Conventional absorption spectroscopy is not nearly sensitive enough for quantitative overtone measurements on submonolayer coatings. While cavity-enhanced absorption detection methods using microresonators have the potential to provide quantitative absorption cross sections of even weakly absorbing submonolayer films, this potential has not yet been fully realized. To determine the absorption cross section of a submonolayer film of ethylene diamine (EDA) on a silica microsphere resonator, we use phase-shift cavity ringdown spectroscopy simultaneously on near-IR radiation that is Rayleigh backscattered from the microsphere and transmitted through the coupling fiber taper. We then independently determine both the coupling coefficient and the optical loss within the resonator. Together with a coincident measurement of the wavelength frequency shift, an absolute overtone absorption cross section of adsorbed EDA, at submonolayer coverage, was obtained and was compared to the bulk value. The smallest quantifiable absorption cross section is . This absorption cross section is comparable to the extinction coefficients of, e.g., single gold nanoparticles or aerosol particles. We therefore propose that the present method is also a viable route to absolute extinction measurements of single particles.
© 2014 Optical Society of America
Single-molecule detection and single-atom detection rely largely on the measurement of excited-state fluorescence [1,2]. While single-particle absorption measurements, especially in the IR fingerprint region , are generally applicable and provide more chemical specificity, conventional absorption spectroscopy is not nearly sensitive enough for single-molecule measurements. In most commercial spectrometers absorption spectroscopy requires the measurement of a small intensity change on a large intensity background. While direct single-particle absorption detection therefore appears impossible with this approach, Celebrano et al. succeeded in detecting the shadow of a strongly absorbing molecule by focusing the light to a diffraction-limited spot . Of course, surface-enhanced Raman scattering [5,6], surface-plasmon-resonance-enhanced detection , and near-field scanning optical microscopy also have approached and occasionally reached single-molecule or single-particle detection limits.
Optical microresonators of differing geometries have also been used previously as label-free and ultrasensitive chemical sensors reaching single-particle or single-molecule detection limits [8–18]. The resonance frequencies of the “whispering gallery” cavity modes (WGMs) are sensitive to the surface coverage and the refractive index of the adsorbed chemical species [11,19], while the optical absorption of the surface layer leads to a decrease of the quality () factor  and can be retrieved either from the reduction of power that is transferred to the resonator mode , from the decrease of the cavity ringdown time, or from the broadening of the resonance line. These cavity-enhanced absorption detection methods have, therefore, the potential to provide quantitative absorption cross sections of single particles. For microresonators this potential has, to the best of our knowledge, not yet been realized, although Pipino et al. measured absolute overtone absorption cross sections using a large monolithic folded optical cavity . In most previous studies the presence of a particle placed in the mode field of a microresonator was inferred from, e.g., stepwise resonance frequency shifts  or incremental transfer of thermal energy into the resonator [8,9] and could not be readily quantified. In addition, a measurement of the total optical loss in the microresonator obtained from resonance lifetime or linewidth measurements does not permit us to distinguish losses due to molecular absorption from changes in the cavity coupling coefficient.
As we show in the present paper, the signal enhancement, which is provided here by an optical microcavity, is indeed quantifiable and provides a route to absolute absorption cross sections of either single particles or—here—of weak transitions at submonolayer coverages. We combined “conventional” phase-shift cavity ringdown measurements of Rayleigh backscattered light with phase-shift measurements of light bypassing the cavity and thereby obtain absolute values for the coupling coefficient and the cavity loss. The optical loss measurement can then be related to the surface coverage, which is obtained from the frequency shift of the WGM. With the assumptions made about the molecular dimensions, it is possible to calculate the absorption cross section.
Time-domain measurements have routinely been used to measure optical lifetimes in a variety of resonator configurations  including monolithic silica resonator cavities [22,24] and microresonators [25,26]. For such cavity ringdown time measurements the time-dependent intensity decay of a short optical pulse injected into the resonator is monitored. We apply an alternative approach that, instead, uses intensity-modulated light from a cw source and then measure the phase shift of light exiting the resonator. This approach is referred to as phase-shift cavity ringdown (PS-CRD) spectroscopy and has been used for mirror cavities [27,28], fiber-optic loops , and, more recently, silica microsphere resonators [30,31]. To demonstrate the sensitivity of the method we use the PS-CRD technique to measure the optical absorption of near-IR light through a weak overtone transition of ethylene diamine (EDA), , that is adsorbed on the surface of a high- silica microsphere with a coverage of less than four monolayers. The compound was selected because its absorption spectrum and refractive index at 1.5 μm are well known. Also, the adsorption kinetics of EDA on silica have previously been characterized , and its vapor pressure is comparably high, allowing for a controlled dosing experiment.
2. EXPERIMENTAL SETUP
The silica microsphere (diameter of 273 μm, measured using the microscope built into the fusion splicer) was formed by melting the end of a single-mode optical fiber (Corning SMF-28E) in the electric arc of a fusion splicer. Another strand of single-mode optical fiber was tapered to a waist diameter of about 3 μm and used to couple light into the evanescent field of the microsphere’s WGMs. A detailed description of the experimental setup regarding the microsphere and tapered waveguide may be found elsewhere .
The amplitude- and frequency-modulated light is coupled into either TE or TM WGMs of the microsphere. Rayleigh backscattering, from imperfections in the silica microsphere, equilibrates degenerate counterpropagating WGMs. Rayleigh backscattered light is coupled into the fiber taper and detected using a photodetector (Fig. 1) [33,34]. In addition, WGM resonances are observed by monitoring the light transmitted through the tapered waveguide using a second photodetector. A spectrum of a typical WGM resonance, viewed simultaneously in backscatter and transmission modes, is shown in references [35,36]. Frequency locking of the diode laser was achieved using the Pound–Drever–Hall (PDH) technique , as described previously . The control signal was continuously acquired and is readily converted into the WGM frequency shift.
A distributed feedback (DFB) laser (Avanex 1905 LMI, linewidth: 2 MHz), amplified to a power of 9 mW using an erbium-doped fiber amplifier (Keopsys OI-BT-C-18-Sd-B-GP-FA), was employed to interrogate the microsphere. An ILX Lightwave ultra-low-noise current source (LDX-3620) was used with the DFB laser. At a fixed temperature, this laser can be continuously current tuned over a wavelength range of 0.15 nm. The laser output was sinusoidally intensity modulated using a Mach–Zehnder modulator (JDS Uniphase) to a maximum frequency of 20 MHz. A polarization controller positioned after the modulator allowed the TE or TM resonator mode to be selectively excited. The mode polarization was determined by placing an InGaAs detector [Detector (1): Thorlabs DET10C] above the microsphere and recording the scattered radiation through an IR polarizer.
WGM resonances were detected through the Rayleigh backscattering of light coupled into the delivery waveguide. It is well known that Rayleigh backscattering from imperfections in the silica microsphere quickly equilibrates degenerate counter-propagating cavity modes . A fiber-optic circulator directed the backscattered light to a fiber-coupled 150 MHz bandwidth InGaAs detector [Detector (2): Thorlabs PDA10CF]. Light transmitted though the delivery fiber was monitored using another InGaAs detector [Detector (3): Thorlabs DET10C]. RF lock-in amplifiers (Stanford Research Systems Model SR844) processed the detector outputs, providing intensity and phase angle measurements that were referenced to the laser intensity modulation.
A quartz crystal microbalance (QCM) was placed under the microsphere and taper. The fiber taper, microsphere, and microbalance sensor element were located under a glass dosing chamber into which EDA vapor was introduced. A low flow of nitrogen was passed over neat EDA (vapor pressure of 11.3 Torr at room temperature), carrying the vapor through a Teflon valve into the dosing chamber. This entire apparatus was contained within a Plexiglas enclosure and purged with dry nitrogen, which served to reduce contamination and the adsorption of water vapor onto the microsphere.
3. POUND–DREVER–HALL FREQUENCY LOCKING
To lock the laser to a WGM, we use the PDH method  as described earlier [38,39]. Briefly, the DFB laser is current modulated, resulting in a frequency modulation (FM) of 10–50 MHz in addition to the 1–20 MHz amplitude modulation (AM) described above. When the resulting detector signal, which contains the beat notes at the FM frequency, is mixed with the FM oscillator and low-pass filtered, a dispersive-like error signal is obtained that is returned to the laser driver and used to lock the laser center frequency.
We select the FM frequency such that the error signal remains proportional to the derivative of the WGM line shape, i.e., we work in a regime in which the modulation frequency is small compared to the WGM linewidth. The polarity of the error signal indicates the relative tuning of the laser with respect to the resonance center frequency. This signal is applied to a servo circuit, where it is amplified, integrated, and fed back to the current driver as a correction signal. As a consequence, the laser frequency locks tightly to the WGM resonance with an electrical bandwidth of 35 kHz. If the WGM shifts in frequency due to, for example, adsorption of molecules on the microsphere surface, the magnitude of the correction signal applied to the laser changes accordingly. Knowledge of the transfer function of the laser driver (mA/mV), as supplied by the manufacturer (ILX Lightwave), together with the measured tuning characteristics of the DFB laser (pm/mA), allows us to calculate the frequency shift from the control voltage change.
4. REAL-TIME MEASUREMENT OF THE SURFACE COVERAGE
The surface coverage of the silica sphere with EDA was measured simultaneously using both the frequency shift of the WGM and a QCM. The QCM was positioned directly below the fiber taper and microsphere. The surface of the quartz crystal supports a gold electrode, which occupies about 25% of the surface area. While the gold electrode of the QCM presents a different surface compared to the silica microsphere, both are expected to adsorb EDA and coverages may be compared. Surface coverages of the QCM were calculated from the quartz crystal resonance shifts using the Sauerbrey equation . An analog-to-digital converter was used to simultaneously measure the servo-control voltage, the QCM frequency, the backscattered signal intensity, and the phase angles from the lock-in amplifiers, while the laser was locked to the WGM. These values were displayed, and simultaneously recorded, on a computer through a LabView program (Fig. 2).
We note that with a number of assumptions it is also possible to independently determine the coverage from the wavelength shift of the WGM. Teraoka and co-workers have derived an expression describing the wavelength shift of a WGM due to molecules adsorbed on a microsphere surface [10,19,41]. Their calculation is based on the polarization induced in an adsorbed molecule by the evanescent tail of the WGM. Using a perturbation approach for calculating the wavelength shift induced by a change, , in the dielectric medium external to the microsphere with radius , they derived the expression for the fractional change in the TE-mode wave vector (see also Appendix A):
For the first-order TM mode one requires a correction term,1) can be used to relate the wavelength shift , to the surface coverage, . The transverse component of the polarizability of the adsorbed molecule, , and the radial component of the polarizability, , depend on the components of the polarizability tensor and on the orientation of the adsorbed molecule on the surface . Using calculated values for the diagonal tensor components for gas phase EDA, it can be shown that varies by, at most, 6% from the isotropic polarizability value of EDA () . Hence, orientation effects can be ignored in this case. Also, given the low concentration of EDA, the thermal conductivity of the vapor surrounding the microsphere differs insignificantly from that of pure nitrogen present before the dosing. Therefore, frequency shifts due to a change in thermal conductivity are expected to be negligible.
5. RESULTS AND ANALYSIS
Figures 2(a) and 2(b) give the surface coverage values obtained from the QCM and those calculated from the WGM resonance wavelength shift using Eq. (1). The maximum dosage level indicated by the QCM is a factor of 4 greater than that based on the WGM wavelength shift. This difference is not surprising, since the microsphere surface is atomically smooth silica, whereas the sensitive region of the QCM is principally a comparably rough evaporated gold surface.
It has been shown that gold reversibly adsorbs amines  in a manner highly dependent on surface roughness. We therefore use the more reliable coverages obtained from Eq. (1) instead of the values given by the QCM. It is also known that EDA adsorbs strongly to silica through interaction with surface silanol groups . Given the response from the QCM [Fig. 2(a)], we can assume that in our case the observed perturbations of the WGM cavity resonance are due to adsorbed EDA, rather than vapor. In addition, we have to consider that water adsorbs to silica and the silica surface may originally be covered with a few monolayers of water that are partially displaced by EDA.
As can be seen in Fig. 2(a), the QCM response is discretized due to its 1 Hz frequency resolution, whereas the microsphere frequency shift is continuous. Figure 2(b) also shows that upon exposing the sphere to EDA, the WGM resonance frequency shifts to longer wavelengths as expected.
EDA adsorbs onto silica through interactions with surface silanol groups, which are the major surface species, even in the presence of water vapor . The average surface density of silanol groups on silica is estimated at , which suggests that, based on the resonance shift data, about four monolayers of EDA are deposited on the microsphere over the course of this experiment. By comparison, the “footprint” of an EDA molecule in the bulk liquid phase can be estimated from the density () and the molar mass () as , which is somewhat larger than expected from the ab initio “diameter” of the isolated molecule (). The density of the bulk EDA layers () is therefore comparable to the surface density of the silanol groups (about ).
Figure 2(b) shows a pronounced change in deposition rate after about two monolayers were deposited. We speculate that the fast formation of the first two monolayers is driven by the strong hydrogen bonds between the silanol groups and the amine moiety of the EDA, whereas the slower formation of the next two monolayers is governed by weaker EDA/EDA interactions. It has been shown that EDA strongly binds through chemisorption on silica via a proton transfer reaction with the surface silanol groups . Additional physisorbed layers will bond through amine hydrogen bonding interactions, which have a lower energy on the order of . The oscillations in Figs. 2(c) and 2(d) were found to occur in almost all dosing experiments and are not yet understood. While we expect that the frequency shift (coverage), as well as absorption and coupling coefficients, will approach an asymptotic value given by the vapor pressure of the gas, the free energy of adsorption, and the temperature of the gas and the substrate, it is not required that this limit is reached monotonously. The oscillations may then be a reflection of reorientation and spatial redistribution processes.
In our experiment, optical absorption of EDA through its N–H stretch overtone band at 1549 nm is measured with the PS-CRD technique. In a previous application of the phase-shift technique to microspheres, the ring-cavity model of Rezac  was used to calculate the phase shift observed in the light transmitted through the delivery fiber . This transmitted light represents the superposition of a portion of the incident field and the forward scattered field of the microsphere. The phase shift observed in the transmitted light is given by 35,36].
The coupling constant, , was assumed to remain unchanged throughout the adsorption process. This was verified experimentally by measuring the frequency-dependent phase shift of a microsphere WGM with first a clean surface and then a surface covered by approximately two monolayers of EDA. It was found that the ringdown time decreased with dosing, as expected, while the coupling constant, , remained unchanged (Fig. 3). It appears that the clockwise/counterclockwise modal coupling is dominated by intrinsic scattering centers within the microsphere and not by adsorbed species on the microsphere surface.
From Eq. (4) one expects that the phase shift of the intensity-modulated backscattered light varies approximately linearly with the AM frequency for low modulation frequencies, . For high modulation frequencies deviations from linearity are expected, as described in Ref. . A fit of the phase-shift values obtained at different AM frequencies to Eq. (4) yields the ringdown time and the coupling constant . The quality factor is given by (Fig. 3), where is the optical frequency of the light.
Based on the ringdown time at zero coverage, the -factor is for the particular TE mode used. Calculating -factors based on ringdown time eliminates complications due to thermal effects, which are known to influence -factor determinations based on linewidth measurements .
By recording the phase shift in transmission mode, , and backscatter mode, , simultaneously at a fixed , one can use Eqs. (3)–(5) to calculate the ringdown time (), the absorption coefficient (), and the coupling coefficient () throughout the dosing process [Figs. 2(c) and 2(d)]. These measurements can then be correlated to the coverage of the microsphere with EDA, which is obtained from the frequency shift [Fig. 2(b)] to obtain Fig. 4.
6. PHOTOTHERMAL EFFECTS
Photothermal effects, such as desorption of EDA upon heating of the sphere on resonance, have to be considered. When the laser is locked on a WGM resonance, imperfections in the microsphere absorb part of the circulating light, leading to heating of the microsphere. We found that with increasing input power, the resonance shifts to longer wavelengths, and attribute that shift to an increase in the microsphere’s temperature . Using published values for the thermo-optic coefficient and linear expansion coefficient of silica , it is estimated that the temperature of the microsphere is higher than the QCM when the laser is locked to the WGM resonance. Given the relatively high binding energies involved, the 10 K temperature increase of the microsphere is expected to have a negligible effect on the degree of adsorption of the first two monolayers but may affect the physisorbed EDA layers at higher coverage.
In Fig. 4(a) the coupling coefficient, , governing the interaction between the taper and the microsphere resonator is seen to increase linearly until a coverage of about , i.e., roughly two monolayers, is reached. This may appear surprising, since, to the best of our knowledge, in all previous studies the coupling parameter is assumed to be independent of the surface coverage. It appears that this premise is not necessarily true. The change of with the surface coverage may be explained by the adsorbed layer of EDA on the sphere and fiber that will, especially in the narrow fiber taper, influence the index of the propagated mode and thereby the phase-matching condition.
As expected, the overtone absorption, , increases approximately linearly but is then found to decrease gradually as more than about one or two monolayers are deposited [Fig. 4(b)]. Oscillations of the absorption were observed beyond about two monolayers of coverage and presently lack a definitive explanation. These oscillations may be due to restructuring and reorientation of the adsorbate layers as a function of surface coverage. Oscillations were observed in all experiments but were sometimes found at lower coverages.
The overtone absorption cross section of one monolayer is estimated fromB).
Using the value for the absorption coefficient at one monolayer of coverage (), the experimental absorption cross section is calculated as . By comparison, the bulk absorption cross section of EDA liquid at 1550 nm is . For molecules as small as EDA, light attenuation by scattering is negligible .
The small difference between the measured cross section and the bulk value is readily explained. We emphasize that many of the values used in this estimate of the absorption cross section, such as , , , and , have errors estimated to be in the 10%–20% range, and even the bulk absorption cross section of liquid EDA, , , may be slightly inaccurate.
Using Eq. (6) one can readily calculate the molecular absorption cross section at other coverages [Fig. 4(c)]. We find a gradual decrease in the absorption cross section after a coverage of one or two monolayers has been reached. This effect can again be explained using reorientation effects, or possibly using clustering and island formation. The TE-WGM used in this experiment has its electric field parallel to the microsphere surface. As a consequence, N–H bonds oriented parallel to the surface will be preferentially excited. Deviation from this optimal orientation will cause a reduced interaction with the mode field and reduced absorption. While it may appear that oscillations at submonolayer coverages are then attributable to a reorientation of the surface-bound amine group, one has to consider that the unbound amine group remains free to rotate. Similarly, the decrease in the apparent absorption cross section at higher coverage is likely not due to orientation effects, which cannot explain an absorption cross section that is so much lower than the bulk value. Other geometric effects such as a reduced density of the topmost layer appear to be a more likely cause for the decreased effective absorption cross section. Since we are dealing with only a few layers of molecules, it is possible that subsequent deposition may affect already deposited layers, causing a reconstruction of layers that interact more or less favorably with the microresonator field, and thereby lead to a variable absorption cross section.
By analogy to the adsorption isotherms of ammonia on silica , we expect that the interaction of EDA with surface silanol groups on the thermally annealed silica sphere results in an initial chemisorbed layer, which is strongly bound by hydrogen bonds or by electrostatic interactions after proton transfer (Fig. 5). Subsequent layers are physisorbed. It is therefore likely that EDA follows a Brunauer–Emmett–Teller-type adsorption isotherm. This hypothesis is consistent with the reduced effective absorption cross section after about two monolayers are formed [Fig. 4(c)].
When benchmarking the sensitivity of the PS-CRD measurements against those reported before, we calculate from Fig. 2(c) or Fig. 4(b) that the minimal detectable absorption loss is about , or . From Eq. (4) one can determine that the smallest quantifiable absorption cross section is . Assuming a coverage of (i.e., one particle in the evanescent mode volume), it is then apparent that one should be able to perform an absolute measurement of the absorption cross section of a single particle with this method as long as the optical loss per particle exceeds (). This absorption cross section and the molecular dimensions are comparable to those of, e.g., single gold nanoparticles, or the scattering cross sections of aerosol particles. We therefore propose that the present method is a viable route to absolute absorption or scattering measurements of single particles.
The above method requires some prior knowledge about the adsorbed molecule. To determine the absorption cross section as was done here, one needs a reliable value for the transverse polarizability (TE mode) or both transverse and radial polarizabilities (TM mode). For most molecules with a flexible carbon frame, the value for the isotropic polarizability is expected to be quite similar to both values and is readily accessible through the refractive index and, e.g., the Clausius–Mosotti relation. Of course, one may invert the problem and calculate the polarizability from a known absorption cross section.
APPENDIX A: DERIVATION OF EQ. (1)
Teraoka et al. have derived an expression describing the wavelength shift of a WGM due to molecules adsorbed on a microsphere surface [10,19,41]. Their calculation is based on the polarization induced in an adsorbed molecule by the evanescent tail of the WGM. The interaction energy between the induced dipole and the evanescent field provides a first-order correction to the WGM energy. Using a perturbation approach for calculating the wavelength shift induced by a change, , in the dielectric medium external to the microsphere, they derived the following expression for the fractional change in the wave vector:A2) can be related to the surface coverage, , through the equation 42]. Equations (1) and (A3) depend on the value of the transverse polarizability of the adsorbed molecule for TE modes and on both radial and transverse polarizabilities for TM modes. In our case of EDA, theoretical values are available for the diagonalized polarizability tensor components . From these values we determined the transverse and radial polarizability components as and , respectively. Our estimate for the isotropic polarizability of is therefore close to the value for and also agrees well with the isotropic polarizability calculated from the refractive index using the Clausius–Mosotti relation, . Note that in all calculations the small correction to the real part of the complex polarizability due to the absorption band at 1550 nm was neglected.
APPENDIX B: ESTIMATE OF THE VOLUME FRACTION, , OF THE EVANESCENT WAVE IN EQ. (6)
To estimate the fraction of the WGM volume that interacts with the adsorbed molecular layer, we require the fraction of the WGM propagating in the evanescent wave. Assuming first that the layer is homogeneous and thick compared to the penetration depth of the evanescent wave, we can, for a TE mode, write the ratio of the evanescent field to the field inside the sphere as 54] and made use of the evanescent field decay length .
The refractive index of the microresonator sphere material at was calculated from the Sellmeier coefficients for silica as . Assuming that a sphere with a 300 μm diameter is suspended in vacuum (), only 0.14% of the TE-WGM field is in the evanescent wave. This number increases to 1.3% if the surrounding medium is water () and 7.3% if .
The present case is slightly more complicated, since the WGM interacts only with the thin EDA layer of subwavelength thickness with a refractive index that is close to that of the silica microsphere, . Given that only a small fraction of the WGM power resides in air, we can approximate the fraction of the TE mode field in the overlayer as the ratio between the field in the EDA layer and that inside the sphere, i.e., asB2). For a TM-polarized WGM the fraction, , depends on the value assumed for , and the expression is more complicated.
Consiglio Nazionale delle Ricerche; Natural Sciences and Engineering Research Council of Canada (NSERC).
We thank John Saunders for writing the LabView program and Saverio Avino for his contributions to the PDH-laser locking setup.
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