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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 1, Iss. 11 — Nov. 13, 2006
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Finesse and sensitivity gain in cavity-enhanced absorption spectroscopy of biomolecules in solution

Timothy McGarvey, André Conjusteau, and Hideo Mabuchi  »View Author Affiliations


Optics Express, Vol. 14, Issue 22, pp. 10441-10451 (2006)
http://dx.doi.org/10.1364/OE.14.010441


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Abstract

We describe a ‘wet mirror’ apparatus for cw cavity-enhanced absorption measurements with Bacteriochlorophyll a (BChla) in solution and show that it achieves the full sensitivity gain (≈ 2.3 × 104) afforded by the finesse (3.4 × 104) and loss distribution of our optical resonator. This result provides an important proof-of-principle demonstration for solution-phase cavity-enhanced spectroscopy; straightforward extrapolation to a system with state-of-the-art low-loss mirrors and shot-noise-limited performance indicates that single molecule sensitivity in liquids is within reach of current technology. With the probe laser locked to the cavity resonance, our instrument achieves a sensitivity ≈ 3.4 × 10-8/√Hz (for a sample of length 1.75 mm) with 100 kHz bandwidth and can reliably detect sub-nM concentrations of BChla with 1 ms integration time.

© 2006 Optical Society of America

1. Introduction

Efforts to improve the sensitivity of solution-phase optical absorption spectroscopy are motivated by applications in label-free biosensing [1

1. R. E. Kunz, “Optimizing integrated optical chips for label-free (bio-)chemical sensing,” Anal. Bioanal. Chem. 384, 180–190 (2006); [CrossRef]

1. N. Kinrot and M. Nathan, “Investigation of a Periodically-Segmented Waveguide Fabry-Pérot Interferometer for Use as a Chemical/Biosensor,” J. Lightwave Technol. 24, 2139–2145 (2006).

] and in the characterization of low-concentration chemical reaction kinetics [2

2. A. J. Hallock, E. Berman, and R. N. Zare, “Ultratrace Kinetic Measurements of the Reduction of Methylene Blue,” J. Am. Chem. Soc. 125, 1158–1159 (2003). [CrossRef] [PubMed]

]. Approaches based on the use of high-finesse optical resonators are motivated by results achieved in analogous gas-phase experiments— experiments involving vibrational overtones of gas-phase molecules [3

3. J. Ye, L.-S. Ma, and J. L. Hall, “Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy,” J. Opt. Soc. Am. B 15, 6–15 (1998). [CrossRef]

] have achieved detection thresholds as low as 1.5 × 10-13/√Hz. For largely technical reasons, it has proven quite difficult for experiments on molecules in solution to approach such levels of sensitivity.

Here we present a significant technical advance in cw solution-phase optical absorption spectroscopy, in which we demonstrate that it is possible in practice to realize the full sensitivity gain that is made available via incorporation of a high-finesse Fabry-Perot cavity. In gas-phase experiments one can effectively take such finesse-limited sensitivity gains for granted, but the introduction of liquids into the intracavity volume can substantially complicate the requirements for performing reliable optical absorption measurements. In our scenario with a Fabry-Perot resonator, e.g., mechanical and thermal stability of the cavity are substantially compromised by the presence of liquid between the mirrors. Mechanical couplings and hydrodynamic phenomena associated with sample injection likewise introduce various difficulties that would not arise in an analogous gas-phase experiment. Setups based on evanescent-wave coupling to light circulating in a dielectric resonator [4

4. A. C. R. Pipino, “Monolithic folded resonator for evanescent wave cavity ringdown spectroscopy,” Appl. Opt. 39, 1449–1453 (2000). [CrossRef]

, 5

5. J. L. Nadeau, V. S. Ilchenko, D. Kossokovski, G. H. Bearman, and L. Maleki, “High-Q whispering-gallery mode sensor in liquids,” Proc. SPIE 4629, 172–180 (2002). [CrossRef]

] are less vulnerable to such effects, but would seem to have an ultimate sensitivity disadvantage as the molecules of interest can access only a weak tail of the optical mode function.

Our experiment incorporates a short (l = 1.75 mm) high-finesse (F 0 ≈ 5 × 104 when empty) Fabry-Perot resonator that is entirely filled with liquid sample, such that the mirror surfaces are in direct contact with fluid. This type of ‘wet mirror’ configuration (which is similar to that of Van der Sneppen et al. [6

6. L. van der Sneppen, A. Wiskerke, F. Ariese, C. Gooijer, and W. Ubachs, “Improving the sensitivity of HPLC absorption detection by cavity ring-down spectroscopy in a liquid-only cavity” Anal. Chim. Acta 558, 2–6 (2006). [CrossRef]

]) allows us to avoid the presence of optically-lossy surfaces within the cavity, and preserves the full finesse afforded by mirror losses provided the solvent itself has sufficiently low absorption. In the work described here we chose to test our instrument’s performance with ultra-dilute samples of Bacteriochlorophyll a (BChla) dissolved in d 6-acetone. We achieve an optical absorption sensitivity of ≈ 3.4 × 10-8/√Hz and find that with 1 ms integration time we are able reliably to measure BChla concentrations as low as ~ 200 pM. In comparison with other high-sensitivity optical absorption techniques that have been applied to liquid samples, such as cavity ring-down [7

7. S. Xu, G. Sha, and J. Xie, “Cavity ring-down spectroscopy in the liquid phase,” Rev. Sci. Instrum. 73, 255–258 (2002). [CrossRef]

, 8

8. K. L. Bechtel, R. N. Zare, A. A. Kachanov, S. S. Sanders, and B. A. Paldus, “Moving beyond Traditional UV-Visible Absorption Detection: Cavity Ring-Down Spectroscopy for HPLC,” Anal. Chem. 77, 1177–1182 (2005). [CrossRef] [PubMed]

, 6

6. L. van der Sneppen, A. Wiskerke, F. Ariese, C. Gooijer, and W. Ubachs, “Improving the sensitivity of HPLC absorption detection by cavity ring-down spectroscopy in a liquid-only cavity” Anal. Chim. Acta 558, 2–6 (2006). [CrossRef]

], incoherent broad-band cavity-enhanced absorption [9

9. S. E. Fiedler, A. Hese, and A. A. Ruth, “Incoherent broad-band cavity-enhanced absorption spectorscopy of liquids,” Rev. Sci. Instrum. 76, 023107 (2005). [CrossRef]

], thermal lens effect [10

10. M. E. Long, R. L. Swofford, and A. C. Albrecht, “Thermal Lens Technique - New Method of Absorption Spectroscopy,” Science 191, 183–185 (1976). [CrossRef] [PubMed]

] and photo-acoustic [11

11. C. K. N. Patel and A. C. Tam, “Pulsed optoacoustic spectroscopy of condensed matter,” Rev. Mod. Phys. 53, 517–550 (1981). [CrossRef]

] spectroscopy, we note that our approach achieves comparable (and is capable of better) sensitivity while requiring only small amounts of sample (several ml). In its current configuration, which exhibits a fair amount of excess technical noise, our setup has an absorption detection threshold ≈ 7 × 10-6 cm-1 with 1 ms integration time; further improvements to the laser and cavity stabilization would make it possible to approach a shot-noise-limited value ≈ 3.5 × 10-8 cm-1 (the works cited above report detection thresholds in the range ~ 10-5╌10-7 cm-1).

Fig. 1. Schematic diagram of the experimental setup. PBS: polarizing beam-splitter; NBPS: non-polarizing beam-splitter; λ/4: quarter-wave plate; HV: high voltage. See text for other designations.

Setting aside absolute sensitivity, however, we consider the main result of this paper to be the quantitative analysis that matches our observed sensitivity gain (≈ 2.3 × 104 relative to single-pass absorption) with theoretical predictions based on our cavity finesse 3.4 × 104 and internal losses. We believe that this agreement provides a proof of concept such that we may reasonably extrapolate a prediction of the performance that could be achieved with state-of-the-art low-loss mirrors and shot-noise-limited readout. In this way we find that sensitivities approaching 10-12/√Hz could be achievable, which would make room temperature, liquid-phase single-BChla-molecule absorption spectroscopy a real possibility (see Discussion). Such a setup would require a very short (l ~ 10 μm) cavity in order to suppress solvent-induced losses; this dimension emphasizes the possibility of integration with microfluidic sample delivery [12

12. F. J. Blanco, M. Agirregabiria, J. Berganzo, K. Mayora, J. Elizalde, A. Calle, C. Dominguez, and L. M. Lechuga, “Microfluidic-optical integrated CMOS compatible devicesfor label-free biochemical sensing,” J. Micromech. Microeng. 16, 1006–1016 (2006). [CrossRef]

].

2. Apparatus

A schematic of our setup is shown in Figure 1. The BChla-doped d 6-acetone sample is injected into the intracavity volume of a hermetically-sealed Fabry-Perot (FP) resonator (see below). A Verdi-pumped MBR-110 Titanium Sapphire laser (Ti:S) provides laser light at 783nm (cor responding to the Qy transition in BChla, with expected extinction coefficient ≈ 6 × 104 M-1 cm-1 in acetone [13

13. I. Eichwurzel, H. Stiel, K. Teuchner, D. Leupold, H. Scheer, Y. Salomon, and A. Scherz, “Photophysical Consequences of Coupling Bacteriochlorophyll a with Serine and its Resulting Solubility in Water,” Photochem. Photobiol. 72, 204–209 (2000); [CrossRef] [PubMed]

13. J. S. Connolly, E. B. Samuel, and A. F. Janzen, “Effects of solvent on the fluorescence properties of bacteriochlorophyll a,” Photochem. Photobiol. 36, 565–574 (1982).

]; the Qy peak sits at 770nm but our Ti:S did not operate stably there with the mirror set we have) for probing the cavity response. The Ti:S laser is pre-stabilized to an internal reference cavity and an acousto-optic modulator (AO) driven by a voltage-controlled oscillator (VCO) is utilized to produce a frequency-shifted beam that can be locked to the FP (with 100 kHz bandwidth). The error signal for the latter servo is derived by the usual demodulation of frequency modulation (FM) sidebands produced by an electro-optic modulator (EO). We additionally apply integral feedback to a piezo-electric actuator of the FP cavity length in order to compensate for slow drift. Some intensity stabilization is implemented via feedback to a variable-gain amplifier (VGA) on the rf input of the VCO driving the AO.

The beam reflected from the FP cavity is split and directed to two different photodetectors (PD): one for measuring and recording the time-dependent reflectivity and one for generating the FM error signal. Note that we used a rather weak probe beam (incident power 6 × 10-8 W, essentially the lowest at which we could stay locked to the cavity) in order to avoid potential nonlinearities; we therefore utilized avalanche photodiodes (APD’s) for both purposes (a Menlo Systems APD-210 for the error signal and a Hamamatsu C5460-01 for the data acquisition, neither of which operate in Geiger mode). The analog bandwidth of the data acquisition photodetector was 100 kHz and we digitized at 1 MHz sampling rate at 14 bit resolution.

The FP mirrors were fabricated by Research Electro-Optics (Boulder, Colorado), with specified loss < 20 ppm (in air) at a center wavelength of 770nm for the high-reflectivity coating run. The super-polished substrates had 10 cm radius of curvature. The mechanical assembly of the FP incorporates a solvent-tight glass window to allow optical access to one side of the cavity (fixed mirror), but the scanning-mirror side is sealed by a flexible sheet of (opaque) Kalrez; the piezo-actuator pushes the scanning mirror mount through the flexible Kalrez sheet. This construction allowed us to ensure that no solvent could reach the associated electrical components, but limited us to making optical reflection (as opposed to transmission) measurements for detecting intracavity absorption. A clean ‘plumbing’ system was integrated with the FP assembly so that solution could be pulled up through the cavity by applying suction from above (this proved to be the best technique for filling the cavity with bubble-free liquid sample). Great care had to be taken to ensure mechanical stability of the entire assembly and to suppress control vibrational coupling from the plumbing components. Also, since the solvent we employed (d 6-acetone) to carry the BChla molecules is sufficiently transparent only before prolonged exposure to air, we found it necessary to purge the cavity with dry nitrogen before each experiment.

3. Cavity-enhanced absorption measurements

Our discussion here will focus on characterizing the expected sensitivity gain in cavity-enhanced absorption measurements, with an implicit assumption that what one wants to achieve is the ability to measure absorption caused by a small number of molecules with as high a bandwidth as possible (which is quite different than in methods that achieve high sensitivity with long averaging times, such as [14

14. M. Tokeshi, M. Uchida, A. Hibara, T. Sawada, and T. Kitamori, “Determination of Subyoctomole Amounts of Nonfluorescent Molecules Using a Thermal Lens Microscope: Subsingle-Molecule Determination,” Anal. Chem. 73, 2112–2116 (2001). [CrossRef] [PubMed]

]). Ultimately, we hope that cavity-enhanced spectroscopy with ultra-high finesse can enable single molecule studies in which one continuously monitors the absorption of a non-fluorescing, wild-type molecule at one or more optical wavelengths to detect reactions or conformational changes in real time (as can already be done with strongly absorbing gas-phase alkali atoms [15

15. H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B 68, 1095–1108 (1999). [CrossRef]

]). Towards that end, the current study is mainly intended to demonstrate that high-finesse cavities can indeed be utilized for liquid-phase absorption spectroscopy, provided great care is taken to suppress background losses associated with solvent and sample containment.

3.1. Absorption estimators and the operational sensitivity gain

Consider a single-pass measurement of absorption in a sample of length l. We assume that the sample consists of dopant molecules suspend in a solvent, and that it is possible to make measurements of either plain solvent or doped solvent under otherwise identical conditions. If the power absorption coefficient of the substance of interest is α, and the solvent/sample-holder contribute background loss e -δ, we have a total transmitted power

Psp=Pinceδ
(1)

with undoped solvent and

Psp+=Pinceδeαl
(2)

with doped solvent. It is straightforward to estimate αl from measurements of P sp- and P sp+:

(αl)sp=In[Psp]In[Psp+].
(3)

The sensitivity of (αl)sp to uncertainties in the measured optical powers is easy to compute:

Δ(αl)sp={(αl)spPsp}ΔPsp+{(αl)spPsp+}ΔPsp+
(4)
=ΔPspPspΔPsp+Psp+.
(5)

We thus see that the fractional uncertainties in P sp- and P sp+ translate directly into absolute uncertainties in (αl)sp . Hence, for very small absorption, the detection threshold for single-pass measurement is equal to the fractional uncertainty of the optical power measurements. The aim of cavity-enhanced absorption is to improve upon this, i.e., to obtain a (much) lower detection threshold for the same sample length l and fractional uncertainty in measuring optical power.

Here we consider cavity-enhanced absorption measurements performed via detection of reflected optical power from a cavity of length l, filled with the liquid sample. (The reason for considering reflection rather than transmission measurements has to do with the way we chose to construct a cavity whose length can be controlled by a piezo-actuator and yet is completely leak-tight.) The reflected power is [16

16. A. E. Siegman, Lasers (University Science Books, Sausalito, 1986).

]

Pce=Pinc(r12grt)2r12(1grt)2,grt=r1r2eδ/2
(6)

with undoped solvent and

Pce+=Pinc(r12grt+)2r12(1grt+)2,grt+=r1r2eδ/2eαl=grteαl
(7)

with doped solvent. Here r 1 = √1-t12 and r 2 = √1-t22, where t12 and t22 are the power transmission coefficients of the first and second cavity mirror (we assume we are reflecting off of the first mirror), and δ includes background power losses from both the solvent and the mirror coatings. Note that the equation relating P ce+ and αl contains three other parameters, {P inc,r 1,grt-}. It is thus necessary to measure at least three additional quantities to form an estimator. In cavity-reflection measurements the most natural set is {P inc,P ce-,F -}, where F - is the cavity finesse with undoped solvent (see below). Tedious but straightforward calculations then yield a corresponding cavity-enhanced absorption estimator:

(αl)ce=In[1π2F1+π2FR]+In[Q+π2FR+Qπ2F],
(8)

where

RPcePinc,R+Pce+Pinc,Q1R+1R.
(9)

For αl ≪ 1 and to leading order in π/2F - this can be approximated by

(αl)ce=πF(R+R1R+)=πF(Pce+PcePincPce+).
(10)

If we want to account for a mode-matching efficiency ε < 1, we can set

PincεPinc,PcePrfl(1ε)Pinc,Pce+Prfl+(1ε)Pinc,
(11)
RPrfl(1ε)PincεPincRε,R+Prfl+(1ε)PincεPincR+ε,
(12)

where P rfl± represent the total power measured in reflection from the cavity with undoped and doped solvent. So then

(αl)ceπF(Prfl+(1ε)PincPrfl(1ε)PincεPincPrfl+(1ε)Pinc),
(13)

and similarly for the exact (αl)ce.

Returning now to the case ε = 1 for simplicity, we note that

(αl)cePce+=π2FPincPcePce+(PincPce+)2,
(14)
(αl)cePce+ΔPce+=π2F1R1R+R+1R+(ΔPce+Pce+).
(15)

From the latter expression we may thus define an ‘uncertainty suppression factor’ U ce≈:

(αl)cePce+ΔPce+=Uce1(ΔPce+Pce+).
(16)

Since we saw above that the corresponding uncertainty suppression factor of single-pass measurement is U sp = - 1, we conclude that the operational sensitivity gain of cavity-enhanced absorption relative to single-pass is

GopUceUsp=Uce=(π2F1R1R+R+1R+)1.
(17)

Under the mild condition {R -,R +} < 1/2, which implies r 1r 2 and δ + αlt1,22, we have

1R1R+R+1R+<2,
(18)

in which case the contribution of ∆P ce+ to ∆(αl)ce≈ is bounded by

(αl)cePce+ΔPce+<πF(ΔPce+Pce+).
(19)

Indeed, if αl ≪ 1 then R -R + and we can solve for the condition U ce≈ > F -, which requires

π21R1R+R+1R+π2R+1R+<1,
(20)

hence R + ≲ 0.4. Under this condition (which is still relatively mild, being satisfied, e.g., by δ = t12 = t22 and αlδ) we achieve a suppression ≳ F - in the effect of a fractional uncertainty in power measurement on our ability to estimate αl. Compared to the single-pass method, our detection threshold is thus smaller (better) by a factor of order F1 for the same sample length l and fractional power uncertainty.

For completeness we include

(αl)ceFΔF=πFRR+1R+(ΔFF),
(21)
(αl)cePincΔPinc=π2FRR+1R+11R+(ΔPincPinc),
(22)
(αl)cePceΔPce=π2FR1R+(ΔPcePce),
(23)

all of which have uncertainty suppression factors comparable to (in the case of P ce-) or better (in the case of F - and Pinc) than that for P ce+ considered above. The corresponding expressions are much more cumbersome, though still calculable, in case of ε < 1. For P ce+, for example,

(αl)cavPtr+ΔPtr+=π2F1Rε1R+εR+ε1R+ε(ΔPtr+Ptr+(1ε)Pinc),
(24)

where R ±ε are as defined in Eq. (12).

Note that in general we may assume F - and ε to be fixed parameters. As a result, any uncertainty about them will result in a corresponding ‘calibration’ uncertainty in cavity-enhanced measurement of αl. However, long as P inc can be held constant (presumably by some sort of active servo-control) and P ce- is well known (by virtue of long integration time in a ‘set-up’ phase of the experiment), it follows that ∆P ce+ will determine the overall measurement uncertainty. Ultimately one could hope to reach the shot-noise limited value,

ΔPce+Pce+(S/q)Pce+τ(S/q)Pce+τ=1(S/q)Pce+τ,
(25)
(αl)cePce+ΔPce+Uce1(S/q)Pce+τ.
(26)

Here S is the photodetection sensitivity (in units of A/W), q is the electron charge and τ is the integration time. Note that (S/q) is bounded above by the inverse photon energy (h̅ω)-1.

3.2. Theoretical sensitivity gain

Given a fractional uncertainty η in measuring optical power, we have

Δ(αl)ce=((αl)cePce+)ΔPce+((αl)cePce+)ηPce+,
(27)
Δ(αl)sp=((αl)spPsp+)ΔPsp+((αl)spPsp+)ηPsp+.
(28)

We can thus define a theoretical uncertainty suppression factor for each method,

Uth:ce=(Pce+(αl)cePce+)1=1lPce+(Pce+α)Pce+,
(29)
Uth:sp=(Psp+(αl)spPsp+)1=1lPsp+(Psp+α)Psp+.
(30)

Pce+=Pinc(r12grt+)2r12(1grt+)2,
(31)

we can compute

Pce+α=2lPincgrt+(r12grt+)(1r12)r12(1grt+)3,
(32)
(Pce+α)Pce+=2lPce+grt+(1r12)(1grt+)(r12grt+)
(33)
Uth:ce=2grt+(1r12)(1grt+)(r12grt+).
(34)

It follows that the theoretical sensitivity gain is

GthUth:ceUth:sp=2grt+(1r12)(1grt+)(r12grt+),
(35)

and it can be verified numerically that G thG op over an appropriate parameter range. The theoretical expression is useful for design purposes, whereas G op is more useful in evaluating the performance of laboratory devices since it can be computed from directly measurable quantities only.

Note that U th:ce can be used to provide a theoretical expression (analogous to the operational version, Eq. (26)) for the minimum measurable absorption:

Δ(αl)th:ceUth:ce1(S/q)Pce+τ
(36)
2(1grt)(r12grt)grt(1r12)(Pceτ)/(h̅ω).
(37)

3.3. Determination of finesse and mode-matching efficiency

Above we have presented several equations that account for the effects of imperfect mode-matching efficiency ε < 1. In practice it can be difficult to determine ε accurately, especially if one cavity mirror is physically inaccessible as in our hermetically sealed setup. Our approach was to match absorption estimates obtained at high BChla concentrations from the reflection dip, via Eq. (13), with estimates from the change in finesse, via Eq. (41) below (which does not depend on ε). At relatively high BChla concentrations (such that αl ≳ 2π/F -) both methods are reliable, whereas at low concentrations only the reflection dip yields precise measurements because the change-in-finesse approach is limited by laser/cavity jitter and nonlinearity of the piezo-actuator. Since ε is fixed by laser alignment, a determination from high-concentration measurements should remain valid for any αl.

L=1grt2(1r12)+(1r22)+δ,
(38)
L+=1grt+2(1r12)+(1r22)+δ+2αl.
(39)

Assuming the mirror and solvent losses are independent of the concentration of BChla, the resonance widths ∆f ± can be measured in the presence and absence of a given concentration of BChla to directly determine the loss it induces:

2πF+2πF=2π(Δf+Δf)=2αl,
(40)

so

(αl)Δf=π(Δf+Δf).
(41)

This estimator for the induced absorption does not depend on the TEM00 mode-matching efficiency, and may thus be used to calibrate ε in a reflection-dip measurement taken at the same concentration of BChla. Explicitly, we equate expression (13) for (αl)ce≈ to the measured value of (αl)f and solve for ε in terms of the measured quantities F -, Pinc, P ce- and P ce+.

4. Data Summary

Aside from the linear behavior at high concentrations, the salient feature of our data plot is the flattening at low concentrations. The flattening occurs because the absorption signal induced by very low concentrations dips below our technical noise floor for measuring the reflected optical power; at very low concentrations, the apparent absorption inferred from the data via the estimator (αl)ce≈ is dominated by the optical noise and is thus independent of the concentration. The concentration at which the data points begin to deviate from linear behavior thus indicates the detection threshold of our device, and is seen to be ~ 200 pM. The corresponding sensitivity gain relative to single-pass measurements, from Eq. (17), is G op ≈ 2.3 × 104 ≈ 2F -\/π.

Fig. 2. Cavity-enhanced estimate (αl)ce≈ versus nominal BChla concentration (see text).

5. Discussion

The shot-noise limit (dash-dot line in Fig. 2) actually sits below our demonstrated detection threshold by a factor ~ 200, meaning that much better performance could in principle be obtained in our setup without any changes to the FP cavity itself. With a finesse of 3.4 × 104 and mode-matched optical power of 60 nW, the shot-noise limited absorption detection threshold would be ~ 2 × 10-10/√Hz. With 1 s integration time this would correspond to ~ 200 BChla molecules in the cavity mode volume (which in our current device is ~ 10-5 cm3). The best commercially available mirrors achieve t12 + t22 ≈ 10-6 and δ ≈ 2.2 × 10-6 [17

17. G. Rempe, R. J. Thompson, H. J. Kimble, and R. Lalezari, “Measurement of ultralow losses in an optical interferometer,” Opt. Lett. 17, 363–365 (1992). [CrossRef] [PubMed]

]; assuming these parameters and adding solvent-induced losses of 5 × 10-7 (scaled from our existing device) for a cavity with l = 10 μm, we find P ce- ≈ 0.53P inc while the circulating power would be P circ ≈ 1.46 × 105 P inc [16

16. A. E. Siegman, Lasers (University Science Books, Sausalito, 1986).

]. With 1 m radius-of-curvature mirrors the intracavity spot size would be ≈ 1.7 × 10-12 cm2, so for a intracavity intensity of 105 W/cm2 (which should keep us below saturation [18

18. A. M. van Oijen, M. Ketelaars, J. Köhler, T. J. Aartsma, and J. Schmidt, “Spectroscopy of Individual Light-Harvesting 2 Complexes of Rhodopseudomonas acidophila: Diagonal Disorder, Intercomplex Heterogeneity, Spectral Diffusion, and Energy Transfer in the B800 Band,” Biophys. J. 78, 1570–1577 (2000). [CrossRef] [PubMed]

]) we could have P ce- ≈ 7 × 10-7 W. The shot-noise limited sensitivity would then be ≈ 1.5 × 10-12/√Hz. This would make it possible to monitor the absorption of an individual BChla molecule with ~ 2 kHz bandwidth (near the peak extinction coefficient ≈ 7 × 104 M-1 cm-1 at 770 nm). One potential technical issue with this extrapolation, however, is the question of what photothermal disturbances might arise at this level of circulating power and finesse; if they turn out to be significant then it could be interesting to investigate high-finesse, liquid-phase cavity-enhanced photothermal spectroscopy [19

19. H. A. Schuessler, S. H. Chen, Z. Rong, Z. C. Tang, and E. C. Benck, “Cavity-enhanced photothermal spec-troscopy: dynamics, sensitivity and spatial resolution,” Appl. Opt. 31, 2669–2677 (1992). [CrossRef] [PubMed]

, 20

20. E. D. Black, I. S. Grudinin, S. R. Rao, and K. G. Libbrecht, “Enhanced photothermal displacement spectroscopy for thin-film characterization using a Fabry-Perot resonator,” J. Appl. Phys. 95, 7655–7659 (2004). [CrossRef]

] as an alternative.

Acknowledgments

We thank Michael Armen for invaluable technical assistance, as well as Dirk Englund, Orkun Aiken and Muhammed Yildirim for contributions to early stages of this work. This research was supported by the National Science Foundation and the W. M. Keck Foundation.

References and links

1.

R. E. Kunz, “Optimizing integrated optical chips for label-free (bio-)chemical sensing,” Anal. Bioanal. Chem. 384, 180–190 (2006); [CrossRef]

N. Kinrot and M. Nathan, “Investigation of a Periodically-Segmented Waveguide Fabry-Pérot Interferometer for Use as a Chemical/Biosensor,” J. Lightwave Technol. 24, 2139–2145 (2006).

2.

A. J. Hallock, E. Berman, and R. N. Zare, “Ultratrace Kinetic Measurements of the Reduction of Methylene Blue,” J. Am. Chem. Soc. 125, 1158–1159 (2003). [CrossRef] [PubMed]

3.

J. Ye, L.-S. Ma, and J. L. Hall, “Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy,” J. Opt. Soc. Am. B 15, 6–15 (1998). [CrossRef]

4.

A. C. R. Pipino, “Monolithic folded resonator for evanescent wave cavity ringdown spectroscopy,” Appl. Opt. 39, 1449–1453 (2000). [CrossRef]

5.

J. L. Nadeau, V. S. Ilchenko, D. Kossokovski, G. H. Bearman, and L. Maleki, “High-Q whispering-gallery mode sensor in liquids,” Proc. SPIE 4629, 172–180 (2002). [CrossRef]

6.

L. van der Sneppen, A. Wiskerke, F. Ariese, C. Gooijer, and W. Ubachs, “Improving the sensitivity of HPLC absorption detection by cavity ring-down spectroscopy in a liquid-only cavity” Anal. Chim. Acta 558, 2–6 (2006). [CrossRef]

7.

S. Xu, G. Sha, and J. Xie, “Cavity ring-down spectroscopy in the liquid phase,” Rev. Sci. Instrum. 73, 255–258 (2002). [CrossRef]

8.

K. L. Bechtel, R. N. Zare, A. A. Kachanov, S. S. Sanders, and B. A. Paldus, “Moving beyond Traditional UV-Visible Absorption Detection: Cavity Ring-Down Spectroscopy for HPLC,” Anal. Chem. 77, 1177–1182 (2005). [CrossRef] [PubMed]

9.

S. E. Fiedler, A. Hese, and A. A. Ruth, “Incoherent broad-band cavity-enhanced absorption spectorscopy of liquids,” Rev. Sci. Instrum. 76, 023107 (2005). [CrossRef]

10.

M. E. Long, R. L. Swofford, and A. C. Albrecht, “Thermal Lens Technique - New Method of Absorption Spectroscopy,” Science 191, 183–185 (1976). [CrossRef] [PubMed]

11.

C. K. N. Patel and A. C. Tam, “Pulsed optoacoustic spectroscopy of condensed matter,” Rev. Mod. Phys. 53, 517–550 (1981). [CrossRef]

12.

F. J. Blanco, M. Agirregabiria, J. Berganzo, K. Mayora, J. Elizalde, A. Calle, C. Dominguez, and L. M. Lechuga, “Microfluidic-optical integrated CMOS compatible devicesfor label-free biochemical sensing,” J. Micromech. Microeng. 16, 1006–1016 (2006). [CrossRef]

13.

I. Eichwurzel, H. Stiel, K. Teuchner, D. Leupold, H. Scheer, Y. Salomon, and A. Scherz, “Photophysical Consequences of Coupling Bacteriochlorophyll a with Serine and its Resulting Solubility in Water,” Photochem. Photobiol. 72, 204–209 (2000); [CrossRef] [PubMed]

J. S. Connolly, E. B. Samuel, and A. F. Janzen, “Effects of solvent on the fluorescence properties of bacteriochlorophyll a,” Photochem. Photobiol. 36, 565–574 (1982).

14.

M. Tokeshi, M. Uchida, A. Hibara, T. Sawada, and T. Kitamori, “Determination of Subyoctomole Amounts of Nonfluorescent Molecules Using a Thermal Lens Microscope: Subsingle-Molecule Determination,” Anal. Chem. 73, 2112–2116 (2001). [CrossRef] [PubMed]

15.

H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B 68, 1095–1108 (1999). [CrossRef]

16.

A. E. Siegman, Lasers (University Science Books, Sausalito, 1986).

17.

G. Rempe, R. J. Thompson, H. J. Kimble, and R. Lalezari, “Measurement of ultralow losses in an optical interferometer,” Opt. Lett. 17, 363–365 (1992). [CrossRef] [PubMed]

18.

A. M. van Oijen, M. Ketelaars, J. Köhler, T. J. Aartsma, and J. Schmidt, “Spectroscopy of Individual Light-Harvesting 2 Complexes of Rhodopseudomonas acidophila: Diagonal Disorder, Intercomplex Heterogeneity, Spectral Diffusion, and Energy Transfer in the B800 Band,” Biophys. J. 78, 1570–1577 (2000). [CrossRef] [PubMed]

19.

H. A. Schuessler, S. H. Chen, Z. Rong, Z. C. Tang, and E. C. Benck, “Cavity-enhanced photothermal spec-troscopy: dynamics, sensitivity and spatial resolution,” Appl. Opt. 31, 2669–2677 (1992). [CrossRef] [PubMed]

20.

E. D. Black, I. S. Grudinin, S. R. Rao, and K. G. Libbrecht, “Enhanced photothermal displacement spectroscopy for thin-film characterization using a Fabry-Perot resonator,” J. Appl. Phys. 95, 7655–7659 (2004). [CrossRef]

OCIS Codes
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(300.6250) Spectroscopy : Spectroscopy, condensed matter

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: September 5, 2006
Revised Manuscript: October 12, 2006
Manuscript Accepted: October 20, 2006
Published: October 30, 2006

Virtual Issues
Vol. 1, Iss. 11 Virtual Journal for Biomedical Optics

Citation
Timothy McGarvey, André Conjusteau, and Hideo Mabuchi, "Finesse and sensitivity gain in cavity-enhanced absorption spectroscopy of biomolecules in solution," Opt. Express 14, 10441-10451 (2006)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-14-22-10441


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References

  1. R. E. Kunz, "Optimizing integrated optical chips for label-free (bio)chemical sensing," Anal. Bioanal. Chem. 384, 180-190 (2006);N. Kinrot and M. Nathan, "Investigation of a Periodically-Segmented Waveguide Fabry- Pérot Interferometer for Use as a Chemical/Biosensor," J. Lightwave Technol. 24, 2139-2145 (2006). [CrossRef]
  2. A. J. Hallock, E. Berman and R. N. Zare, "Ultratrace Kinetic Measurements of the Reduction of Methylene Blue," J. Am. Chem. Soc. 125, 1158-1159 (2003). [CrossRef] [PubMed]
  3. J. Ye, L.-S. Ma and J. L. Hall, "Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy," J. Opt. Soc. Am. B 15, 6-15 (1998). [CrossRef]
  4. A. C. R. Pipino, "Monolithic folded resonator for evanescent wave cavity ringdown spectroscopy," Appl. Opt. 39, 1449-1453 (2000). [CrossRef]
  5. J. L. Nadeau, V. S. Ilchenko, D. Kossokovski, G. H. Bearman and L. Maleki, "High-Q whispering-gallery mode sensor in liquids," Proc. SPIE 4629, 172-180 (2002). [CrossRef]
  6. L. van der Sneppen, A. Wiskerke, F. Ariese, C. Gooijer and W. Ubachs, "Improving the sensitivity of HPLC absorption detection by cavity ring-down spectroscopy in a liquid-only cavity" Anal. Chim. Acta 558, 2-6 (2006). [CrossRef]
  7. S. Xu, G. Sha and J. Xie, "Cavity ring-down spectroscopy in the liquid phase," Rev. Sci. Instrum. 73, 255-258 (2002). [CrossRef]
  8. K. L. Bechtel, R. N. Zare, A. A. Kachanov, S. S. Sanders and B. A. Paldus, "Moving beyond Traditional UVVisible Absorption Detection: Cavity Ring-Down Spectroscopy for HPLC," Anal. Chem. 77, 1177-1182 (2005). [CrossRef] [PubMed]
  9. S. E. Fiedler, A. Hese and A. A. Ruth, "Incoherent broad-band cavity-enhanced absorption spectorscopy of liquids," Rev. Sci. Instrum. 76, 023107 (2005). [CrossRef]
  10. M. E. Long, R. L. Swofford and A. C. Albrecht, "Thermal Lens Technique — New Method of Absorption Spectroscopy," Science 191, 183-185 (1976). [CrossRef] [PubMed]
  11. C. K. N. Patel and A. C. Tam, "Pulsed optoacoustic spectroscopy of condensed matter," Rev. Mod. Phys. 53, 517-550 (1981). [CrossRef]
  12. F. J. Blanco, M. Agirregabiria, J. Berganzo, K. Mayora, J. Elizalde, A. Calle, C. Dominguez and L. M. Lechuga, "Microfluidic-optical integrated CMOS compatible devicesfor label-free biochemical sensing," J. Micromech. Microeng. 16, 1006-1016 (2006). [CrossRef]
  13. I. Eichwurzel, H. Stiel, K. Teuchner, D. Leupold, H. Scheer, Y. Salomon and A. Scherz, "Photophysical Consequences of Coupling Bacteriochlorophyll a with Serine and its Resulting Solubility in Water," Photochem. Photobiol. 72, 204-209 (2000);J. S. Connolly, E. B. Samuel and A. F. Janzen, "Effects of solvent on the fluorescence properties of bacteriochlorophyll a," Photochem. Photobiol. 36, 565-574 (1982). [CrossRef] [PubMed]
  14. M. Tokeshi, M. Uchida, A. Hibara, T. Sawada and T. Kitamori, "Determination of Subyoctomole Amounts of NonfluorescentMolecules Using a Thermal LensMicroscope: Subsingle-Molecule Determination," Anal. Chem. 73, 2112-2116 (2001). [CrossRef] [PubMed]
  15. H. Mabuchi, J. Ye and H. J. Kimble, "Full observation of single-atom dynamics in cavity QED," Appl. Phys. B 68, 1095-1108 (1999). [CrossRef]
  16. A. E. Siegman, Lasers (University Science Books, Sausalito, 1986).
  17. G. Rempe, R. J. Thompson, H. J. Kimble and R. Lalezari, "Measurement of ultralow losses in an optical interferometer," Opt. Lett. 17, 363-365 (1992). [CrossRef] [PubMed]
  18. A. M. van Oijen, M. Ketelaars, J. K¨ohler, T. J. Aartsma and J. Schmidt, "Spectroscopy of Individual Light- Harvesting 2 Complexes of Rhodopseudomonas acidophila: Diagonal Disorder, Intercomplex Heterogeneity, Spectral Diffusion, and Energy Transfer in the B800 Band," Biophys. J. 78, 1570-1577 (2000). [CrossRef] [PubMed]
  19. H. A. Schuessler, S. H. Chen, Z. Rong, Z. C. Tang and E. C. Benck, "Cavity-enhanced photothermal spectroscopy: dynamics, sensitivity and spatial resolution," Appl. Opt. 31, 2669-2677 (1992). [CrossRef] [PubMed]
  20. E. D. Black, I. S. Grudinin, S. R. Rao and K. G. Libbrecht, "Enhanced photothermal displacement spectroscopy for thin-film characterization using a Fabry-Perot resonator," J. Appl. Phys. 95, 7655-7659 (2004). [CrossRef]

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