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We describe the fabrication of integrated hollow waveguides through guided self-assembly of straight-sided, thin film delamination buckles within a multilayer system of chalcogenide glass and polymer. The process is based on silver photodoping, which was used to control both the stress and adhesion of the chalcogenide glass films. Straight, curved, crossing, and tapered microchannels were realized in parallel. The channels are cladded by omnidirectional dielectric reflectors designed for low-loss, air-core guiding of light in the 1550-1700 nm wavelength range. Loss as low as ~15 dB/cm was measured for channels of height ~2.5 μm, in good agreement with both an analytical ray optics model and finite difference numerical simulations. The loss is determined mainly by the reflectivity of the cladding mirrors, which is ~0.995 for the as-fabricated devices.
©2007 Optical Society of America
1. Introduction
Low-loss hollow waveguides with periodic claddings, in both fiber [1-2] and integrated [3] form, are emerging as an important class of optical devices. Potential applications include temperature-insensitive and tunable telecommunication devices [3], optical analysis of small volumes of gases or liquids [4], nonlinear optics in gases [5], novel slow light and optomechanical structures [3,6], and chip-scale optical interconnects [7-8]. Integrated hollow waveguides have traditionally been fabricated by wafer bonding [4,7] or by selective etching of a sacrificial material [9-10]. Here we describe a new approach, wherein hollow microchannels are fabricated by controlled formation of thin film delamination buckles within a multilayer stack. The microchannels are surrounded by omnidirectional dielectric reflector (ODR) claddings [11-15] comprising thin films of chalcogenide glass and polymer, making them an integrated planar analogue of the so-called ‘Omniguide’ fibers [1]. Light guiding experiments have confirmed that propagation loss is relatively low (as low as ~15 dB/cm) over the omnidirectional bandwidth of the cladding mirrors, in the 1550-1700 nm wavelength region. Straight, curved, tapered and crossing channels were realized on a single wafer. We believe that the approach described might enable new opportunities for gas- and liquid-phase photonic integrated circuits.
2. Brief background on delamination buckles
Buckling delamination of thin films is a fairly well understood phenomenon [16-17]. Within the regime of elastic deformation, the buckled areas are characterized by an increase in bending strain energy but a decrease in compressive strain energy. Buckling of a film can occur spontaneously, provided: (i) the compressive energy exceeds the bending energy for a given buckled width, and (ii) the energy release rate (per unit area under the buckle) is higher than the adhesion energy per unit area between the film (or stack of films) and its substrate. Beautiful and intriguing patterns often arise, as reviewed elsewhere [16-18]. Since film delamination causes catastrophic failure of microelectronic circuits or of protective barrier coatings, buckling has traditionally been studied as a problem to be avoided.
Recently, a few researchers [18-21] have investigated means to control the formation of buckles and some [18,21] have suggested applications in microfluidics. The desired buckle morphology for microfluidic channels and hollow waveguides is a straight-sided blister, commonly known as the Euler column [18]. Within elastic limits, and for a given equi-biaxial, pre-buckle stress level, the Euler column arises for only a restricted range of buckle width [18,22]. However, if compressive, bending, or shear stresses exceed the yield stresses of the films undergoing delamination, plastic deformation also plays a role in determining the buckle shape [17].
3. Process description and fabrication details
To control the location and shape of delamination buckles, two distinct properties must be engineered. First, a technique for creating regions of low and high adhesion [18] is required. Second, some means is required for accurately controlling the stress within the layers to be buckled. Our process is essentially guided self-assembly of straight-sided, Euler-like buckles by delamination of a multilayer stack, as illustrated in Fig. 1. Control over both adhesion energy and compressive stress was achieved through the well-known silver photodoping phenomenon [14,23], where illumination of a silver film in contact with a chalcogenide glass causes the silver to be dissolved into the glass. We have found that we can tune the compressive stress in a chalcogenide glass film by photodoping varying amounts of silver, as shown in the inset of Fig. 1. Furthermore, we have found that, under the right conditions (as described below), dissolution of an embedded Ag layer results in loss of adhesion between the adjacent chalcogenide film and an underlying polymer layer.
Fig. 1. Schematic of the process used to form hollow waveguides. PAI is polyamide-imide and IG2 is Ge33As12Se55 glass. Inset: evolution of the compressive stress in a single IG2 layer on a silicon substrate versus the number of Ag layers (~25 nm thick) sequentially photodoped into the glass. The origin of the horizontal axis corresponds to the as-deposited film.
A representative process flow (Fig. 1) is described briefly in the following; more details on film deposition can be found elsewhere [13-15]. First we deposited a series of alternating Ge33As12Se55 chalcogenide glass (IG2, Vitron AG) and polyamide-imide (PAI) polymer (Torlon AI-10, Solvay Advanced Polymers) layers (~150 nm and 290 nm thick, respectively), starting and ending with a polymer layer, to form an 8.5 period ODR. A thin silver layer (~50 nm thick) was patterned by liftoff on the top surface of this mirror. A second (4.5 period) ODR was then deposited, starting with a thicker (~260 nm) IG2 glass layer (first layer only, as explained in Section 5). In this ODR, a thin (~20 nm) silver layer was deposited following each IG2 glass layer. Aside from tuning the stress, dissolved Ag increases the refractive index of the IG2 layers, thereby increasing the peak reflectivity and omnidirectional bandwidth of the upper ODR [14]. The PAI layers in the upper mirror were soft-baked only (5 min at 90 °C). As is typical for spun cast and cured polymer films, the PAI layers are under tensile stress at room temperature (in the 10-20 MPa range, as determined by studying single PAI layers). The tensile stress of these layers offsets the compressive stress in the IG2 layers, and inhibits the buckling of the stack during its deposition.
Following deposition of the entire structure, the sample appeared essentially flat and featureless. A two-step process was used to initiate post-deposition buckling. First, the sample was exposed to a high intensity (~0.1 W/cm2) white light source for approximately 1 day, to drive dissolution of Ag into the IG2 glass films. Second, the sample was heated on a hot plate in a flowing nitrogen atmosphere. Any previously undissolved Ag diffuses into adjacent IG2 films during this baking process [14], increasing the stress of the IG2 layers in the upper mirror. In a typical baking process, empirically optimized by testing numerous samples, the temperature was ramped at ~5 °C/min up to 120 °C, and then at ~ 1 °C/min until nearly all of the intended features had buckled. While we often observe some localized buckling after the white light exposure, most of the buckling features arise above some critical temperature (~160 °C) during the baking process. As the temperature rises, the compressive stress of all layers increases (in addition to the stress increase caused by Ag dissolution) due to the higher thermal expansion coefficients of IG2 (~12×10-6 K-1) and PAI (~30×10-6 K-1) relative to the Si substrate (~3×10-6 K-1). Furthermore, the layers are more prone to deform plastically at elevated temperature, as discussed below. The end result is that the upper ODR buckles in locations defined by the patterned Ag layer, producing hollow channels (similar to Euler columns) surrounded by ODR mirrors (see Figs. 1 and 2). After buckling, the sample was slowly cooled to room temperature, and spun-cast with an overlayer of epoxy (Norland Optical Adhesive, NOA-73). Samples were cleaved after a brief immersion in liquid nitrogen, which improves the tendency of the PAI layers to fracture in a brittle manner on cleaving [14]. Nevertheless, some stretching of the PAI layers is evident in the SEM images (see Figs. 2 and 4). In spite of this, the IG2 layers cleave well and the glass and polymer layers within the upper and lower mirrors remain well adhered. This is quite remarkable given the range of temperature (-196 °C to > 200 °C) to which samples were exposed during processing.
Dissolution of the Ag strips into the bottom IG2 layer of the upper mirror is believed to be akin to a ‘disappearance’ of the interfacial bonds in these regions; anecdotal evidence of decohesion accompanying Ag photodoping has been reported previously [24]. Within the upper mirror, delamination between the PAI and Ag-doped IG2 layers is avoided by restricting the Ag thickness. Because of the order of deposition, sufficiently thin Ag layers are dissolved into the IG2 layers during sputtering deposition (due to the kinetic energy of arriving Ag ions) or shortly afterward (due to routine light exposure), and subsequent PAI layers are found to adhere very well.
An optimized process enabled the fabrication of a variety of structures on a single sample, as shown in Fig. 2. Straight-sided channels of width 10 to 80 μm were realized in parallel, although the wider channels (60 and 80 μm) exhibit some localized wrinkling along the channel (see Fig. 5), likely due to the onset of a secondary buckling mode [18,22]. The ring structures shown in Figs. 2(a) and (c) are somewhat unique, as they derive from embedded circles of Ag. These regions delaminate entirely during the baking step, forming a dome shape at high temperature. On cooling to room temperature, the centers of the domes collapse resulting in the self-assembled, ring-shaped channels shown in Fig. 2(c). We have verified that these channels are hollow by cleaving through rings and inspecting their cross-section using an SEM. They resemble the ring resonators proposed by Scheuer et al.[25]. The tapered channels (Fig. 2(f)) are tapered in both width and height, as per the discussion below. Such waveguides have been studied theoretically in the context of slow light effects [3,6].
Fig. 2. Images of a chip after the buckling process. (a) Low magnification photograph showing straight-sided buckles with nominal widths from 10 to 80 μm (in groups of 5), 80 to 20 μm and 80 to 10 μm tapers, sinusoidal s-bends, and rings with diameters 500 and 1000 μm. (b) SEM image of the cleaved facet of a nominally 20 μm wide hollow waveguide. Inset: higher magnification image of the upper mirror. (c)-(f) Optical microscope photographs of various features: (c) 500 μm diameter rings, (d) 20 and 40 μm straight-sided guides, with buckled alignment mark features (crosses and squares) in between, (e) s-bends in 40 μm wide guides, and (f) sections of two adjacent tapers (centre-to-centre spacing 250 μm). The defects visible in some of the images are discussed in the main text.
Part of the work described (including all of the glass deposition steps) was conducted outside of a clean room environment. Efforts were made to avoid contamination of the samples (by dust particles, etc.), but a low density of debris-related defects was typically visible under the microscope (as in Fig. 2). Also, localized rough edges along the Ag strips (due to imperfect liftoff) produced obviously correlated defects along the buckled channels. As a result, every hollow waveguide tested had defects along its length, some of which cause significant scattering of light (see Section 5). This limited our light guiding experiments to samples less than ~ 1 cm in length. We expect that a more tightly controlled process, conducted entirely in a clean room environment, would increase the yield and allow for arbitrarily long hollow channels.
4. Analysis of the buckling process
To theoretically analyze the buckling of the multilayers, we used bulk material properties for Ge33As12Se55 (IG2) glass [26-27] and Torlon polyamide-imide (PAI) polymer [28-29]. It should be noted that the elastic modulus and other mechanical properties of a thin film might be different than the bulk counterparts. Furthermore, Ag doping of the IG2 glass likely modifies its mechanical properties. An exact treatment incorporating these details is left for future work.
The elastic modulus, Poisson’s ratio, and coefficient of thermal expansion (CTE) of IG2 glass are approximately 21.9 GPa, 0.27, and 12×10-6 K-1, respectively [26], and its tensile and flexural yield strengths are on the order of 20-100 MPa [26-27]. The elastic modulus, Poisson’s ratio, and CTE of Torlon AI-10 (an unfilled grade of Torlon) are approximately 3 GPa, 0.4, and 30×10-6 K-1, respectively [28-29]. Its tensile and flexural strengths are on the order of ~150 MPa at room temperature and ~100 MPa at 150 °C. Torlon PAI is amongst the toughest and strongest of all polymers, and exhibits exceptional retention of mechanical properties over a wide range of temperature (from cryogenic temperatures up to ~250 °C). This poses a challenge with respect to facet preparation, as mentioned above. When extensively cured, the PAI layers (such as in the lower mirror of the devices described) have a tendency to stretch and deform on cleaving (even after a bath in liquid nitrogen). Soft-baked layers are less tough and cleave more readily.
Fig. 3. Buckling delamination of a single IG2 film. (a) Buckling atop a 1 mm diameter Ag circle. The movie file (0.57 MB) shows the real-time evolution of the buckling pattern as light induces photodoping of the underlying Ag into the IG2 film (and thus loss of adhesion of the IG2 film). Outside the Ag circle, the IG2 film remains well adhered to the polymer underlayer. (b) Buckling in a region where the Ag underlayer is continuous. The movie file (1.37 MB) shows real-time migration of the buckle pattern.
In early phases of the work, we studied the buckling delamination of single layer chalcogenide films. Figs. 3(a) and (b) (and the associated movie files) show the delamination and buckling of a single IG2 layer (~500 nm thick). The layer was deposited on top of a patterned Ag layer (~40 nm thick), which in turn lies atop a 500 nm PAI layer on a silicon wafer. The Ge33As12Se55 layer was subsequently deposited with a second (non-patterned) Ag layer (also ~40 nm thick) and then stored in a refrigerator for several months. The sample was removed from the refrigerator, allowed to return to room temperature, and then placed under the microscope. The microscope light-source immediately induced photodoping of the Ag layers into the glass, causing loss of adhesion at the locations of the underlying Ag features. Figure 3(a) shows a circular Ag feature, over which the IG2 film is partially delaminated at the start of the movie. When the intensity of the microscope light is increased, Ag photodoping drives further delamination of the IG2 film and changes in the buckle patterns. Note that the delamination does not extend outside the perimeter of the underlying Ag circle. We have observed (although did not record) straight-sided Euler buckles forming overtop straight-sided Ag strips on similar samples. Figure 3(b) shows buckling in a region where the Ag underlayer is continuous. Silver photodoping might be a powerful technique for studying the dynamic properties of thin film buckle formation.
The critical (minimum) compressive stress required to elastically buckle a thin isotropic plate or film (assuming sufficiently low adhesion in the latter case) is given by the well known expression [18,22]:
where b is the half-width of the buckle, and h, E, and v are the thickness, elastic modulus, and Poisson’s ratio of the plate or film, respectively. The Euler column arises for b0<b<2.5*b0 [18,22] (approximately), where b0 is the minimum half-width for buckle formation given a pre-buckle stress level σ0. Furthermore, the Euler buckle has a raised cosine shape [17-18] with peak amplitude (ie. the height of the buckle at its centre) given by
Our buckling experiments on single IG2 films over pre-patterned Ag strips verified these relationships. For multilayers, buckling can be analyzed using either an effective medium approach or by considering each sub-layer individually [30]. Based on the latter approach, and using the material parameters described above and layer thicknesses described in Section 5, predictions of the elastic buckling theory (for representative stress levels, see Fig. 1 inset) are plotted in Fig. 4(a) along with experimentally measured buckle heights.
Fig. 4. Analysis of the buckling process for the 4.5 period upper mirror. (a) Peak buckle height versus half-width (both in units of μm) according to the elastic buckling theory described in reference [30] (solid line). After photodoping and at ~160 °C, the bottom and remaining IG2 layers of the upper mirror were assumed to possess 200 and 100 MPa compressive stress, respectively (see Fig. 1). Stress in the PAI layers was assumed negligible. The markers show some experimentally measured buckle heights for each of the nominal half-widths studied. (b) SEM image of a nominally 10 μm wide buckle, showing sharp bending and some cracking near the buckle peripheries. The PAI layers appear somewhat stretched and deformed after cleaving, as discussed in the main text.
The disagreement between the elastic theory and the experimental data is larger than can be explained by uncertainties in the moduli or compressive stresses of the films. Rather, it is likely due to the neglect of plastic deformation in the purely elastic theory, as follows. First, the stress levels employed are comparable to the yield stresses [17] of both the PAI polymer and the IG2 glass (see above), particularly at elevated temperature. Second, the aspect ratio (h/b, with h the total thickness of the upper ODR) for our buckled structures is outside the ‘thin plate’ limits [17] specified for application of the elastic theory. It is known [31] that buckling of ‘thick’ plates is accompanied by plastic deformation, and that the corresponding critical buckling stress is well below that predicted by the purely elastic theory. The shape of the smallest buckled features (see Fig. 4(b)) supports this conclusion. The profile is not well described by a raised cosine function, and there is sharp bending (and even evidence of cracking in some cases) near the edges of the buckle [32]. Plastic deformation is somewhat beneficial in the present context, as it enables straight-sided buckles with aspect ratios that could not be produced by elastic deformation alone.
As mentioned above, for elastic buckling of a thin film (or stack of films), there is a restricted range of delamination widths that produce a straight-sided Euler buckle. This is because the initial buckling releases compressive strain in the direction normal to the buckle axis only. For sufficiently wide Euler columns, residual compressive strain along the axis causes secondary wrinkling in that direction [22]. Even though the buckling deviates from a purely elastic process in the present case, we observed evidence for a similarly restricted range of straight-sided buckle widths. Figure 2 shows 10, 20, and 40 μm wide buckles, which were consistently straight-sided for the process described. Figure 5 shows typical sets of 60 μm and 80 μm wide buckles from the same process. These exhibit regions of secondary wrinkling, and the wrinkling is most significant for the widest channels. This is likely the reason that the 40 μm wide waveguides exhibited the lowest loss (see below), in spite of the fact that the wider waveguides have larger (especially taller) hollow cores.
Fig. 5. Microscope photographs of straight-sided buckles with: (a) 60 and (b) 80 μm base width. The color difference is due to the use of a different microscope filter in each case. The 60 μm features show some localized, small-scale wrinkling along the axis of the channels. The wrinkling is more extensive and significant for the 80 μm features.
5. Light guiding analysis
Waveguides with Bragg reflector claddings (Bragg waveguides) were originally proposed 30 years ago [33], and have received renewed interest [1,6-9] due to the recent discovery of ODRs [11-12]. Cladding a Bragg waveguide with an ODR enables higher confinement of light to the core, improved robustness to defect induced scattering, better fabrication tolerance, and potential for low-loss waveguide bends [8].
For Bragg waveguides with small (wavelength scale) core dimensions, low propagation loss is dependent on highly reflective (R~1) cladding mirrors [3,7-9,34]. Guidance of linearly polarized light is particularly challenging, due to the lower reflectivity of a Bragg mirror for TM polarized light (especially at high angles of incidence). A reduction in the polarization dependence of mirror reflectivity can be achieved by tuning the thickness of the layer nearest the air core [3,9]. For in-plane polarized light guidance in the buckle waveguides, the flat bottom mirror effectively sees TE polarized light. The upper (buckled) mirror is curved, making it necessary to consider both polarization states. To reduce radiation loss at the ‘sidewalls’, the first layer of the upper mirror was designed to be approximately a half wavelength thick [9].
Given the self-assembled shape of the hollow waveguides, an accurate theoretical analysis requires a numerical solution (see below). However, because the waveguides of interest (particularly the 40 μm wide channels) have a low height to width ratio, a simplified slab model can be expected to provide some insight. Figure 6 shows the reflectivity (predicted by a planar transfer matrix model) for the upper and lower cladding mirrors at various angles of incidence and for both TE and TM polarization. Details of the modeling, including refractive index dispersion curves, can be found elsewhere [13]. The layer thicknesses were estimated from SEM images, and Ag photodoping was assumed to increase the refractive index of the IG2 layers in the upper mirror by 0.35 [14].
Fig. 6. Simulated reflectivity for various incidence angles (from normal) for (a) the bottom ODR (with IG2 and PAI layer thickness 145 nm and 290 nm, respectively) and (b) the Ag-doped top ODR (with Ag:IG2 and PAI layer thickness 150 and 290 nm, respectively, except for a 260 nm thick Ag:IG2 first layer). The mirrors were designed to provide overlapping omnidirectional stop bands near 1600 nm.
Using a ray-optics model for a slab Bragg waveguide, the loss due to sub-unity mirror reflectivity is [3]
where α is the loss in dB/cm, R is the mirror reflectivity (assumed equal for both mirrors) at the ray’s angle of incidence, and M is the number of reflections per centimeter of waveguide length. For the fundamental mode and a core size considerably larger than the wavelength of light, and neglecting penetration of light into the cladding mirrors (which is reasonable for high index contrast mirrors), it follows that [3]
where λ is the free-space wavelength in cm, and D is the thickness of the hollow core (ie. the mirror separation) in cm.
For the waveguides described here, the upper and lower cladding mirrors are not identical. Using the same approximations as above, the loss due to sub-unity mirror reflectivity is then
where RT and RB are the reflectivities of the top and bottom mirrors, respectively.
The 40 μm wide waveguides described below have a peak core height of ~2.5 μm. Using this as the core thickness in the slab model, the incident angle for the fundamental mode ray is ~72 degrees from normal at a wavelength of 1600 nm (ie. by applying a half-transverse-wavelength condition). From the data in Fig. 6, the relevant reflectivities for TE polarized light are RB~0.999 and RT~0.996. Using these numbers in (5) produces α~14 dB/cm. Note that this estimate is approximately valid for all of the low-loss TE modes discussed below, since they are single-moded in the vertical direction.
The buckled waveguides have a laterally tapered shape, which results in an index guiding mechanism in that direction [3,10]. Furthermore, the effective width of the waveguides in the lateral direction (while difficult to define exactly) is relatively large and the use of a λ/2 first layer in the upper mirror results in a reasonably high reflectivity (~0.98) for TM light at near-glancing incidence. The net result is that the radiation of TM polarized light through ‘sidewalls’ of the waveguide is of secondary importance. This is evinced by assuming a lateral effective core width of ~10 μm (a somewhat arbitrary but conservative value) and an effective mirror reflectivity of 0.98 in the expressions above.
Since the slab model is only a rough approximation of the actual structures (with curved upper mirrors), a more accurate numerical solution was obtained using commercial finite difference software (Mode Solutions 2.0, Lumerical Solutions Inc.). For modeling purposes, we assumed the buckles to have a raised cosine shape. From profilometer measurements, this was verified to be a good assumption for the wider (> 20 μm wide) buckles. Perfectly matched layer boundary conditions were used, and the simulation grid size was varied until further reduction produced no significant changes in the modal solutions. We used the same refractive index dispersion expressions and layer thicknesses as above, and neglected material absorption. Figure 7 shows the 3 lowest-order TE mode solutions at 1600 nm wavelength for a waveguide with base width 40 μm and peak height 2.5 μm, along with their predicted loss (due to radiation through the mirrors) versus wavelength.
Fig. 7. Results from a commercial finite difference mode solver. (a) The intensity distributions for the 3 lowest order TE modal solutions at 1600 nm. (b) The predicted radiation loss versus wavelength for the modes in part (a).
The low-loss bands in Fig. 7(b) correlate well with the overlapping omnidirectional stop bands shown in Fig. 6. From the ray optics viewpoint, it is expected that the low loss propagation band should be determined mainly by the overlap of the TE stop bands (of the lower and upper mirror) at ~72 degrees incidence. The low-loss propagation band is also expected to correspond approximately to the omnidirectional stop band of the upper mirror, since guided light is effectively incident on the upper mirror with a range of angles and for both polarization states. Both interpretations are consistent with the numerical and experimental results.
The numerical solution predicted ~ 7 air-guided TE modes; the lowest order (lowest loss) modes are summarized in Table 1. Note that the losses of the TE modes are in reasonable agreement with the predictions of the ray optics model as expected. However, the low-loss bandwidth reduces slightly with increasing mode order. Predicted losses for TM polarized modes are much higher, consistent with our experimental observations.
Table 1. Low-order air-guided modes for a 40 μm wide buckled waveguide with raised cosine profile and peak height 2.5 μm, as predicted by a finite difference mode solver at 1600 nm wavelength.
6. Light guiding results
Light propagation was studied experimentally using both a tunable laser (Santec) and a broadband light source (Koheras SuperK Red). Source light 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 at the output facet. Output light was delivered to one of a photodetector, an infrared camera, or an optical spectrum analyzer (Anritsu), in the latter case via an iris, a fiber collimating optic, and a short length of standard single mode fiber. To obtain experimental mode field profiles, magnified near-field images were focused onto an InGaAs CCD camera. The system was calibrated by imaging light from optical fibers with known mode-field diameters. For loss measurements, a multimode fiber (attached to a micropositioner) was used to scan the surface of a chip under test. Further details on the experimental setup can be found elsewhere [35].
Guiding was verified for buckle base widths in the 20 to 80 μm range. However, we could not propagate light down the 10 μm wide channels, likely because their height is near the λ/2 cutoff condition for this type of waveguide [3]. For the reasons discussed above, we focus on results for waveguides with 40 μm base width and for in-plane (TE) polarized light. Experimental near field mode profiles at the output facet of an approximately 5 mm long waveguide are shown in Figs. 8(a)-(c). Consistent with the prediction of several low-loss TE modes, we observed multimode interference effects. By adjusting the input coupling position and laser wavelength, it was possible to excite different mode patterns at the output. The 3 lowest-order mode patterns shown are in good qualitative agreement with the results from the finite difference mode solver, and evidence of higher order modes was also observed. An exact quantitative comparison between experiment and theory was limited by the resolving power of the optics and by nonlinearities in the infrared camera [35].
Propagation loss estimated from scattered light was as low as ~15 dB/cm (see Fig. 8(d)). This is in reasonable agreement with the theoretical predictions above, suggesting that the loss is mainly determined by the reflectivity of the cladding mirrors. Light guiding through s-bends was also observed (Fig. 8(e)), although further work is required to ascertain the relative contributions to loss from finite mirror reflectivity, bending, and defect-induced scattering.
Fig. 8. Results for guidance of TE polarized light in buckled waveguides with 40 μm base width. (a)-(c) Near field mode profiles: (a) fundamental mode at 1610 nm, (b) first order mode at 1610 nm, and (c) second order mode at 1586 nm. (d) Loss estimate from plot of scattered light versus distance along a straight, 40 μm wide waveguide. To ensure a conservative estimate, data points associated with a scattering defect near 2.4 mm were removed. (e) Scattered light (1595 nm wavelength) from a nominally 40 μm wide hollow waveguide (~ 5 mm in length) captured by an infrared camera. The sinusoidal s-bend is 500 μm long with a 250 μm offset. Light is coupled at left and the output facet is visible at right.
In Figs. 9(a) and (b), selected theoretical reflectivity curves for the lower and upper cladding mirrors are repeated from Fig. 6. Experimental verification (not shown) was obtained for the bottom mirror, revealing near-perfect agreement above the electronic band edge of the materials as in our previous work [14-15]. Figure 9(c) shows the typical transmission versus wavelength through a hollow waveguide, with the wavelength response of the test setup removed. A low-loss band in the 1550 to 1700 nm wavelength range was found, with out of band rejection on the order of 40 dB. The position and bandwidth of the transmission passband are well correlated with the omnidirectional reflection bands of the cladding mirrors [1], in good agreement with the predictions of the finite difference simulation above. Note that the Ag-doped mirrors do not exhibit high reflectivity in the vicinity of the theoretically predicted (neglecting material loss) third order stop band near 700 nm [14]. As a result, the waveguides do not efficiently transmit light in that range.
Fig. 9. Wavelength dependence of TE polarized light guidance. (a) Simulated reflectivity of the lower ODR cladding, for TE polarized light at normal (green) and near-glancing (blue) incidence. (b) Simulated reflectivity of the upper ODR cladding, for normal incidence (green), and near-glancing incidence for TE (blue) and TM (red) light. (c) Measured transmission versus wavelength through a typical 40 μm wide hollow waveguide, ~ 5 mm in length.
The loss of the waveguides is comparable to that for other integrated air-core waveguides (with similar core size) reported in the literature [7,9-10]. Nevertheless, it is always desirable to reduce loss. This could be achieved by employing higher index contrast mirror materials (implying new process development) or by increasing the number of periods in the mirrors (implying increased process complexity and cost). However, Katagiri et al. [36] have shown that the reflectivity and bandwidth of finite period Bragg mirrors can be greatly increased by adding an ‘outer’ metallic layer. Preliminary analyses using the models described above predict that, for core dimensions similar to those described here, loss below 1 dB/cm can be achieved using 4-5 period mirrors ‘capped’ by a thin (~50 nm) metal film. This would require only a slight modification to the process described, and will be explored in future work.
7. Conclusions
Compared to conventional methods for fabricating hollow waveguides and microchannels, the approach described has potential advantages. The delamination buckles are driven by energy minimization, form spontaneously, and are quite stable. We have handled some samples extensively and verified their light guiding properties over the course of several months. Long and complex channel layouts (curved, crossing, and tapered channels, etc.) can be realized in a straightforward and parallel process. While not yet verified, it seems likely that the inner walls of buckled channels could exhibit roughness characterized by the film deposition process (which can be sub-nm), highly advantageous for low-loss light guiding and efficient fluid flow. The specific materials used here provide further advantages, including toughness, flexibility, resistance to cracking [15], and a processing temperature regime that is compatible with back-end integration on electronics. However, the general idea (ie. fabricating hollow waveguides by buckling delamination within a multilayer stack) should be transferable to other material systems, provided means to control compressive stress and interfacial adhesion are available.
One limitation is that the ability to engineer the core dimensions (for example, to realize single mode propagation) and aspect ratio is somewhat restricted by the conditions for straight-sided buckle formation. Furthermore, challenges related to process repeatability, precision, and controllability are expected, especially since plastic deformation plays a role in the self-assembly. Nevertheless, the approach represents a new option for fabrication of hollow channels and waveguides on planar platforms.
Acknowledgments
We thank Ying Tsui, Blair Harwood, and Prabhat Dwivedi for assistance with fabrication processes, Jim McMullin for helpful discussions, and George Braybrook for SEM images. The work was supported by the Natural Sciences and Engineering Research Council of Canada and by TRLabs. Devices were fabricated at the Nanofab of the University of Alberta.
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