Open Access
Add to BibSonomy
Abstract
We present an optical-trapping scheme based on an on-resonance photonic nanojet (PNJ) excited using a plane wave. A two-dimensional numerical simulation demonstrates that a PNJ is enhanced through resonance with whispering gallery modes (WGMs) and achieves a larger spatial distribution, providing a stable trapping region for nanoparticles nearly four times larger than those of the WGM nodes without broadening by the PNJ. To further enlarge the trapping region, an asymmetric micro-resonator lengthens the mode field of the on-resonance PNJ. We also propose an effective method for addressing the nanoparticle-induced resonance detuning through exciting high-order WGMs of a larger-mode field volume.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
At present, an optical tweezer is an extremely powerful tool for a noninvasive manipulation of microscale or nanoscale particles such as bacteria, cells, and viruses in biological and medical sciences [1–5]. A traditional optical tweezer often becomes inefficient when applied to the trapping of nanoscale particles owing to a diffraction limit that fundamentally prohibits the focus of the beam into an infinitely small spot. Near-field photonics devices have paved the way to enabling effective nanoparticle trapping regardless of the diffraction limit [6]. The optical forces of this trapping scheme result from the strong gradient of the optical intensity of the evanescent fields outside the devices. Several types of photonics devices, such as planar waveguides [7–10], micro-ring resonators [11–13], silica microspheres [14], and plasmonic devices [15–17], have been exploited to trap and manipulate the nanoparticles. However, because the evanescent fields decay quickly outside the devices, the above trapping schemes have extremely short working distances. This implies that they only work when the nanoparticles are moving very close to the surface of the device, which becomes inefficient for a low concentration particle flow.
An interesting near-field distribution of an optical field, called a photonics nanojet (PNJ), was discovered in 2004 [18]. A PNJ arises on the shadow side of a dielectric microcylinder or microsphere illuminated by a plane wave. Because a PNJ has a sub-diffraction-limit beam waist and a small divergence, it has many potential applications including the use in a super-resolution microscope [19–21], nanomanufacturing [22], and particle detection [23]. The highly localized optical field also makes a PNJ a promising candidate for the trapping of nanoparticles [24–26]. The most competitive advantage of this optical trapping scheme based on a PNJ over an evanescent field is that the PNJ often has a length of several, and even tens, of the incident wavelengths, which provides a much larger region for nanoparticle trapping. However, because a PNJ is a type of radiative mode rather than a resonance mode, the intensity enhancement is not obvious, which seriously hinders the further development of the PNJ-based trapping techniques. Some studies have recently demonstrated that a whispering gallery mode (WGM) and PNJ can be excited simultaneously in dielectric microcylinders or microspheres [27–29]. As a result, the intensity of a PNJ is resonantly enhanced owing to the mode field overlap with the WGM. As an application for the detection of nanoparticles, the on-resonance PNJ also shows an enhanced resolution [30]. The motivation of this paper is the use of an on-resonator PNJ for nanoparticle trapping. The on-resonance PNJ has not only an elongated optical field but also a strong intensity, which will provide a larger scale and more efficient optical trapping scheme.
In this paper, we describe an optical trapping scheme based on an on-resonance PNJ. The remainder of this paper is organized as follows: The theoretical description of the trapping system is given briefly in section 2. In section 3, we calculate the optical field distribution of the on-resonance PNJ and the optical forces on the nanoparticles. The broadening of the stable trapping region in an asymmetric micro-resonator is demonstrated in section 4. In section 5, we study the attenuation of the optical forces caused by the nanoparticle itself owing to a detuning from the resonance frequency. This effect is relieved by exciting the high-order WGM. Finally, section 6 summarizes the main points of this study.
2. Theoretical description of the trapping system
The optical force on a particle when illuminated by light originates from the electromagnetic radiation pressure, which can be calculated through an integral of the Maxwell stress tensor over the particle surface [26]. For a nanoparticle, whose size is much smaller than the wavelength of the light, the optical force is mainly from the optical intensity gradient. The formulas for the force can be expressed in a simple form under the following dipole approximation [6]:
where α = V(ε-εm)/(ε + 2εm) is the polarizability of the particle, V is the particle volume, c and λ are the speed and wavelength of light, and ε and εm are dielectric constants of a particle and the background medium, respectively. In the next two sections, we use Eq. (1) to calculate the optical forces on the nanoparticles. If the particle diameter increases to nearly one hundred nanometers, another type of optical force from the momentum transferred from the incident photons to the particle becomes sufficient.Particularly in a PNJ where the optical flux is confined in a narrow path, the optical scattering will be further enhanced. Moreover, the influence of the particle on the optical field is unavoidable, and it is unreasonable to regard the particle as an electric dipole. In this case, the optical force calculation should use the Maxwell stress tensor, which will be discussed in detail in Section 5.
Figure 1 demonstrates the optical trapping process schematically. A z-polarized plane wave propagates along the x-axis, which will excite the transverse electric (TE) WGM inside the microcylinder. The mode field E of the WGM in the microcylinder can be separated as E = Er•Eφ•Ez in cylindrical coordinates. The azimuthal and radial distributions are written as follows:
where m and l are the azimuthal and radial quantum numbers of the WGM, respectively, R is the radius of the microcylinder, n and nm are the refractive index of the microcylinder and background medium, Jm and Hm(1) are the mth Bessel and first-kind of Hankel functions, and kφ(m,l) is the φ-component of the wave vector of the resonance mode with the quantum number (m, l). The coefficients A and B are determined through the continuity condition at the interface between the microcylinder and background medium.For the field distribution in the z-direction, we can use a three-layer planar waveguide to calculate Ez for a thin microcylinder. To achieve an effective simulation, a 3D microcylinder structure can be transferred into 2D mode using the effective index method. This mode is also suitable for a microcylinder of infinite height. Note that the field distributions of the WGM inside the microcylinder and microsphere differ. However, the key features of both the WGM and PNJ excited inside the resonator are similar. Apart from some depolarization effects, the light scattering by objects has the same features as the full 3D mode [31]. In this study, it was reasonable to solve the 2D problem in the optical trapping scheme based on an on-resonance PNJ.
3. Optical trapping in on-resonance PNJ
We first calculate the optical field distributions of the PNJ and WGM when the microcylinder is illuminated by a z-polarized plane wave using the 2D finite element method (FEM). A microcylinder with a refractive index of 2 and a diameter of 3 μm is placed inside a water environment (nm = 1.33). Figures 2(a) and 2(b) show an off- and on-resonance PNJ at incident wavelengths of 760 and 760.8034 nm, respectively. At resonance, the azimuthal and radial quantum numbers of the WGM are 22 and 1, respectively. The intensity of a PNJ is enhanced through resonance with the WGM owing to the mode overlap between them. Figure 2(d) shows a zoom-in image of the field distribution outside the microcylinder, corresponding to the dashed line box in Fig. 2(b). One of the WGM nodes overlapping with a PNJ (i.e., an on-resonance PNJ; see the middle node in Fig. 2(b)) has a larger mode field outside the microcylinder than the other WGM nodes. For comparison, Fig. 3 shows the intensity distributions of the off- and on-resonance PNJ and a WGM node without a PNJ along the dashed line labeled “1” in Fig. 2(a), and “2” and “3” in Fig. 2(b), respectively. The on-resonance PNJ has a strong intensity and large area outside the microcylinder, both of which show the favorability of the optical trapping scheme.
Fig. 2 Optical intensity distributions of (a) off- and (b) on-resonance PNJ. (c) Force field distribution for a 20-nm particle. The white arrows indicate the directions of the forces. (d) Zoomed-in image of the optical intensity distribution outside the microcylinder. The white lines present the trapping edge. In addition, (c) and (d) are amplified images for the dashed box in (b).
Fig. 3 Optical intensity of on- and off-resonance PNJs and WGM decay based on the distance from the edge of the microcylinder.
Before we calculate the optical force on a nanoparticle, the power of the incident plane wave is assumed to be 1 W with an area of 10 × 10 μm2. Figure 2(c) shows the force distribution on a 20-nm particle, the region of which is consistent with that in Fig. 2(d). The white arrow indicates the direction of the optical force. Because the optical forces are all pointing toward the microcylinder surface, it implies that the nanoparticle will finally be trapped onto the surface of the microcylinder. As expected, the area of the optical force field produced by the on-resonance PNJ is also larger than that of the other WGM nodes.
Because the nanoparticle is inside a water environment, the Brownian diffusion should be considered, which will degrade the trapping stability. The nanoparticle will escape from the optical trapping through Brownian motion. This is an effective method for describing the trapping stability quantitatively by calculating the stability number [32,33]:
where Wtrap is the work needed to release a particle from a trapping region, kB is the Boltzmann constant, and T is the temperature in Kelvin, and is assumed to be 300 K. The trapping edge is defined as S = 10, which is indicated by the white line in Fig. 2(d). This means that the nanoparticle has a stable trapping status inside the region enclosed by the white line. From Fig. 2(d), the stable trapping region in the on-resonance PNJ is nearly 4-times larger than that in the WGM.4. Enlarging the trapping region in the deformed micro-resonator
The PNJ can be effectively elongated in a two-layer microcylinder, and then broadened in the trapping region [26]. In this case, however, an elongated PNJ cannot been enhanced resonantly with the WGM because its field distribution is separate from that of the WGM inside the microcylinder. In this section, the motivation to elongate the on-resonance PNJ is to improve the overlapping between the WGM and PNJ. The deformed micro-resonator will break the circular symmetrical distribution of the WGM [34]. In a properly designed micro-resonator, the mode field of the WGM can incline toward the side of the PNJ. Here, we introduce a symmetric half-spiral resonator (SHSR) to elongate the on-resonance PNJ [34,35]. Figure 4(a) shows the mode field distribution of an on-resonance PNJ in an SHSR with a diameter of 3 μm and a deformation parameter of ε = 0.5. The WGM of this resonator has the same quantum numbers with that in Fig. 2, i.e., m = 22 and l = 1. We define the length of the on-resonance PNJ lp, which indicates the distance from the microcylinder to the position where the intensity of the PNJ decays to 1/e. As shown in Fig. 4(c), lp increases with the deformation parameter ε. This implies that the mode field overlapping between the WGM and the PNJ is increased owing to the microcylinder moving gradually away from a perfect circular shape with an increased ε. Indeed, the elongated on-PNJ is in favor of large-region optical trapping. However, a microcylinder with a large ε will suffer from severe Q spoiling, thereby weakening the optical forces. Here, we also define another characteristic length ls for the distance from the microcylinder surface to the trapping edge (i.e., S = 10 as indicated by the white line in Fig. 4(b)). As shown in Fig. 4(d), the stable trapping region represented by ls will decrease within the range of a large ε, which means there is a trade-off between the Q factor and overlapping with the PNJ for the WGM as the deformation parameter of the microcylinder increases. Based on the calculation results, the best value of ε is approximately 0.2.
Fig. 4 (a) Optical intensity distribution of an on-resonance PNJ in a symmetric half-spiral resonator. (d) Zoomed-in image of the optical intensity distribution outside the microcylinder. The white line indicates the trapping edge, S = 10. In addition, (c) and (d) are the two characteristic lengths ls and lp as functions of the deformation parameter ε for the microcylinder, respectively.
5. Detuning from resonance induced by nanoparticles
In the previous section, the nanoparticle size is set to 20 nm, which is too small to influence the optical field. However, for a larger sized particle we cannot neglect its effect on the resonance mode. According to the perturbation theory, the resonance detuning induced by the nanoparticle can be written as follows [36]:
where Ep is the electric field at the particle position. The denominator of the above equation is the integral of the mode field over its entire spatial distribution, and ε’ refers to the relative dielectric constant distribution of the resonator. From Eq. (5), the resonance detuning is dependent on the particle size included in Re(α) and its location in the mode field implied by Ep. To study the influence of the particle on the optical force, Eq. (1) is not reasonable owing to the derivation process of this equation, which assumes that the particle has no effect on the resonance mode. In this case, we should calculate the optical field distribution with the nanoparticle, and then use the Maxwell stress tensor to calculate the optical force. It should be point out that in this 2D mode, the optical force on the nanoparticle is newton per unit length (N/m). Therefore, we regard the nanoparticle as a “nanorod” whose height is equal to it radius for the force calculation. Figure 5(a) shows the optical forces on nanoparticles with different sizes because they are moving along line “2,” as indicated in Fig. 2(b). For particles with small sizes, the optical forces continuously increase when approaching a microcylinder. The strength of the optical force also increases with the particle size. This case is consistent with Eq. (1), implying that the particle is sufficiently small to produce no effect on the optical field. However, the optical forces on particles of 80 and 100 nm in size are very different from the forces on smaller particles. The forces will decrease quickly when the particles reach close to the microcylinder. In particular, the sign of the force on the 100-nm particle changes from negative to positive. This means that the light will “push” the particle away from the microcylinder if the particle is too close. This phenomenon is attributed to two aspects: first, when a particle moves close to the microcylinder, the resonance detuning increases, thereby weakening the optical force. Second, the optical scattering force will increase quickly with the particle size. The scattering force is in the x-axis direction of the light propagation. Because the positive forces are not favorable to the trapping stability, it is necessary to analyze the stability for different particle sizes. Figure 5(b) shows the stability number as a function of the particle size. For small particles, the stability number increases with the particle size but no longer increases or even drops if the particle is too large.Fig. 5 (a) Optical forces vs. the distance between the microcylinder edge and the particles of different sizes. (b) Stability number as a function of the particle size.
We can see that the denominator in Eq. (5) implies that a resonance mode with a larger volume will mitigate the resonance detuning induced by the nanoparticle. The high-order WGM has multiple nodes in radial directions whose mode volume is larger than the fundamental WGM. In the formation of a PNJ, the microcylinder can be regarded as a spherical lens. The PNJ is simply the result of focusing the incident plane wave at the edge of the microcylinder. If the refractive index of the microcylinder is increased, the focus will appear inside the microcylinder. Figure 6(a) shows that a part of the PNJ is distributed inside the microcylinder with the larger refractive index of 2.4. If the incident wavelength is at approximately 736.594 nm, the WGM of the second radial order, i.e., l = 2 is excited, as shown in Fig. 6(b). This selective excitation of the high-order WGM is owing to the overlap of the mode field between the PNJ and desired WGM. In this case, the field distribution of the PNJ has a larger overlap with the WGM of radial quantum number l = 2 than that of l = 1. The mode field of this on-resonance PNJ clearly has a larger spatial distribution than that shown in Fig. 2(b).
Fig. 6 Optical intensity distribution of (a) off- and (b) on-resonance PNJ. The PNJ is resonant with the radial second-order WGM. (c) Optical forces on particles with different sizes when they are approaching the microcylinder along the dashed line in (b). (d) Stability number as a function of the particle size.
Figure 7 shows the resonance detuning for the first and second radial order WGM induced by a 100-nm particle. As analyzed above, the particle perturbs the high-order WGM slightly more than the fundamental WGM.
The optical forces on particles with different sizes are shown in Fig. 6(c). The optical forces continuously increase as the particle approaches the microcylinder. This indicates that the particle has little effect on the forces when the PNJ is resonant with the second-order WGM. Similarly, Fig. 6(d) demonstrates that the stability number is a monotonic increasing function with the particle size when below 100 nm.
6. Conclusion
In summary, we proposed a novel optical trapping scheme using an on-resonance PNJ. The results indicate that this scheme achieves both a large trapping region and a high trapping efficiency owing to the resonance of the PNJ and WGM inside the microcylinder. The stable trapping region of this scheme is over 4-times larger than that of the WGM when calculating the stability number. A deformed microcylinder has a symmetric half-spiral structure introduced to elongate the on-resonance PNJ. According to the calculation results, the optimal deformation parameter for the deformed microcylinder is found to be 0.2. Moreover, resonance detuning will be induced by the nanoparticles, thereby weakening the optical forces on them. In particular, the scattering forces will “push” the large nanoparticles away from the microcylinder. To address this problem, we can selectively excite a high-order WGM of a large mode field to mitigate the resonance detuning. Moreover, to experimentally realize the trapping system, a tunable laser with an ultra-narrow linewidth can be used to excite an on-resonance PNJ. Silicon nitride is a suitable material for fabricating the microcylinder resonator owing to its refractive index lager than two at visible waveband and excellent property in micro-nano-fabrication technology. We believe that the results presented in this paper will help make better use of a PNJ for the trapping of nanoparticles.
Funding
National Natural Science Foundation of China (61805112); Natural Science Foundation of Jiangsu Province (BK20181003); Special Project of National Key Technology R&D Program of the Ministry of Science and Technology of China (2016YFC0201401).
References
1. 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(5), 288–290 (1986). [CrossRef] [PubMed]
2. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987). [CrossRef] [PubMed]
3. S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348(6299), 348–352 (1990). [CrossRef] [PubMed]
4. J. Zhu, Ş. K. Özdemir, and L. Yang, “Optical detection of single nanoparticles with a subwavelength fiber-taper,” IEEE Photonics Technol. Lett. 23(18), 1346–1348 (2011). [CrossRef]
5. X. C. Yu, B. B. Li, P. Wang, L. Tong, X. F. Jiang, Y. Li, Q. Gong, and Y. F. Xiao, “Single nanoparticle detection and sizing using a nanofiber pair in an aqueous environment,” Adv. Mater. 26(44), 7462–7467 (2014). [CrossRef] [PubMed]
6. D. Erickson, X. Serey, Y. F. Chen, and S. Mandal, “Nanomanipulation using near field photonics,” Lab Chip 11(6), 995–1009 (2011). [CrossRef] [PubMed]
7. K. Grujic, O. Hellesø, J. Hole, and J. Wilkinson, “Sorting of polystyrene microspheres using a Y-branched optical waveguide,” Opt. Express 13(1), 1–7 (2005). [CrossRef] [PubMed]
8. A. 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(7225), 71–75 (2009). [CrossRef] [PubMed]
9. A. H. J. Yang, T. Lerdsuchatawanich, and D. Erickson, “Forces and transport velocities for a particle in a slot waveguide,” Nano Lett. 9(3), 1182–1188 (2009). [CrossRef] [PubMed]
10. H. Cai and A. W. Poon, “Optical trapping of microparticles using silicon nitride waveguide junctions and tapered-waveguide junctions on an optofluidic chip,” Lab Chip 12(19), 3803–3809 (2012). [CrossRef] [PubMed]
11. S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010). [CrossRef] [PubMed]
12. A. H. J. Yang and D. Erickson, “Optofluidic ring resonator switch for optical particle transport,” Lab Chip 10(6), 769–774 (2010). [CrossRef] [PubMed]
13. H. Cai and A. W. Poon, “Optical manipulation of microparticles using whispering-gallery modes in a silicon nitride microdisk resonator,” Opt. Lett. 36(21), 4257–4259 (2011). [CrossRef] [PubMed]
14. 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(8), 6230–6238 (2009). [CrossRef] [PubMed]
15. K. Wang, E. Schonbrun, and K. B. Crozier, “Propulsion of gold nanoparticles with surface plasmon polaritons: evidence of enhanced optical force from near-field coupling between gold particle and gold film,” Nano Lett. 9(7), 2623–2629 (2009). [CrossRef] [PubMed]
16. W. Zhang, L. Huang, C. Santschi, and O. J. F. Martin, “Trapping and sensing 10 nm metal nanoparticles using plasmonic dipole antennas,” Nano Lett. 10(3), 1006–1011 (2010). [CrossRef] [PubMed]
17. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Scannable plasmonic trapping using a gold stripe,” Nano Lett. 10(9), 3506–3511 (2010). [CrossRef] [PubMed]
18. Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12(7), 1214–1220 (2004). [CrossRef] [PubMed]
19. A. Darafsheh, G. F. Walsh, L. Dal Negro, and V. N. Astratov, “Optical super-resolution by high-index liquid-immersed microspheres,” Appl. Phys. Lett. 101(14), 141128 (2012). [CrossRef]
20. Z. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2(1), 218 (2011). [CrossRef] [PubMed]
21. X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013). [CrossRef]
22. E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008). [CrossRef] [PubMed]
23. A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, “Experimental confirmation of backscattering enhancement induced by a photonic jet,” Appl. Phys. Lett. 89(22), 221118 (2006). [CrossRef]
24. X. Cui, D. Erni, and C. Hafner, “Optical forces on metallic nanoparticles induced by a photonic nanojet,” Opt. Express 16(18), 13560–13568 (2008). [CrossRef] [PubMed]
25. A. A. R. Neves, “Photonic nanojets in optical tweezers,” J. Quant. Spectrosc. Radiat. Transf. 162, 122–132 (2015). [CrossRef]
26. H. Wang, X. Wu, and D. Shen, “Trapping and manipulating nanoparticles in photonic nanojets,” Opt. Lett. 41(7), 1652–1655 (2016). [CrossRef] [PubMed]
27. I. Mahariq and H. Kurt, “Strong field enhancement of resonance modes in dielectric microcylinders,” J. Opt. Soc. Am. B 33(4), 656–662 (2016). [CrossRef]
28. I. Mahariq and H. Kurt, “On- and off-optical-resonance dynamics of dielectric microcylinders under plane wave illumination,” J. Opt. Soc. Am. B 32(6), 1022–1030 (2015). [CrossRef]
29. Z. Chen, A. Taflove, and V. Backman, “Highly efficient optical coupling and transport phenomena in chains of dielectric microspheres,” Opt. Lett. 31(3), 389–391 (2006). [CrossRef] [PubMed]
30. A. Heifetz, J. J. Simpson, S.-C. Kong, A. Taflove, and V. Backman, “Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere,” Opt. Express 15(25), 17334–17342 (2007). [CrossRef] [PubMed]
31. M. Lester and M. Nieto-Vesperinas, “Optical forces on microparticles in an evanescent laser field,” Opt. Lett. 24(14), 936–938 (1999). [CrossRef] [PubMed]
32. A. H. J. Yang and D. Erickson, “Stability analysis of optofluidic transport on solid-core waveguiding structures,” Nanotechnology 19(4), 045704 (2008). [CrossRef] [PubMed]
33. T. J. Davis, “Brownian diffusion of nano-particles in optical traps,” Opt. Express 15(5), 2702–2712 (2007). [CrossRef] [PubMed]
34. H. Cao and J. Wiersig, “Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87(1), 61–111 (2015). [CrossRef]
35. X. Tu, X. Wu, L. Liu, and L. Xu, “High-Q unidirectional emission properties of the symmetric half-spiral microcavities,” J. Opt. Soc. Am. B 27(2), 300–304 (2010). [CrossRef]
36. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003). [CrossRef] [PubMed]
