3. Experimental setup

In Eqs. (3) and (4), k<sup>0</sup> is the wavenumber in vacuum, k<sup>0</sup> ¼ 2π=λ, Jm is the Bessel

<sup>m</sup> is its first derivative. We have considered that the

<sup>m</sup> is the second class Hankel

<sup>R</sup> ¼ 1508:25 nm,

eff ¼ 1:3800. Thus, the resonances for each

<sup>m</sup> is its first derivative, Hð Þ<sup>2</sup>

external medium does not present any anisotropy (in our case, it will be air). By following this procedure, it is possible to calculate the dispersion curves of several WGMs propagating in a cylindrical, silica MR of 125 μm diameter (the parameters of conventional optical fibers). Sellmeier dispersion of the silica was taken into account for the refractive index of the material. It is worth to note that the dispersion curves are not truly a curve, but a series of discrete solutions that have a particular radial order l and azimuthal order m. For a standard optical fiber and 1550 nm optical wavelength, the azimuthal orders will be relatively high (m � 300). Figure 2 shows the calculations of the resonant wavelengths for the first radial orders, as a function of the azimuthal order m for the TM polarization. The curves for the TE polarization follow the same trend, but the values of the resonant wavelengths are slightly different. By using Eq. (1), it is possible to relate the resonant wavelength with the effective index of the WGM resonance. For the azimuthal order m ¼ 360 and the first radial order, l ¼ 1, the resonant wavelengths

Resonant wavelength of WGMs with azimuthal orders from 250 to 370. Only a selection of the solutions to

(a) Optical field of a m ¼ 40 and l ¼ 1 WGM in a silica, cylindrical MR. (b) Field amplitude of the WGM as

a function of the radial coordinate, for m ¼ 40 and l ¼ 1; 2; 3.

function of order m and J

nTM

Figure 2.

Figure 3.

140

highlight their discrete nature is shown.

eff <sup>¼</sup> <sup>1</sup>:3826 and <sup>λ</sup>TE

function of order m, and Hð Þ<sup>2</sup> <sup>0</sup>

Applications of Optical Fibers for Sensing

0

and the effective indices of both polarization families are λTM

<sup>R</sup> <sup>¼</sup> <sup>1505</sup>:39 nm, <sup>n</sup>TE

polarization are not overlapped in wavelength.

The general setup used in the experiments is shown in Figure 4a. The light source is a tunable diode, linearly polarized laser (TDL) with a narrow linewidth (<300 kHz). The tuning range covers from 1515 to 1545 nm. The laser integrated a piezoelectric-based fine frequency tuning facility that allows continuous scanning of the emitted signal around a given wavelength, with subpicometer resolution. A polarization controller (PC) after the laser allows rotating the polarization of the light, and, as a consequence, it allows exciting TE- and TM-WGMs separately. The optical signal is then launched through an optical circulator, which enables measuring the WGM resonances in reflection by means of a photodetector (PD).

The MR will consist on a section of the bare optical fiber under test (FUT). Depending on the experiment, it will be a conventional telecom fiber, a rare-earth doped fiber, a photosensitive fiber, or a fiber where a grating has been previously inscribed. It is carefully cleaned and mounted on a three-axis flexure stage. WGMs are excited around the FUT by using the evanescent optical field of an auxiliary microtaper with a waist of 1–2 μm in diameter and a few millimeters in length. This is not the only method that allows exciting WGMs in MRs: for example, one of the first techniques consisted on using a prism to excite the resonances in a spherical MR [15], but the efficiency was very poor. More recently, a fused-tapered fiber tip fabricated using a conventional fiber splicer was demonstrated to be capable of exciting WGMs in a cylindrical MR [16]. However, the highest efficiencies are achieved by using microtapers, with coupling efficiencies higher than 99% [8]. These microtapers are fabricated by the fuse-and-pull technique from conventional

Figure 4. (a) Scheme of the experimental setup. (b) Typical reflection spectrum of a WGM.

telecom fiber [17]. The microtaper and the MR are placed perpendicularly (see in the inset Figure 4a). Since the optical field of the WGMs is not axially localized (its extension is around 200 μm in length [7]), this setup allows exciting the WGM at different positions along the MR: by sweeping the microtaper along the MR, it is possible to detect variations of the parameters of the MR in the axial direction by measuring the shift of the resonances—radius [13, 18], temperature, or strain. Variations can be characterized along several centimeters of the MR.

power that these systems can provide [22]. Another example is the shift in wavelength observed in distributed Bragg reflectors (DBR) and distributed feedback (DFB) lasers due to a pump-induced increment of temperature [23]. The heat is due to the non-radiative processes related to the electronic relaxation of some dopants: for example, this effect is less important in ytterbium-doped fibers, while Er/Ybcodoped and erbium-doped fibers exhibited a high increase of temperature with pump, due to its specific electronic-level system [24]. Thus, it is an intrinsic characteristic of the doped fibers that one needs to evaluate in order to design the proper

Whispering Gallery Modes for Accurate Characterization of Optical Fibers' Parameters

DOI: http://dx.doi.org/10.5772/intechopen.81259

In the experiments presented here, several commercially available single-mode, core-pumped doped fibers from Fibercore were investigated. Specifically, the FUTs were three Er-doped fibers (DF-1500-F-980, M12-980/125, and I25-980/125), a Ybdoped fiber (DF-1100), and an Er/Yb-codoped fiber (DF-1500 Y). The values for absorption coefficients at the pump wavelength were 5.5 dB/m (DF-1500-F-980), 12 dB/m (M12-980/125), 21.9 dB/m (I25-980/125), 1000 dB/m (DF-1100), and 1700 dB/m (DF-1100). Short sections of 2 cm in length of each FUT were used as the MR where the WGMs were excited. The FUTs were pumped with a singlemode, fiber-pigtailed laser diode that emitted a maximum power of 380 mW at 976 nm. As the pump launched to the FUT was increased, the WGM resonance shifted toward longer wavelengths in all cases, as it was expected, since the thermooptic and the thermal expansion coefficients of silica are both positives. As an example, Figure 5 shows the shift in wavelength of a resonance as a function of the pump launched to the fiber DF-1500-F-980. In our experiments, we did not investigate in detail the temporal response of the phenomenon, which will be ruled by the mechanisms that convert the pump power to heat, the heat conduction in silica, and the transfer of heat to the air. Typically, it will be on the range of a few tens of

At this point, several features of this technique must be clarified. First, it is worth to point out that the shift in wavelength is virtually independent of the particular resonance used for the measurements, that is, it does not depend on its radial and azimuthal order nor on its polarization. The sensitivity to thermal variations of different WGM resonances was theoretically calculated around 1.53 μm, taking into account both the thermal expansion of the fiber and the thermo-optic effect. The results showed that the difference in sensitivity between different resonances differs in less than 1/10000 per each ºC of temperature increase. This

The second aspect to highlight is related to the fact that the dopants in the active fibers are located in their core, while WGMs are highly confined in the outer region of the cladding (see Figure 3). From the study of heat conduction in doped fibers

Wavelength shift of the resonant wavelength as the pump power is increased. From left to right: pump power

optical system.

microseconds [25].

Figure 5.

143

simplifies the utility of this technique.

0 mW, 40 mW, 110 mW, 180 mW, 270 mW, and 370 mW.

The transmission of the taper was measured using a photodetector, and the signal was registered by an oscilloscope synchronized with the TDL. A typical transmission trace consists on a signal that will present a series of notches at the resonant wavelengths. For MRs of 125 μm in diameter, the free spectral range between two consecutive azimuthal orders m is � 4 nm at 1550 nm, and it is the same for both polarizations. Figure 4b shows the reflection spectrum of a resonance in an optical fiber (a ¼ 62:5 μm): its linewidth is 36 fm, which corresponds to a <sup>Q</sup>-loaded factor of 4 � <sup>10</sup><sup>7</sup> .

As it was mentioned before, the position of the resonances will depend on the value of the refractive index of the material. In the next sections, we will study the characterization of different fibers and fiber components by means of the measurement of the shift of WGM resonances as the effective index of the MR is modified.
