Optofluidic transformation optics for innovative devices

Transformation optics, a new paradigm for light manipulation using materials that exhibit spatially varying permittivity (an electric characteristic) and permeability (a magnetic characteristic) to alter the electromagnetic space, is an area of intense investigation. For example, a transformation optics approach can improve the optical properties of conventional refractive and gradient-index (GRIN) optical imaging devices. Recently, a number of systems have been identified by spatially varying the permittivity of the medium, offering new and exciting opportunities for controlling and manipulating light. However, experimental transformation optics research has so far been limited to solid materials, which require complicated fabrication processes.

Optofluidics is a fast-growing technology that aims to manipulate light and fluids at the microscale, exploiting their interaction to create highly versatile devices and integrated systems.¹ The ability to tune, reconfigure, and manipulate small amounts of fluids (10⁻⁹ to 10⁻¹⁸ liters)—and to use those fluids to control light—enables new solutions and opportunities for a wide range of traditional micro-optical components and devices from microlenses² and gratings³ to prisms⁴ and waveguides. As a result, the hindrance imposed by solid conventional optical components is easily solved.

Figure 1. Light focusing and interference in an optofluidic waveguide. (a) Optofluidic waveguide consisting of three laminar flows in the microchannel. (b) Gradient-index (GRIN) profile of the microchannel in the transverse direction to realize light focusing. (c) Bi-directional GRIN profile to realize light interference. The intensity scale describes the refractive index distribution. (d) Simulated light propagation in the waveguide with the index profile shown in (b). Light is bent and focused periodically in the optofluidic waveguide. (e) Simulated light propagation in the waveguide with the index profile shown in (c). Light interference is clearly seen in the optofluidic waveguide.

Figure 2. Interference patterns in the optofluidic waveguide. (a) Zoomed views of the first section from the experimental observation (top) and from the simulation using the finite-difference time-domain method (bottom). (b) Observed (top) and simulated (bottom) interference patterns in the optofluidic waveguide.

We recently demonstrated a controllable transformation optics device based on a liquid medium. Specifically, we achieved chirped focusing of light and interference in an optofluidic waveguide underpinned by a unique bi-directional refractive index gradient profile in a flow channel (see Figure 1).⁵ This effect depends on the waveguide's characteristics, the liquid composition, and the flow rate. Figure 1(a) shows an optofluidic waveguide design with three flow streams. A liquid with a relatively high refractive index is injected into the central flow stream instead of a side flow stream. Optofluidic waveguides provide an easy means of varying the spatial distribution of the refractive index in the microchannel by tuning the flow rates. In our experiments, we injected ethylene glycol (n_core=1.432) and de-ionized water (n_clad=1.332) as the core and cladding liquid streams, respectively.

In such a waveguide, two different light-propagation phenomena designed using a transformation optics approach were realized. First, a light-focusing phenomenon in the waveguide can be observed with a gradient refractive index profile in the transverse direction: see Figure 1(b). Figure 1(d) shows the curved light ray trajectories converging to a focus 300μm from the core inlet. To achieve a longer focal distance, a milder GRIN profile is required. Second, a strong interference effect with analogous discrete diffraction in the waveguide can be observed with a bi-directional GRIN profile in both the transverse and propagation directions: see Figures 1(c) and 1(e).

We compared the experimentally observed light focusing and interference with simulations (see Figure 2). Figure 2(a) shows the light distribution between the first two focal points. Beyond the first focal point, most rays bend in quickly to the second focal point, but some fan out and converge slowly, forming fin-like patterns. The intensity in the focal section exhibits a large variation resulting from the interference effect. A close-up of the region just beyond the focal point shows the interference patterns in which regular bright spots appear within an open angle of 12°: see Figure 2(b). The interference effect originates from the rays entering from different positions on the input side and following different trajectories.

In conclusion, our observations of lightwave bending and manipulation demonstrate a controllable transformation optics device based on a liquid medium. With inherent real-time tunability and reconfigurability, such waveguides may be versatile platforms for many scientific studies, particularly in dynamically controlled transformation optics systems. These new phenomena have potential applications in GRIN-like optical elements for optical modulation and signal routing. The interference patterns may also be applied to single-molecule sorting and dynamic assembling. In the near future, we plan to use optofluidic transformation optics for single-molecule detection and manipulation.

This work was supported by the Environmental and Water Industry Development Council of Singapore through grant MEWR C651/06/171.