Abstract

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 σmin=2.7×1012cm2. 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

1. INTRODUCTION

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 [3], 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 [4]. Of course, surface-enhanced Raman scattering [5,6], surface-plasmon-resonance-enhanced detection [7], 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 [818]. 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 (Q) factor [20] and can be retrieved either from the reduction of power that is transferred to the resonator mode [21], 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 [22]. 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 [19] 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 [23] 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 [29], 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), H2NCH2CH2NH2, that is adsorbed on the surface of a high-Q 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 [32], 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 [30].

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 [37], as described previously [38]. The control signal was continuously acquired and is readily converted into the WGM frequency shift.

 figure: Fig. 1.

Fig. 1. Schematic representation of the experimental setup. The output of a distributed feedback (DFB) laser at 1549 nm is directed through an optical isolator and an erbium-doped fiber amplifier to a Mach–Zehnder modulator. The polarization of the amplitude-modulated beam is then polarization controlled before being coupled into a silica microsphere resonator. The Rayleigh backscattered light is directed though a circulator to a photodetector (PD) (3). The intensity and phase of the signal from the PD is measured using a lock-in amplifier. Photodiode (2) and another lock-in amplifier are used to measure the intensity and phase of light that is transmitted through the fiber taper. The backscattered light is also used to lock the center frequency of the laser to the cavity resonance with the Pound–Drever–Hall (PDH) method. The coverage is obtained from the frequency shift of the WGM as described below. The FM and AM frequencies are kept sufficiently different to allow the lock-in amplifiers to accurately extract intensity and, simultaneously, phase angle values without cross talk. Typically the Rayleigh-backscattered signal is used to lock the laser to the WGM resonance.

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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 [34]. 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 5cm3 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 [37] 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 [40]. 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).

 figure: Fig. 2.

Fig. 2. Response of WGM to dosing of EDA onto the silica microsphere surface. Very low concentrations of EDA have been mixed into a stream of dry nitrogen starting at t=300s. (a) Frequency response of the QCM. The readout is digitized with 1 Hz resolution. (b) Wavelength shift, δλ, of the WGM resonance as measured by the correction voltage supplied to the PDH-locked DFB laser, (c) absorption coefficient, αm, and (d) coupling coefficient, κ, calculated from the observed phase shifts and Eqs. (3)–(5).

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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, δεr, in the dielectric medium external to the microsphere with radius R, they derived the expression for the fractional change in the TE-mode wave vector (see also Appendix A):

(δkk0)TE=αtθε0R1(n12n22).

For the first-order TM mode one requires a correction term,

(δkk0)TM(δkk0)TE[2(n2n1)2],
and would have to use both the tangential and the radial component to the polarizability instead of αt as is appropriate for a TE mode. This expression holds for a surface layer that is much thinner than the wavelength of the light—as is the case in the present experiments. Here, n1=1.444 is the microsphere refractive index, and n2=1.0 is that of the surroundings. If the refractive index of the adsorbed material is assumed constant, Eq. (1) can be used to relate the wavelength shift δλ/λ0=δk/k0, to the surface coverage, θ. The transverse component of the polarizability of the adsorbed molecule, αt, and the radial component of the polarizability, αr, depend on the components of the polarizability tensor and on the orientation of the adsorbed molecule on the surface [42]. Using calculated values for the diagonal tensor components for gas phase EDA, it can be shown that αt varies by, at most, 6% from the isotropic polarizability value of EDA (αiso=6.7×1024cm3) [43]. 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 [44] 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 [32]. 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 [32]. The average surface density of silanol groups on silica is estimated at 4.9nm2 [45], 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 (0.9g/mL) and the molar mass (60.1g/mol) as 0.23nm2/molecule, which is somewhat larger than expected from the ab initio “diameter” of the isolated molecule (0.13nm2/molecule). The density of the bulk EDA layers (47molecules/nm2) is therefore comparable to the surface density of the silanol groups (about 4.9nm2).

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 [32]. Additional physisorbed layers will bond through amine hydrogen bonding interactions, which have a lower energy on the order of 13kJ/mole [46]. 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 [47] was used to calculate the phase shift observed in the light transmitted through the delivery fiber [30]. 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 [30]

ΔΦtrans=2tan1[ΩneffL2c2lnΓ(lnΓ)2(αmL/2)2],
where Ω is the angular laser intensity modulation frequency, neff is the effective refractive index of the WGM, L is the circumference of the microsphere, κ=1Γ2 is the coupling constant between the taper and microsphere, and αm is the attenuation coefficient.

In addition, we also recorded the phase shift of the backscattered field. It has been shown recently that the phase shift for the backscattered light is [35,36]

ΔΦbs=2tan1[2Ω/τΩ2(1/τ2+1/γ2)],
where τ is the ringdown time of the microsphere, given as
τ=Lneffc0(αmL2lnΓ),
and γ is the coupling constant between near-degenerate clockwise and counterclockwise WGMs [35,36].

The coupling constant, γ, 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, γ, 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.

 figure: Fig. 3.

Fig. 3. Observed phase delay of the amplitude-modulated light of a WGM of a clean microresonator (solid black circles) and after dosing (open blue circles). From a fit to Eq. (4) (lines), ringdown times of τ=12.3±0.2 and 11.4±0.2ns were obtained, respectively. At a vacuum wavelength of 1.549 μm (ν=1.93×1014Hz), this corresponds to a Q-factor of about 1.5×107. The coupling constants of γ=31±3 and 30±4ns were unchanged.

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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, Ω. For high modulation frequencies deviations from linearity are expected, as described in Ref. [35]. A fit of the phase-shift values obtained at different AM frequencies to Eq. (4) yields the ringdown time τ and the coupling constant γ. The quality factor is given by Q=2πντ (Fig. 3), where ν is the optical frequency of the light.

Based on the ringdown time at zero coverage, the Q-factor is 1.5×107 for the particular TE mode used. Calculating Q-factors based on ringdown time eliminates complications due to thermal effects, which are known to influence Q-factor determinations based on linewidth measurements [48].

By recording the phase shift in transmission mode, ΔΦtrans, and backscatter mode, ΔΦbs, simultaneously at a fixed Ω, one can use Eqs. (3)–(5) to calculate the ringdown time (τ), the absorption coefficient (αm), and the coupling coefficient (κ) 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.

 figure: Fig. 4.

Fig. 4. Data shown in Fig. 2 were processed using Eqs. (3)–(5) to obtain (a) the coupling coefficient, κ, (b) the attenuation coefficient, αm, and (c) the molecular absorption cross section, σ, as a function of the surface coverage, which was calculated from the frequency shift of the WGM [Fig. 2(b)] and Eq. (4). The vertical dashed line indicates the approximate coverage corresponding to one monolayer, and the horizontal line in (c) indicates the absorption cross section of bulk liquid EDA, σbulk.

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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 [49]. Using published values for the thermo-optic coefficient and linear expansion coefficient of silica [50], it is estimated that the temperature of the microsphere is 10K 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.

7. DISCUSSION

In Fig. 4(a) the coupling coefficient, κ, governing the interaction between the taper and the microsphere resonator is seen to increase linearly until a coverage of about 10molecules/nm2, 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 κ 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, αm, 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 from

σ=(αmα0)lEDAfthinθ,
where α0=0.0020cm1 is the optical loss of the WGM before dosing, lEDA=360pm is the estimated length of an EDA molecule and our estimate for the thickness of one monolayer, and fthin=1.05×105 is the fraction of the TE-WGM interacting with a film of 360 pm thickness (see Appendix B).

Using the value for the absorption coefficient at one monolayer of coverage (θ=4.9×1014molecules/cm2), the experimental absorption cross section is calculated as σ=2.7×1021cm2. By comparison, the bulk absorption cross section of EDA liquid at 1550 nm is σbulk=2.9×1021cm2 [51]. For molecules as small as EDA, light attenuation by scattering is negligible [52].

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 lEDA, f, θ, and αmL, have errors estimated to be in the 10%–20% range, and even the bulk absorption cross section of liquid EDA, σbulk, [51], 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 [53], 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)].

 figure: Fig. 5.

Fig. 5. Schematic depiction of EDA molecules adsorbed to silica through either hydrogen bonding to a surface silanol group (left molecule), electrostatic interactions following proton transfer (right), or weak dispersion forces (top). (Image inspired by Fig. 3 of Ref. [32]).

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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 αmin=5×105cm1, or αminL=4.2×106. From Eq. (4) one can determine that the smallest quantifiable absorption cross section is σmin=2.7×1012cm2. Assuming a coverage of θ=1/1500μm2 (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 σmin=2.7×1012cm2 (270nm2). 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, δεr, in the dielectric medium external to the microsphere, they derived the following expression for the fractional change in the wave vector:

(δkk0)=VpδεrE0*·Epdr2VεrE0*·E0dr,
where E0 is the unperturbed field of the microsphere and Ep is the perturbed field. The integral in the numerator is over the volume of the external perturbing medium, and that in the denominator is over all space. This expression applies to both TE and TM modes. For the adsorption of a thin layer (ΔRλ0) of molecules onto a microsphere of radius R, this expression reduces to
(δkk0)TE=1R(n12n22)RR+ΔR(np(r)2n22)dr,
where n1=1.444 is the microsphere’s refractive index, n2=1.0 is that of the surrounding air, and np(r) is that of the adsorbed material, here EDA. If the refractive index of the adsorbed material is assumed constant, Eq. (A2) can be related to the surface coverage, σ, through the equation
(δkk0)TE=αtσε0R1(n12n22),
where αt is the transverse polarizability of the adsorbed molecule. The transverse component of the polarizability depends on the components of the polarizability tensor and on the orientation of the adsorbed molecule on the surface [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 [43]. From these values we determined the transverse and radial polarizability components as 6.7×1024cm3<αt<7.1×1024cm3 and 5.7×1024cm3<αr<6.6×1024cm3, respectively. Our estimate for the isotropic polarizability of 6.7×1024cm3 is therefore close to the value for αt and also agrees well with the isotropic polarizability calculated from the refractive index using the Clausius–Mosotti relation, 7.0×1024cm3. 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, f, 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 [19]

fthick=εmr=Rjl2(k0nsR)exp(2(rR)/rev)r2drϕ=02πθ=0π[Ylm(ϕ,θ)]2sinθdθdϕεsr=0Rjl2(k0nsr)r2drϕ=02πθ=0π[Ylm(ϕ,θ)]2sinθdθdϕε0nm2jl2(k0nsR)r=Rexp(2(rR)/rev)r2drε0ns2jl2(k0nsR)R32ns2nm2ns2(R2rev/2+Rrev2/2+rev3/4)2R3nm2ns2nm2revRnm2ns2nm2λ02πRnm2(ns2nm2)3/2,
where we integrated the spherical Bessel function jl according to Lam et al. [54] and made use of the evanescent field decay length rev(λ0/2π)(ns2nm2)1/2R.

The refractive index of the microresonator sphere material at λ=1.55μm was calculated from the Sellmeier coefficients for silica as ns=1.444. Assuming that a sphere with a 300 μm diameter is suspended in vacuum (nm=1), 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 (nm=1.31) and 7.3% if nm=1.40.

The present case is slightly more complicated, since the WGM interacts only with the thin EDA layer of subwavelength thickness with a refractive index nEDA=1.4413 that is close to that of the silica microsphere, ns. 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., as

fthinεEDAr=RR+ΔRjl2(k0nsR)r2drϕ=02πθ=0π[Ylm(ϕ,θ)]2sinθdθdϕεsr=0R+ΔRjl2(k0nsr)r2drϕ=02πθ=0π[Ylm(ϕ,θ)]2sinθdθdϕε0nEDA2jl2(k0nsR)((R+ΔR)33R33)ε0ns2jl2(k0ns(R+ΔR))(R+ΔR)32ns2nm2ns223(R+ΔR)3R3(R+ΔR)3nEDA2ns2nm2.
Here, we assumed that the field (value of the squared spherical Bessel function) is constant over the thickness of the EDA layer and that nsnEDA. Using ns=1.4439, nEDA=1.4413, nm=1.0,R=136μm, and, for one monolayer, ΔR=0.36nm, one obtains fthin=1.05×105 independent of the wavelength of the light. The actual fraction of the total WGM residing in the overlayer is slightly less, since we neglected the fraction of the light traveling outside the overlayer in the denominator of Eq. (B2). For a TM-polarized WGM the fraction, f, depends on the value assumed for l, and the expression is more complicated.

FUNDING INFORMATION

Consiglio Nazionale delle Ricerche; Natural Sciences and Engineering Research Council of Canada (NSERC).

ACKNOWLEDGMENTS

We thank John Saunders for writing the LabView program and Saverio Avino for his contributions to the PDH-laser locking setup.

REFERENCES

1. J. Goldwin, M. Trupke, J. Kenner, A. Ratnapala, and E. A. Hinds, “Fast cavity-enhanced atom detection with low noise and high fidelity,” Nat. Commun. 2, 418 (2011). [CrossRef]  

2. M. Pirchi, G. Ziv, I. Riven, S. S. Cohen, N. Zohar, Y. Barak, and G. Haran, “Single-molecule fluorescence spectroscopy maps the folding landscape of a large protein,” Nat. Commun. 2, 493 (2011). [CrossRef]  

3. X. J. G. Xu, M. Rang, I. M. Craig, and M. B. Raschke, “Pushing the sample-size limit of infrared vibrational nanospectroscopy: from monolayer toward single molecule sensitivity,” J. Phys. Chem. Lett. 3, 1836–1841 (2012). [CrossRef]  

4. M. Celebrano, P. Kukura, A. Renn, and V. Sandoghdar, “Single-molecule imaging by optical absorption,” Nat. Photonics 5, 95–98 (2011). [CrossRef]  

5. P. G. Etchegoin and E. C. Le Ru, “A perspective on single molecule SERS: current status and future challenges,” Phys. Chem. Chem. Phys. 10, 6079–6089 (2008). [CrossRef]  

6. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997). [CrossRef]  

7. P. Zijlstra, P. M. R. Paulo, and M. Orrit, “Optical detection of single non-absorbing molecules using the surface plasmon resonance of a gold nanorod,” Nat. Nanotechnol. 7, 379–382 (2012). [CrossRef]  

8. A. M. Armani, “Label-free, single-molecule detection with optical microcavities (August, pg 783, 2007),” Science 334, 1496 (2011). [CrossRef]  

9. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007). [CrossRef]  

10. I. Teraoka, S. Arnold, and F. Vollmer, “Perturbation approach to resonance shifts of whispering-gallery modes in a dielectric microsphere as a probe of a surrounding medium,” J. Opt. Soc. Am. B 20, 1937–1946 (2003). [CrossRef]  

11. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008). [CrossRef]  

12. M. Pelton, M. Z. Liu, H. Y. Kim, G. Smith, P. Guyot-Sionnest, and N. E. Scherer, “Optical trapping and alignment of single gold nanorods by using plasmon resonances,” Opt. Lett. 31, 2075–2077 (2006). [CrossRef]  

13. J. Zhu, S. K. Ozdemir, L. He, D. R. Chen, and L. Yang, “Single virus and nanoparticle size spectrometry by whispering-gallery-mode microcavities,” Opt. Express 19, 16195–16206 (2011). [CrossRef]  

14. J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010). [CrossRef]  

15. J. D. Swaim, J. Knittel, and W. P. Bowen, “Detection of nanoparticles with a frequency locked whispering gallery mode microresonator,” Appl. Phys. Lett. 102, 183106 (2013). [CrossRef]  

16. L. Stern, I. Goykhman, B. Desiatov, and U. Levy, “Frequency locked micro disk resonator for real time and precise monitoring of refractive index,” Opt. Lett. 37, 1313–1315 (2012). [CrossRef]  

17. T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. USA 108, 5976–5979 (2011). [CrossRef]  

18. V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, and S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101, 043704 (2012). [CrossRef]  

19. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272–274 (2003). [CrossRef]  

20. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996). [CrossRef]  

21. G. Farca, S. I. Shopova, and A. T. Rosenberger, “Cavity-enhanced laser absorption spectroscopy using microresonator whispering-gallery modes,” Opt. Express 15, 17443–17448 (2007). [CrossRef]  

22. A. C. R. Pipino, J. P. M. Hoefnagels, and N. Watanabe, “Absolute surface coverage measurement using a vibrational overtone,” J. Chem. Phys. 120, 2879–2888 (2004). [CrossRef]  

23. M. Mazurenka, A. J. Orr-Ewing, R. Peverall, and G. A. D. Ritchie, “Cavity ring-down and cavity enhanced spectroscopy using diode lasers,” Ann. Rep. Prog. Chem. C 101, 100–142 (2005). [CrossRef]  

24. A. C. R. Pipino, “Ultrasensitive surface spectroscopy with a miniature optical resonator,” Phys. Rev. Lett. 83, 3093–3096 (1999). [CrossRef]  

25. V. S. Ilchenko, X. S. Yao, and L. Maleki, “Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery modes,” Opt. Lett. 24, 723–725 (1999). [CrossRef]  

26. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003). [CrossRef]  

27. J. M. Herbelin, J. A. McKay, M. A. Kwok, R. H. Ueunten, D. S. Urevig, D. J. Spencer, and D. J. Benard, “Sensitive measurement of photon lifetime and true reflectances in an optical cavity by a phase-shift method,” Appl. Opt. 19, 144–147 (1980). [CrossRef]  

28. R. Engeln, G. von Helden, G. Berden, and G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105–109 (1996). [CrossRef]  

29. Z. G. Tong, A. Wright, T. McCormick, R. K. Li, R. D. Oleschuk, and H. P. Loock, “Phase-shift fiber-loop ring-down spectroscopy,” Anal. Chem. 76, 6594–6599 (2004). [CrossRef]  

30. J. A. Barnes, B. Carver, J. M. Fraser, G. Gagliardi, H. P. Loock, Z. Tian, M. Wilson, S. S. H. Yam, and O. Yastrubshak, “Loss determination in microsphere resonators by phase-shift cavity ring-down measurements,” Opt. Express 16, 13158–13167 (2008). [CrossRef]  

31. M. I. Cheema, S. Mehrabani, A. A. Hayat, Y. A. Peter, A. M. Armani, and A. G. Kirk, “Simultaneous measurement of quality factor and wavelength shift by phase shift microcavity ring down spectroscopy,” Opt. Express 20, 9090–9098 (2012). [CrossRef]  

32. M. Xu, D. F. Liu, and H. C. Allen, “Ethylenediamine at air/liquid and air/silica interfaces: protonation versus hydrogen bonding investigated by sum frequency generation spectroscopy,” Environ. Sci. Technol. 40, 1566–1572 (2006). [CrossRef]  

33. M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B 17, 1051–1057 (2000). [CrossRef]  

34. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669–1671 (2002). [CrossRef]  

35. J. A. Barnes, G. Gagliardi, and H. P. Loock, “Phase-shift cavity ring-down spectroscopy on a microresonator by Rayleigh backscattering,” Phys. Rev. A 87, 053843 (2013). [CrossRef]  

36. J. A. Barnes, G. Gagliardi, and H. P. Loock, “Erratum: Phase-shift cavity ring-down spectroscopy on a microsphere resonator by Rayleigh backscattering [Phys. Rev. A 87, 053843 (2013)],” Phys. Rev. A 88, 059905 (2013). [CrossRef]  

37. E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys. 69, 79–87 (2001). [CrossRef]  

38. S. Avino, J. A. Barnes, G. Gagliardi, X. J. Gu, D. Gutstein, J. R. Mester, C. Nicholaou, and H. P. Loock, “Musical instrument pickup based on a laser locked to an optical fiber resonator,” Opt. Express 19, 25057–25065 (2011). [CrossRef]  

39. G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010). [CrossRef]  

40. V. Tsionsky and E. Gileadi, “Use of the quartz crystal microbalance for the study of adsorption from the gas phase,” Langmuir 10, 2830–2835 (1994). [CrossRef]  

41. I. Teraoka and S. Arnold, “Theory of resonance shifts in TE and TM whispering gallery modes by nonradial perturbations for sensing applications,” J. Opt. Soc. Am. B 23, 1381–1389 (2006). [CrossRef]  

42. I. Teraoka and S. Arnold, “Estimation of surface density of molecules adsorbed on a whispering gallery mode resonator: utility of isotropic polarizability,” J. Appl. Phys. 102, 076109 (2007). [CrossRef]  

43. L. V. Lanshina, M. N. Rodnikova, and K. T. Dudnikova, “Structure of liquid ethylene diamine according to data on molecular-scattering of light,” J. Struct. Chem. 30, 684–687 (1990). [CrossRef]  

44. M. T. S. R. Gomes, M. I. S. Verissimo, and J. A. B. P. Oliveira, “Detection of volatile amines using a quartz crystal with gold electrodes,” Sens. Actuators B 57, 261–267 (1999). [CrossRef]  

45. V. Dong, S. V. Pappu, and Z. Xu, “Detection of local density distributions of isolated silanol groups on planar silica surfaces using nonlinear optical molecular probes,” Anal. Chem. 70, 4730–4735 (1998). [CrossRef]  

46. J. D. Lambert and E. D. T. Strong, “The dimerization of ammonia and amines,” Proc. R. Soc. A 200, 566–572 (1950). [CrossRef]  

47. J. Rezac, “Properties and applications of whispering-gallery mode resonances in fused silica microspheres,” Ph.D. thesis (Oklahoma State University, 2002).

48. C. Schmidt, A. Chipouline, T. Pertsch, A. Tunnermann, O. Egorov, F. Lederer, and L. Deych, “Nonlinear thermal effects in optical microspheres at different wavelength sweeping speeds,” Opt. Express 16, 6285–6301 (2008). [CrossRef]  

49. J. A. Barnes, H. P. Loock, and G. Gagliardi, “Phase shift cavity ring-down measurements on silica sphere microresponators,” in Cavity Enhanced Spectroscopy and Sensing, H. P. Loock and G. Gagliardi, eds. (Springer, 2013).

50. G. Adamovsky, S. F. Lyuksyutov, J. R. Mackey, B. M. Floyd, U. Abeywickrema, I. Fedin, and M. Rackaitis, “Peculiarities of thermo-optic coefficient under different temperature regimes in optical fibers containing fiber Bragg gratings,” Opt. Commun. 285, 766–773 (2012). [CrossRef]  

51. M. Buback and H. P. Vogele, FT-NIR Atlas (VCH, 1993).

52. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).

53. B. Fubini, V. Bolis, A. Cavenago, E. Garrone, and P. Ugliengo, “Structural and induced heterogeneity at the surface of some SiO2 polymorphs from the enthalpy of adsorption of various molecules,” Langmuir 9, 2712–2720 (1993). [CrossRef]  

54. C. C. Lam, P. T. Leung, and K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992). [CrossRef]  

References

  • View by:

  1. J. Goldwin, M. Trupke, J. Kenner, A. Ratnapala, E. A. Hinds, “Fast cavity-enhanced atom detection with low noise and high fidelity,” Nat. Commun. 2, 418 (2011).
    [Crossref]
  2. M. Pirchi, G. Ziv, I. Riven, S. S. Cohen, N. Zohar, Y. Barak, G. Haran, “Single-molecule fluorescence spectroscopy maps the folding landscape of a large protein,” Nat. Commun. 2, 493 (2011).
    [Crossref]
  3. X. J. G. Xu, M. Rang, I. M. Craig, M. B. Raschke, “Pushing the sample-size limit of infrared vibrational nanospectroscopy: from monolayer toward single molecule sensitivity,” J. Phys. Chem. Lett. 3, 1836–1841 (2012).
    [Crossref]
  4. M. Celebrano, P. Kukura, A. Renn, V. Sandoghdar, “Single-molecule imaging by optical absorption,” Nat. Photonics 5, 95–98 (2011).
    [Crossref]
  5. P. G. Etchegoin, E. C. Le Ru, “A perspective on single molecule SERS: current status and future challenges,” Phys. Chem. Chem. Phys. 10, 6079–6089 (2008).
    [Crossref]
  6. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
    [Crossref]
  7. P. Zijlstra, P. M. R. Paulo, M. Orrit, “Optical detection of single non-absorbing molecules using the surface plasmon resonance of a gold nanorod,” Nat. Nanotechnol. 7, 379–382 (2012).
    [Crossref]
  8. A. M. Armani, “Label-free, single-molecule detection with optical microcavities (August, pg 783, 2007),” Science 334, 1496 (2011).
    [Crossref]
  9. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
    [Crossref]
  10. I. Teraoka, S. Arnold, F. Vollmer, “Perturbation approach to resonance shifts of whispering-gallery modes in a dielectric microsphere as a probe of a surrounding medium,” J. Opt. Soc. Am. B 20, 1937–1946 (2003).
    [Crossref]
  11. F. Vollmer, S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
    [Crossref]
  12. M. Pelton, M. Z. Liu, H. Y. Kim, G. Smith, P. Guyot-Sionnest, N. E. Scherer, “Optical trapping and alignment of single gold nanorods by using plasmon resonances,” Opt. Lett. 31, 2075–2077 (2006).
    [Crossref]
  13. J. Zhu, S. K. Ozdemir, L. He, D. R. Chen, L. Yang, “Single virus and nanoparticle size spectrometry by whispering-gallery-mode microcavities,” Opt. Express 19, 16195–16206 (2011).
    [Crossref]
  14. J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
    [Crossref]
  15. J. D. Swaim, J. Knittel, W. P. Bowen, “Detection of nanoparticles with a frequency locked whispering gallery mode microresonator,” Appl. Phys. Lett. 102, 183106 (2013).
    [Crossref]
  16. L. Stern, I. Goykhman, B. Desiatov, U. Levy, “Frequency locked micro disk resonator for real time and precise monitoring of refractive index,” Opt. Lett. 37, 1313–1315 (2012).
    [Crossref]
  17. T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. USA 108, 5976–5979 (2011).
    [Crossref]
  18. V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101, 043704 (2012).
    [Crossref]
  19. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272–274 (2003).
    [Crossref]
  20. M. L. Gorodetsky, A. A. Savchenkov, V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996).
    [Crossref]
  21. G. Farca, S. I. Shopova, A. T. Rosenberger, “Cavity-enhanced laser absorption spectroscopy using microresonator whispering-gallery modes,” Opt. Express 15, 17443–17448 (2007).
    [Crossref]
  22. A. C. R. Pipino, J. P. M. Hoefnagels, N. Watanabe, “Absolute surface coverage measurement using a vibrational overtone,” J. Chem. Phys. 120, 2879–2888 (2004).
    [Crossref]
  23. M. Mazurenka, A. J. Orr-Ewing, R. Peverall, G. A. D. Ritchie, “Cavity ring-down and cavity enhanced spectroscopy using diode lasers,” Ann. Rep. Prog. Chem. C 101, 100–142 (2005).
    [Crossref]
  24. A. C. R. Pipino, “Ultrasensitive surface spectroscopy with a miniature optical resonator,” Phys. Rev. Lett. 83, 3093–3096 (1999).
    [Crossref]
  25. V. S. Ilchenko, X. S. Yao, L. Maleki, “Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery modes,” Opt. Lett. 24, 723–725 (1999).
    [Crossref]
  26. D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
    [Crossref]
  27. J. M. Herbelin, J. A. McKay, M. A. Kwok, R. H. Ueunten, D. S. Urevig, D. J. Spencer, D. J. Benard, “Sensitive measurement of photon lifetime and true reflectances in an optical cavity by a phase-shift method,” Appl. Opt. 19, 144–147 (1980).
    [Crossref]
  28. R. Engeln, G. von Helden, G. Berden, G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105–109 (1996).
    [Crossref]
  29. Z. G. Tong, A. Wright, T. McCormick, R. K. Li, R. D. Oleschuk, H. P. Loock, “Phase-shift fiber-loop ring-down spectroscopy,” Anal. Chem. 76, 6594–6599 (2004).
    [Crossref]
  30. J. A. Barnes, B. Carver, J. M. Fraser, G. Gagliardi, H. P. Loock, Z. Tian, M. Wilson, S. S. H. Yam, O. Yastrubshak, “Loss determination in microsphere resonators by phase-shift cavity ring-down measurements,” Opt. Express 16, 13158–13167 (2008).
    [Crossref]
  31. M. I. Cheema, S. Mehrabani, A. A. Hayat, Y. A. Peter, A. M. Armani, A. G. Kirk, “Simultaneous measurement of quality factor and wavelength shift by phase shift microcavity ring down spectroscopy,” Opt. Express 20, 9090–9098 (2012).
    [Crossref]
  32. M. Xu, D. F. Liu, H. C. Allen, “Ethylenediamine at air/liquid and air/silica interfaces: protonation versus hydrogen bonding investigated by sum frequency generation spectroscopy,” Environ. Sci. Technol. 40, 1566–1572 (2006).
    [Crossref]
  33. M. L. Gorodetsky, A. D. Pryamikov, V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B 17, 1051–1057 (2000).
    [Crossref]
  34. T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669–1671 (2002).
    [Crossref]
  35. J. A. Barnes, G. Gagliardi, H. P. Loock, “Phase-shift cavity ring-down spectroscopy on a microresonator by Rayleigh backscattering,” Phys. Rev. A 87, 053843 (2013).
    [Crossref]
  36. J. A. Barnes, G. Gagliardi, H. P. Loock, “Erratum: Phase-shift cavity ring-down spectroscopy on a microsphere resonator by Rayleigh backscattering [Phys. Rev. A 87, 053843 (2013)],” Phys. Rev. A 88, 059905 (2013).
    [Crossref]
  37. E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys. 69, 79–87 (2001).
    [Crossref]
  38. S. Avino, J. A. Barnes, G. Gagliardi, X. J. Gu, D. Gutstein, J. R. Mester, C. Nicholaou, H. P. Loock, “Musical instrument pickup based on a laser locked to an optical fiber resonator,” Opt. Express 19, 25057–25065 (2011).
    [Crossref]
  39. G. Gagliardi, M. Salza, S. Avino, P. Ferraro, P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
    [Crossref]
  40. V. Tsionsky, E. Gileadi, “Use of the quartz crystal microbalance for the study of adsorption from the gas phase,” Langmuir 10, 2830–2835 (1994).
    [Crossref]
  41. I. Teraoka, S. Arnold, “Theory of resonance shifts in TE and TM whispering gallery modes by nonradial perturbations for sensing applications,” J. Opt. Soc. Am. B 23, 1381–1389 (2006).
    [Crossref]
  42. I. Teraoka, S. Arnold, “Estimation of surface density of molecules adsorbed on a whispering gallery mode resonator: utility of isotropic polarizability,” J. Appl. Phys. 102, 076109 (2007).
    [Crossref]
  43. L. V. Lanshina, M. N. Rodnikova, K. T. Dudnikova, “Structure of liquid ethylene diamine according to data on molecular-scattering of light,” J. Struct. Chem. 30, 684–687 (1990).
    [Crossref]
  44. M. T. S. R. Gomes, M. I. S. Verissimo, J. A. B. P. Oliveira, “Detection of volatile amines using a quartz crystal with gold electrodes,” Sens. Actuators B 57, 261–267 (1999).
    [Crossref]
  45. V. Dong, S. V. Pappu, Z. Xu, “Detection of local density distributions of isolated silanol groups on planar silica surfaces using nonlinear optical molecular probes,” Anal. Chem. 70, 4730–4735 (1998).
    [Crossref]
  46. J. D. Lambert, E. D. T. Strong, “The dimerization of ammonia and amines,” Proc. R. Soc. A 200, 566–572 (1950).
    [Crossref]
  47. J. Rezac, “Properties and applications of whispering-gallery mode resonances in fused silica microspheres,” Ph.D. thesis (Oklahoma State University, 2002).
  48. C. Schmidt, A. Chipouline, T. Pertsch, A. Tunnermann, O. Egorov, F. Lederer, L. Deych, “Nonlinear thermal effects in optical microspheres at different wavelength sweeping speeds,” Opt. Express 16, 6285–6301 (2008).
    [Crossref]
  49. J. A. Barnes, H. P. Loock, G. Gagliardi, “Phase shift cavity ring-down measurements on silica sphere microresponators,” in Cavity Enhanced Spectroscopy and Sensing, H. P. Loock, G. Gagliardi, eds. (Springer, 2013).
  50. G. Adamovsky, S. F. Lyuksyutov, J. R. Mackey, B. M. Floyd, U. Abeywickrema, I. Fedin, M. Rackaitis, “Peculiarities of thermo-optic coefficient under different temperature regimes in optical fibers containing fiber Bragg gratings,” Opt. Commun. 285, 766–773 (2012).
    [Crossref]
  51. M. Buback, H. P. Vogele, FT-NIR Atlas (VCH, 1993).
  52. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).
  53. B. Fubini, V. Bolis, A. Cavenago, E. Garrone, P. Ugliengo, “Structural and induced heterogeneity at the surface of some SiO2 polymorphs from the enthalpy of adsorption of various molecules,” Langmuir 9, 2712–2720 (1993).
    [Crossref]
  54. C. C. Lam, P. T. Leung, K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992).
    [Crossref]

2013 (3)

J. D. Swaim, J. Knittel, W. P. Bowen, “Detection of nanoparticles with a frequency locked whispering gallery mode microresonator,” Appl. Phys. Lett. 102, 183106 (2013).
[Crossref]

J. A. Barnes, G. Gagliardi, H. P. Loock, “Phase-shift cavity ring-down spectroscopy on a microresonator by Rayleigh backscattering,” Phys. Rev. A 87, 053843 (2013).
[Crossref]

J. A. Barnes, G. Gagliardi, H. P. Loock, “Erratum: Phase-shift cavity ring-down spectroscopy on a microsphere resonator by Rayleigh backscattering [Phys. Rev. A 87, 053843 (2013)],” Phys. Rev. A 88, 059905 (2013).
[Crossref]

2012 (6)

M. I. Cheema, S. Mehrabani, A. A. Hayat, Y. A. Peter, A. M. Armani, A. G. Kirk, “Simultaneous measurement of quality factor and wavelength shift by phase shift microcavity ring down spectroscopy,” Opt. Express 20, 9090–9098 (2012).
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L. Stern, I. Goykhman, B. Desiatov, U. Levy, “Frequency locked micro disk resonator for real time and precise monitoring of refractive index,” Opt. Lett. 37, 1313–1315 (2012).
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X. J. G. Xu, M. Rang, I. M. Craig, M. B. Raschke, “Pushing the sample-size limit of infrared vibrational nanospectroscopy: from monolayer toward single molecule sensitivity,” J. Phys. Chem. Lett. 3, 1836–1841 (2012).
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P. Zijlstra, P. M. R. Paulo, M. Orrit, “Optical detection of single non-absorbing molecules using the surface plasmon resonance of a gold nanorod,” Nat. Nanotechnol. 7, 379–382 (2012).
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G. Adamovsky, S. F. Lyuksyutov, J. R. Mackey, B. M. Floyd, U. Abeywickrema, I. Fedin, M. Rackaitis, “Peculiarities of thermo-optic coefficient under different temperature regimes in optical fibers containing fiber Bragg gratings,” Opt. Commun. 285, 766–773 (2012).
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2011 (7)

S. Avino, J. A. Barnes, G. Gagliardi, X. J. Gu, D. Gutstein, J. R. Mester, C. Nicholaou, H. P. Loock, “Musical instrument pickup based on a laser locked to an optical fiber resonator,” Opt. Express 19, 25057–25065 (2011).
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M. Celebrano, P. Kukura, A. Renn, V. Sandoghdar, “Single-molecule imaging by optical absorption,” Nat. Photonics 5, 95–98 (2011).
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T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. USA 108, 5976–5979 (2011).
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J. Zhu, S. K. Ozdemir, L. He, D. R. Chen, L. Yang, “Single virus and nanoparticle size spectrometry by whispering-gallery-mode microcavities,” Opt. Express 19, 16195–16206 (2011).
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J. Goldwin, M. Trupke, J. Kenner, A. Ratnapala, E. A. Hinds, “Fast cavity-enhanced atom detection with low noise and high fidelity,” Nat. Commun. 2, 418 (2011).
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M. Pirchi, G. Ziv, I. Riven, S. S. Cohen, N. Zohar, Y. Barak, G. Haran, “Single-molecule fluorescence spectroscopy maps the folding landscape of a large protein,” Nat. Commun. 2, 493 (2011).
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2010 (2)

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
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G. Gagliardi, M. Salza, S. Avino, P. Ferraro, P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
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2008 (4)

2007 (3)

G. Farca, S. I. Shopova, A. T. Rosenberger, “Cavity-enhanced laser absorption spectroscopy using microresonator whispering-gallery modes,” Opt. Express 15, 17443–17448 (2007).
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A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
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I. Teraoka, S. Arnold, “Estimation of surface density of molecules adsorbed on a whispering gallery mode resonator: utility of isotropic polarizability,” J. Appl. Phys. 102, 076109 (2007).
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2006 (3)

2005 (1)

M. Mazurenka, A. J. Orr-Ewing, R. Peverall, G. A. D. Ritchie, “Cavity ring-down and cavity enhanced spectroscopy using diode lasers,” Ann. Rep. Prog. Chem. C 101, 100–142 (2005).
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2004 (2)

A. C. R. Pipino, J. P. M. Hoefnagels, N. Watanabe, “Absolute surface coverage measurement using a vibrational overtone,” J. Chem. Phys. 120, 2879–2888 (2004).
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Z. G. Tong, A. Wright, T. McCormick, R. K. Li, R. D. Oleschuk, H. P. Loock, “Phase-shift fiber-loop ring-down spectroscopy,” Anal. Chem. 76, 6594–6599 (2004).
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2003 (3)

2002 (1)

2001 (1)

E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys. 69, 79–87 (2001).
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2000 (1)

1999 (3)

A. C. R. Pipino, “Ultrasensitive surface spectroscopy with a miniature optical resonator,” Phys. Rev. Lett. 83, 3093–3096 (1999).
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V. S. Ilchenko, X. S. Yao, L. Maleki, “Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery modes,” Opt. Lett. 24, 723–725 (1999).
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1998 (1)

V. Dong, S. V. Pappu, Z. Xu, “Detection of local density distributions of isolated silanol groups on planar silica surfaces using nonlinear optical molecular probes,” Anal. Chem. 70, 4730–4735 (1998).
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1997 (1)

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
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1996 (2)

M. L. Gorodetsky, A. A. Savchenkov, V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996).
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1994 (1)

V. Tsionsky, E. Gileadi, “Use of the quartz crystal microbalance for the study of adsorption from the gas phase,” Langmuir 10, 2830–2835 (1994).
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1993 (1)

B. Fubini, V. Bolis, A. Cavenago, E. Garrone, P. Ugliengo, “Structural and induced heterogeneity at the surface of some SiO2 polymorphs from the enthalpy of adsorption of various molecules,” Langmuir 9, 2712–2720 (1993).
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1992 (1)

1990 (1)

L. V. Lanshina, M. N. Rodnikova, K. T. Dudnikova, “Structure of liquid ethylene diamine according to data on molecular-scattering of light,” J. Struct. Chem. 30, 684–687 (1990).
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M. Xu, D. F. Liu, H. C. Allen, “Ethylenediamine at air/liquid and air/silica interfaces: protonation versus hydrogen bonding investigated by sum frequency generation spectroscopy,” Environ. Sci. Technol. 40, 1566–1572 (2006).
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A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
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Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
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J. A. Barnes, G. Gagliardi, H. P. Loock, “Phase-shift cavity ring-down spectroscopy on a microresonator by Rayleigh backscattering,” Phys. Rev. A 87, 053843 (2013).
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S. Avino, J. A. Barnes, G. Gagliardi, X. J. Gu, D. Gutstein, J. R. Mester, C. Nicholaou, H. P. Loock, “Musical instrument pickup based on a laser locked to an optical fiber resonator,” Opt. Express 19, 25057–25065 (2011).
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E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys. 69, 79–87 (2001).
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Chen, D. R.

J. Zhu, S. K. Ozdemir, L. He, D. R. Chen, L. Yang, “Single virus and nanoparticle size spectrometry by whispering-gallery-mode microcavities,” Opt. Express 19, 16195–16206 (2011).
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J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
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X. J. G. Xu, M. Rang, I. M. Craig, M. B. Raschke, “Pushing the sample-size limit of infrared vibrational nanospectroscopy: from monolayer toward single molecule sensitivity,” J. Phys. Chem. Lett. 3, 1836–1841 (2012).
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V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101, 043704 (2012).
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K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
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V. Dong, S. V. Pappu, Z. Xu, “Detection of local density distributions of isolated silanol groups on planar silica surfaces using nonlinear optical molecular probes,” Anal. Chem. 70, 4730–4735 (1998).
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L. V. Lanshina, M. N. Rodnikova, K. T. Dudnikova, “Structure of liquid ethylene diamine according to data on molecular-scattering of light,” J. Struct. Chem. 30, 684–687 (1990).
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R. Engeln, G. von Helden, G. Berden, G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105–109 (1996).
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K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
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T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. USA 108, 5976–5979 (2011).
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G. Adamovsky, S. F. Lyuksyutov, J. R. Mackey, B. M. Floyd, U. Abeywickrema, I. Fedin, M. Rackaitis, “Peculiarities of thermo-optic coefficient under different temperature regimes in optical fibers containing fiber Bragg gratings,” Opt. Commun. 285, 766–773 (2012).
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Fraser, S. E.

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. USA 108, 5976–5979 (2011).
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B. Fubini, V. Bolis, A. Cavenago, E. Garrone, P. Ugliengo, “Structural and induced heterogeneity at the surface of some SiO2 polymorphs from the enthalpy of adsorption of various molecules,” Langmuir 9, 2712–2720 (1993).
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J. A. Barnes, G. Gagliardi, H. P. Loock, “Erratum: Phase-shift cavity ring-down spectroscopy on a microsphere resonator by Rayleigh backscattering [Phys. Rev. A 87, 053843 (2013)],” Phys. Rev. A 88, 059905 (2013).
[Crossref]

J. A. Barnes, G. Gagliardi, H. P. Loock, “Phase-shift cavity ring-down spectroscopy on a microresonator by Rayleigh backscattering,” Phys. Rev. A 87, 053843 (2013).
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S. Avino, J. A. Barnes, G. Gagliardi, X. J. Gu, D. Gutstein, J. R. Mester, C. Nicholaou, H. P. Loock, “Musical instrument pickup based on a laser locked to an optical fiber resonator,” Opt. Express 19, 25057–25065 (2011).
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G. Gagliardi, M. Salza, S. Avino, P. Ferraro, P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
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J. A. Barnes, B. Carver, J. M. Fraser, G. Gagliardi, H. P. Loock, Z. Tian, M. Wilson, S. S. H. Yam, O. Yastrubshak, “Loss determination in microsphere resonators by phase-shift cavity ring-down measurements,” Opt. Express 16, 13158–13167 (2008).
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B. Fubini, V. Bolis, A. Cavenago, E. Garrone, P. Ugliengo, “Structural and induced heterogeneity at the surface of some SiO2 polymorphs from the enthalpy of adsorption of various molecules,” Langmuir 9, 2712–2720 (1993).
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J. Goldwin, M. Trupke, J. Kenner, A. Ratnapala, E. A. Hinds, “Fast cavity-enhanced atom detection with low noise and high fidelity,” Nat. Commun. 2, 418 (2011).
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J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
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V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101, 043704 (2012).
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K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
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J. Goldwin, M. Trupke, J. Kenner, A. Ratnapala, E. A. Hinds, “Fast cavity-enhanced atom detection with low noise and high fidelity,” Nat. Commun. 2, 418 (2011).
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T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. USA 108, 5976–5979 (2011).
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V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101, 043704 (2012).
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A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
[Crossref]

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref]

Sens. Actuators B (1)

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[Crossref]

Other (4)

J. Rezac, “Properties and applications of whispering-gallery mode resonances in fused silica microspheres,” Ph.D. thesis (Oklahoma State University, 2002).

J. A. Barnes, H. P. Loock, G. Gagliardi, “Phase shift cavity ring-down measurements on silica sphere microresponators,” in Cavity Enhanced Spectroscopy and Sensing, H. P. Loock, G. Gagliardi, eds. (Springer, 2013).

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Figures (5)

Fig. 1.
Fig. 1. Schematic representation of the experimental setup. The output of a distributed feedback (DFB) laser at 1549 nm is directed through an optical isolator and an erbium-doped fiber amplifier to a Mach–Zehnder modulator. The polarization of the amplitude-modulated beam is then polarization controlled before being coupled into a silica microsphere resonator. The Rayleigh backscattered light is directed though a circulator to a photodetector (PD) (3). The intensity and phase of the signal from the PD is measured using a lock-in amplifier. Photodiode (2) and another lock-in amplifier are used to measure the intensity and phase of light that is transmitted through the fiber taper. The backscattered light is also used to lock the center frequency of the laser to the cavity resonance with the Pound–Drever–Hall (PDH) method. The coverage is obtained from the frequency shift of the WGM as described below. The FM and AM frequencies are kept sufficiently different to allow the lock-in amplifiers to accurately extract intensity and, simultaneously, phase angle values without cross talk. Typically the Rayleigh-backscattered signal is used to lock the laser to the WGM resonance.
Fig. 2.
Fig. 2. Response of WGM to dosing of EDA onto the silica microsphere surface. Very low concentrations of EDA have been mixed into a stream of dry nitrogen starting at t=300s. (a) Frequency response of the QCM. The readout is digitized with 1 Hz resolution. (b) Wavelength shift, δλ, of the WGM resonance as measured by the correction voltage supplied to the PDH-locked DFB laser, (c) absorption coefficient, αm, and (d) coupling coefficient, κ, calculated from the observed phase shifts and Eqs. (3)–(5).
Fig. 3.
Fig. 3. Observed phase delay of the amplitude-modulated light of a WGM of a clean microresonator (solid black circles) and after dosing (open blue circles). From a fit to Eq. (4) (lines), ringdown times of τ=12.3±0.2 and 11.4±0.2ns were obtained, respectively. At a vacuum wavelength of 1.549 μm (ν=1.93×1014Hz), this corresponds to a Q-factor of about 1.5×107. The coupling constants of γ=31±3 and 30±4ns were unchanged.
Fig. 4.
Fig. 4. Data shown in Fig. 2 were processed using Eqs. (3)–(5) to obtain (a) the coupling coefficient, κ, (b) the attenuation coefficient, αm, and (c) the molecular absorption cross section, σ, as a function of the surface coverage, which was calculated from the frequency shift of the WGM [Fig. 2(b)] and Eq. (4). The vertical dashed line indicates the approximate coverage corresponding to one monolayer, and the horizontal line in (c) indicates the absorption cross section of bulk liquid EDA, σbulk.
Fig. 5.
Fig. 5. Schematic depiction of EDA molecules adsorbed to silica through either hydrogen bonding to a surface silanol group (left molecule), electrostatic interactions following proton transfer (right), or weak dispersion forces (top). (Image inspired by Fig. 3 of Ref. [32]).

Equations (11)

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(δkk0)TE=αtθε0R1(n12n22).
(δkk0)TM(δkk0)TE[2(n2n1)2],
ΔΦtrans=2tan1[ΩneffL2c2lnΓ(lnΓ)2(αmL/2)2],
ΔΦbs=2tan1[2Ω/τΩ2(1/τ2+1/γ2)],
τ=Lneffc0(αmL2lnΓ),
σ=(αmα0)lEDAfthinθ,
(δkk0)=VpδεrE0*·Epdr2VεrE0*·E0dr,
(δkk0)TE=1R(n12n22)RR+ΔR(np(r)2n22)dr,
(δkk0)TE=αtσε0R1(n12n22),
fthick=εmr=Rjl2(k0nsR)exp(2(rR)/rev)r2drϕ=02πθ=0π[Ylm(ϕ,θ)]2sinθdθdϕεsr=0Rjl2(k0nsr)r2drϕ=02πθ=0π[Ylm(ϕ,θ)]2sinθdθdϕε0nm2jl2(k0nsR)r=Rexp(2(rR)/rev)r2drε0ns2jl2(k0nsR)R32ns2nm2ns2(R2rev/2+Rrev2/2+rev3/4)2R3nm2ns2nm2revRnm2ns2nm2λ02πRnm2(ns2nm2)3/2,
fthinεEDAr=RR+ΔRjl2(k0nsR)r2drϕ=02πθ=0π[Ylm(ϕ,θ)]2sinθdθdϕεsr=0R+ΔRjl2(k0nsr)r2drϕ=02πθ=0π[Ylm(ϕ,θ)]2sinθdθdϕε0nEDA2jl2(k0nsR)((R+ΔR)33R33)ε0ns2jl2(k0ns(R+ΔR))(R+ΔR)32ns2nm2ns223(R+ΔR)3R3(R+ΔR)3nEDA2ns2nm2.

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