High sensitivity pH sensing by using a ring resonator laser integrated into a microfluidic chip

We present a chip-scale integrated pH sensor with high sensitivity by using an optofluidic ring resonator (OFRR) laser. An optical fiber with a high refractive index (RI) is employed both as an optical cavity and the sensing reactor along a microchannel, while disodium fluorescein (DSF) aqueous solution with a low RI is served as the cladding gain medium and fluorescent probes. The pump light is introduced along the fiber axis and guided by the total internal reflection at the fiber/cladding interface. The evanescent field of the pump light extends out of the fiber surface and efficiently excites the dye molecules residing in the evanescent field region of the Whispering Gallery Modes (WGMs) of the OFRRs to produce lasing emission. This pumping scheme provides a uniform excitation to the gain medium and significantly increases the signal-to-noise ratio, ensuring a low lasing threshold and highly sensitive sensing. The lasing threshold property under different pH conditions is experimentally and theoretically conducted to evaluate the sensing performance, which shows that the lasing threshold highly depends on the pH value of the cladding solution due to the increasing deprotonation process. We further verify that the intensity of the lasing emission and the pH value shows good linearity in the pH range 6.51-8.13, with a 2-order-of-magnitude sensitivity enhancement compared to fluorescence measurement. The proposed OFRR lasing platform shows excellent robustness and low sample consumption, providing a powerful sensing strategy in medicine, and hazardous/toxic/volatile sensing, which require label-free, real-time, and in situ detection.


Ⅰ. Theoretical analysis of optofluidic ring resonator dye lasers
The optofluidic dye laser can be modeled as a four-energy-level laser system. Let N1 be dye concentration in the exited state and nt be total dye concentration. Qabs, Qleak, and Qscat are the quality factors of a ring resonator related to the energy losses caused by the cavity absorption, light leakage, and scattering, respectively. The total quality factor (Qtol) of a Whispering Gallery Mode (WGM) in a ring resonator can be written as: Q -1 tol = Q -1 abs + Q -1 leak + Q -1 scat [1]. Then, the population inversion condition can be expressed as [2][3][4] where σa(λ) and σe(λ) are the dye absorption cross-section and the dye emission cross-section at the lasing wavelength λL, respectively. m = n1/n2 is the effective refractive index (RI) of the WGMs, where n1, and n2 are the RIs of the optical fiber and the gain cladding solution, respectively. At threshold, Eq. (S1) can be written as: where γ is defined as the fraction of gain molecules in the excited state at the threshold. Qabs = 2πm/ηλntσa(λ), η is the ratio of the evanescent-field volume to that of the whole WGM, which is estimated to around 0.02 [1]. In our experiment, n1 = 1.458, n2 = 1.333, and the diameter of the optical fiber is 200 µm. Then, the calculated Qleak will be beyond 10 19 [1], which can be neglected as compared to the Qabs~10 6 . According to Ref. [5], Qscat is of the order of 10 12 and can also be neglected. Figure S2 presents the calculated Qabs under different pH conditions.
According to the laser theory, the lasing threshold, Ith, is determined by: . 1 Through Eqs. (S2)-(S3), one can calculate the lasing threshold, in which the σa(λ) and σe(λ) of disodium fluorescein (DSF) aqueous solution are measured in the experiments detailed below in section Ⅱand Ⅴ, respectively.

Ⅱ. Absorption cross-section measurement
The measurement of absorbance is used to characterize the dye absorption cross-section. A UV-Visible spectrophotometer (Specord-200, Analytik Jena AG) is used to measure the absorption spectrum [6]. The absorbance spectra of 20 μM DSF with different pHs are measured [7]. The σa(λ) is calculated based on equation: where l is the length of light path, n is the concentration of dye, and A is the absorbance. The absorption cross-section is shown in Figure S1. The σa(λ) at the lasing wavelength (523 nm) is estimated to be 5.31×10 −18 to 7.96×10 −18 in the pH range 6.51-12.30.

Ⅲ. Fluorescence lifetime measurement
A fluorescence lifetime measurement system is used to characterize the lifetime of DSF. We measure their transient photoluminescence (PL) decay spectra under different pH values using fluorescence lifetime spectrometer (C11367, Hamamatsu). The processed data is then fitted to an exponential decay function to extract the lifetime value. As shown in Figure S3, the fluorescence lifetime of DSF increases from 4.92 to 5.38 ns in the pH range 6.51-12.30.

Ⅳ. Quantum yield measurement
To determine the quantum yield of DSF, we measured the absorbance and fluorescence of DSF aqueous solution with different pH value in parallel with Rhodamine 6G (R6G) (in methanol). The absorbance tests are performed with an UV-Visible spectrophotometer (Specord-200, Analytik Jena AG). The fluorescence spectrum is examined using a fluorescence spectrophotometer. The absorption (or excitation) wavelength is fixed at 470 nm. The quantum yield can be calculated as below [8] where the subscripts x and ref represent the sample to be tested and the standard reference solution, respectively. Φ is the quantum yield, F is the integrated area of the fluorescence emission spectra, n is RI of the solvent, f = 1-10 -A , A is the absorbance at the excitation wavelength 8 . We calculate that the Φ increases from 0.29 to 0.92 in the pH range 6.51 -12.3 (Φref = ΦR6G = 0.93 for R6G in methanol) [9].

Ⅴ. Emission cross-section measurement
The σe(λ) is obtained from the fluorescence emission spectra of DSF aqueous solution using equation [10] ( ) where c is the speed of light in vacuum, τF is the fluorescence lifetime of DSF molecule, g(λ) = I(λ)/∫I(λ)dλ is the normalized line-shape function of the fluorescence spectra, and Φ is the fluorescence quantum yield of the dye molecules. Using experimentally measured data as detailed previously, the emission cross-section under different pH conditions is plotted in Figure S4. The σe(λ) at the lasing wavelength (523 nm) is estimated to be 3.83×10 −17 to 1.61×10 −16 in the pH range 6.51-12.30.

Ⅵ. Sensitivity analysis
According to the laser theory, a normalized pumping rate relative to threshold value is given by [11] , , p p th where Rp is pumping rate in atoms per second, Rp,th is threshold pumping rate in atoms per second. The below-threshold region(r＜1) is then described by the approximate results [11] . 1 ss r n r ≈ − below threshold, r＜1 (S8) The approximate formulas for the laser behavior above threshold are thus [11] The sensitivity capabilities of optofluidic sensing can be predicted by calculating the effect of the dye parameters on the lasing threshold, defined as [12] , dI I S d α α α = (S11) where α is the parameter examined (α = σa, τ, Φ) Through Eqs. (S10)-(S11), the sensitivity below and above the threshold can be calculated by ( ) ( ) ( ) below threshold 1 1 . above threshold 1 1