# Dynamically reconfigurable liquid-core liquid-cladding lens in a microfluidic channel

Original entry: Sorell Massenburg, APPHY 226, Spring 2009

Sindy K. Y. Tang, Claudiu A. Stan and George M. Whitesides., Lab Chip, 2008, 8, 395–401

# Soft Matter Keywords

Liquid interfaces. Interfacial tension. Microfluidics, PDMS

# Abstract

This paper describes the design and operation of a liquid-core liquid-cladding (L2) lens formed by the laminar flow of three streams of liquids in a microchannel whose width expands laterally in the region where the lens forms. Two streams of liquid with a lower refractive index (the cladding) sandwich a stream of liquid with a higher refractive index (the core). As the core stream enters the expansion chamber, it widens and becomes biconvex in shape, for some rates of flow. This biconvex fluidic element focuses light.Manipulating the relative rates of flow of the streams reconfigures the shape, and therefore the focal distance, of the L2 lens. This paper also describes a technique for beam tracing, and for characterization of a lens in an enclosed micro-scale optical system. The use of a cladding liquid with refractive index matched to that of the material used in the fabrication of the microfluidic system (here, poly(dimethylsiloxane)) improves the quality of the focused beam.

# Soft Matter Example

The authors have utilized PDMS on chip microfluidic device to create a liquid-core liquid-cladding lens ($L^2$) to create a dynamically changing lens. This technique makes use of the flexibility of PDMS to change the curvature between two liquids (core and cladding). Specifically a liquid filled rounded 1mm by 1mm rectangular expansion chamber is utilized to change the curvature without altering the convergence of light. The expansion chamber height was 100$\mu m$ to accommodate the insertion of optical fiber which served as the light source. In front of the expansion chamber there is an aperture which is one third of the size of the expansion chamber and is made from channels filled with black ink.

Fig.1 Schematic of $L^2$ lens and picture of itsoperation.

The two outer cladding liquid layers are made of a trifluoroethanol (index of refraction of 1.291), methanol (index of refraction: 1.327), ethylene glycol (1.429) and ethanol (1.360). This gave an overall refractive index of 1.4 which matches the PDMS. The authors also employed a 53.6% trifluoroethanol, 31.5% benzothiazole and 14.9% ethanol mixture which also matched the PDMS. This matching limits the light loss due to scattering due to PDMS. Benzothiazole was used as the core liquid. All liquids were chosen to minimize swelling in the PDMS.

To test the lens, the authors used a 95mW, 532nm Nd:YAG laser coupled via an optical fiber with a nominal aperture of 0.12. The authors were able to modify the lens curvature by varying flow rates as shown in the graph below. With increasing flow rate, the curvature first increased then decreased. With a fixed flow rate, increasing the ratio of viscosities led to a similar, though less significant, change in curvature. To change the shape of the lens, the relative flow rates between the two claddings were varied.

Fig.2 Variation of interface curvature with core flow rate..

The authors used the flow rate of the expandable core to modulate the focal distance as shown in the graph below.

Fig.2 Variation of focal point with the left cladding flow rate.

Like conventional lens, the $L^2$ lens is also susceptible to aberrations due to deviations in the core-cladding interface. This should be correctable by adjusting the expansion chamber and shape of the lens, like in conventional lenses. There was also some light scattering. Overall quality of the $L^2$ lens is comparable to lenses that are tunable via electrowetting.