Bessel light modes have the physical characteristic of diffraction immunity [1,2], a property that has utilization in a diverse range of applications, including optical traps [3–5], optical coherence tomography [6,7], and nonlinear physics [8,9]. It is widely understood that such beams can be physically realized through use of an axicon, which acts to create linear phase retardation in the direction transverse to the optical axis [10]. Beams emanating from particularly designed axicons are termed “non-diffracting,” which in reality are of only discreet distance due to energy conservation arguments.

Commonly, axicon lenses have an obtuse apex, but acute angled axicons have also been reported. A recent theoretical study by Khonina et al. classifies a family of beam types arising from a range of apex angled axicons [11]. The formation of a quasi-Bessel beam occurs specifically when the half apex angle is greater than the incident angle for the condition of total internal reflection, illustrated in Fig. 1(a). For apex angles smaller in magnitude, the diffracting beams that emerge can be classified as evanescent hollow; evanescent at tip; and halo and hollow [11]. For acute angled axicons, classification is defined as collimated, focused, and hollow beams. This latter classification is cyclical with respect to the number of internal reflections made [12], schematically illustrated for the case of one internal reflection in Figs. 1(b)–1(d).

 

Fig. 1. Schematic illustration of ray paths for axicon lenses, including (a) obtuse apex-angle and (b)–(d) acute apex axicon with single internal reflection.

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This Letter reports the self-assembly of an integrated micrometer-scale oblate axicon refractive lens. This sits within a special class of axicons termed “micro-axicon,” an area that has gained increasing interest, with lens demonstrations upon planar [13], fiber [14,15], and bulk material [16]. The fabrication approach reported is unique and effectively forms two concatenated axicons, the first with an acute apex, formed by a tapered optical fiber and the second with an obtuse apex formed at the distal end of the fiber. The distal lens is fabricated primarily through self-assembly.

The fabrication method reported monolithically attaches an optical fiber to an optical planar substrate through use of consolidated high-purity glass soot. The soot is deposited via flame hydrolysis deposition (FHD), which can manipulate the refractive index, stress, and thickness of the resulting glass through mass flow controllers. So far, the platform, termed integrated optical fiber (IOF), has demonstrated environmental stability [17], physical monitoring [18,19], and refractometry [20,21]. This work expands applications much further, by demonstrating for the first time direct transitional coupling of optical power from the fiber constituent to its planar constituent, opening up new avenues of research and development of the platform. This could, for example, enable a route for ruggedized connectorization of silica fiber to silica planar platforms.

Figure 2 illustrates the process used for component fabrication in this work. It begins by linearly tapering an optical fiber, SMF-28e, to a diameter of 10 μm, using a micro-heater assembly. The optical fiber is subsequently placed upon a single-side-polished silicon wafer with a 15 μm thermally grown oxide. The oxide layer acts principally as an optical buffer (underclad) between the FHD and silicon. The FHD process uses a torch with four sheath flows. Through the central input flows chloride-based precursors, namely, ${\mathrm{PCl}}_3$, ${\mathrm{BCl}}_3$, and ${\mathrm{GeCl}}_4$, at rates of 100 sccm, 80 sccm, and 100 sccm, respectively. The precursors enter a hydrogen and oxygen flame with flow rates of 5.4 l/min and 2.7 l/min, respectively. The flame is shaped using a single argon sheath of flow 8.0 l/min. After deposition, the resulting soot is consolidated in a furnace that is ramped in temperature at a rate of 5°C/min to 1360°C and then cooled at a rate of equal magnitude. The high-temperature FHD consolidation step occurs $>1100°\mathrm{C}$, Fig. 2(e). This promotes the self-assembly of a lens at the distal end of the tapered fiber and integrates the taper to the planar layer. The lens is self-formed through meniscus effects in the consolidated FHD soot that is subsequently “frozen-in” when the device is returned to room temperature, observable in Fig. 3. The properties of the formed lens depend upon the diameter of the optical fiber, thickness of glass deposited, and composition of the soot (which affect its fluidic behavior, e.g., viscosity and surface tension). This enables a wide range of design freedom.

 

Fig. 2. Schematic illustration showing consecutive steps (a)–(f) of integrated optical fiber fabrication and self-assembly of the axicon lens.

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Fig. 3. Scanning electron micrograph images of the attached optical fiber, showing distal end of the fiber, with a self-assembled lens.

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After consolidation, the thickness and refractive index of the resultant FHD glass layers are measured using a prism coupler (Metricon). The thickness is taken as $6.10\pm 0.05\mathrm{\mu m}$ and refractive index of $1.4516\pm 0.0001$ (at 1.553 μm wavelength) and $1.4533\pm 0.0001$ (at 633 nm wavelength). The topology of the consolidated surface is analyzed using a stylus profiler (KLA Tencor P16+), illustrated in Fig. 4. The apex angle, $\alpha$, for the distal lens can be approximated as 113.9°. It should also be noted that the optical fiber itself forms an “acute axicon lens” with an angle of 0.08°, as shown in Fig. 4(a).

 

Fig. 4. Profilometry of the attached optical fiber, showing the topology of (a) acute angled axicon formed by the tapered fiber and (c) distal end of the fiber with a self-assembled lens, formed from consolidated FHD glass. Analytical approximation for the topology is shown in (b) and (d), respectively.

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In Fig. 4, it is noted that frozen-in surface tension features result in a trench around the optical fiber, where material is “pulled in” during consolidation. As expected, trench depth is a function of fiber diameter, principally on the order 0.4 μm in depth.

To observe guidance in the planar layer of the chip, a thin (30 nm) layer of gold is deposited on the top surface. This enables a plasmon–hybrid mode [22] to be supported as a TM modal solution in the planar layer. Light is launched into the optical fiber from a superluminescent-LED (centered on 780 nm). The observed diffraction pattern into the planar layer is captured from above using a complementary metal-oxide semiconductor (CMOS) camera (IDS UI-1240ML_NIR). It should be noted that this technique is non-destructive and through investigating different gold coverages, it was concluded that the presence of the gold layer itself had negligible influence on beam output, other than associated ohmic losses expected, which limit the extent of propagation.

The output captured in Fig. 5 shows a characteristic central beam and two accompanying spatial side beams that are angularly offset from the optical axis by 13°. Modulation in intensity is also observed, with a period of approximately 115 μm. It should be noted that such a feature is characteristic of a Bessel-like beam formed by an oblate axicon [10], understood to result from a co-propagating wavevector along the optical axis. Here, the obtuse oblate axicon is formed at the distal end of the fiber. The spatial sideband features are characteristic of an acute apex axicon forming a focused beam [16], consistent with the form of the linear tapered optical fiber.

 

Fig. 5. Images from CMOS camera taken (a) prior to launch, (b) upon launch at the distal end of the fiber, (c) upon launch at 3 mm offset upon the optical axis, and (d) upon a 6 mm offset (scale for all images equivalent).

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There are several approaches reported to model non-idealized axicons. Hankel transforms are one such approach [10], which are essentially two-dimensional circularly symmetric Fourier transforms, utilizable due to the typical rotational symmetry of an axicon. However, due to design complexity for this planar arrangement, a full three-dimensional Fourier-based beam propagation method is used to model system output. The simulation utilizes a fast Fourier transform beam propagation method (FFT-BPM) with perfectly matched layers (PMLs) for boundary conditions. The measured topology of the device is analytically approximated for the simulation, as shown in Fig. 4. The simulation does not include the thin gold layer that was used to observe the emerging beam, as it was experimentally verified that the presence of the gold did not alter the form of the emerging beam.

Figure 6 depicts the simulated modal power distribution just before light enters the distal lens. For clarity, the silicon, thermal oxide, FHD, and fiber layers have been marked. It is clear from the simulation that this particular geometry has power leakage, principally into the silicon substrate below and laterally into the planar FHD layer, indicated in the image with arrows showing direction of power flow. Leakage occurs for two reasons. First, after tapering, the power in the fiber guides principally in the cladding layer of the fiber. As the FHD has a higher refractive index, power leaks laterally but is partially contained by the self-assembled trench, previously discussed. Furthermore, the fiber cladding and the oxide buffer layer are comparable in refractive index, meaning that power is able to leak into the oxide layer and in turn the silicon. Future geometries that could reduce or remove such effects may include, for example, development of an initial FHD layer that is lower in refractive index than the optical fiber clad and can be used in place of the thermal oxide.

 

Fig. 6. Cross-sectional view of a three-dimensional FFT-BPM, showing the modal intensity just before light enters the integrated lens. Arrows indicate directional flow of power.

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Figure 7 is a top view simulation of light propagation from the distal lens and is comparable to the empirical data captured in Fig. 5. To achieve the image, power is integrated over a 4 μm spatial thickness in proximity to the device surface. Several features are common in both simulated and experimental data, including an intensity undulation, central power distribution, and two spatial side-band features. Deviations do occur between the simulation observed, due in part to differences between approximated and actual form. Consistent with mechanisms proposed, the central and side-band features are primarily influenced by the distal lens and fiber taper, respectively.

 

Fig. 7. Three-dimensional FFT-BPM showing the intensity distribution after the integrated lens.

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This work demonstrates, for the first time, power coupling from an optical fiber to an IOF platform. This is achieved through self-assembly around an optical fiber, forming structures that approximate axicons. Through a non-destructive approach gold deposition approach the optical propagation in the fabricated device is imaged.

Here, we enable future integrated applications monolithically combining and coupling light effectively into integrated components within the planar substrate.