nm). For wavelengths at 1573.5 nm ( ≈ 107 @1573.5 nm) and beyond, the measurement error may increase considerably due to the limited spectral resolution. We are aware of this and therefore, we choose probe wavelength at 1572 nm in our gas detection experiments, instead of a longer wavelength (corresponding to larger ) to enhance more of the PTS signal. In addition, as shown in Supplementary Fig. S8, three linear relationships of phase modulation on n , n , and n ×n are obtained with R2 all above 94%, confirming the reliability of the linear relationship between phase modulation and n ×n .\nThermal drift mainly affects the stability of operating point (i.e., quadrature point or Q-point) of the MZI. We stabilized the operating point by controlling the external temperature of the packaged gas cell, with on-chip MZI inside of it. As shown in Supplementary Fig. S9, we have conducted stability evaluation under realistic laboratory environment, and the Q-point fluctuation was less than 1% under controlled temperature of 25 ℃. In addition, as shown in Supplementary Fig. S11(c), Kerr induced background has negligible influence on our PTS measurement as it was removed by periodically scanning the pump wavelength across the absorption line, thanks to the wavelength independence of the Kerr effect within the small scanning range of the pump wavelength.\nComment 3.4: Editorial fit – The manuscript would suit a specialized photonics or sensor journal. It does not deliver the conceptual advance or broad impact required by Nature Communications. For these reasons, I recommend rejection.\nResponse: We appreciate the reviewer’s constructive comment. We have demonstrated a dual slow-light enhancement in PTS sensing on a suspended silicon PhCW. We believe it is a novel and interdisciplinary work as it encompasses many disciplines, including photonics, thermodynamics, sensing, spectroscopy, nanoscale device manufacturing, chip integration and package, etc. To be more specific, we have developed a new type of on-chip PTS based on PhCW, which generates structural dual slow-light by tailoring the dispersion of PhCW to enhance pump absorption and probe phase modulation. The pump slow-light effect enhances heat generation due to gas absorption by a factor of n ; the suspended PhCW enhances heat accumulation, leading to an increased temperature change around the waveguide region, which modulates the phase of the probe beam via the enhanced overlap of the temperature and probe fields. The probe slow-light effect further enhances the phase modulation by a factor of n . These combined effects lead to a significantly enhanced phase modulation proportional to n ×n .\nThe optimized PTS silicon chip was fabricated with a nanoscale CMOS-compatible manufacturing, and a suspended 2D-PhCW was fabricated using multi-layer wet-etching process. We further packaged the PTS chip into a compact gas chamber for portable sensing applications. Such a miniaturization and integration level are not achievable with traditional fiber and free-space systems, positioning our device for future sensor-on-a-chip that could integrate light source, detector and electronics on a single chip, with potential applications in smart homes, point-of-care diagnostics, environmental monitoring, wearable devices, etc."}, {"round": 3, "reviewer_comments": {"reviewer_1": "I thank the reviewers for their answers that mostly addressed my comments. I recommend publication.\nI must, however, still insist that they are unable to explain their fluctuations due to finite sample effects and should therefore remove their speculations about Bloch-Floquet modes entirely, not commenting on ng fluctuations as these are common in experiments and likely caused by combination of multiple effects.", "reviewer_3": "The revision and rebuttal address several earlier technical issues. In particular, the detection-limit analysis has been corrected: the Allan–Werle evaluation now yields a 1σ MDL of ~12–15 ppm for C₂H₂ at ~200 s (on-/off-line), consistent between the main text (Fig. 5e) and the new rebuttal plots (Fig. R3).\nThe removal of constant-absorption simulations improves clarity, and the dual-slow-light scaling is reasonably evidenced by the linear dependence of Δφ on ngp×ngb (R²≈0.96) together with the choice to operate the probe at 1572 nm to avoid under-sampling of fringes.\nThat said, several points remain only partially convincing:\n1. Novelty and significance. The device combines established elements—slow-light PhCWs and on-chip PTS—into a careful integration. The perturbative derivation and experimental validation of the ngp×ngb scaling are expected from standard theory, so the conceptual advance appears incremental.\n2. Performance claims. While the reported NEA·L of 1.4×10⁻⁶ cm⁻¹·m (L = 1 mm) is competitive and collated as best-in-class among waveguide sensors in Table 1, the absolute MDL remains above leading MIR waveguide and cavity/fiber systems summarized by the authors (Tables 1 and S2). Please moderate language such as “benchmark/unprecedented” and expand quantitative comparisons (e.g., normalized to optical path, bandwidth, and total SWGC loss).\n3. High‑ng fluctuations. The origin of the observed fluctuations in the high‑ng regime is still not firmly established. The rebuttal acknowledges that direct simulation at the experimental length (N≈2000) is infeasible and softens the wording to a hypothesis (Bloch–Floquet modes or measurement limits). This remains speculative; additional evidence (or neutral phrasing) would avoid over-interpretation.\nMethodology/reproducibility. Experimental details are largely sufficient (e.g., SWGC losses ~9 dB/facet; temperature‑stabilized packaged cell). Sharing raw Allan traces and ng‑extraction scripts would further aid transparency.\nOverall assessment. The authors have improved the manuscript and provided more robust MDL analysis. However, I still have doubts about the manuscript’s novelty and about the degree of performance advance over the state of the art. I recommend tempering claims, strengthening head‑to‑head comparisons (including MIR platforms and cavity/fiber systems), and clarifying the high‑ng analysis."}, "author_response": "Point-by-point response to referees\nWe sincerely thank the editor and reviewers for the professional evaluations and efforts to help to improve the manuscript. In the following, we provide detailed responses to the concerns raised by the reviewers, and highlight the corresponding revisions in yellow in the main manuscript and supplementary information.\nReviewer #1 (Remarks to the Author):\nComment 1.1: I thank the reviewers for their answers that mostly addressed my comments. I recommend publication. I must, however, still insist that they are unable to explain their fluctuations due to finite sample effects and should therefore remove their speculations about Bloch-Floquet modes entirely, not commenting on ng fluctuations as these are common in experiments and likely caused by combination of multiple effects.\nResponse: We sincerely appreciate the reviewer’s comment. We have now removed the speculative comments of ng fluctuations from the manuscript.\nReviewer #3 (Remarks to the Author):\nComment 3.1: The revision and rebuttal address several earlier technical issues. In particular, the detection limit analysis has been corrected: the Allan–Werle evaluation now yields a 1σ MDL of ~12–15 ppm for C₂H₂ at ~200 s (on /off line), consistent between the main text (Fig. 5e) and the new rebuttal plots (Fig. R3). The removal of constant absorption simulations improves clarity, and the dual slow light scaling is reasonably evidenced by the linear dependence of Δφ on ngp×ngb (R²≈0.96) together with the choice to operate the probe at 1572 nm to avoid under sampling of fringes.\nResponse: We sincerely thank the reviewer’s thoughtful evaluation and continuous encouragement and suggestions, which have indeed improved the manuscript.\nComment 3.2: That said, several points remain only partially convincing: That said, several points remain only partially convincing: Novelty and significance. The device combines established elements—slow light PhCWs and on chip PTS—into a careful integration. The perturbative derivation and experimental validation of the ngp×ngb scaling are expected from standard theory, so the conceptual advance appears incremental.\nResponse: We sincerely appreciate the reviewer for this constructive comment. We would like to further clarify that our research is focus on on-chip sensors, where the short optical path length is a limiting factor. We proposed the concept of dual slow-light enhancement to achieve high sensitivity despite of the limited path length. We specifically employed PhCW as the waveguide platform to realize the dual-slow-light due to its flexibility in tailoring dispersion. Theoretically, we analyzed the pump and probe light fields in the slow-light modes, the thermal-conduction field, and the refractive index modulation induced by the photo-thermal effect. It is a multi-physical process involving coupled light-heat-light interactions, distinguishing our work as a cross-disciplinary contribution rather than a simple incremental extension. Experimentally, we specifically designed and fabricated the PhCW that is compatible with on-chip PTS and achieves high PT phase modulation efficiency. We integrated the sensing PhCW into an on-chip MZI, which enabled phase measurement in a compact form. We also verified that the on-chip photothermal efficiency is proportional to ngp×ngb, and confirmed that the sensitivity of the on-chip PTS sensor can indeed be enhanced by the dual slow-light method.\nComment 3.3: Performance claims. While the reported NEA·L of 1.4×10 ⁶ cm ¹·m (L = 1 mm) is competitive and collated as best-in-class among waveguide sensors in Table 1, the absolute MDL remains above leading MIR waveguide and cavity/fiber systems summarized by the authors (Tables 1 and S2). Please moderate language such as “benchmark/unprecedented” and expand quantitative comparisons (e.g., normalized to optical path, bandwidth, and total SWGC loss).\nResponse: We thank the reviewer for this valuable comment. Following your suggestion, we have moderated the claims and removed \"benchmark/unprecedented\" in the revised manuscript. We expand quantitative comparisons with previous reported results in the revised Tables S1 and S2. For a fair comparison with other waveguide and cavity/fiber sensors, we use both NEA∙L and NNEA∙L. NEA∙L is already used in previous manuscript, which is normalized by the optical path (L). NNEA∙L represents the normalized noise equivalent absorption coefficient and length product, which is obtained by normalizing the NEA∙L by the bandwidth (BW) and optical pump power (P). The total SWGC loss is included in the pump power delivered into the waveguide. The calculation of NNEA∙L requires the knowledge of the detection bandwidth. In Table S1, many of the referenced papers did not clearly state the bandwidth values, hence we could not obtain a value for the NNEA∙L. For those papers with given detection bandwidth (or can be deduced form the information provided in the paper), the NNEA∙L is in the range of 10⁻6 to 10⁻7 W∙Hz-1/2. Our current on-chip PTS sensor achieves 1.8×10⁻8 W∙Hz-1/2. For other free-space and optical fiber-based systems, we have also compared the sensitivity in terms of NNEA∙L, as shown in Table S2. Free-space sensors based on cavities and multi-pass cells (MPCs) typically reach levels of 10⁻4−10⁻6 W∙Hz-1/2, while fiber-based PTS sensors show NNEA·L ranging from 10⁻7 to 10⁻9 W∙Hz-1/2.\nTable S1 Performance comparison of photonic waveguide gas sensors\nMethods Gases & λ (nm) Range Chip types L (cm) BW (Hz) P (mW) NEA∙L NNEA∙L (W∙Hz-1/2)\nDAS CH @1650 nm NIR Si-strip 10 5.7 10 4.6×10-4 1.9×10-6\n2 2 2 5\nDAS CH @3270 nm MIR Si-Slot 1.15 Not stated 1 1.7×10-5 Not stated\n7 8\nDAS CHO @7330 nm MIR Si-SWG 1 Not stated Not stated 1.1×10-4 Not stated\n3 6\nDAS 1.5×10-4 9.6×10-7\nCH @1531 nm NIR ChG-strip 2 0.94 6.3\nOff-chip PTS 2 2 9.3×10-6 6×10-8\nOff-chip PTS CO @2004 nm NIR LN-strip 9.12 1.44 8 1.1×10-3 7.3×10-6\n2 2\nTable S2 Comparison of the on-chip sensor with free-space/optical fiber sensors\nSensor Year& Methods Gas & Gas cell & L (m) BW (Hz) P (mW) NEA∙L NNEA∙L (W∙Hz-1/2) Dynamic\neff\ntypes ref. λ(nm) length (W∙Hz-1/2) range\nCH\nCH\nspace 2019 OA-ICOS 4 28 cm cavity 27000 0.02 12 1.9×10-3 1.6×10-4 >2.6×102\n1654\nsensors\nNH\nOptical 2021 PTS-FPI 2 2 5.5 cm HC-ARF 0.055 0.094 125 1.3×10-8 5.3×10-9 6.2×104\n1532\nfiber\nCH\nsensors 2015 PTS-MZI 2 2 10 m HC-PBF 10 0.094 15.3 2.3×10-6 1.2×10-7 5.3×105\n2 2 1 mm PhCW 0.001 0.94 12.5 1.4×10-6 1.8×10-8 >2.5×104\nsensor work chip MZI 1531\nComment 3.4: High ng fluctuations. The origin of the observed fluctuations in the high ng regime is still not firmly established. The rebuttal acknowledges that direct simulation at the experimental length (N≈2000) is infeasible and softens the wording to a hypothesis (Bloch–Floquet modes or measurement limits). This remains speculative; additional evidence (or neutral phrasing) would avoid over interpretation.\nResponse: We agree with the reviewer that a definitive confirmation of the origin of high-ng fluctuations is not established. We would like to clarify that this does not affect the main conclusions of the manuscript regarding the dual-slow-light enhancement and the detection sensitivity. To avoid over interpretation, we followed your and reviewer #1’s suggestion, and removed, in the manuscript, the speculative hypothesis of ng fluctuation.\nComment 3.5: Methodology/reproducibility. Experimental details are largely sufficient (e.g., SWGC losses ~9 dB/facet; temperature-stabilized packaged cell). Sharing raw Allan traces and ng-extraction scripts would further aid transparency.\nResponse: We thank the reviewer’s insightful suggestion. The raw Allan traces can be found in Fig. 5(e) in the manuscript and Fig. S15 in the supporting information. The ng-extraction script is uploaded in the link [1].\n[1] https://github.com/PolyU-EEE/ng-extraction-script\nComment 3.6: Overall assessment. The authors have improved the manuscript and provided more robust MDL analysis. However, I still have doubts about the manuscript’s novelty and about the degree of performance advance over the state of the art. I recommend tempering claims, strengthening head-to-head comparisons (including MIR platforms and cavity/fiber systems), and clarifying the high-ng analysis.\nResponse: We appreciate the reviewer’s insightful comment. Following your suggestions, we have briefly explained the novelty in the response to Comment 3.2, revised the claims and comparisons in the response to Comment 3.3 and clarified the high ng analysis in Comment 3.4."}, {"round": 4, "reviewer_comments": {"reviewer_3": "My suugestion is: paper acceptance as it is."}, "author_response": ""}]

Decision letter