1. Introduction

Self-assembly is a promising enabler of micro- and nano-scale devices [1], and is starting to play a role in mainstream technologies [2]. One category of self-assembly techniques employs thin film stresses, which can cause films to wrinkle [3], buckle [4, 5], or roll [6] in a predictable and controllable manner. Within this category, numerous optical devices have been demonstrated, including microcavities [7,8], microlenses [9], and integrated hollow waveguides [10].

Integrated hollow waveguides [11–13] have applications to optical sensing [13, 14] and fundamental physics studies [15], and as chip-scale optical communication channels [11, 12, 16, 17]. Recently, we reported [10] that stress-induced buckling of thin films could be exploited for the self-assembly of hollow Bragg waveguides on a silicon platform. A low temperature (<300 °C) fabrication process using a chalcogenide glass and a high performance polymer produced hollow waveguides with height ~2.5 μm and loss ~15 dB/cm. Compared to traditional methods for manufacturing integrated hollow microchannels and waveguides, our approach has the advantage of not requiring wafer bonding or sacrificial etch steps. However, the mechanics of buckle formation (which can involve both elastic and plastic deformations) result in a restricted range of size and shape for straight-sided buckles. Furthermore, this range scales with the thickness of the multilayer to be buckled. Since the buckled multilayer becomes the upper mirror of the waveguides, there are tradeoffs between the achievable core dimensions and the upper cladding reflectance. Given these geometrical restrictions and in the interest of fabrication simplicity, it is desirable to minimize the required number of layers while maintaining high reflectance.

It is known [18–21] that terminating a Bragg mirror by a metal layer can result in ultra-high reflectance for only a small number of dielectric bi-layers. We recently studied the metallic termination of omnidirectional dielectric reflectors (ODRs) [22], and showed that such an approach can deliver higher angle-averaged reflectance, wider omnidirectional bandwidth, and a reduction in the required number of layers. Here, we describe the application of hybrid mirrors to the self-assembled hollow waveguide process reported previously [10]. This approach reduces the overall number of layers by ~30%, while simultaneously reducing the propagation loss by nearly one order of magnitude.

2. Fabrication process and analysis of the fabricated structures

The waveguides were fabricated with only slight modifications to the previously described process [10], as shown schematically in Fig. 1. We first deposited a 5.5 period Bragg mirror comprising Ge₃₃As₁₂Se₅₅ (IG2) glass and polyamide-imide (PAI) polymer, onto a metal-coated Si substrate. The metal layer consisted of ~5 nm Cr (as an adhesion layer) followed by ~40 nm Au (selected for its high reflectance in the near infrared). The film deposition details were provided elsewhere [22]. Note that one of the attributes of the PAI polymer used is its good adherence to many metals (including Au) [23]. A thin Ag layer was subsequently patterned on the top (polymer) surface of the hybrid mirror, using a liftoff process.

 

Fig. 1. The sequence of steps is shown for producing a buckled hollow waveguide with metal layers terminating the upper and lower cladding mirrors. Light and heat are applied after deposition of the multilayer, to drive the dissolution of Ag into adjacent IG2 films. The main modifications to the established process [10] are that a metal-coated silicon substrate is used as a base and that a capping metal layer is added following the formation of the hollow channels.

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When an IG2 film is deposited overtop the patterned Ag layer, the Ag regions define the locations of subsequently formed delamination buckles. This is due to a loss of adhesion (between the overlying IG2 layer and the underlying PAI layer) following the light or heat driven dissolution of the Ag into the IG2 layer. From numerous trials, reliable and controllable buckle formation has been found to depend on the complete dissolution of the Ag strips at some desired stage of the process (i.e. such as after the deposition of the upper cladding mirror). We have inspected the polymer surface underneath buckled features (after mechanically removing the buckled overlayers), and confirmed that no significant amount of elemental Ag remains. A continuous Ag film was deposited following each IG2 layer in the upper mirror in order to increase the overall compressive stress, which is the other prerequisite for buckle formation [10]. As shown in Fig. 1, the first (bottom) IG2 layer in the upper mirror is designed to dissolve both the Ag strips and a continuous Ag overlayer. Thus, the thickness of the Ag strips plus the thickness of the Ag overlayer must be below some maximum, determined by the solubility limit and thickness of the IG2 layer. The solubility limit of thermally doped or photodoped Ag depends on the chalcogenide glass alloy [24], and is ~20 at. % for Ge₃₃As₁₂Se₅₅ [25]. We find that if the Ag strips are too thin, some buckles form prematurely (typically as ‘telephone cord’ buckles [4]) during the deposition of the upper mirror. In this case, it seems that the moderate temperature (~100 °C) used to soft-bake the PAI layers is sufficient to induce complete dissolution of the Ag strips. Conversely, if the Ag strips are too thick, we find that no delamination buckles will form, even after the sample is extensively exposed to light and heat.

In the samples described below, the first IG2 layer in the upper mirror was ~250 nm thick and it was deposited with an Ag overlayer ~10 nm thick. The three remaining IG2 layers were ~125 nm thick and each was followed by an Ag overlayer ~15 nm thick. A PAI layer (~290 nm thick) was spin-coated and soft-baked following the deposition of each IG2/Ag bi-layer. Keeping these details constant, this same upper mirror was deposited onto 4 bottom mirror samples patterned with Ag strips of different thicknesses: ~25 nm, ~35 nm, ~45 nm, and ~50 nm. Each sample was finally subjected to an identical light exposure and baking procedure to induce buckling, as described in [10]. After buckling, the samples were coated by ~40 nm Au to complete the upper hybrid mirror, and then in some cases spun-cast by a protective epoxy overlayer. All of the samples produced a reasonably high yield (>70 %) of straight-sided delamination buckles, but the best results (approaching 100% yield) were obtained for the Ag strip thicknesses of 45 and 50 nm. In these cases, there was no premature buckling of features, and nearly all of the intended features buckled during the final baking step. Photographs of these samples, showing buckles with base widths in the 10 to 80 μm range, are shown in Fig. 2. Unlike the results in [10], the wider channels do not exhibit secondary wrinkling along their axis, suggesting the compressive stress was better optimized in the present case.

 

Fig. 2. Digital camera images of a sample after the buckling process. (a) Low magnification photograph showing arrays of straight-sided buckles and 500 μm diameter microrings, after deposition of the upper Au layer. (b)-(c) Microscope images captured prior to deposition of the upper Au layer: (b) a pair of 500 μm diameter rings and (c) sections of 80 to 10 μm and 80 to 20 μm tapers. (d)-(e) Microscope images captured after deposition of the upper Au layer: (d) an array of 60 μm wide channels, with a single 40 and 80 μm channel also visible, and (e) s-bends in 80 μm wide channels. (f) Microscope image showing the facet (top view) of an array of 60 μm wide channels, cleaved after deposition of an epoxy overlayer.

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The geometrical properties of the buckled channels were studied using a contact profilometer (Alphastep), a non-contact optical profilometer (Zygo), and by SEM and AFM. Figure 3(a) shows the profile of typical buckles, as obtained using the contact profilometer. The peak buckle height varies from ~0.7 μm for the nominally 10 μm wide buckles to ~3.8 μm for the nominally 80 μm wide buckles. The wider buckles exhibited a larger variation in their peak height, as was observed previously [10]. However, the buckle heights generally exhibited less variation for the present samples. Figure 3(b) shows a contact profilometer scan across 5 adjacent buckles of 20 and 40 μm base width. The variation in buckle height is <10 %, and could probably be reduced in a more carefully controlled process. Some of the variation in height is attributable to unintended variations in the Ag strip widths (and thus the width of the buckles), which is in turn due to imperfect lithography and liftoff.

 

Fig. 3. Contact profilometer scans showing the approximate cross-section of the buckles. (a) Scans for nominally 10, 20, 40, 60, and 80 μm wide buckles. The flat top of the scans for the 10 and 20 μm wide buckles is an artifact due to the finite size of the profilometer tip, and is not present in AFM scans of the same buckles. (b) Scans for sets of 5 buckles, with nominal base width of 20 and 40 μm.

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Figure 4(a) shows an AFM surface plot for one of the 40 μm buckles. From short-range scans on the top surface of many buckles (of all sizes), the RMS roughness was consistently found to be below 1 nm. This was corroborated by the optical profilometer results (not shown). As evidenced by the SEM image in Fig. 4(b), the upper mirror buckles as a single structure without loss of interlayer adhesion. Thus, we postulate that a similar level of roughness would characterize the inner surface of the hollow channels.

 

Fig. 4. (a). AFM surface plot of a nominally 40 μm wide buckle. (b) SEM image (scale bar: 100 nm) showing the cleaved facet of a buckled multilayer (i.e. the upper mirror). Deformation of the PAI layers on cleaving obscures the IG2/PAI interfaces to some extent. The Au layer is visible as the bright line separating the last PAI layer from the epoxy overlayer.

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3. Ray-optics analysis of slab hollow waveguides

To gain insight into the air-guiding mechanism, we employed a simple ray-optics model for a slab Bragg waveguide [12, 26] as shown schematically in Fig. 5. The slab model is justified by the low height to width aspect ratio and laterally tapered shape of the buckle guides. The gradual tapering produces a relatively weak index guiding mechanism in the lateral direction [12, 13].

 

Fig. 5. A schematic illustration of the ray optics model for a slab hollow waveguide is shown. The structure is representative of the buckled waveguides with metal-terminated Bragg cladding mirrors.

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We made the simplest possible assumptions for an air-guided mode, as follows. First, we considered modes with a single anti-node in the vertical (transverse) direction (i.e. only the fundamental slab mode is modeled). Second, we assumed a hard boundary at the interface between the air core and each of the upper and lower cladding mirrors. The latter assumption is open to question, especially since neither the upper nor the lower mirror of our waveguides has a quarter-wave, high index layer adjacent to the core (i.e. non-negligible penetration of the guided mode field into each mirror is likely [26]). Nevertheless, the agreement with experiment is good as shown below. The effective angle of incidence for a guided ray was estimated by setting the air core thickness equal to half the transverse wavelength of the guided mode, leading to:

where λ ₀ is the free-space wavelength and d is the air-core thickness. Using (1) to estimate the effective angle of incidence, the effective ray reflectance of each cladding mirror was calculated. Then, considering the number of ray reflections per unit length, the propagation loss of the air-guided modes was approximated as [10, 12]:

where R_U (R_L) is the effective reflectance of the upper (lower) cladding mirror, and α is in dB/cm provided λ ₀ and d are expressed in centimeters. TE and TM modes were considered separately, by calculating the appropriate mirror reflectance for each case.

We calculated R_U and R_L versus wavelength using a standard transfer matrix model. The real part of the refractive indices of IG2 glass and PAI polymer were modeled using the dispersion expressions provided elsewhere [27]. The Ag-doped IG2 layers in the upper mirror were assumed to have a fixed (wavelength independent) increase in their refractive index, with the exact value of the increase dependent on the Ag concentration. Since we did not have an established model for the loss of these dielectric layers, we simply introduced a wavelength-independent extinction coefficient as a means to assess the relative impact of dielectric loss [22]. The complex optical constants of the metal layers were modeled using the closed-form expressions provided by Rakic et al. [28].

As a first test of the model, we considered the waveguides reported in [10]. In those waveguides, the lower mirror comprised 8.5 periods of alternating PAI polymer and undoped IG2 glass layers (on silicon), and the upper mirror comprised 4.5 periods of alternating Ag-doped IG2 glass and PAI polymer layers (with an epoxy overlayer). Neither mirror was terminated with a metal layer. Using the estimated layer thicknesses and other details provided in [10], the propagation loss versus wavelength predicted by (2) is plotted in Fig. 6, along with an experimental result for the transmission of TE polarized light.

 

Fig. 6. Results of a ray-optics model for the propagation loss of the buckled hollow waveguides reported in [10]. (a) The effective reflectance of the upper mirror versus wavelength, for a TE polarized ray (solid blue line) and a TM polarized ray (dashed red line). Lossless dielectric layers were assumed. (b) As in (a), but for the bottom mirror. (c) Comparison of the predicted and measured (black dotted line) insertion loss versus wavelength for the TE case, for a hollow waveguide 0.5 cm in length and with peak core height 2.5 μm. The dash-dot blue line was obtained assuming lossless dielectric layers. The solid blue line was obtained assuming nonzero loss in the dielectric layers, as described in the main text.

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The ray optics model provides an accurate prediction of the width and position of the low loss propagation band, and thus affords useful insight into the air-guiding mechanism. The experimental data is an insertion loss measurement on a 40 μm buckle waveguide, ~0.5 cm in length, and thus includes contributions from both coupling and propagation losses. For comparison, the theoretical estimate of propagation loss was simply scaled to a waveguide of the same length. Their good agreement suggests that the coupling loss makes a relatively small contribution to the overall insertion loss in this case. While we have not estimated the coupling losses directly, the results in Section 4 place an upper limit of ~3 dB for waveguides of similar core size. It is also worth noting that the rapid oscillation in the experimental pass band varies between samples and to some extent between scans on the same sample (for example, compare Fig. 6(c) to the scan on a similar waveguide in [10]). We attribute this to experimental instabilities and modal effects; the hollow waveguides support several propagation modes (see below), but the spectral scans are performed with single mode optics at the input and output.

The ray optics model predicts a minimum propagation loss for TE polarized light of ~13 dB/cm at 1620 nm, in good agreement with the results reported in [10]. For TM polarized light, the minimum predicted loss exceeds 300 dB/cm due to low reflectance from the upper cladding. We also considered the impact of a non-zero extinction coefficient for the dielectric layers, as discussed in greater detail in Section 4. As an example, Fig. 6(c) also shows the insertion loss for the case where the PAI layers have an extinction coefficient κ_P=10^-4 and the Ag-doped IG2 layers in the upper mirror have an extinction coefficient κ_IU=3×10^-4. This level of dielectric loss has a modest impact on the air-guided modes, increasing the minimum predicted propagation loss to ~15 dB/cm. This is due to the fact that the propagation loss is dominated by radiation through the cladding mirrors.

4. Experimental results for buckled hollow waveguides with metal-terminated claddings

To facilitate light guiding experiments, the samples shown in Fig. 2 were immersed in a liquid nitrogen bath and cleaved. Light guiding was studied using fiber pigtailed laser sources of various wavelengths, as well as a broadband supercontinuum source (Koheras SuperK Red). The input light source was passed through fiber-based polarization control optics and then coupled into the hollow waveguides using an objective lens. A second objective lens was used to collect light from the output facet, for delivery to a photodetector, an optical spectrum analyzer (Anritsu), or an infrared camera. System base scans were obtained without a sample in place, and sample insertion loss was estimated accordingly. Air guiding of light was observed for all buckle sizes; a more complete set of results will be reported elsewhere. Here, we focus on results for guides with ~60 μm base width and ~3 μm peak core height. Very similar results, including good agreement with the ray-optics theory, were obtained for 20, 40, and 80 μm wide waveguides. The high insertion loss of the 10 μm wide waveguides made comparison with theory difficult.

As for the waveguides in [10], single-wavelength excitation of the guides revealed the presence of multiple propagation modes. Figure 7(a) shows evidence of the four lowest order TE modes at a wavelength of 1320 nm, obtained by slightly adjusting the position of the objective lens relative to the input facet of the waveguide. For TE polarized light, 1320 nm is near the loss minimum of the waveguides as discussed below. Figure 7(b) shows a top view of a 1.2 cm long waveguide under these excitation conditions, with the input coupled power ~1 mW. The two bright spots are the input and output facets of the waveguide. No light streak is visible, suggesting low radiation and scattering of light through the upper cladding mirror. Light guiding was also studied at 1480 nm wavelength, since this lies near the loss minimum for TM polarized modes as discussed below. Figures 7(c) and 7(d) show captured light streaks for TM and TE polarized input light, respectively, facilitated in part by a higher available launch power (~20 mW). At 1480 nm, the ray-optics model (below) predicts high radiation of TE polarized light through the upper cladding. This is consistent with the bright, decaying light streak shown in Fig. 7(d).

 

Fig. 7. Light guiding in a buckle waveguide with 60 μm base width, as imaged by an infrared camera. (a) A series of end facet images for light at 1320 nm, with slight adjustments in the input coupling position. (b)-(d) Top view images showing scattered/radiated light streaks for a waveguide of length ~1.2 cm: (b) TE polarized light at 1300 nm. (c) TM polarized light at 1480 nm. (d) TE polarized light at 1480 nm.

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The supercontinuum source was used to obtain broadband scans. Light from the output facet of a waveguide under test was delivered to the optical spectrum analyzer via an iris, a fiber collimating optic, and a short length of standard single mode fiber. For measurements over such a broad wavelength range, considerable variation in the input coupling efficiency is possible. Furthermore, coupling a multimode waveguide to a single mode (for most of the wavelength range considered) fiber is expected to produce some ripple and artifacts in the experimental data (see Section 3). For simplicity, we neglected these details. Figure 8(a) shows an experimental insertion loss measurement for TE polarized light plotted alongside the predictions of the ray optics model, and Fig. 8(b) shows the analogous results for TM polarized light. For the model, layer thicknesses were estimated from SEM images and from fits to spectrophotometer data [22]. A thickness of 290 nm was used for all PAI layers, except as mentioned below for the TM case. In the bottom mirror, a thickness of 130 nm was used for the IG2 layers. In the top mirror, a thickness of 270 nm (140 nm) was used for the first (remaining) IG2 layers. All IG2 layers in the upper mirror were assumed to have the same wavelength independent increase in refractive index due to Ag doping, Δn_Ag=0.4 [25]. Finally, an air core thickness of 3 μm was used (see Fig. 3).

As for the result discussed in Section 3, the gross details of the modeled and experimental spectra are well matched. In the TE case, even the 3 satellite bands in the 900–1200 nm range are reproduced. For the TM experimental data, the plateau in the 1200–1300 nm wavelength range is actually due to residual transmission of TE light; the fiber-based polarization control optics used provide an extinction ratio on the order of 20 dB.

 

Fig. 8. Plots in the top (middle) row show the predicted ray reflectance for the upper (lower) cladding mirror of a 60 μm wide waveguide. Plots in the bottom row show the loss predictions of the ray optics model alongside the experimental insertion loss (black dotted line). In all cases, the dash-dot lines correspond to an assumption of lossless dielectric layers, while the solid lines correspond to an assumption of non-zero dielectric loss (κ_p=10^-4, κ_IU=3×10^-4, as explained in the main text). (a) TE polarized light. (b) TM polarized light. The square symbols in the bottom plots indicate the loss estimated from scattered light decay at 1480 nm.

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In order to improve agreement between the experimental and theoretical results, in particular for the TE case, it was necessary to introduce dielectric loss into the ray optics model. As shown in Fig. 8(a), both the upper and lower cladding mirrors of the waveguides exhibit a notch in reflectance within their main stop band. For the upper mirror, the notch is essentially due to the thicker IG2 layer nearest the core, and the depth of the notch is found to be very sensitive to the extinction coefficient of the Ag-doped IG2 layers (κ_IU). Ag doping of chalcogenide glasses is known to increase their sub-bandgap absorption [29]. For the lower mirror, the notch is due to the use of a low index (PAI) incident layer, and its depth is correspondingly sensitive to the extinction coefficient of PAI (κ_P). As shown in Fig. 8, reasonable agreement was obtained using fixed extinction coefficients of κ_P=10^-4 and κ_IU=3×10^-4 in the ray-optics model. However, the TE propagation loss is still underestimated in the 1600 to 1800 nm wavelength region, probably due to strong C-H overtone absorption in the PAI layers [22]. Also, the best fit for the TM case (as shown) was obtained for slightly reduced PAI layer thickness (280 nm). We attribute this to non-negligible birefringence, not taken into account by our dispersion model for PAI [27].

The use of fixed (wavelength-independent) extinction coefficients is simplistic, but nevertheless provides some insight into the experimental spectra. The extinction coefficient used for PAI is based on measurements reported elsewhere [22]. Independent determination of optical constants for the Ag-doped IG2 films is challenging, since such measurements should be performed on films with thickness similar to those used in the multilayers (~100–200 nm). This is because the properties (including homogeneity and uniformity, etc.) of an Ag doped layer depend on the thickness of the starting Ag and chalcogenide layers [24]. Furthermore, a rigorous understanding of the loss mechanisms would require more insight into the variation of the input coupling loss with wavelength. Some of the experimentally observed roll-off in transmission (for example within the 1200–1800 nm range for TE light) might be attributable to increased coupling loss with increasing wavelength. Indeed, preliminary loss measurements (using the scattered light technique described in [10]) at 1480 nm (the square symbols in Fig. 8) suggest that the impact of material loss was overestimated in the preceding analysis. We hope to clarify the relative contributions of absorptive, scattering, radiation, and coupling losses in future work.

Note that the omnidirectional reflection band of the bottom (top) cladding mirror lies in the 1450 to 1600 nm (1450 to 1800 nm) range [22], and that the air guiding of light exhibits minimum loss outside of this band. As is well known [12], the air guiding of light in a straight and uniform Bragg waveguide does not depend on omnidirectionality. However, guiding within the omnidirectional bands of the mirrors can provide additional functionality, including novel slow light devices [15] and low-loss, sharp waveguide bends [16].

Even at liquid nitrogen temperature, the PAI layers retain high toughness [23,25] and do not consistently fracture in a brittle manner on cleaving. Preparation of high quality facets is thus a challenge, making it difficult to estimate losses by the cut-back technique. Temelkuran et al. [30] reported similar challenges for hollow fibers based on chalcogenide glass and polymer. Furthermore, since very little light is radiated or scattered through the top mirror, it was not possible to estimate the minimum propagation loss (i.e. for TE polarized light near 1300 nm wavelength) from scattered light measurements. However, we can place an upper limit on propagation loss by considering the insertion loss and neglecting input coupling losses. Insertion loss as low as ~4.7 dB was measured (using both the broadband source and narrow linewidth sources) for waveguides with base width 60 μm and length ~1.2 cm, indicating that the propagation loss near 1300 nm is less than 4 dB/cm. From the ray-optics model, this corresponds to mirror reflectance (for both claddings) on the order of 0.999.

The propagation loss is amongst the lowest reported for integrated hollow waveguides. Modeling indicates that improved mirror design could result in even lower losses. For example, tuning the thickness of the layers adjacent to the air core can minimize the impact of dielectric losses. Furthermore, it would be beneficial to align the omnidirectional bands of the claddings with the low loss windows of the polymer. We hope to explore such improvements in future work.

5. Summary and conclusions

We have shown that metal termination of few-period Bragg cladding mirrors can greatly reduce the loss of integrated hollow waveguides. This approach allows the use of thinner cladding mirrors and simplifies the fabrication process. Furthermore, for self-assembled buckle waveguides, reduced cladding thickness can ultimately enable straight-sided buckles with smaller hollow cores.