1. Introduction

Surface nanoscale axial photonics (SNAP) is a new platform for fabrication of complex miniature photonic circuits with the record small loss and accuracy [1–5]. SNAP explores whispering gallery modes (WGMs), which are launched along the transverse direction of an optical fiber and experience slow propagation along the fiber axis. Having very small propagation constant, these modes are sensitive to dramatically small variation of the fiber radius and its refractive index. The success of SNAP is predominately attributed to the ability of strong micron-scale localization of light with nanometer-scale variation of the optical fiber radius [1, 2] and the possibility of the fiber radius variation with unprecedented accuracy at sub-nanoscale [3, 4]. This accuracy is substantially higher than the accuracy achieved in lithographic fabrication of microphotonic devices [6–9]. For comparison, while the characteristic reproducibility of lithographic fabrication has achieved a few nanometers [6, 7], it can be less than an angstrom, i.e., at least an order of magnitude smaller, in SNAP [3]. In addition, the attenuation of light in SNAP microdevices is similar to silica microresonators, i.e., it can be at least two orders of magnitude smaller than the attenuation of lithographically fabricated microdevices [6–9]. The attenuation and the fabrication accuracy were the main impediments for application of coupled microresonator series as optical buffers [6]. It is expected that fabrication of coupled microresonator series based on the SNAP platform can solve this problem. Generally, the further development of SNAP will open its new intriguing applications both of fundamental and practical importance.

To date, two methods of super-accurate modification of the optical fiber radius at nanoscale and, in particular, reproducible fabrication of microresonator chains were demonstrated [3, 4]. The first method is based on local annealing with a CO₂ laser beam. In this approach, the nanoscale modification of the optical fiber radius is performed by the release of tension, which is frozen in during the fiber drawing. The second method is applicable to photosensitive fibers and explores variation of the optical fiber refractive index and its radius due to the UV laser exposure [3].

Previously, the series of identical UV-induced microresonators was demonstrated in a Ge-doped optical fiber exposed though an amplitude mask [3]. Due to the relatively weak photosensitivity, the introduced effective fiber radius variation was fairly small, around 0.5 nm. The effective radius variation similar to that demonstrated in [1] can be also introduced in chalcogenide glasses with stronger natural photosensitivity [10]. However, applications of chalcogenide microresonators are limited by higher attenuation of light, which is comparable to that in planar microresonators [6–9], refractive index instability, and aging [11]. To solve the problem, the photosensitivity of a Ge-doped fiber can be increased by hydrogen loading, the process successfully employed in the fiber grating inscription technique [12]. The advantage of fabrication of multiple series of coupled microresonators using the UV exposure compared to the CO₂ laser heating approach is in simplicity of simultaneous multiple resonator fabrication with an amplitude mask and a better accuracy (less than an angstrom compared to 2 angstroms [3]). However, as opposed to the fiber gratings, in SNAP, the periphery rather than the core of the fiber should be modified with the UV exposure. Because of the hydrogen leakage through the fiber surface, it was not clear if the concentration of hydrogen remaining near the fiber surface is sufficient for the efficient variation of the optical fiber radius.

In this paper, we show that the hydrogen loading of the Ge-doped fiber allows to increase the introduced effective fiber radius variation by an order of magnitude compared to the unloaded case. In addition, it is demonstrated that this variation can be increased further by a factor of two with a CO₂ laser beam annealing, which releases the tension frozen in during the fiber drawing. The fabricated chains of microresonators have the effective fiber radius variation up to 5 nm and enable mutual coupling. It is shown that, within the accuracy of measurement, the similarity of microresonators is affected by the background fiber radius variation rather than the fabrication process. Overall, we demonstrate the fabrication of coupled microresonators using the UV exposure of the Ge-doped hydrogen loaded optical fiber through an amplitude mask, a method of post-processing of these microresonators with a CO₂ laser beam exposure, and temporary tuning of these microresonators with a wire heat source.

2. UV-inscription of SNAP microresonator chains

A 15 µm radius coreless optical fiber used in our experiments was drawn from a uniformly doped 12.5% mol GeO₂ concentration silica preform. The photosensitivity of the fiber was increased by hydrogen loading [12]. The setup for fabrication of a SNAP microresonator chain is shown in Fig. 1(a) . The series of SNAP microresonators were created along the fiber surface with the exposure of 248 nm pulsed excimer laser beam through the amplitude mask having 100 μm period and 50% duty cycle. The inscription of microresonators was followed by 30 min annealing at 150°C.

 

Fig. 1 Illustration of fabrication, post-processing and tuning of SNAP microresonator changes. (a) Fabrication of microresonators with a UV exposure through the amplitude mask; (b) Trimming of microresonator chains with a CO2 laser beam; (c) Tuning of microresonator chains with a wire heater.

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The UV exposure results in modification of the optical (e.g., refractive index) and mechanical (e.g., density) and and geometric parameters of the photosensitive fiber [13, 14]. In SNAP, these modifications are taken into account by the summarized contribution to the effective fiber radius variation,

The characterization of the effective radius variation, Eq. (1), was performed with a microfiber scanning method [2, 16, 17]. A transverse biconical fiber taper with a micron diameter waist was connected to the light source and detector. The microfiber waist was translated along the test fiber and touched it in 5 μm steps evanescently exciting the resonant whispering gallery modes (WGMs) as illustrated in Fig. 2 . The WGM transmission power spectra were measured with a 3 pm wavelength resolution using the JDS tunable laser source and detector. These spectra allowed us to determine the variation of the effective fiber radius, Eq. (1), by enveloping the regions with WGM resonances as described in [2].

 

Fig. 2 Characterization of a SNAP fiber using the microfiber scanning method. The intensity of field distribution in microresonators and in the microfiber is illustrated in red.

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Figure 3(a) shows the results of measurement and characterization of a 1 mm length fiber segment, which contain the series of 10 SNAP microresonators created by the UV exposure through an amplitude mask as explained above. Figure 3(b) shows the magnified section of Fig. 3(a) containing two microresonators enveloped by the radius variation profile. It is seen that the characteristic effective radius variation of created microresonators is around 5 nm. This is an order of magnitude greater than that demonstrated for a similar fiber without hydrogen loading [3]. Each microresonator contains 3 axial modes. While the coupling of ground state modes of microresonators is not resolved, the second modes experience weak coupling, and the third modes are strongly coupled to each other. Due to smaller barriers which separate the third modes, the splitting of their resonances into a multiplet is clearly resolved. On the contrary, the resonances of the second modes are split into doublets only. This is explained by the larger barriers separating the second modes and also by the tilt (chirp) of the resonance positions, which is approximately 0.1 nm in wavelength and 1 nm in effective radius variation over 1 mm length of the fiber (Fig. 3(a)). As the result of tilt, the coupling between microresonators is additionally weakened.

 

Fig. 3 (a) Characterization of a 1 mm long UV-inscribed microresonator chain; (b) Magnified part of Fig. 3(a) containing two microresonators; (c) Characterization of a 1 mm long unexposed fiber section adjacent to the section shown in Fig. 3(a); (d) Magnified part of Fig. 3(c); (e) Characterization of a 1 mm long UV-inscribed microresonator chain, which was fabricated with 30% smaller UV power at a more uniform fiber section than that shown in Fig. 3(a); (f) Magnified part of Fig. 3(e) with two microresonators.

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The tilt of the microresonators in Fig. 3(a) is explained by the original variation of the optical fiber radius. In fact, Fig. 3(c) and 3(d) show characterization of the fiber segment, which was adjacent to that shown in Fig. 3(a) but was not UV exposed. The slope of the radius variation in Fig. 3(c) coincides with the average slope of the radius variation in Fig. 3(a) within the measurement accuracy.

For comparison, Fig. 3(e) and (f) shows characterization of another 1 mm long optical fiber section containing 10 microresonators. A better original uniformity of this section allowed us to create a series of similar microresonators with a significantly smaller tilt. In addition, reduction of the UV power resulted in decreased quantum well depth of the inscribed microresonators and in the smaller potential barriers between them. This caused stronger coupling between the second axial modes and, as the result, the multiplet splitting of their resonances.

3. Modification of SNAP microresonators with a CO₂ laser beam exposure

Another way to modify and trim the effective radius of a fiber at nanoscale, which is not limited by the fiber photosensitivity, is annealing [3, 4]. Here we investigate the combined effect of the UV exposure described in the previous section and annealing. To this end, we applied an unfocused CO₂ laser beam having 2 mm FWHM (Synrad, 48-2 series) to the microresonator chain shown in Fig. 3(a) and adjusted the laser power so that the microresonator in the center of the beam was erased. The duration of the exposure was 4 s and the switching time was ~0.1 s. The results of the experiment are shown in Fig. 4(a) . Characterization of the microresonator chain in this figure was performed similarly to those in Fig. 3. Crucially, while the heating temperature gradually decreased with the distance from the center of the CO₂ laser beam, the effect of the annealing was not monotonic. We explain this effect by saturation of the tension release. In fact, the temperature of the beam in the center was high enough to completely erase the UV introduced effective radius variation. With the decrease of local temperature in the ~$\pm 0.5$mm vicinity of the center, the depth of the microresonator quantum wells increases achieving the saturation value with effective radius variation of ~10 nm (Fig. 4(c)), i.e., two times greater than that before the CO₂ laser treatment (Fig. 3(b) and Fig. 2(b)). Presumably, the annealing of the fiber released the tension, which was frozen in during the fiber drawing [3, 4, 18, 19], and also the tension which was introduced by the photoelastic deformation of the fiber in the process of the UV exposure [13, 14]. The photoelastic tension caused negative variation of the refractive index and, thus, the release of this tension caused the local growth of the refractive index. In addition, the release of tension, which was introduced during fiber drawing, caused increase in both the refractive index and fiber radius [18, 19]. In the region, which is around 0.5 mm from the beam center (Figs. 3(a) and 3(c)), the relaxation of the total tension achieves saturation, which is manifested by the maximum radial shift and maximum depth of the quantum wells. Further decrease of the local heating temperature outside the $\pm 0.5$mm vicinity of the center leads to gradual decrease of the quantum well depth down to the depth of microresonators with were not exposed to the CO₂ laser radiation.

 

Fig. 4 (a) Characterization of a UV-inscribed microresonator chain, which was post-processed by a CO2 beam exposure; (b) Magnified part of Fig. 4(a) containing two microresonators in the region of vanishing CO2 beam power; (c) Magnified part of Fig. 4(a) in the region where the tension release was saturated.

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Thus, using the local CO₂ laser beam annealing (as well as other similar heat sources) can be employed for post-processing of SNAP microresonators and other SNAP devices. Remarkably, it is shown here that increasing or decreasing the depth of multiple microresonators can be performed simultaneously by a heating beam having the axial dimensions much greater than the dimensions of an individual microresonator. Presumably, further development of this demonstration will allow to introduce the predetermine modification of the effective radius variation at nanoscale. In addition, the UV correction of the SNAP devices fabricated at the photosensitive fibers is also possible [20].

4. Temperature dependence and temporary modification of microresonators with a wire heater

The spectral and transmission characteristics of resonant photonic circuits strongly depend on temperature. In particular, the performance of SNAP devices are affected by temperature through the effective radius variation

The performance of a microresonator chain depends both on temporal and spatial temperature variation along the fiber axis. From Eq. (2), the temperature dependence of the effective fiber radius ($r_0=15$µm) is ~0.12 nm/K. Thus, only several degrees of the temperature gradient over a millimeter of the fiber length is enough to compensate for the tilt ~1nm/mm of microresonator positions in Fig. 3(a). To demonstrate this, we employed a simple wire heater next to the SNAP fiber with series of microresonators characterized in Fig. 3. The heater was placed normal to the SNAP fiber and was enclosed into a silica capillary to protect the microresonators from contamination as illustrated in Fig. 1(c). The results of the experiment are shown in Fig. 5 . It is seen that by local heating of the microresonator chain we were able to modify the tilt of their original positions (compare Fig. 3(a) and Fig. 5(a)). The local spectra of microresonators away from the heater (Fig. 5(b)) resemble those in Fig. 3(b). However, the behavior of spectra in the vicinity of the heater experience severe noise (Fig. 5(c)). The latter is explained by fluctuations of local temperature in time, common for microresonator devices with temperature control (see e.g. [5, 21]). This noise is further dramatized in our experiment due to a large time interval between the successive spectral measurements equal to 1 minute. Substantial reduction of the observed spectral noise requires a much better temporal stabilization of the temperature and is beyond the scope of this paper.

 

Fig. 5 (a) Characterization of a UV-inscribed microresonator chain, which was temporary tuned by a wire heater; (b) Magnified part of Fig. 5(a) containing two microresonators in the unheated region; (c) Magnified part of Fig. 5(a) in the heated region.

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5. Summary

Thus, the Ge-doped and hydrogen loaded thin photosensitive fiber is a promising platform for fabrication of SNAP microdevices and, in particular, for integrated chains of coupled microresonators. The additional post-processing of these devices with a CO₂ laser allowed us to modify their profile and contrast. In the developed approach, the achieved variation of the effective radius of a microresonator was as large as 10 nm. Potentially, this will allow us to increase the density of coupled microresonator integration from 10 per mm, demonstrated in this paper, to up to 50 per mm by employing amplitude masks with smaller periods and programmed CO₂ laser post-processing, which enables correction of the original fiber radius variation. The mode coupling and resonance spacing of individual microresonators can be controlled by choosing the appropriate period and duty cycle of the amplitude mask and the laser beam power. The demonstrated approach can be also useful for the fundamental investigation of the effect of photosensitivity.