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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 8 — Apr. 13, 2009
  • pp: 6230–6238
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Whispering gallery mode carousel – a photonic mechanism for enhanced nanoparticle detection in biosensing

S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer  »View Author Affiliations


Optics Express, Vol. 17, Issue 8, pp. 6230-6238 (2009)
http://dx.doi.org/10.1364/OE.17.006230


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Abstract

Individual nanoparticles in aqueous solution are observed to be attracted to and orbit within the evanescent sensing ring of a Whispering Gallery Mode micro-sensor with only microwatts of driving power. This Carousel trap, caused by attractive optical gradient forces, interfacial interactions, and the circulating momentum flux, considerably enhances the rate of transport to the sensing region, thereby overcoming limitations posed by diffusion on such small area detectors. Resonance frequency fluctuations, caused by the radial Brownian motion of the nanoparticle, reveal the radial trapping potential and the nanoparticle size. Since the attractive forces draw particles to the highest evanescent intensity at the surface, binding steps are found to be uniform.

© 2009 Optical Society of America

1. Introduction

2. The Whispering Gallery Mode Carousel Phenomenon

Nanoparticles suspended in an aqueous environment normally appear to be in Brownian motion. However, we observe in the vicinity of a bare silica microsphere (oblate microspheroid, eccentricity < 5%, equatorial radius R ≈ 50 um) excited into a circulating WGM (quality factor Q ~ 106), nanoparticles as small as 140 nm radius (a) are trapped for hundreds of seconds in orbit within the sensing volume with driving light power P ≈ 50 µW. As shown in Fig. 1(a), these nanoparticles appear to circumnavigate in the direction that light takes within the WGM. The nanoparticle concentration was ≈ 1 fM in D2O. D2O (Aldrich, 99.9%) was used to minimize absorption loss in the infrared. The particle recorded in the video was seen to orbit for over two revolutions before escaping, Fig. 2.

A tapered fiber which coupled power into the microsphere was positioned a few microns to one side of the equator. At resonance, a dip was observed in the power transmitted through the fiber at wavelength λr as the laser was tuned. The power P driving the WGM was estimated from this dip depth [5

5. J. C. Knight, G. Chung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131(1997). [CrossRef] [PubMed]

, 6

6. L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86, 091114 (2005). [CrossRef]

]. In addition to the deterministic propulsion, the trapped particle is also under the influence of Brownian motion, revealed as a blinking of the elastic scattering signal from the particle, as well as by the delimited fluctuations in λr (Fig. 1(b)). In what follows we will show that the physical interpretation of these fluctuations reveals the trapping potential and the size of the nanoparticle. This potential is responsible for increased transport of target nanoparticles to the sensing volume.

Fractional fluctuations in the resonance wavelength from the background level Δλrr are clearly due to perturbations in the WGM as the result of nanoparticle’s interaction with the microcavity, and are equal at each instant to the ratio of the energy polarizing the particle Wp to the energy in the cavity W c (reactive sensing principle, RSP) [7

7. 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] [PubMed]

],

Δλr/λr=Wp/Wc
(1)
Fig. 1. WGM-Carousel-Trap. (a) WGM excited in a microsphere (radius R = 53 μm) with Q = 1.2×106 by a 1060nm tunable laser using fiber-evanescent-coupling. The resonance wavelength is tracked from a dip in the transmitted light (PD). An elastic scattering image shows a polystyrene particle (radius a = 375 nm) trapped and circumnavigating at 2.6 μm/s using a drive power of 32 μW. (b) A particle is sensed through resonance wavelength fluctuations Δλr that identify its size/mass. These fluctuations are recorded from before the particle enters the Carousel-trap until after it escapes ≈ 6 min later.
Fig. 2 (Media 1) This is a sped-up video (16× real time) of a single nanoparticle (a = 375 nm) being trapped and propelled by the WGM momentum flux. The fiber is coupled to the microsphere (R = 48 µm) by contact slightly off the equator on the backside. The WGM has Q = 1.5 ×106, and is driven with a power P = 25 μW. Light travels in the fiber from right to left (WGM scatter can be seen on the left edge of the microsphere). The trapped particle is observed through elastic scattering as a bright spot in front and in back of the microsphere. The ring pattern around the bright spot is caused by diffraction by the microscope objective. The nanoparticle is trapped, and propelled for just over two revolutions with a period of 140s before escaping. The particle appears to move faster on the backside due the transverse magnification in the microsphere image.

Δλr(h+a)Δλr(a)exp[(h+a)/L]exp[a/L]=exp[h/L].
(2)

Equation (2) enables wavelength shift statistics to be transformed into separation statistics. The results are particularly revealing.

3. Trapping potential well

Figure 3(a) shows the separation histogram taken on a nanoparticle (a = 140 nm) that circumnavigated a microsphere for just over two orbits. A pronounced maximum is seen at h ≅ 35 nm from the sensing surface. The peak is indicative of a surface repulsion that becomes more evident by translating these separation statistics into a potential curve using equilibrium statistical mechanics.

Under the assumption of thermal equilibrium the Boltzmann distribution relates the potential U(h) to the probability density p(h); U(h) = -kBTln[p(h)/p(h ref)], where href is a reference separation for which U (href) = 0. Figure 3(b) shows the result. The particle is clearly trapped in a radial potential well with its minimum 35 nm from the surface as it is driven to orbit by the WGM’s tangential momentum flux. These potential points were fit by a sum of two exponentials: a short-range repulsive interaction Us/kBT = 6.2exp[-h/(17.6 nm)], and a long-range attractive interaction Up/kBT = -8.0exp[-h/(142.7 nm)]. The latter supports our hypothesis that the particle’s motion is principally radial since its characteristic length of 143 nm is close to the evanescent length in the radial direction (146 nm). The attractive force arising from this potential is similar to the gradient force in optical tweezer experiments, for which the potential in the equatorial plane is expected to be the negative of the polarization energy, Up(h) ≈ - (αex/4)E 2 0(a) exp(-h/L) where αex is the nanoparticle’s polarizability [9

9. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a Single-Beam Gradient Force Optical Trap for Dielectric Particles,” Opt. Lett. 11, 288–290 (1986). [CrossRef] [PubMed]

]. Indeed, a series of experiments show that the value of this “polarization potential” at the surface Up(0) is proportional to the power P entering the mode. The gradient force is aided in keeping the particle on an equatorial track by a transverse phase-gradient contribution [10

10. Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008). [CrossRef] [PubMed]

]. The positive potential Us is independent of power, and appears to be due to repulsion between ionized silanol groups on the bare silica surface (pH = 7), and the negatively charged polystyrene nanoparticle (the particles used were slightly sulfonated). The characteristic length of Us is close to the Debye length λD arrived at from the measured conductivity of our medium [11

11. J. N. Izraelachvili, Intermolecular And Surfaces Forces. 173–191 (Academic Press, Inc. , San Diego, CA, 1987).

], λD ≈ 20 nm, assuming monovalent ions. By varying the ionic conductivity of the solution one can effectively change the range of Us. In contrast, Up is independent of ionic conductivity and reaches much deeper into the solution. In effect the combined potential forms a “sink-hole” that draws particles toward the optimal region in the sensing volume.

Fig. 3. Separation histogram and trapping potential. (a) separation histogram collected from a single tapping event of a polystyrene (PS) particle (from mean radius <a> =140 nm hydrosol). The WGM with Q = 7.3×105 was excited with P = 233 μW at λ ≈ 1060 nm in a microsphere with R = 44 μm. The statistics were comprised of 1000 points. (b) Potential plot arrived at from the histogram in (a). These points are fit to a sum of two potentials (in red).

It is important to point out that not all forces in the optical problem may be considered conservative. [10

10. Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008). [CrossRef] [PubMed]

] Our description of a potential associated with the separation statistics is strictly meant to apply to conservative forces in the equatorial plane.

The value of the polarization potential at zero separation, Up(0), may be calculated directly in terms of the maximum wavelength shift (Δλr)max = Δλr(a), the power P driving the mode, and its resonant Q by using the RSP, Eq. (1). [7

7. 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] [PubMed]

] The polarization energy at zero separation Wp(0) = - Up(0) and the energy in the cavity Wc is the driving power P times the photon lifetime Q/ωr. Consequently, the potential at zero separation is

Up(0)=(Δλr)maxPQ/(2πc),
(3)

where c is the speed of light. Whereas (Δλr)max is independent of P or Q, the attractive potential grows as their product. If we suppose Us is very short range, then the minimum power to perceive trapping, P min, can be estimated by setting ∣Up(0)∣≈ kBT;

PminkBT(2πc)/[Q(Δλr)max].
(4)

Since all of the parameters on the right in Eq. (4) are measurable, the thermal escape hypothesis is testable by measuring P min.

A series of five experiments were performed in order to detect the minimum power to keep a particle in orbit. In each the power driving a WGM was lowered as an orbiting particle’s velocity was measured from a video recording. Figure 4 shows the results of one of these experiments for which the power was lowered from 42 μW over a period of 1200 s. The particle was lost as the power reached 7.3 μW. At this power the normalized potential from Eq. (3) ∣Up(0)∣ /kBT ≈ 1, consistent with thermal escape (as indicated by the top horizontal scale in the Fig. 4). The recorded velocities in the Fig. 4 do not appear to be heading toward an intercept at the origin as might be expected. The reason lies in the fact that although the momentum flux at a given height decreases in proportion to drive power, the flux seen by the particle falls more rapidly, since the particle moves outward as the drive power decreases. The other four experiments showed similar results. The picture that evolves is of a particle attracted to the orbit and rapidly fluctuating radially above the equator by Brownian forces. This trapping mechanism also leads to enhanced detection rates in the WGM biosensor.

Fig. 4. Particle velocity as a function of drive power P. A nanoparticle of radius a = 375 nm was trapped in a Carousel of a microsphere with R = 45 μm and Q = 1.5 × 106. The power was gradually reduced over a period of 1200 s. Upon reaching 7.3 μW the particle escapes within 10 s, as seen by imaging and through the cessation of wavelength fluctuations. The upper horizontal scale is calculated from Eq. (3).

(Δλr)maxDλr1/2R5/2a3ea/L
(5)

Table 1. Nanoparticle Sizing by WGM Carousel. Size determined for each of four Carousel trapped nanoparticles from their delimited wavelength shift (Δλr)max using Eq. (5) (far right) as compared with the mean size given by the manufacturer for the associated hydrosol <a>.

table-icon
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Although the experiments were for resonators of different sizes and driven by different lasers, the nanoparticle size obtained by inverting Eq. (5) agreed with the manufacturer’s mean size <a> within the uncertainties in the experiment and the standard deviation in the manufactured hydrosols. This clearly opens the door for a nanoparticle size/mass spectrometer in solution [14

14. The translation from a size to a mass spectrum requires knowledge of mass density.

]. With a microsphere for which R = 40 μm and Q ≈ 107 individual bioparticles having a mass of HIV (600 attograms, a ≈ 50 nm) should be easily sizable with P ≈ 50 μW at λ, ≈ 780 nm. For a power of 2 mW using the same resonator a smaller virus with a = 15 nm (mass ≈ 15 attograms, e.g. Poliovirus) is within reach.

Fig. 5. Particle separation histograms for two different NaCl concentrations (0.5 mM and 5 mM). Note that the particle is closer to the surface for higher salt concentration, indicated by the peak position of the statistics.

Fig. 6. (a) First three binding steps of nanoparticles (a = 375 nm) on a microsphere with R = 45 μm and P = 150 μW, Q = 2×105, Note the uniformity in step height. Red dash separation is set to 0.45 pm. (b) Image of a = 140 nm particles trapped and bound in the Carousel orbit, R = 39 μm.

4. Conclusions

Acknowledgments

S. A. thanks D. G. Grier of NYU for useful discussions. This work was principally supported by the National Science Foundation - Division of Bioengineering and Environmental Systems Grant No: 0522668. D.K. thanks an NYU-POLY seed grant for partial support. F.V. was supported by a Rowland Junior Fellowship.

References and links

1.

A. Ashkin and J. M. Dziedzic, “Optical Trapping and Manipulation of Viruses and Bacteria,” Science 235, 1517–1520 (1987). [CrossRef] [PubMed]

2.

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

3.

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] [PubMed]

4.

T. M. Squires, R. J. Messinger, and S. R. Manalis, “Making it stick: convection, reaction and diffusion in surface-based biosensors,” Nature Biotechnol. 26, 417–426 (2008). [CrossRef]

5.

J. C. Knight, G. Chung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131(1997). [CrossRef] [PubMed]

6.

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86, 091114 (2005). [CrossRef]

7.

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] [PubMed]

8.

L ≈ (λ/4π)(ns2-nm2)-1/2, D=2nm2(2ns)1/2(nnp2 - nm2)/(ns2 - nm2)(nnp2 + 2nm2), where ns, nm, and nnp are the refractive indices of the microsphere (1.45), aqueous medium (1.33), and nanoparticle (1.5 for virus and 1.59 for polystyrene; D = 1.50 and 2.26 respectively).

9.

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a Single-Beam Gradient Force Optical Trap for Dielectric Particles,” Opt. Lett. 11, 288–290 (1986). [CrossRef] [PubMed]

10.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008). [CrossRef] [PubMed]

11.

J. N. Izraelachvili, Intermolecular And Surfaces Forces. 173–191 (Academic Press, Inc. , San Diego, CA, 1987).

12.

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]

13.

F. Vollmer, S. Arnold, and D. Keng, “Single Virus Detection from the Reactive Shift of a Whispering-Gallery Mode,” Proc. Natl. Acad. Sci. USA 105, 20701–20704 (2008). [CrossRef] [PubMed]

14.

The translation from a size to a mass spectrum requires knowledge of mass density.

15.

H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 71–75 (2009) [CrossRef] [PubMed]

OCIS Codes
(020.7010) Atomic and molecular physics : Laser trapping
(040.1880) Detectors : Detection
(230.3990) Optical devices : Micro-optical devices

ToC Category:
Optical Trapping and Manipulation

History
Original Manuscript: February 25, 2009
Revised Manuscript: March 31, 2009
Manuscript Accepted: March 31, 2009
Published: April 1, 2009

Virtual Issues
Vol. 4, Iss. 6 Virtual Journal for Biomedical Optics

Citation
S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer, "Whispering gallery mode carousel – a photonic mechanism for enhanced nanoparticle detection in biosensing," Opt. Express 17, 6230-6238 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-6230


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References

  1. A. Ashkin and J. M. Dziedzic, "Optical Trapping and Manipulation of Viruses and Bacteria," Science 235,1517-1520 (1987). [CrossRef] [PubMed]
  2. F. Vollmer and S. Arnold, "Whispering-gallery-mode biosensing: label-free detection down to single molecules," Nature Methods 5, 591-596 (2008). [CrossRef] [PubMed]
  3. 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] [PubMed]
  4. T. M. Squires, R. J. Messinger, and S. R. Manalis, "Making it stick: convection, reaction and diffusion in surface-based biosensors," Nature Biotechnol. 26, 417-426 (2008). [CrossRef]
  5. J. C. Knight, G. Chung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131(1997). [CrossRef] [PubMed]
  6. L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, "Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process," Appl. Phys. Lett. 86, 091114 (2005). [CrossRef]
  7. 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] [PubMed]
  8. L ? (?/4?)(ns2-nm2)-1/2, D = 2nm2 (2ns)1/2(nnp2 - nm2)/(ns2 - nm2)(nnp2 + 2nm2), where ns, nm, and nnp are the refractive indices of the microsphere (1.45), aqueous medium (1.33), and nanoparticle (1.5 for virus and 1.59 for polystyrene; D = 1.50 and 2.26 respectively).
  9. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a Single-Beam Gradient Force Optical Trap for Dielectric Particles," Opt. Lett. 11,288-290 (1986). [CrossRef] [PubMed]
  10. Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100,013602 (2008). [CrossRef] [PubMed]
  11. J. N. Izraelachvili, Intermolecular And Surfaces Forces. 173-191 (Academic Press, Inc., San Diego, CA, 1987).
  12. 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]
  13. F. Vollmer, S. Arnold, and D. Keng, "Single Virus Detection from the Reactive Shift of a Whispering-Gallery Mode," Proc. Natl. Acad. Sci. USA 105,20701-20704 (2008). [CrossRef] [PubMed]
  14. The translation from a size to a mass spectrum requires knowledge of mass density.
  15. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, "Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides," Nature 457,71-75 (2009) [CrossRef] [PubMed]

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