OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 6 — Mar. 24, 2014
  • pp: 6881–6898
« Show journal navigation

Quasi-droplet microbubbles for high resolution sensing applications

Yong Yang, Jonathan Ward, and Síle Nic Chormaic  »View Author Affiliations


Optics Express, Vol. 22, Issue 6, pp. 6881-6898 (2014)
http://dx.doi.org/10.1364/OE.22.006881


View Full Text Article

Acrobat PDF (1470 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Optical properties and sensing capabilities of fused silica microbubbles were studied numerically using a finite element method. Mode characteristics, such as quality factor (Q) and effective refractive index, were determined for different bubble diameters and shell thicknesses. For sensing applications with whispering gallery modes (WGMs), thinner shells yield improved sensitivity. However, the Q-factor decreases with reduced thickness and this limits the final resolution. Three types of sensing applications with microbubbles, based on their optimized geometrical parameters, were studied. Herein the so-called quasi-droplet regime is defined and discussed. It is shown that best resolution can be achieved when microbubbles act as quasi-droplets, even for water-filled cavities at the telecommunications C-band.

© 2014 Optical Society of America

1. Introduction

For the sake of general discussion, let us consider refractive index sensing as an example. The sensitivity of a resonator to changes in refractive index relies on the portion of electromagnetic (EM) field distributed outside it or, in another words, the tunneling depth of the evanescent field. To extend the evanescent field, several methods have been developed, such as deformed microspheres [19

19. T. Oo, C. Dong, V. Fiore, and H. Wang, “Evanescently coupled optomechanical system with SiN nanomechanical oscillator and deformed silica microsphere,” Appl. Phys. Lett. 103, 031116 (2013). [CrossRef]

] or plasmonic enhancement in metal-coated microresonators [20

20. Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. H. Gong, “High-Q Exterior Whispering-Gallery Modes in a Metal-Coated Microresonator,” Phys. Rev. Lett. 105, 153902 (2010). [CrossRef]

22

22. Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. H. Gong, “Strongly enhanced light-matter interaction in a hybrid photonic-plasmonic resonator,” Phys. Rev. A 85, 031805 (2012). [CrossRef]

]. By having different dielectric layers, the WGM EM field distribution can be tailored. Liquid core optical ring resonator (LCORR) sensors [23

23. I. M. White, H. Oveys, and X. D. Fan, “Liquid-core optical ring-resonator sensors,” Opt. Lett. 31, 1319–1321 (2006). [CrossRef] [PubMed]

] are an alternative type of WGM resonator. Such devices can be viewed as hybrid microresonators, since the evanescent light field can penetrate into the liquid in the core. In LCORRs, however, a high Q is maintained because most of the WGM energy still propagates in the shell structure. Therefore, LCORRs have outstanding sensing properties.

2. FEM simulations of microbubbles

Images of typical microbubbles are shown in Fig. 1(a) and the schematic cross-section of a microbubble is shown in Fig. 1(b). For simplicity we assume that the microbubble is a spherical shell formed by fused silica and surrounded by air with core materials that can be varied. A working wavelength of 1.55 μm was chosen, as it is commonly used in WGM experiments. FEM simulations of a 3D structure consume a lot of computational resources even for micron-scale objects. The microbubble is rotationally and axially symmetric, so by utilizing a newly developed FEM [28

28. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theory Tech. 55, 1209–1218 (2007). [CrossRef]

], the 3D problem is reduced to 2D and is solvable in seconds with smaller computational memory requirement. The method in [28

28. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theory Tech. 55, 1209–1218 (2007). [CrossRef]

] is based on the weak form of the Helmholtz equation [29

29. M. I. Cheema and A. G. Kirk, “Accurate determination of the quality factor and tunneling distance of axisymmetric resonators for biosensing applications,” Opt. Express 21, 8724–8735 (2013). [CrossRef] [PubMed]

], given by:
dV((×H˜*)ε1(×H)α(H˜*)(H)+c2H˜2Ht2)=0.
(1)
where ε is the effective permittivity and α is the penalty factor first introduced in [28

28. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theory Tech. 55, 1209–1218 (2007). [CrossRef]

].

Fig. 1 (a) Images of double-pass and single-pass microbubbles. (b) Whispering gallery modes propagate along the surface of a microbubble (red trace). For purpose of illustration, a microbubble is cut transversely along the polar axis. R is the outer radius of the microbubble and t is the shell thickness. The mode number, m, determines the relationship between the azimuthal field, E, and the azimuthal coordinate, ϕ, as E ∝ exp(imϕ). Therefore, the solution of the 3D FEM problem can be reduced to 2D along the bubble’s symmetry axis. Radial mode distribution patterns are shown in (c), (d) and (e). (c) is the first radial order fundamental mode, (d) is the second radial order mode, and (e) is a higher transverse mode. All are quasi-TE modes. To derive Q-factor values, perfectly matched layers (PMLs) are required (c) – (e).

In spherical coordinates (r, θ, ϕ), WGMs propagate azimuthally to the rotational symmetric axis, as illustrated in Fig. 1(b). This gives rise to a field phase varying term, exp(imϕ). Here, m is the azimuthal mode order of the WGM. In the simulation, m is varied and eigenfrequencies of corresponding fundamental modes are determined for different EM field distributions along the radial direction (Fig. 1(c)–(e)). The effective index of the mode is estimated by Neff = /2πR, where R is the outer radius of the microbubble.

For WGRs, the Q-factor is a very important parameter. The total intrinsic loss of a WGR originates from radiation loss (tunneling loss), material loss, surface roughness, and contamination. Here, only radiation and material losses are considered. The surface roughness is very small due to the fabrication method used. In experiments, a high Q absorption limit for microbubbles has been reported [30

30. G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013). [CrossRef] [PubMed]

]. Radiation loss is caused by leakage from evanescent light into a free space mode. The upper and lower bounds of the Q-factor can be estimated with a closed resonator model. In this work, a more precise method was used, in which a perfectly matched layer (PML) along the boundary of the computation domain is introduced, see Fig. 1(c) – (e). A properly set PML can be treated as an anisotropic absorber, simulating radiation tunneling to infinity within a limited domain calculation space. An accurate determination of the Q-factor in a microsphere has been reported recently using this modified method [29

29. M. I. Cheema and A. G. Kirk, “Accurate determination of the quality factor and tunneling distance of axisymmetric resonators for biosensing applications,” Opt. Express 21, 8724–8735 (2013). [CrossRef] [PubMed]

]. In order to match the model with a realistic situation, material absorption is introduced as an additional imaginary part to the resonator permittivity. For fused silica and a 1.55 μm wavelength, the imaginary part is estimated to be εi = −3.56 × 10−10, which is calculated from the absorption coefficient. As will be demonstrated in the following, the radiation loss is dominant when the diameter of the microbubble is less than ∼ 30μm. The Q-factor exponentially increases with diameter such that it is saturated when R >30 μm, and is then only limited by the material absorption loss.

When solving the eigen-equations using FEM software, such as COMSOL©, with complex material permittivity and PMLs, the eigenfrequencies (fr) are complex, with the real parts representing resonant frequencies and the imaginary parts representing total intrinsic losses. Therefore, the Q-factor is defined as Q = Re(fr)/2Im(fr). For the material absorption term, the upper bound is limited to around 109, which will be shown in the following simulation results. For investigating WGM properties, air (ε = 1) is initially chosen as the core material in this section.

Microbubbles with different diameters (10–50 μm) and wall thicknesses (800 nm and 2 μm) were simulated (Fig. 2). Similar to solid microspheres, Q-factors increase with diameter. Exponential curves for diameters below 30 μm indicate that radiation losses dominate. When microbubbles are larger, radiation losses diminish and become negligible compared to material losses. As expected, Q-factors for large diameters do not exceed absorption Q-factors of solid microspheres (< 1010). Two microbubbles with different shell thicknesses were compared. It is clear that when the shell is thinner, the mode tunnels more into the core, increasing the radiation loss and reducing the Q-factor. Therefore, to design high Q-factor microbubbles, larger diameters and thicker shells are required. In the following calculations, 50 μm has been selected as a reasonable microbubble size, since it can be easily fabricated and shell thickness can be controlled in fabrication [12

12. J. Ward, Y. Yang, and S. Nic Chormaic, “Highly sensitive temperature measurements with liquid-core microbubble resonators,” IEEE Photon. Technol. Lett. 25, 2350 (2013). [CrossRef]

].

Fig. 2 Q-factors of microbubbles drop exponentially with decreasing radii due to greater radiation loss for smaller WGM cavities. This is illustrated on the plot with quasi TE fundamental modes. Two different shell thicknesses, 800 nm (black square) and 2 μm (blue circle), are compared. The red dotted line represents the absorption Q limit of a silica microsphere calculated using the same FEM simulation method with a diameter of 50 μm. Due to material loss, the Q-factor is limited by the absorption Q.

Before discussing the shell thickness relationship, it is necessary to note that in addition to fundamental modes, other modes also exist in microbubbles (c.f. Fig. 1(d) and 1(e)). These can be denoted as higher radial (q = 2, 3,...) or higher polar (l = m ± 1, m ± 2,...) modes. For the first radial, fundamental TE mode, when the thickness is less than 1 μm, the Q-factor drops extremely sharply (Fig. 3). The TM mode has a lower Q-factor and it drops when the shell thickness is less than 1.3 μm. At a wall thickness of ∼ 600 nm, the Q of the TM mode drops to a very low value, implying that the microbubble can only hold the TE mode. For shell thickness less than 500 nm, even the TE mode has a very low Q-factor and microbubbles cannot hold any high Q WGMs. It is worth noting that, when the thickness is larger than the working wavelength (1.55 μm in this paper), microbubbles can even hold second order radial modes (q = 2). Radial mode distribution is dependent on the medium along the radial direction. If the shell becomes even thicker, microbubbles should be able to hold even higher radial modes until they become the same as solid microspheres. In other words, single radial mode operation is only possible for microbubbles with subwavelength shells.

Fig. 3 Three different types of modes coexist in microbubbles, represented as squares (TE), circles (TM) and triangles (q = 2 TE). However, due to inner surface tunneling loss, higher radial modes have lower Q-factors than lower modes. The diameter of the microbubble for this plot is 50 μm. The TE mode is higher than the TM mode, especially when the shell is thin. The maximum Q-factor is limited by the silica absorption.

For real sensing applications, light has to be coupled in and out of the WGR for detection. Many coupling methods have been developed and, among them, tapered fibers exhibit high efficiency as evanescent probes that are widely used for WGRs [31

31. M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000). [CrossRef] [PubMed]

]. In order to effectively couple light, the cavity mode must be sufficiently spatially overlapped with the mode from the tapered fiber and a phase matching condition must be met, i.e. the effective index of the WGM must equal that of the tapered fiber mode. To verify efficient coupling in the microbubble tapered fiber system, the effective index of a 50 μm microbubble fundamental TE mode was calculated (Fig. 4). For comparison, the index for different tapered fiber diameters is also shown. Note that this index is calculated when the fiber is in contact with the microbubble. To tune the effective index, one can control the taper/microbubble gap or change the taper diameter.

Fig. 4 Effective index of a 50 μm diameter microbubble for different shell thickness and different modes. Black squares are the fundamental TE mode and red circles are the TM mode. The effective index of the second radial order is plotted in blue triangles for a shell thickness from 1.1 μm, where the air-filled bubble starts to support high order modes. The taper effective index for a fiber waist of 0.5–1.0 μm radius is also presented (dashed pink line). Once the geometry of a microbubble is set, a proper taper size can be chosen to satisfy the phase matching condition.

From Fig. 4 it is clear that, for thinner microbubbles, the effective index decreases, which is also due to more EM field distributed in the core. For a 50 μm microbubble, the effective index of the TE mode varies from 1.20 to 1.35. Phase matching can be realized if the taper diameter is controlled between 1.4 μm and 1.8 μm. The second order mode has an even lower effective index, ranging from 1.05 to 1.28, so a thinner taper is required to efficiently couple with this mode. In the following discussion for an air-filled microbubble, we assume that only the first order fundamental TE mode is of concern, since it has a larger Q-factor than the higher order modes. Efficient coupling to such modes is realized and controlled by selecting the size of tapered fiber.

3. Quasi droplet regime of microbubbles

The foregoing discussion has been centered on WGM properties of empty (air-filled) microbubbles; however, it is of more significance to investigate the microbubbles filled with liquid. The refractive index of liquid is higher than air and a spherical boundary can be shaped if the liquid forms a droplet, therefore WGMs can be found in such a droplet. Droplet WGRs have been studied for lasing [32

32. S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: Highlighting the liquid-air interface by laser emission,” Science 231, 486–488 (1986). [CrossRef] [PubMed]

] and nonlinear effects [33

33. S. Uetake, R. S. D. Sihombing, and K. Hakuta, “Stimulated raman scattering of a high-q liquid-hydrogen droplet in the ultraviolet region,” Opt. Lett. 27, 421–423 (2002). [CrossRef]

]. Indeed, droplet-like WGMs can also be found in microbubbles.

If the shell of a microbubble is very thick, most of the EM field of the mode will propagate within the shell, so the microbubble behaves like a solid microsphere. As it gets thinner, mode gets extended more into the core. For an extreme situation, t → 0, the mode is almost entirely propagating in the liquid core, where a droplet like condition is satisfied, given that the inner boundary is spherical. Between these two situations, there exists a region where the shell starts to lose the ability to confine WGMs. This region has been dubbed the quasi-droplet regime [34

34. W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, “A quasi-droplet optofluidic ring resonator laser using a micro-bubble,” Appl. Phys. Lett. 99, 091102 (2011). [CrossRef]

]. It is worth noting that higher radial modes occupy more space than first order modes; therefore, they cannot exist in air-filled microbubbles with very thin shells. However, the core of a liquid-filled bubble provides the space required for higher order modes to propagate, so higher modes can be supported in thin-walled, liquid-filled bubbles. For example, in Lee et al. [34

34. W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, “A quasi-droplet optofluidic ring resonator laser using a micro-bubble,” Appl. Phys. Lett. 99, 091102 (2011). [CrossRef]

], the quasi-droplet regime mentioned is only for the q = 2 mode. Therefore, it is very important to clarify the definition of the quasi-droplet regime for different modes. In the following, the quasi-droplet regime is described in terms of the effective index, the spatial extent of the EM field, and the percentage of light distributed in the core.

The estimated percentage of the WGM’s EM field in the core was found by integrating the EM field intensity in the core and shell separately. The percentage of energy in the core for the first three radial modes for a shell thickness varying from 300 nm to 3 μm is calculated for fixed diameter microbubbles, see Fig. 5(e). It can be seen that, when the shell thickness is 500 nm or less, up to 85% of the q = 1 WGM propagates in the core, while if the shell thickness is more than half of the working wavelength (1.55 μm), more than 80% of the light travels in the shell. To describe the quasi-droplet regime more precisely, we resorted to a quantified definition for the fundamental TE mode. The idea is based on the well-known interpretation of the radial mode number. For a liquid microsphere, i.e. a droplet, the radial field distribution has a maximum inside the droplet close to the boundary. Analogous to a droplet, when the peak is inside the core of a microbubble, the core is equivalent to the droplet while the shell is the new boundary. This can be used as a criterion for the quasi-droplet regime. It can be physically interpreted that light is traveling in the water and the field distributed in the shell is the evanescent component tunneling into the shell. According to this definition, for a shell thickness of less than 300 nm, the microbubble is driven into the quasi-droplet regime for its fundamental TE mode (see Fig. 5(c) and 5(d)). However, such defined thickness does not apply for the q = 2 and q = 3 modes, as those modes have multiple peaks along the radial direction so they are more complicated than the q = 1 case. Where the percentage of the EM field for the q = 2 and q = 3 modes are plotted, even when the shell is as thick as 1 μm and 1.5 μm, respectively, the proportion of the EM field in the core does not drop to less than 80% (Fig. 5(e)).

Fig. 5 Radial field distribution for a water-filled, 50 μm microbubble. From (a) to (d) shell thickness decreases from 500 nm to 200 nm. The y-axis represents |E|2 along the radius r, for the TE fundamental modes. When the shell is less than 300 nm thick, the maximum shifts completely inside the core and this is defined as the quasi-droplet regime. In (e), the percentage of light intensities for different radial modes inside the core are calculated. It can been seen that higher order modes have more light distributed in the core, even for microbubbles with thicker shells.

To have a general definition that applies to different radial modes, the effective indices for the q = 1, 2, and 3 modes in microbubbles were calculated. For comparison, the effective index of a droplet of the same diameter was simulated and is shown together with those for a solid silica microsphere (Fig. 6). The effective index for a microbubble mode in the quasi-droplet regime, as defined above, is only slightly higher than for the droplet modes, proving that, in this case, the shell is negligible and the microbubble acts like a droplet. For thicker shells >2.5 μm, the effective indices of all bubble modes are the same as the corresponding modes in a solid silica microsphere of the same size. The q = 1 mode does not reach the droplet index unless the shell thickness is less than 500 nm. On the other hand, higher order modes, especially the q = 2 modes, exhibit a much wider range of effective indices corresponding to those of the droplet. The effective index of the q = 2 mode changes abruptly to more closely resemble a solid microsphere when the shell is thicker than 1.5 μm. Accordingly, a new definition for the quasi-droplet regime could be the range of shell thicknesses until the point where the effective index starts to rapidly approach that of a silica microsphere.

Fig. 6 The effective refractive indices of microbubbles with shell thicknesses from 200 nm to 3 μm. First (black squares), second (red circles) and third (blue triangles) order radial modes are shown and compared with those of a liquid droplet (horizontal dashed lines) and a silica microsphere (horizontal solid lines) of the same diameter. Water was chosen as the liquid and the structures are 50 μm in diameter.

So far the quasi-droplet has been defined in two ways and we have shown that, for a very thin shell, a microbubble filled with liquid behaves very similarly to a droplet WGR. This may be useful in applications such as sensing or nonlinear optics. The quasi-droplet resonator has advantages since its shape is protected by the shell. Changes to resonator shape through surface evaporation can thereby be avoided, and coupling to external waveguides is easier instead of low efficiency, free space excitation [32

32. S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: Highlighting the liquid-air interface by laser emission,” Science 231, 486–488 (1986). [CrossRef] [PubMed]

].

4. Optimizing microbubble geometry for high resolution sensing applications

4.1. Pressure sensing

The resonant frequency of a microbubble WGR can be tuned by manipulating the compression or tension on the device [35

35. M. Sumetsky, Y. Dulashko, and R. S. Windeler, “Super free spectral range tunable optical microbubble resonator,” Opt. Lett. 35, 1866–1868 (2010). [CrossRef] [PubMed]

]. Alternatively, a mode frequency shift of hundreds of GHz can be generated in a microbubble by gas pressure [13

13. R. Henze, T. Seifert, J. Ward, and O. Benson, “Tuning whispering gallery modes using internal aerostatic pressure,” Opt. Lett. 36, 4536–4538 (2011). [CrossRef] [PubMed]

]. In this case, two different mechanisms are dominant. The first is size expansion by applying aerostatic pressure from inside the bubble. The second is a possible refractive index change due to strain and stress in the resonator material. For a given material the elasto-optic coefficient (C) and shear modulus (G) are constants, so the pressure sensitivity is given by [13

13. R. Henze, T. Seifert, J. Ward, and O. Benson, “Tuning whispering gallery modes using internal aerostatic pressure,” Opt. Lett. 36, 4536–4538 (2011). [CrossRef] [PubMed]

, 36

36. R. Henze, J. M. Ward, and O. Benson, “Temperature independent tuning of whispering gallery modes in a cryogenic environment,” Opt. Express 21, 675–680 (2013). [CrossRef] [PubMed]

] (neglecting external pressure):
dλ(pi)λ=2n0(Rt)3+12CG(Rt)34Gn0(R3(Rt)3)pi.
(3)
where n0 is the refractive index. In [13

13. R. Henze, T. Seifert, J. Ward, and O. Benson, “Tuning whispering gallery modes using internal aerostatic pressure,” Opt. Lett. 36, 4536–4538 (2011). [CrossRef] [PubMed]

], Eq. 3 was fitted to experimental results. An example of the measured sensitivity to changes in internal pressure for a typical microbubble, with a shell thickness of 1.25 μm and a diameter of 74 μm, was ∼7 GHz/bar. From Eq. 3, the sensitivity of pressure sensing is proportional to the geometrical parameters R and t and a relative sensitivity, Sr, can be defined by:
Sr=λpR3R3(Rt)3.
(4)
For simplicity, in the following, Sr is used for sensitivity, and relative sensitivity is not distinguished from absolute sensitivity. Using Eq. 2 and Eq. 4, ℜ can be calculated. Note that since it is deduced from relative sensitivity, it is a relative resolution. Again, for simplicity, ℜ represents relative resolution in the following sections. The resolution, ℜ, is plotted in Fig. 7 as a function of shell thickness, and the graph incorporates the Q-factor plotted in Fig. 3. It can be seen that the best resolution is obtained with a shell thickness of about 1.4 μm. The resolution worsens when the shell thickness is less than 1 μm. This is due to the exponentially decreasing value of Q with decreasing shell thickness. When the shell is thicker than 1.5 μm, the resolution also worsens, as the sensitivity to pressure diminishes with increasing shell thickness. The Q-factor reaches the material limit when the shell thickness is more than 1.4 μm. Sensitivity changes as the inverse cube of the shell thickness, which causes less severe deterioration of the resolution.

Fig. 7 Resolution ℜ versus shell thickness for a microbubble used in pressure sensing. The diameter of the microbubble is 50 μm. The blue line shows the minimum range of resolution. It corresponds to an optimized thickness around 1.4 μm. Lines joining the data points are simply guides for the eye.

4.2. Refractive index sensing

Fig. 8 (a) Sensitivity is higher for thinner shells while (b) Q-factors drop for microbubbles filled with water for different bubble diameters (20 μm to 50 μm) and shell thicknesses (500 nm to 3 μm). For a certain thickness, an optimized resolution, defined by Eq. 2, can be achieved in (c) (horizontal, blue dashed line shows the minimum). Diameters in the Fig. are: 20 μm (black squares), 30 μm (red circles), 40 μm (purple triangles) and 50 μm (blue spades). (d) Comparison of ℜ with q = 1 (black squares) and q = 2 (red circles) for the same microbubbles. Lines joining the data points are simply guides for the eye.

So far it has been shown that high resolution refractive index sensing can be obtained by using a microbubble operating close to the quasi-droplet regime. It is assumed that index changes occur only in the core region. In some other situations, such as thermal sensing [37

37. J. D. Suter, I. M. White, H. Y. Zhu, and X. D. Fan, “Thermal characterization of liquid core optical ring resonator sensors,” Appl. Opt. 46, 389–396 (2007). [CrossRef] [PubMed]

], changes in both shell and core refractive index must be considered. The thermo-optical coefficient of silica is positive, which leads to a red shift of the modes if the temperature rises. The core is often filled with a negative thermo-optical liquid, such as water, ethanol, or acetone. The net thermal shifting of a bubble is determined by the proportion of intensity in the shell and core, as in Eq. 5. This can be tuned by selecting the shell thickness. Recent experimental results have proven that a thermally induced red shift of silica can be compensated for [37

37. J. D. Suter, I. M. White, H. Y. Zhu, and X. D. Fan, “Thermal characterization of liquid core optical ring resonator sensors,” Appl. Opt. 46, 389–396 (2007). [CrossRef] [PubMed]

] and it is even possible to obtain a large inverse blue shift [12

12. J. Ward, Y. Yang, and S. Nic Chormaic, “Highly sensitive temperature measurements with liquid-core microbubble resonators,” IEEE Photon. Technol. Lett. 25, 2350 (2013). [CrossRef]

].

4.3. Nanoparticle sensing

As an extension of the optimization method discussed in this paper, let us now consider nanoparticle sensing in microbubbles as a final example. Nanoparticle detection and bimolecular sensing have been realized in other WGRs [9

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

,15

15. 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]

,41

41. 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,” Nature Photon. 4, 122(2010). [CrossRef]

] and have also been generally discussed in LCORRs [27

27. H. Li, Y. Guo, Y. Sun, K. Reddy, and X. Fan, “Analysis of single nanoparticle detection by using 3-dimensionally confined optofluidic ring resonators,” Opt. Express 18, 25081–25088 (2010). [CrossRef] [PubMed]

]. Usually, the particles, the WGR, and the evanescent coupler are in an aqueous environment so that the particles can be delivered to the sensing devices. In practice, microbubbles can benefit from their hollow structure, so that various liquids can be passed inside the device while the optical readout occurs outside (by taper coupling, for example) without being influenced by the liquid. For a simple estimation of this effect, suppose a nanoparticle with a radius, r0, is attached to the inner surface of the shell and the core is filled with water (see inset of Fig. 9(a)). The nanoparticle possesses a refractive index difference to water, Δε (r0) in permittivity. This small perturbation by the particle can cause a frequency shift, δω, as follows:
Δωω=d3rΔε(|E(r)|)22d3rε(|E(r)|)2.
(6)
On calculation, the frequency shift of the fundamental TE mode is calculated assuming that Δε is a very small perturbation (Δε = 0.005) in the above Eq. 6. The sensitivity is plotted in Fig. 9(a).

Fig. 9 (a) Sensitivity of a microbubble for nanoparticle sensing. A relative frequency shift to the WGM is caused by a spherical nanoparticle (diameter 500 nm) attached to a water-filled 50 μm microbubble. Inset: schematic picture of the simulation condition. (b) ℜ versus shell thickness for a 50 μm microbubble for sensing the 500 nm nanoparticle. The axis of resolution is plotted on a log scale, which implies that the resolution improves nearly exponentially for a thinner shell for the first order fundamental mode (black squares). Here, the first order mode is plotted as black squares while the red circles represent the second order mode. Lines joining the data points are simply guides for the eye.

For thinner shells the sensitivity is much higher, because the nanoparticle changes the refractive index in the evanescent field that penetrates into the liquid core. Subwavelength thickness is required for particle sensing, otherwise the sensitivity goes to zero. The resolution determined from the sensitivity and the Q-factor data presented in Fig. 8(b) is plotted in Fig. 9(b). The resolution worsens exponentially when the shell thickness increases for a 50 μm microbubble. This is quite similar to the refractive index sensing situation, but with even more sensitive dependency on thickness. It can be understood by considering the concepts discussed in Section 3. From Eq. 6, the nanoparticle is sensed by the value of |E(r)|2, which means that a high sensitivity is achieved when the radial maximum covers the position of the nanoparticle. As discussed in Section 3 and shown in Fig. 5, if the microbubble is in the quasi-droplet regime, the maximum is shifted from inside the shell to the inner boundary of the microbubble near the position of the nanoparticle. If the relative position of the maximum to the nanoparticle changes, it leads to an exponential increase in |E((r))|2. This is the origin of exponentially improved resolution. Sensing nanoparticles with second order modes is also shown in Fig. 9. The simulation shows that there is an increase in sensitivity when the shell thickness is around 1.5 μm and the best resolution is achieved for a shell thickness of 1 μm. This corresponds to the multi maxima in the core discussed in Section 3. It is also obvious that, for microbubbles with the same shell thickness, both the sensitivity and resolution of the q = 2 mode are better than for the q = 1 mode. Within the simulation range from 500 nm to 1.5 μm, the microbubble is in the quasi-droplet regime for the q = 2 mode while out of this regime for the q = 1 mode, thereby proving that the quasi-droplet regime is quite important for high sensitivity particle sensing. Microbubbles in the quasi-droplet regime have other advantages. For example, for higher order modes in the quasi-droplet regime, more mode maxima lie in the core, implying a deeper penetration of the mode into the liquid. Even if one requires a method for sensing particles that are not attached to the inner surface, high sensitivity is still achievable if it is done using the appropriate higher order mode and a carefully designed shell thickness. This is of more practical significance in biochemical sensing applications.

Here, the absolute frequency shift due to the presence of a single particle was not discussed since the specific material and geometrical properties of the nanoparticle were not assigned in our simulations. Therefore, such a simple model based on perturbation theory cannot provide more information. For example, here the nanoparticle is a dielectric sphere with a diameter of 500 nm. Intuitively, as described in Eq. 6, sensitivity should decrease in an approximately cubic relationship to the size of the particle. However, an exact lower bound to the detectable particle size cannot be given due to lack of absolute sensitivity. It is worth noting that the FEM used herein is universal and, therefore, it should be capable of simulating such a case. A complicated modification to introduce arbitrary nanoparticles near the surface of a toroidal cavity to break the axial symmetry has been reported [42

42. A. Kaplan, M. Tomes, T. Carmon, M. Kozlov, O. Cohen, G. Bartal, and H. G. L. Schwefel, “Finite element simulation of a perturbed axial-symmetric whispering-gallery mode and its use for intensity enhancement with a nanoparticle coupled to a microtoroid,” Opt. Express 21, 14169–14180 (2013). [CrossRef] [PubMed]

]. With some modifications, this method should also be suitable for microbubbles.

5. Conclusions

WGM optical properties of microbubble WGRs have been studied with numerical simulation results based on FEM. When the shell thickness diminishes to a certain scale, the WGMs are dominated by the presence of the liquid core and the microbubble modes operate in the so-called quasi-droplet regime. This provides an ultra-sensitive way to detect liquid optical properties. Optimization was performed to achieve the best resolution for three types of sensing applications. This method can be further developed for a wide range of optimization designs with microbubbles besides sensing, such as newly developed optomechanical, microfluidic devices [30

30. G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013). [CrossRef] [PubMed]

] and group velocity dispersion control for utilization in optical frequency comb generation [43

43. M. Li, X. Wu, L. Liu, and L. Xu, “Kerr parametric oscillations and frequency comb generation from dispersion compensated silica micro-bubble resonators,” Opt. Express 21, 16908–16913 (2013). [CrossRef] [PubMed]

].

Acknowledgments

This work is supported by OIST Graduate University. We thank Dr. Yongping Zhang for fruitful discussions and Mr. Nitesh Dhasmana for his help in preparing this manuscript.

References and links

1.

K. J. Vahala, “Optical microcavities,” Nature (London) 424, 839–846 (2003). [CrossRef]

2.

L. N. He, S. K. Ozdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photon. Rev. 7, 60–82 (2013). [CrossRef]

3.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature (London) 415, 621–623 (2002). [CrossRef]

4.

Y. Q. Wu, J. M. Ward, and S. Nic Chormaic, “Ultralow threshold green lasing and optical bistability in ZBNA (ZrF4 − BaF2 − NaF− AlF3) microspheres,” J. Appl. Phys. 107, 033103 (2010). [CrossRef]

5.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature (London) 443, 671–674 (2006). [CrossRef]

6.

Y. S. Park, A. K. Cook, and H. L. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006). [CrossRef] [PubMed]

7.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics,” Opt. Express 15, 17172–17205 (2007). [CrossRef] [PubMed]

8.

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

9.

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

10.

M. Gregor, C. Pyrlik, R. Henze, A. Wicht, A. Peters, and O. Benson, “An alignment-free fiber-coupled micro-sphere resonator for gas sensing applications,” Appl. Phys. Lett. 96, 231102 (2010). [CrossRef]

11.

C. H. Dong, L. He, Y. F. Xiao, V. R. Gaddam, S. K. Ozdemir, Z. F. Han, G. C. Guo, and L. Yang, “Fabrication of high-Q polydimethylsiloxane optical microspheres for thermal sensing,” Appl. Phys. Lett. 94, 231119 (2009). [CrossRef]

12.

J. Ward, Y. Yang, and S. Nic Chormaic, “Highly sensitive temperature measurements with liquid-core microbubble resonators,” IEEE Photon. Technol. Lett. 25, 2350 (2013). [CrossRef]

13.

R. Henze, T. Seifert, J. Ward, and O. Benson, “Tuning whispering gallery modes using internal aerostatic pressure,” Opt. Lett. 36, 4536–4538 (2011). [CrossRef] [PubMed]

14.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J. M. Raimond, and S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145, 86–90 (1998). [CrossRef]

15.

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]

16.

T. Beck, S. Schloer, T. Grossmann, T. Mappes, and H. Kalt, “Flexible coupling of high-Q goblet resonators for formation of tunable photonic molecules,” Opt. Express 20, 22012–22017 (2012). [CrossRef] [PubMed]

17.

M. Sumetsky and Y. Dulashko, “SNAP: fabrication of long coupled microresonator chains with sub-angstrom precision,” Opt. Express 20, 27896–27901 (2012). [CrossRef] [PubMed]

18.

C.-L. Zou, F.-W. Sun, C.-H. Dong, F.-J. Shu, X.-W. Wu, J.-M. Cui, Y. Yang, Z.-F. Han, and G.-C. Guo, “High-Q and unidirectional emission whispering gallery modes: Principles and design,” IEEE J. Sel. Top. Quantum Electron. 19, 1–6 (2013). [CrossRef]

19.

T. Oo, C. Dong, V. Fiore, and H. Wang, “Evanescently coupled optomechanical system with SiN nanomechanical oscillator and deformed silica microsphere,” Appl. Phys. Lett. 103, 031116 (2013). [CrossRef]

20.

Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. H. Gong, “High-Q Exterior Whispering-Gallery Modes in a Metal-Coated Microresonator,” Phys. Rev. Lett. 105, 153902 (2010). [CrossRef]

21.

M. R. Disfani, M. S. Abrishamian, and P. Berini, “Teardrop-shaped surface-plasmon resonators,” Opt. Express 20, 6472–6477 (2012). [CrossRef] [PubMed]

22.

Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. H. Gong, “Strongly enhanced light-matter interaction in a hybrid photonic-plasmonic resonator,” Phys. Rev. A 85, 031805 (2012). [CrossRef]

23.

I. M. White, H. Oveys, and X. D. Fan, “Liquid-core optical ring-resonator sensors,” Opt. Lett. 31, 1319–1321 (2006). [CrossRef] [PubMed]

24.

M. Sumetsky, Y. Dulashko, and R. S. Windeler, “Optical microbubble resonator,” Opt. Lett. 35, 898–900 (2010). [CrossRef] [PubMed]

25.

A. Watkins, J. Ward, Y. Q. Wu, and S. Nic Chormaic, “Single-input spherical microbubble resonator,” Opt. Lett. 36, 2113–2115 (2011). [CrossRef] [PubMed]

26.

S. Berneschi, D. Farnesi, F. Cosi, G. N. Conti, S. Pelli, G. C. Righini, and S. Soria, “High Q silica microbubble resonators fabricated by arc discharge,” Opt. Lett. 36, 3521–3523 (2011). [CrossRef] [PubMed]

27.

H. Li, Y. Guo, Y. Sun, K. Reddy, and X. Fan, “Analysis of single nanoparticle detection by using 3-dimensionally confined optofluidic ring resonators,” Opt. Express 18, 25081–25088 (2010). [CrossRef] [PubMed]

28.

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theory Tech. 55, 1209–1218 (2007). [CrossRef]

29.

M. I. Cheema and A. G. Kirk, “Accurate determination of the quality factor and tunneling distance of axisymmetric resonators for biosensing applications,” Opt. Express 21, 8724–8735 (2013). [CrossRef] [PubMed]

30.

G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013). [CrossRef] [PubMed]

31.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000). [CrossRef] [PubMed]

32.

S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: Highlighting the liquid-air interface by laser emission,” Science 231, 486–488 (1986). [CrossRef] [PubMed]

33.

S. Uetake, R. S. D. Sihombing, and K. Hakuta, “Stimulated raman scattering of a high-q liquid-hydrogen droplet in the ultraviolet region,” Opt. Lett. 27, 421–423 (2002). [CrossRef]

34.

W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, “A quasi-droplet optofluidic ring resonator laser using a micro-bubble,” Appl. Phys. Lett. 99, 091102 (2011). [CrossRef]

35.

M. Sumetsky, Y. Dulashko, and R. S. Windeler, “Super free spectral range tunable optical microbubble resonator,” Opt. Lett. 35, 1866–1868 (2010). [CrossRef] [PubMed]

36.

R. Henze, J. M. Ward, and O. Benson, “Temperature independent tuning of whispering gallery modes in a cryogenic environment,” Opt. Express 21, 675–680 (2013). [CrossRef] [PubMed]

37.

J. D. Suter, I. M. White, H. Y. Zhu, and X. D. Fan, “Thermal characterization of liquid core optical ring resonator sensors,” Appl. Opt. 46, 389–396 (2007). [CrossRef] [PubMed]

38.

I. M. White, H. Oveys, X. Fan, T. L. Smith, and J. Y. Zhang, “Integrated multiplexed biosensors based on liquid core optical ring resonators and antiresonant reflecting optical waveguides,” Appl. Phys. Lett. 89, 191106 (2006). [CrossRef]

39.

I. M. White, H. Y. Zhu, J. D. Suter, N. M. Hanumegowda, H. Oveys, M. Zourob, and X. D. Fan, “Refractometric sensors for lab-on-a-chip based on optical. ring resonators,” IEEE Sensors J. 7, 28–35 (2007). [CrossRef]

40.

H. Li and X. Fan, “Characterization of sensing capability of optofluidic ring resonator biosensors,” Appl. Phys. Lett. 97, 011105 (2010). [CrossRef]

41.

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,” Nature Photon. 4, 122(2010). [CrossRef]

42.

A. Kaplan, M. Tomes, T. Carmon, M. Kozlov, O. Cohen, G. Bartal, and H. G. L. Schwefel, “Finite element simulation of a perturbed axial-symmetric whispering-gallery mode and its use for intensity enhancement with a nanoparticle coupled to a microtoroid,” Opt. Express 21, 14169–14180 (2013). [CrossRef] [PubMed]

43.

M. Li, X. Wu, L. Liu, and L. Xu, “Kerr parametric oscillations and frequency comb generation from dispersion compensated silica micro-bubble resonators,” Opt. Express 21, 16908–16913 (2013). [CrossRef] [PubMed]

OCIS Codes
(140.4780) Lasers and laser optics : Optical resonators
(140.3948) Lasers and laser optics : Microcavity devices
(280.4788) Remote sensing and sensors : Optical sensing and sensors

ToC Category:
Sensors

History
Original Manuscript: February 3, 2014
Revised Manuscript: March 7, 2014
Manuscript Accepted: March 7, 2014
Published: March 17, 2014

Citation
Yong Yang, Jonathan Ward, and Síle Nic Chormaic, "Quasi-droplet microbubbles for high resolution sensing applications," Opt. Express 22, 6881-6898 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-6881


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. K. J. Vahala, “Optical microcavities,” Nature (London) 424, 839–846 (2003). [CrossRef]
  2. L. N. He, S. K. Ozdemir, L. Yang, “Whispering gallery microcavity lasers,” Laser Photon. Rev. 7, 60–82 (2013). [CrossRef]
  3. S. M. Spillane, T. J. Kippenberg, K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature (London) 415, 621–623 (2002). [CrossRef]
  4. Y. Q. Wu, J. M. Ward, S. Nic Chormaic, “Ultralow threshold green lasing and optical bistability in ZBNA (ZrF4 − BaF2 − NaF− AlF3) microspheres,” J. Appl. Phys. 107, 033103 (2010). [CrossRef]
  5. T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature (London) 443, 671–674 (2006). [CrossRef]
  6. Y. S. Park, A. K. Cook, H. L. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006). [CrossRef] [PubMed]
  7. T. J. Kippenberg, K. J. Vahala, “Cavity optomechanics,” Opt. Express 15, 17172–17205 (2007). [CrossRef] [PubMed]
  8. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, F. Vollmer, “Shift of whispering-gallery modes in micro-spheres by protein adsorption,” Opt. Lett. 28, 272–274 (2003). [CrossRef] [PubMed]
  9. F. Vollmer, S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008). [CrossRef] [PubMed]
  10. M. Gregor, C. Pyrlik, R. Henze, A. Wicht, A. Peters, O. Benson, “An alignment-free fiber-coupled micro-sphere resonator for gas sensing applications,” Appl. Phys. Lett. 96, 231102 (2010). [CrossRef]
  11. C. H. Dong, L. He, Y. F. Xiao, V. R. Gaddam, S. K. Ozdemir, Z. F. Han, G. C. Guo, L. Yang, “Fabrication of high-Q polydimethylsiloxane optical microspheres for thermal sensing,” Appl. Phys. Lett. 94, 231119 (2009). [CrossRef]
  12. J. Ward, Y. Yang, S. Nic Chormaic, “Highly sensitive temperature measurements with liquid-core microbubble resonators,” IEEE Photon. Technol. Lett. 25, 2350 (2013). [CrossRef]
  13. R. Henze, T. Seifert, J. Ward, O. Benson, “Tuning whispering gallery modes using internal aerostatic pressure,” Opt. Lett. 36, 4536–4538 (2011). [CrossRef] [PubMed]
  14. V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J. M. Raimond, S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145, 86–90 (1998). [CrossRef]
  15. 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] [PubMed]
  16. T. Beck, S. Schloer, T. Grossmann, T. Mappes, H. Kalt, “Flexible coupling of high-Q goblet resonators for formation of tunable photonic molecules,” Opt. Express 20, 22012–22017 (2012). [CrossRef] [PubMed]
  17. M. Sumetsky, Y. Dulashko, “SNAP: fabrication of long coupled microresonator chains with sub-angstrom precision,” Opt. Express 20, 27896–27901 (2012). [CrossRef] [PubMed]
  18. C.-L. Zou, F.-W. Sun, C.-H. Dong, F.-J. Shu, X.-W. Wu, J.-M. Cui, Y. Yang, Z.-F. Han, G.-C. Guo, “High-Q and unidirectional emission whispering gallery modes: Principles and design,” IEEE J. Sel. Top. Quantum Electron. 19, 1–6 (2013). [CrossRef]
  19. T. Oo, C. Dong, V. Fiore, H. Wang, “Evanescently coupled optomechanical system with SiN nanomechanical oscillator and deformed silica microsphere,” Appl. Phys. Lett. 103, 031116 (2013). [CrossRef]
  20. Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, Q. H. Gong, “High-Q Exterior Whispering-Gallery Modes in a Metal-Coated Microresonator,” Phys. Rev. Lett. 105, 153902 (2010). [CrossRef]
  21. M. R. Disfani, M. S. Abrishamian, P. Berini, “Teardrop-shaped surface-plasmon resonators,” Opt. Express 20, 6472–6477 (2012). [CrossRef] [PubMed]
  22. Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, Q. H. Gong, “Strongly enhanced light-matter interaction in a hybrid photonic-plasmonic resonator,” Phys. Rev. A 85, 031805 (2012). [CrossRef]
  23. I. M. White, H. Oveys, X. D. Fan, “Liquid-core optical ring-resonator sensors,” Opt. Lett. 31, 1319–1321 (2006). [CrossRef] [PubMed]
  24. M. Sumetsky, Y. Dulashko, R. S. Windeler, “Optical microbubble resonator,” Opt. Lett. 35, 898–900 (2010). [CrossRef] [PubMed]
  25. A. Watkins, J. Ward, Y. Q. Wu, S. Nic Chormaic, “Single-input spherical microbubble resonator,” Opt. Lett. 36, 2113–2115 (2011). [CrossRef] [PubMed]
  26. S. Berneschi, D. Farnesi, F. Cosi, G. N. Conti, S. Pelli, G. C. Righini, S. Soria, “High Q silica microbubble resonators fabricated by arc discharge,” Opt. Lett. 36, 3521–3523 (2011). [CrossRef] [PubMed]
  27. H. Li, Y. Guo, Y. Sun, K. Reddy, X. Fan, “Analysis of single nanoparticle detection by using 3-dimensionally confined optofluidic ring resonators,” Opt. Express 18, 25081–25088 (2010). [CrossRef] [PubMed]
  28. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theory Tech. 55, 1209–1218 (2007). [CrossRef]
  29. M. I. Cheema, A. G. Kirk, “Accurate determination of the quality factor and tunneling distance of axisymmetric resonators for biosensing applications,” Opt. Express 21, 8724–8735 (2013). [CrossRef] [PubMed]
  30. G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013). [CrossRef] [PubMed]
  31. M. Cai, O. Painter, K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000). [CrossRef] [PubMed]
  32. S.-X. Qian, J. B. Snow, H.-M. Tzeng, R. K. Chang, “Lasing droplets: Highlighting the liquid-air interface by laser emission,” Science 231, 486–488 (1986). [CrossRef] [PubMed]
  33. S. Uetake, R. S. D. Sihombing, K. Hakuta, “Stimulated raman scattering of a high-q liquid-hydrogen droplet in the ultraviolet region,” Opt. Lett. 27, 421–423 (2002). [CrossRef]
  34. W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, X. Fan, “A quasi-droplet optofluidic ring resonator laser using a micro-bubble,” Appl. Phys. Lett. 99, 091102 (2011). [CrossRef]
  35. M. Sumetsky, Y. Dulashko, R. S. Windeler, “Super free spectral range tunable optical microbubble resonator,” Opt. Lett. 35, 1866–1868 (2010). [CrossRef] [PubMed]
  36. R. Henze, J. M. Ward, O. Benson, “Temperature independent tuning of whispering gallery modes in a cryogenic environment,” Opt. Express 21, 675–680 (2013). [CrossRef] [PubMed]
  37. J. D. Suter, I. M. White, H. Y. Zhu, X. D. Fan, “Thermal characterization of liquid core optical ring resonator sensors,” Appl. Opt. 46, 389–396 (2007). [CrossRef] [PubMed]
  38. I. M. White, H. Oveys, X. Fan, T. L. Smith, J. Y. Zhang, “Integrated multiplexed biosensors based on liquid core optical ring resonators and antiresonant reflecting optical waveguides,” Appl. Phys. Lett. 89, 191106 (2006). [CrossRef]
  39. I. M. White, H. Y. Zhu, J. D. Suter, N. M. Hanumegowda, H. Oveys, M. Zourob, X. D. Fan, “Refractometric sensors for lab-on-a-chip based on optical. ring resonators,” IEEE Sensors J. 7, 28–35 (2007). [CrossRef]
  40. H. Li, X. Fan, “Characterization of sensing capability of optofluidic ring resonator biosensors,” Appl. Phys. Lett. 97, 011105 (2010). [CrossRef]
  41. 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,” Nature Photon. 4, 122(2010). [CrossRef]
  42. A. Kaplan, M. Tomes, T. Carmon, M. Kozlov, O. Cohen, G. Bartal, H. G. L. Schwefel, “Finite element simulation of a perturbed axial-symmetric whispering-gallery mode and its use for intensity enhancement with a nanoparticle coupled to a microtoroid,” Opt. Express 21, 14169–14180 (2013). [CrossRef] [PubMed]
  43. M. Li, X. Wu, L. Liu, L. Xu, “Kerr parametric oscillations and frequency comb generation from dispersion compensated silica micro-bubble resonators,” Opt. Express 21, 16908–16913 (2013). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited