We have demonstrated chirped focussing and light interference that can be seen only in multi-mode optofluidic waveguides and are not possible in a single-mode waveguiding structure (see Supplementary Movie 1
). This work focussed on low-flow-rate optofluidic waveguides, in which a continuous variation of the refractive index occurs. The physics governing light propagation effects in such waveguides differs from that of conventional liquid–liquid waveguides. In low-flow-rate optofluidic waveguides, diffusion has a greater role in creating an inhomogeneous optical medium that allows the new complex phenomena of self-focussing and interference. Indeed, conventional high-flow-rate liquid–liquid waveguides are usually operated at high Pe, often 10–100 times larger than those studied here16
. As a result, in the high-flow-rate waveguides, diffusion has a limited role, and the waveguides act as step-index optical waveguides, as shown in Supplementary Figure S1
. In the study reported here, the optofluidic waveguides operate at a Pe of less than 0.001, leading to the creation of an inhomogeneous optical medium in which variations in the refractive index occur on a scale that is comparable to, but larger than, the wavelength of light (see Supplementary Fig. S2
). When light propagates in a waveguide with a GRIN profile, loss through leakage at the channel/liquid interface occurs. This energy loss has been estimated by the intensity of fluorescent emission and found to be approximately 3 dB in a 2,500-μm microchannel for the case of extreme diffusion (r
=1 μl min−1
). This leakage loss can be reduced by replacing the de-ionized water with an ethylene glycol–water mixture, which has a higher refractive index than PDMS16
. However, this substitution will reduce the index contrast of the two liquid flow streams and will limit the device tunability.
The convection–diffusion process is unique to miscible liquids and is not observed in solid materials. The low-flow-rate optofluidic waveguide system is a new material system with controllable, spatially variable dielectric parameters, and is a good candidate for designing transformation optics experiments with GRIN profiles controllable by the variation of flow rates. The diffraction and interference of light in the optofluidic waveguides occur in a very different manner than in a solid waveguide array; the optofluidic waveguide is a system with spatially variable and actively controllable dielectric characteristics, which can be tuned by changing the fluid flow rate. Here, discrete diffraction patterns arise from the self-focussing effect due to the transverse index-gradient profiles.
In conclusion, two distinctive phenomena of the optofluidic waveguides have been demonstrated and controlled: chirped focussing and light interference. These phenomena rely on the continuous GRIN profile, which is controlled by microfluidic manipulation. With inherent real-time tunability and reconfigurability, such waveguides may be the versatile platforms for many scientific studies, particularly in dynamically controlled transformation optics systems. These new phenomena have potential applications in the GRIN-like optical elements for optical modulation and signal routing, which can be achieved by manipulating the light distribution via the control of liquid flow rates. In addition, the interference patterns may be applied to nanoparticle bunching, sorting and dynamic assembling using the optical gradient force28
, which depends on the sizes and refractive indices of the particulates.