A new type of self-coupling multi-port microcoil resonator using a microfiber coupler is presented. The microresonators, a simple combination of a microfiber coupler and microcoil resonator, were fabricated by coiling a four port microfiber coupler around a low index support rod to induce optical resonance via coupling between adjacent turns. Light propagates along the coil whilst the beating between the supermodes of the coupler is still present, giving an increased extinction ratio and an output spectrum strongly dependent on the microfiber coupler diameter. The multiport microcoil resonator was embedded in a low refractive index polymer to improve its robustness and the polarization dependence was further analyzed.
©2012 Optical Society of America
Optical microfiber resonators [1–4] have gained a great interest in a variety of fields, due to their easy configurability with fiberized components, low-cost, ease of manufacture, strong evanescent fields and relatively high quality factor (Q-factor up to 2.2 × 105) . Microfibers with a diameter of a few micrometers are particularly suited for fabricating such compact devices due to their flexibility and ease of bending without any measurable losses [2,4]. Three different types of micro-resonators have been demonstrated from a single strand of microfiber to date, including loop resonators , knot resonators  and microcoil resonators (MCRs) . In particular, MCRs were first proposed theoretically in ref. 3 and then implemented experimentally in ref. 6, with subsequent research introducing a new pack of applications in optical sensing [7, 8], fast/slow light  and optical delay lines . However, some applications in this area (mostly sensors) require multi-port channels and attempts for achieving four port micro-resonators included a reef knot (multiport equivalent of the knot resonator)  and racetrack resonators (equivalent of the loop resonator) . In this paper, we propose a new type of multi-port microcoil resonator (MMCR), which is the multiport equivalent of the MCR. The MMCR is based on a microfiber coupler (MC) wrapped around a low index support rod, thus offering the potential benefits of both the MCR and the fiber coupler. This resonator promises to serve all the applications that utilize the MCR; however the interesting features of MMCR such as the high polarization dependent extinction ratio and/or the physical separation between the output ports could be exploited in applications such as optical sensing, integrated optical switches and modulators.
2. MMCR fabrication
The proposed MMCRs as shown in Fig. 1 were fabricated in three steps: first, a MC was fabricated from two 125 μm diameter standard telecom fibers (Corning SMF-28) using the microheater brushing technique ; then, the MC was wrapped around a low refractive-index support rod in a self-coupling coil; finally, the coiled MC was embedded in a low refractive index polymer matrix which was cured to enhance sturdiness. ~100 mm long sections of two single mode fibers were stripped of their coating and twisted 1.5 turns around each other to ensure the two fibers were in close contact before being fused together using a ceramic heater at an estimated fusing temperature of ~1450 °C. In our experiment, two different microfiber couplers were fabricated with waist diameters of d~3.2 µm (MC1) and d~0.7 µm (MC2) respectively. In both MCs, the lengths of the uniform waist region were 4 mm and the adjacent transition regions were ~3 cm. These dimensions were chosen to facilitate handling and simultaneously provide a large distance (~40 nm) between two consecutive maxima in the output ports spectra, so the coupler’s spectral features can be easily distinguished from the resonator resonances.
First of all, we investigated the output spectra of the microfiber coupler using an optical spectrum analyzer (Yokogawa, AQ6370) while the input port was connected to an incoherent white light source (Bentham, WLS100). Figure 2(a) clearly shows the oscillation pattern typical of beating between supermodes  over the whole investigated spectral range , while Fig. 2(b) presents high frequency oscillations only at wavelengths smaller than λ<1.05 μm, due to higher order mode filtering . The fabricated MCs were coiled around a 1 mm diameter glass rod coated with Teflon (refractive index n~1.31 at λ = 1.55 μm) using a computer controlled set of rotation and linear stages . The distance between adjacent turns was about 3.5 μm and coiling was carried out until sharp resonance peaks appeared (typically after 720°).
Figure 3(a) shows an optical microscope image of the coiled MC1 and a cross sectional scanning electron microscope (SEM) image at the microfiber waist is shown in Fig. (b). In fact, because of the low fabrication temperature, the MC exhibits a dumbbell cross section and longitudinal rotations considerably complicate the overall interloop coupling properties. The final microresonator was packaged with ultra-violet (UV) curable polymer (Luvantix PC-373) to enhance their stability. Normally, a resonance shift and optical loss increase are introduced as a result of the large index difference between the air and polymer, but the latter effect can be minimized using techniques explained in Ref. 5.
3. Experimental MMCR spectral characterization
Figure 4 shows the optical resonance spectra for both output ports in two MMCRs, all exhibiting sharp resonances similar to those previously well-reported MCR . However, the additional degree of coupling present in the MC complicates the MMCR spectra; in fact, the output ports seem to be complementary to each other in sample MC1 Fig. 4(b) and similar in MC2 (Fig. 4(d).The explanation behind the different behaviour may lie in the different number of supermodes supported by the MC used to make the different MMCRs. MMCR1 Fig. (4b) has a relatively large waist diameter; thus it supports several supermodes which beat and give the complementary output characteristic of couplers.
At resonances, light simply traverses a longer optical path within the MMCR and the output spectra depend on the relative phase difference between the two supermodes. For this reason, the maxima of port 3 coincide to the minima of port 4 and vice versa. On the other hand, in MMCR2 Fig. 4(d) output spectra maxima and minima of port 3 and 4 coincide; i.e. no complimentary behaviour was noticed. This could be attributed to the fact that the narrower waist of this coupler can support only one supermode, which makes the spectra of the MMCR2 very similar to the well-known MCR, and power is simply split at the output ports in a similar ratio. However, this device still shows some modulation in the resonance extinction ratio as shown in Fig. 4(c); these oscillations are believed to arise in the transition region of the coupler, where beating between the supermodes could still exist. MMCR2 has considerably higher losses than that of MMCR1 and its fabrication is also more challenging. Similar to loop and knot resonators, MMCRs are expected to be polarization dependent and therefore we investigated the transmission of MMCR1 for linearly polarized light with different polarization angles. As shown in Fig. 5(a) , the change in polarization azimuth results in a small shift in the resonance wavelength (0.0616 nm), accompanied by an enhancement in the extinction ratio, which can reach values >20 dB as shown in Fig. 5(b). Compared to a standard MCR, the MMCR extinction ratio at port 3 is relatively high because power injected in port 1 is reduced both by loss and by power exchange into port 4.
Numerical modelling has been carried out to prove that the secondary resonance peaks and the complimentary behaviour of the resonance peaks in different output ports are an intrinsic feature of the MMCR1 and that they do not arise from external experimental factors such as fabrication tolerances and/or polarization. Simulations focus on MMCR1, as MMCR2 behaves like an MCR, which has been modelled in [3, 6-7, 9-10]: while in a common MCR resonances arise from interloop coupling of the fundamental mode propagating in a single microfiber, in MMCR2 they are created by a single supermode propagating in the coupler. In a coupler, light exchange between the two arms is due to beating between supermodes excited by a single mode at the input port. MMCR1 was modelled using the schematic shown in Fig. 6 .
Equations that describe light propagation/coupling inside an MCR  were adapted to include coupling between different fibres composing the coupler [6, 15] in addition to the conventional coupling to the next/previous turn, as given by Eqs. (1-2):
Here represents the amplitude of the electric field component in the turn of the coil at a distance along the turn which has a total length. Note that each arm of the coupler is assigned a separate field amplitude. represents the propagation constant of the mode . The transmissivity was calculated from numerical solution of Eqs. (1-2) subject to the boundary conditions of field continuity between turns as in . The coupling between neighboring turns of a microcoil is typically of the order of 103 m−1 ; to ensure sharp resonances, was chosen to be 5600 m−1 (i.e. near to critical coupling). The internal coupling of the MC was evaluated from SEM pictures of the MC1 cross section (Fig. 3b). The image of the cross section of the coupler was imported to COMSOL to calculate the effective index of the supermodes and thereby calculate the value of, which resulted to be = 36140 m−1. Figure 7 Shows the odd and even supermode profiles in the MC1 waist. The even supermode in Fig. 7(a) and green line in Fig. 7(c) is similar to the fundamental mode in single mode fibers.
Although could vary considerably with any change in geometry, its value nonetheless remains in the range of 104 m−1. Simulation results are shown in Fig. 8(a) and clearly resemble experimental results: in both experiments and simulations the output power of the output ports are complementary and show closely spaced multiple peaks. This can be ascribed to more light coupling at resonance and less coupling off resonance, as a result of the different effective optical paths experienced by light propagating inside the resonator.
Note that an equivalent MCR with the same and geometry would only show one resonance per free spectral range (FSR), whereas Fig. 8a clearly shows several resonances per FSR. MMCR can therefore exhibit certain traits normally found in MCRs with higher number of turns (N = 6). Figure 8(b) shows the effects of the coupler coupling coefficient on the output over one free spectral range. It is clear that the transmission is strongly dependent on even small variations of. In particular, for near the critical coupling (~3.6 × 104 m−1), the spectrum contains two resonances per FSR, in agreement with Fig. 4(b), whereas further away from each resonance undergoes splitting.
In summary, a new type of a four port micro-resonator (the MMCR) has been fabricated by coiling a micro-coupler with specific dimensions around a support rod. By varying the diameter of the coupler minimum waist, it has been possible to control the output spectra: at a small coupler diameter ~700nm the MMCR behaves exactly as an ordinary MCR. This device can have high extinction ratios (~20 dB) and it is highly polarization dependent. These properties make the MMCR a promising device for microfiber devices and sensors, where sharp resonances and physical separation between output signals are important.
References and links
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