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Figure 14. Sensing mechanism:( a) mode shifting,( b) mode splitting( Dx is the detuning between the symmetric and asymmetric mode, while c is the mode linewidth),( c) mode broadening.
with C mq ¼½E m = ðpÞ2 ð2qþ1Þ ðq! Þ 2 Š 1 = 4
where C mq is a normalization constant. From these equations, we can see that the profile of the resonator will directly influence the axial dependence of the electrical field and the spectral distribution of the axial modes [ 61 ]. The radial dependence is a combination of the Bessel functions and the solution can be written as equation( 10).
4 The sensing mechanism
4.1
Label free mechanisms: mode shift, broadening and splitting
Optical microcavities like WGMR show a high contrast( order of 0.95), a high quality factor( over 10 6) and a narrow FWHM( from MHz to GHz), making them promising for optical sensing. In particular, if a small perturbation has to be detected, the steep resonance fringe allows to read little shifts of the resonance position as significant changes in the system transmission( Fig. 14a, blue curve). Otherwise, if large perturbations have to be detected, the steepness allows to accurately define the position of the resonance on a larger detuning scale( see Fig. 14a, black curve).
The traditional label free sensing mechanisms are based on monitoring the resonance changes such as: mode shift( Fig. 14a), mode splitting( Fig. 14b) and mode broadening( Fig. 14c). Monitoring the mode shift is the most common sensing technique. When an analyte aggregates at the surface of the WGMR, it interacts with the evanescent part of the WGM field, inducing not only a shift in the wavelength, but also a change in the Q-factor. This change is due to the losses that the analyte aggregation introduces: consequently a broadening of the resonance is observed. Mode shift and mode broadening are usually complementary techniques, since the mode shift can be caused by an environmental change not related to the analyte.
Figure 15. Scattered light measured with a hand-held spectrometer from a batch of microspheres with As204-Dylight800 1:2 ratio( As204-Dylight800 covalently bound to the surface microsphere of a diameter of about 140 lm) for two different pump powers: 148 mW( red squares) and 98 mW( black squares). Inset: Laser spectrum measured with an optical spectrum analyser.
Mode splitting is originates from the removal of the degeneracy of the clockwise and counterclockwise modes when a particle aggregates to the WGMR surface. This technique can only be used when the WGMR has ultrahigh Q factors. Mode splitting and mode broadening are selfreferenced techniques which make the detection unaffected by environment. A detailed explanation of these techniques can be found in several review articles or books [ 9, 62 ].
4.2
Fluorescence based detection and spectroscopy
There has been some tentative of demonstrating that WGMR can be effective for fluorescence detection, or labeled approach. The intrinsically small Stokes shift of fluorescence dyes may produce excitation and scattered light interferences, especially when the excitation source is a tunable diode laser. The wide gain profile of the semiconductor easily masks the emitted fluorescence due to the overlap with the emission spectrum of the dye. Pastells et al. [ 63 ] demonstrated that the measured scattered signal is just the excitation laser scattered by the microsphere and convoluted by the filter, and not the linear fluorescence( see Fig. 15). Pastells et al. proposed for the first time the use of nonlinear optical techniques for sensing in WGMR.
Fluorescence or Förster resonance energy transfer( FRET) is another technique that is widely used in sensing and / or imaging. In FRET there are two fluorophores, one acting as donor and the other one as acceptor. The donor and the acceptor have to be very close to each other( around 10 nm), they need to have a good overlap and they must be correctly oriented. FRET can occur at the interface of a WGMR under the condition of very short distance between donor and acceptor. The complexity of the FRET process makes it very sensitive to characteristic of the host environment( e. g. its pH or he concentration of ions, etc). Additionally, the absorption spectrum of the donor must not overlap with the absorption spectrum of the acceptor,