We present the characterization of the optical properties of integrated antiresonant reflecting optical (ARROW) waveguides with arch-shaped liquid cores. Optical mode shapes and coupling, waveguide loss, and polarization dependence are investigated. Waveguide loss as low as 0.26/cm with near-single-mode coupling and mode areas as small as 4.5μm2 are demonstrated. A detailed comparison to ARROW waveguides with rectangular cores is presented, and shows that arch-shaped cores are superior for many applications.
© 2005 Optical Society of America
Hollow waveguides are rapidly gaining attention as they allow for light guiding in gaseous or liquid media with the potential of utilizing the many inherent advantages of solid-state integrated optics. Integrated optical devices based on such waveguides have numerous potential applications, including molecular sensing. In particular, waveguides with micron-sized cross sections and picoliter core volumes have the potential to provide single molecule sensitivity. Achieving optical waveguiding in gases and liquids, however, is nontrivial as their refractive index is lower than that of almost all solid-state materials that can be considered for integration, preventing conventional index guiding. One notable exception is Teflon AF whose index of 1.29 is lower than water (1.33) . However, the large cross sections of Teflon AF-based waveguides make them unsuitable for single molecule detection due to the large core volume . The best way to realize waveguides with picoliter liquid or gaseous cores is to rely on dielectric multilayers surrounding the core, for example periodic structures such as photonic crystals  photonic crystal (holey) fibers , or Bragg waveguides . Antiresonant reflecting optical waveguides (ARROWs) were recently demonstrated as an alternative way to realize hollow-core integrated optics. While also employing multiple dielectric cladding layers, ARROWs do not require periodicity to achieve low propagation loss and rely on antiresonance of the transverse wavevector component for each layer . This provides additional design flexibility that can be used to add integrated wavelength filtering or to realize interconnected two-dimensional waveguide arrays . Hollow-core ARROWs with rectangular air and liquid cores fabricated with a bottom-up, thin film approach on silicon were demonstrated along with highly sensitive fluorescence detection from picoliter cores [8–10]. Other approaches for fabricating liquid-core ARROWs based on wafer bonding and other methods have been proposed, but are multi-mode and not compatible with the volume requirements for single molecule sensitivity [11, 12].
Here, we present a detailed investigation of a new class of hollow-core ARROW waveguides based on arched core cross sections. Arch-shaped ARROWs have numerous structural advantages such as higher mechanical stability, smoother core walls, and uniform layer thicknesses around the entire core which will be discussed in detail elsewhere . In this Letter, we discuss the optical properties of these waveguides. We focus on mode shape and coupling, waveguide loss, and polarization dependence. We draw comparisons to ARROWs with rectangular cores and show that the arched shape yields the best optical properties for liquid-core waveguides to date. Scanning electron microscopy (SEM) images of both core types are shown in Fig. 1. While the results described here were obtained with liquid waveguide cores, the results and conclusions are equally applicable to gaseous cores.
2. Mode shape and coupling
The fabrication of hollow-core ARROWs using silicon microfabrication is based on alternating deposition of dielectric (typically SiO2 and SiN) layers using plasma-enhanced chemical vapor deposition (PECVD) around a lithographically patterned sacrificial core . After deposition is completed, the core is removed with a selective etch. The thickness of each dielectric layer is optimized for low loss light propagation for the desired wavelength and core material. For rectangular cores, metals or SU-8 have been used, whereas the arched shape shown in Fig. 1 can be realized by heating patterned photoresist lines and causing them to reflow into rounded cross sections . In this work, we investigate arch-shaped cores designed for light propagation in water at wavelengths of 633 and 690nm. Three periods of SiN/SiO2 cladding layers of 121/320nm thickness were deposited below and above the core to provide waveguiding. After core removal, the wafers were cleaved into waveguides of varying length with open ends and filled with liquid via capillary action. While open-ended waveguides are ideal for optical characterization, they are connected to microfluidic reservoirs in practical sensors. Microfluidic interfacing has been demonstrated for SiO2 channels fabricated using the same methods and dimensions as our waveguides . All measurements described below were carried out with ethylene glycol as the core material and at an excitation wavelength of 633nm. Ethylene glycol was used because it evaporates more slowly from the waveguides than water. No significant meniscus was visible at the end facets during measurements. The simulations reported below were performed using a commercial software package (FIMMWAVE, ©PhotonDesign). Comparisons between rectangular and arch-shaped cores are carried out with two seta of waveguides with the same core widths (w=9, 12, and 15μm) and core heights of 3.5μm (rectangular) and 4μm (arch-shaped), respectively.
We first analyze the mode structure in the arch-shaped waveguides. Fig 2(a) shows the experimentally observed image at the output facet of a waveguide with a 9μm base width, 6.9mm length, and 4μm core height. The image is obtained by butt-coupling light from a HeNe laser via a single-mode fiber into the liquid core and collecting the transmitted light with a high numerical aperture lens and a CCD camera. Also shown in Fig. 2(b) are the normalized intensity cross sections in the vertical and horizontal directions along with the calculated profile for the fundamental mode. The agreement between experiment and theory is excellent without using any fitting procedure, again indicating that no liquid meniscus is affecting the waveguide properties. This indicates that propagation in this waveguide occurs predominantly in the fundamental mode, resulting in an effectively single-mode liquid-core waveguide. The FWHM mode area for this waveguide is only 4.5μm2, the smallest mode area in a liquid-core waveguide to date.
In order to get a more quantitative understanding of the propagating mode structure, we carried out numerical calculations of the coupling efficiency from the exciting single-mode fiber for a core height of 4μm and various core widths. The results for coupling into the fundamental and third order mode of both arch-shaped (circular symbols) and rectangular (squares) cores are shown in Fig. 3(a). Coupling into even order modes is negligible for both core shapes. We find that in both cases coupling occurs predominantly into the fundamental mode with high efficiency. This observation is in good agreement with experimentally observed values. For wider cores, this efficiency drops off as the mode shape mismatch with the circular single-mode fiber increases and more light is coupled into higher-order modes. In arch-shaped cores, coupling efficiency is higher into the fundamental mode and lower into the third order mode compared to rectangular cores. Together with higher loss in the third order mode (see section 3), this leads to the observed single-mode behavior after a few mm propagation for the arch-shaped cores, whereas contributions from the third order mode can be observed experimentally in rectangular cores of similar length. Arch-shaped cores provide superior coupling properties because the fundamental mode shape is more circular than the elliptical modes in rectangular cores of similar dimensions  and therefore a better match to a circular single-mode fiber. A direct comparison for cores with the same mode area (6.2μm2) is shown in Fig. 3(b) and illustrates this point.
3. Waveguide loss
Ultimately, the most important parameter in characterizing a waveguide is the propagation loss. This is particularly true in hollow-core waveguides where wave propagation occurs via inherently leaky modes, and the waveguide loss determines the useful dimensions of an integrated optical device. In order to characterize and compare the propagation loss in arch-shaped ARROWs, we measured the transmitted power as a function of sample length using a standard cutback method for various core widths as shown in Fig. 4(a). We first concentrate on the case where the transmitted light is polarized in the horizontal (x) direction.
The results of this analysis are summarized in Fig. 4(b) which shows the measured (filled symbols) and calculated (open symbols) loss values for both arch-shaped (circles) and rectangular (squares) cores as a function of the FWHM mode area. The mode area was chosen as the abscissa because it determines the excitation volume in most sensing applications
The figure shows several important trends. First, the measured loss increases characteristically as the mode area, i.e. the core dimension, is reduced. It should be noted that the transmission data for the smallest arch-shaped core were somewhat scattered so that the actual loss is likely lower than Fig. 4 indicates. Secondly, the arch-shaped waveguides exhibit consistently lower loss than their rectangular counterparts. This includes the lowest loss of 0.26/cm measured in liquid-core ARROWs to date. The reasons for this superior performance are the improved smoothness of the top ARROW layers, and the more uniform thickness of the ARROW layers all around the core. In the case of rectangular cores, the top layers have different thicknesses in the x- and y-directions, respectively, which needs to be taken into account during sample design. Thirdly, the calculated values for the loss reproduce the correct trend for both core types, but are substantially lower than experimental values. The discrepancy is mainly due to contributions from residual surface roughness and scattering.
4. Polarization dependence
Propagation loss in ARROW waveguides has been known to exhibit a strong polarization dependence since the first demonstration of solid-core ARROWs with one-dimensional confinement . Experiments in hollow-core ARROWs with rectangular cross section have confirmed this polarization discrimination in a two-dimensional waveguide structure. Such waveguides typically exhibit lower loss for horizontally (x-direction) polarized light . Consequently, these waveguides effectively act as polarization filters, but prevent the propagation of circularly polarized light.
In order to map the polarization dependence in arch-shaped hollow-core ARROWs, we have carried out polarization dependent loss measurements. A half-wave plate was placed after the excitation source to vary the incident linear polarization angle θ continuously from x (0°) to y-polarization (90°). Theoretically, the output intensity Io is given by
where Ii is the input intensity including insertion loss, and αX and αY are the waveguide losses in x and y-directions, respectively. Fig. 5(a) shows the measured transmitted intensity (circles) as a function of polarization angle for a representative waveguide (w=12μm, L=5.4mm). The solid line shows a fit of the transmitted intensity to Eq. (1) in excellent agreement with the data. The fitting parameters are the intensity values at 0° and 90°, respectively. It can be easily shown from Eq. (1) that the ratio of these parameters yields exp[(αY - αX)L]. Consequently, αY can be deduced for a given sample length L and the previously determined αX.. Figure 5(b) shows a comparison of the waveguide loss in the x-direction shown in Fig. 4 and the loss in the y-direction determined by using Eq. (1).
It can be seen that arch-shaped cores are polarization-sensitive as well. Horizontally polarized light exhibits consistently lower loss, similar to cores with rectangular shapes. Measurements on several waveguides show that the error in determining αY is approximately ±5%. A comparison with rectangular cores is difficult because the polarization-dependent loss ratio rP=αX/αY depends on the exact shape of the waveguide for a given mode area. However, a reasonable constraint is to compare waveguides with identical mode area, overall low loss, and high fiber-coupling efficiency. Based on the discussion above, this is fulfilled for w=12μm (arch-shaped) and w=9μm (rectangle). The experimentally determined loss ratios are rP=0.38 (arch-shaped) and rP=0.27 (rectangle). This shows that the polarization selectivity is weaker in arch-shaped cores and it is more easily feasible to find core dimensions that exhibit good mode coupling and equal loss in both polarization directions at the same time. This would facilitate propagation of circularly polarized light with low loss and significantly expand the use of hollow-core waveguides in optical spectroscopy. ARROWs with rectangular cores, on the other hand, are more preferable for polarization filtering.
In summary, we have presented a detailed study of the optical properties of hollow-core ARROW waveguides with arched shapes. In addition to their excellent mechanical properties, they have numerous advantages over waveguides with rectangular cross section in terms of mode coupling, waveguide loss, and polarization sensitivity. Low-loss propagation with near single-mode coupling was demonstrated in these waveguides, including the smallest mode areas (4.5μm2) and lowest loss (0.26/cm) observed in liquid-core ARROWs to date. Further reduction in waveguide loss is possible by adding a substrate pre-etch step to form a pedestal on which the hollow core is placed. This results in a lowering of the top cladding layers below the bottom of the hollow core. The efficacy of such a pre-etch step was recently demonstrated in air-core ARROWs with rectangular cores . These improved properties and future prospects make arch-shaped hollow-core waveguides very attractive for single molecule fluorescence or Raman sensing in two-dimensional waveguide arrays .
The authors wish to thank Z. George and J. Moss for assistance with SEM imaging. This work was supported by the NSF, NIH, and AFOSR under grants ECS-0131945, R21EB003430, and FA-9550-05-1-0432, respectively.
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