Chip-integrated spectroscopy capable of temperature retrieval

Device design and calibration

Figure 1a shows the circuit layout of the MRR filter used in this demonstration. It consists of a high-Q ring resonator and two pulley bus waveguides on the two sides of the ring, respectively^26,27. On one side are the input and output ports, and on the other sides are the add and drop ports. The incoming signal is injected into the input port, and the filtered signal is collected at the drop port. To sweep the filter center wavelength, a zigzag heater surrounding the ring is deposited on top of the MRR, enabling thermal tuning of its resonant wavelengths. The efficiency of this control-termed tunability-is defined as the resonance wavelength shift per unit of heating power ((Delta lambda _{res}/Delta P_h)) and is typically expressed in pm/mW. Here, the zigzag layout is to increase the heating area of the electrode and thus the heating efficiency. Alternatively, instead of the thermo-optic tuning, electro-optic tuning can be applied to utilize LN’s large electro-optic coefficients²³. In comparison, the former is more power efficient, but the latter can achieve ultrahigh tuning speed (at hundreds of GHz, versus hundreds of KHz).

Unlike typical interference filters, the MRR filter has periodic transmission spectral windows, separated by free-spectral range (FSR) given by³⁰

where (lambda) is the center wavelength, R is the ring radius, and (n_g) is the group refractive index at the center wavelength. In typical settings, FSR is on the order of nanometers, so that the filter will admit not only the target signal photons, but also those in other periodic windows. Hence, if there is broad background noise, a coarse filter is needed to apply around the target wavelength for noise suppression.

For the current experiment, we design and fabricate the circuits on a 300-nm TFLN wafer, shallow etched to a height of 180 nm. The ring radius is (R=40) (mu)m. The pulley and ring waveguides have top widths of 280 nm and 480 nm, respectively, with a sidewall angle of 82 degree. The detailed fabrication process and the circuit dimensions of the MRR can be found in the Methods section. These waveguide dimensions ensure that only the fundamental TE mode propagates in the waveguides and all the other modes are suppressed. For the center wavelength (lambda =770) nm, the simulated group refractive index (n_g=2.4038), so that the FSR is 0.98 nm by design.

The microscope image of the fabricated chip is shown in Fig. 1a. To characterize its transmission spectrum, we use a tunable laser (New Focus TLB-6700) whose output wavelength can be swept using both coarse and fine scans, the latter of which significantly enhances the calibration accuracy over our previous measurement to reduce the measurement error from 2 pm to 0.03 pm²⁷. The details of the calibration method can be found in the Methods section.

Because of the 0.98-nm FSR and the limited maximum fine scan range of 150 pm, we first use the laser internal coarse scan to locate the resonance wavelength. Then we perform a fine scan around the resonance wavelength with a scanning range of 51 pm. The measurement results are shown in Fig. 1b, where two TE00 modes are shown with a 0.98 nm FSR, as simulated. The resonance profile has a FWHM of 2-pm as shown in the inset of Fig. 1b, corresponding to a loaded cavity of (Q=0.38times 10^{6}). Also shown in the figure are two wide transmission peaks, which correspond to TM00 modes, which have much higher propagation losses due to the waveguide dimension. The wavemeter measurement details of MRR characterization can be found in the Methods section.

In this experiment, we measure specifically the potassium emission lines for potential wildfire detection. To this end, we use a potassium hollow cathode lamp (HCL), which emits the K-line doublet at 766.5 nm and 769.9 nm, respectively. The spacing between the two is 3.4 nm, so that only one line can be transmitted by the MRR at a time when its resonance is thermo-optically tuned. To simultaneously detect both transmission lines, one may cascade two MRR’s in serial, with each’s resonance tuned to be at one line and the input port of a second MRR connected to the through port of the first. Because of the on-chip integration, there is no insertion loss between the two. By cascading more MRR’s, signals in many emission lines can be measured simultaneously.

In our chip design, the heating electrode will introduce additional loss to the cavity, due to the evanescent light absorption by the metal^21,31. Thus it is desirable to spatially separate the electrode and the waveguide, so that there is little evanescent light reaching the electrode. However, if the gap between the two is large, the heater efficiency will be weak, so that the wavelength tunability is reduced. To achieve both low loss (thus high spectral resolution) and high tunability, we use a zigzag-shaped heater to encircle the ring, to increase the heating area and thus its efficiency. Positioning the zigzag on both sides of the ring waveguide increases the heating area while reducing the temperature gradient to provide uniform heating.

Figure 2 shows the measured trade-off between the cavity linewidth and thermo-optic tunability when the lateral distance is varied between the electrode and waveguide. From the figure, when the distance exceeds 2.8 (mu)m, the linewidth is nearly not affected by metal absorption. Yet the tunability remains sufficiently large for this experiment. In our current design, the distance is 2.8 (mu)m as we are interested in measuring accurately the emission linewidth. To characterize the tunability, we apply voltage manually from 17 to 26 V, at a step size of 0.5 V. For each voltage, the heater power is calculated using (P_{h}(V)=V^2/R_{h}), where (R_{h}) is the heater’s resistance. The shifted resonance wavelength (lambda _{res} (V)) is measured using the tunable the laser. Figure 3 shows tunability of MRR with distance 2.8 (mu m) used for our experiment. The slope of the linear fitting line (Delta lambda _{res}/Delta P_{h}) indicates a tunability of 6.3691 pm/mW. The coefficient of fitting determination, (r^2 = 1), confirms the excellent linearity of the response. For other applications, one may choose an appropriate distance according to the trade-off, based on the specific application needs.

Experiment

The experiment for detecting potassium D lines is illustrated in Fig. 4. A hollow cathode lamp (HCL, Scinteck SI-HC-200042) is used as the light source for the K doublet emission. We apply a current of 8 mA and a voltage of 280 V to generate an intense electric field between the lamp’s cathode and anode, where the inert Ne gas is ionized. The electrons emitted from the cathode, along with Ne ions, form a conducting plasma that excites potassium atoms to higher energy states. As the potassium atoms decay, they emit narrow D lines through a quartz window. A thin lens (L_1) with a focal length of 100 mm collimates the diverging thermal light, which is then focused by a second lens (L_2) with a 75 mm focal length. Short-pass (SP) and long-pass (LP) filters are employed to limit the spectral range to 750–800 nm, while effectively avoiding interference from other emission lines. The light is coupled into a multimode fiber (MMF) via a fiber coupler, where a single-mode fiber (SMF) is spliced with the MMF. The light passes through a fiber polarization controller (FPC) before coupled into the MRR chip via a lensed fiber. The MRR is mounted on a stage equipped with a thermoelectric cooler (TEC, Vescent Photonics, Slice-QTC) that actively stabilizes the temperature at (300pm 0.003) K, which is the same as the stage temperature used during calibration. This ensures a stable thermal environment, effectively mitigating ambient fluctuations that could otherwise induce resonance shifts. A power supply (GWINSTEK GPD-2303S) is used to sweep the resonance wavelength of the MRR by 200 pm by adjusting the applied voltage. When the resonance wavelength aligns with the potassium D-line, the emitted photons will pass through the MRR and reach a single-photon detector (PerkinElmer SPCM-AQR-14-FC-11260) through the drop port. The detector output pulses are registered by a counter (Thorlabs SPCNT) over a 1-second integration time to suppress Poissonian noise. During the process, a computer tunes the MRR resonance wavelength by controlling the power supply and records the photon counts at the same time.

The photon counting results are shown in Fig. 5, where (a) and (b) are for the potassium D2 and D1 lines, respectively. For the D2 line, the power supply voltage is increased from 17 to 26 V, at a step size of 0.1 V scanned automatically by the computer. The computer also automatically converts the applied voltage to the corresponding resonance wavelength by the relationship

where the second term calculates the resonance wavelength shift induced by the heater power difference between the applied voltage V and the initial voltage (V_0). As a result, the D-line profiles directly show photon counts as a function of wavelength. Hence, the accuracy of the calibrated tunability (Delta lambda _{res}/Delta P_{h}) and initial wavelength (lambda _{res}(V_0)), determines the precision of the measured wavelengths of the D-lines. The filtered wavelengths match well with the NIST database values of 766.5 nm and 769.9 nm⁶. The dark count is measured as (147pm 11) Hz.

Temperature retrieval by linewidth

Thus far, the reported method for temperature retrieval of wildfire relies on broadband spectral radiance fitted by the Planck function¹⁰. It is susceptible to errors due to the background spectrum of reflected solar radiance background which is also broadband. On the other hand, temperature in plasma is typically determined by the Boltzmann plot of multiple emission lines, which is prone to significant retrieval errors due to intensity fluctuations²⁹. Similarly, temperature retrieval of stars using luminosity in the Stefan-Boltzmann equation requires stellar radius or angular diameter data³², with radius or distance uncertainty affecting accuracy. Spectral contamination further impacts luminosity accuracy.

Here, we introduce a novel method of temperature retrieval using the fine measurement of emission linewidth with the MRR filter. In this experiment, by varying the lamp current from 8 mA to 40 mA, the cathode temperature is raised, which, in turn, boosts the emitted current from the cathode. This leads to a higher plasma charge density and, consequently, an elevated plasma temperature³³. The increase in temperature enhances the thermal motion of potassium atoms, resulting in greater Doppler broadening of the linewidth. Therefore, linewidth broadening is observed with increasing lamp current.

Figure 6 plots the change of linewidth as the lamp current is varied. The error bar represents the standard deviation of three repeated linewidth measurements taken at each lamp current. The emitted light spectrum from the lamp is a convolution of Doppler broadening, caused by thermal motion, and collision broadening, which arises from the reduced lifetime of the excited state of potassium atoms due to collisions¹¹. This results in a Voigt profile (V_{e}(lambda ,T)=G(lambda ,T)otimes L_1(lambda ,T)), where (G(lambda , T)) is the Gaussian profile describing the Doppler broadening and (L_1 (lambda , T)) is the lamp collision broadening Lorentzian profile. The observed linewidth is the result of a further convolution between the Voigt profile (V_e(lambda ,T)) and the Lorentzian profile of the ring resonator (L_2(lambda )). Associative property of convolution allows us to first convolve the lamp collision Lorentzian with the ring Lorentzian, yielding a combined Lorentzian profile (L(lambda ,T) = L_1(lambda ,T)otimes L_2(lambda )). The total observed spectrum is therefore a Voigt profile

In the retrieval model, we first compute the linewidth of the combined Lorentzian profile (L(lambda ,T)) to simplify the calculation, as the resulting combined Lorentzian profile has a linewidth just equal to the sum of the individual Lorentzian linewidths:

where (Delta lambda _{1,2}) are the FWHM of (L_{1,2}), respectively. The collision broadening linewidth, as given by³⁴, can be extended to address the specific conditions in this work. An illustration of the collision processes is shown in Supplementary Fig. S1a. Here, the Ne gas is partially ionized to form Ne ions. These Ne ions and electrons, present in equal densities, form a conducting plasma between the cathode and anode of the HCL. Therefore, we have (n=n_{Ne}+n_{Ne^+}), where n represents the total number density of particles, that consist of unionized neutral Ne with density (n_{Ne}) and ionized Neon with density (n_{Ne^+}). The density of Neon ions in plasma is equal to the density of electrons, expressed as (n_{Ne^+}=n_e). The collision broadening linewidth is then modified to account for these plasma conditions as

Here (Delta lambda _0) is the potassium natural linewidth, which is 0.012 pm³⁵. The subscript K denotes the potassium atoms, and s represents the species that the potassium atoms collide with in the medium of the HCL glass tube, such as electrons (e), Ne ions (Ne(^+)), or neutral Ne atoms (Ne). The mole fraction of the species s is denoted by (chi _s). The scattering cross section is given by (sigma _{s-K}=pi (a_s+a_K)^2) where (a_s) and (a_K) are the radii of the mole fraction of the species s and potassium atoms, respectively. (bar{v}_{s-K}) is the mean relative speed, with (bar{v}_{s-K}=sqrt{bar{v}_s^2+bar{v}_K^2}), where (bar{v}_s=sqrt{8k_BT/pi M_s}), and (bar{v}_K=sqrt{8k_BT/pi M_K}). (M_s) and (M_K) are masses of species s and potassium atoms, respectively. (k_B) is the Boltzmann constant. In this context, the relations (chi _{Ne}+chi _e=1) and (chi _e=chi _{Ne+}) hold. Given that the lamp plasma is considered to be weakly ionized and assuming local thermal equilibrium (LTE) for particles in the glass tube, the fraction of Ne ions (chi _{Ne+}), or the electron fraction (chi _e), also referred to as the degree of ionization, can be related to the temperature via the Saha equation³⁶.

in which the thermal de Broglie wavelength is (lambda _{text {th}}=h/sqrt{2pi M_e k_B T}). The degeneracy ratio of Neon ion to neutral Neon is given by (g_1/g_0=4)³⁷. The first ionization energy of Ne is (epsilon =21.56454) eV³⁸. In the retrieval calculation we use neutral Ne and Ne ion radii (a_{Ne}=0.02) nm and (a_{Ne+}=0.112) nm, Ne mass (M_{Ne}=M_{Ne+}=20.1797) amu, potassium atomic radius (a_{K}=0.235) nm, potassium mass (M_{K}=39.0983) amu, electron radius (a_{e}=2.8179times 10^{-6}) nm, and electron mass (M_{e}=9.11times 10^{-31}) kg. Because the sealed glass tube has a constant volume and inert gas Ne particle numbers, we can determine the total number density, which is independent of temperature, by applying the ideal gas law, (n=p/kT). By using (p=5) torr at (T=300) K, the calculated total number density is (n=1.61times 10^{23}) m(^{-3}), which is on same order as reported in Ref.²⁹.

The Doppler broadening linewidth is defined as³⁴

Then, by using the approximation relation between the FWHM of Voigt, Gaussian, and Lorentzian profiles, the FWHM of Voigt spectrum for the observed light in Eq. (3) is then given to a very good approximation as³⁹:

The retrieved temperature using plasma model is shown in Fig. 7.

As a comparison, the retrieved temperature is on the same order of magnitude ((times 10^4) K) of the temperature retrieved by Boltzmann plot in Ref. ²⁹, where a similar hollow cathode discharge was employed for a laboratory-scale astrophysics experiment. To verify the validity of the retrieval model and gain insight into broadening mechanisms, we analyze the plasma ionization and the broadening competition in Supplementary Section S1. Note that this retrieved temperature is almost one order of magnitude less than the model without considering plasma (completely unionized); see more discussions in Supplementary Section S2.

The validity of the LTE assumption in this model can be evaluated using Griem’s criterion, which defines the critical electron density required for collisional rates to dominate over radiative decay: (n_egtrsim 9.2times 10^{23}bigl (E_{12}/{E_1^H}bigr )^3sqrt{kT/{E_1^H}}) m(^{-3}), where (E_{12}) is the excitation energy from state 1 to state 2, and (E_H) is the ionization energy (13.6 eV) of the hydrogen atom in the ground state^40,41,42. Taking (E_{12}=1.61) eV of potassium atom and (Tapprox 10^4) K, the criterion gives (n_egtrsim 1.12times 10^{21}) m(^{-3}). Given the total particle density (n=1.61times 10^{23}) m(^{-3}), a degree of ionization (chi _egtrsim 0.7%) would be sufficient to satisfy the LTE condition. Reported electron densities in HCL plasmas ((sim 10^{23}) m(^{-3}))²⁹ and our Supplementary Fig. S1 (showing (chi _e) from (0.0065%) to (18%)) support this. Starting from (I=10) mA, where (chi _e=1.6%>0.7%), the electron densities are beyond the threshold of the Griem’s criterion. At lower currents, plasma density may fall short of LTE conditions. In such non-LTE regimes, applying the Saha equation may lead to temperature errors. A more accurate alternative is to use a collisional–radiative model (CRM), which accounts for both collisional and radiative processes⁴³.

Application

The demonstrated single-photon counting MRR spectroscopy have broad applications, ranging from detecting wildfires, to measuring fusion plasma and celestial bodies such as stars and black hole accretion disks in active galactic nuclei (AGN). For those applications, distinct circuit designs and retrieval models may be required to achieve the optimal performance. Table 1 lists the emission bands, temperature range, emission linewidth, underlying broadening mechanisms, and some key physical properties of various light sources. As seen, most of the bands fall entirely or partially in the transparency window of lithium niobate, which spans from the UV to the mid-IR (MIR) (0.4-5 (mu m))^21,22. This provides an opportunity of applying the current LNOI MRR circuits to those various uses. For all of them, the 2 pm FWHM spectral resolution of the current MRR devices is adequate to quantitatively measure the line broadening effects, from which the source temperature can be retrieved. In Supplementary Section S3, we discuss several simple models for the temperature retrieval in those applications.

The important metrics for temperature retrieval in environmental sensing are the linewidth broadening sensitivity to the temperature change, (d(Delta lambda _{obs})/dT), and the temperature retrieval resolution, (Delta T_{ret}=2 pm/|d(Delta lambda _{obs})/dT|), based on the 2-pm resolution of the MRR spectrometer. In the HCL model, we calculated the sensitivity which ranges from 0.0005 to 0.02 pm/K, yielding a resolution between 106 and 3952 K. While the resolution appears limited, Fig. 7 demonstrates that temperature changes in our HCL are typically hundreds to thousands of Kelvin per 2 mA lamp current step (minimum step is 1 mA). This large change relative to (Delta T_{ret}) ensures our method remains applicable in the HCL temperature retrieval, as evidenced by the discernible linewidth broadening in Fig. 6. In higher-temperature regimes, the linewidth becomes less sensitive to temperature increases, as Doppler broadening dominates ((Delta lambda _Gpropto sqrt{T})), resulting in a sensitivity that approximately scales as (d(Delta lambda _{obs})/dTsim T^{-1/2}). However, such temperatures exceed typical operating conditions of HCL and are more relevant in fusion or astrophysical plasmas, where Stark broadening may enhance sensitivity.

In real-world wildfire detection scenarios, additional techniques may be needed to enhance solar background suppression beyond the laboratory bandpass filters. Initial passive detection of potassium D lines is performed using a combination of bandpass filters and the high-resolution MRR filter. Upon detection, active fluorescence sensing can be triggered, in which a pulsed UV laser excites free potassium atoms in the plume^44,45. Time-gated detection captures only the resulting fluorescence at D line wavelengths, effectively rejecting continuous solar photons during off-gate intervals. The fluorescence signal is subsequently analyzed for spectral linewidth broadening in the 11–17 pm range (see Table 1), arising from Doppler and collisional effects, and for temperature retrieval in the 1000–2500 K range (see Table 1). These spectral characteristics, along with the precise temporal correlation between the excitation pulses and detected emissions, enable robust discrimination of fire-induced potassium fluorescence from background noise.

Furthermore, different applications have different measurement requirements not only on wavelength bands and resolution, but also the scanning range and speed. For the thermo-optic tuning, the tunability is given by⁵⁹

Here, (Delta P_h) is the change of the applied electric power for the heater and (Delta lambda _{res}) is the resultant shift in the resonant wavelength. (L_{h}) is the heater length. R is the ring radius. (Delta T) is the temperature change of the heated ring waveguide. (partial n_{eff}/partial T) is the thermal-optic coefficient. (Delta T/Delta P_{h}) is the heater efficiency (i.e., thermal resistance).

In Eq. (9), the thermal-optic coefficient can be calculated by computing the relevant transverse mode properties using finite-difference time-domain (FDTD) simulations. In our case, (partial n_{eff}/partial T=1.79times 10^{-5}) K(^{-1}). The heater efficiency can be efficiently adjusted by changing the distance between the heater and the MRR waveguide. Figure 8 and its inset plot the heater efficiency versus distance derived from Fig. 2 and Eq. (9), and (n_{eff}) as a function of the temperature from the FDTD simulation.

The heater efficiency depends on the distance and thermal conductivity of the cladding material between the heater and waveguide, and the heater’s electrode material composition and geometry^14,30. It is, however, nearly independent of the waveguide geometry, suggesting that the above result can serve as a good design guideline empirically across a broad range of wavelengths. For field deployment, GHz-rate electro-optic tuning could supplement thermal tuning to more effectively compensate for ambient thermal fluctuations ((ll)1 kHz), albeit with a moderate increase in optical loss. Finally, despite the periodicity in the MRR’s resonant lines, the spectral measurement range can exceed the FSR by adding a tunable coarse filter with bandwidth narrower than FSR to block cross-talk interference from unwanted channels.