Tunable Liquid Gradient Refractive Index Lens

A liquid graded refractive index (L-GRIN) lens can focus light purely by liquid flow, eliminating the need for mechanical or electrical light-manipulating mechanisms. In this example, a calcium chloride solution is mixed with distilled water; the resulting gradient in the concentration in CaCl2 creates a gradient in the refractive index in the channel, which focuses light from a fiber optic cable. The L-GRIN lens is tunable; by changing the flow rate of the distilled water, it is possible to control the refractive index distribution in the channel and change the location of the focal plane.

Model Definition

The lens device is composed of a PDMS (polydimethylsiloxane) substrate that has a channel, a first fluid path and a second fluid path, both made of two independent inlets and sharing two common outlets. The first and second fluid paths are merged in the channel to form laminar flows and establish a calcium chloride concentration distribution that resembles the hyperbolic secant profile; see Ref. 1. Figure 1 shows the 2D geometry and dimensions used for the simulation.

Figure 1: Devices schematics and dimensions (in μm).

An optical fiber light source, is positioned adjacent to the channel. The thickness of PDMS between the aperture of the optical fiber and the microfluidic channel is 25 μm. The wavelength of the source is 532 nm and the core diameter of the multi-mode optical fiber is 50 μm with a numerical aperture of 0.22.

The first fluid path uses a solution of calcium chloride (CaCl2) while the other fluid path uses distilled water. The two fluids have a different refractive index. The refractive index of the mixture depends linearly on the concentration profile in the channel and is defined by:

(1)

where c1 = 3.5 mol·l-1 and n1 = 1.41 are respectively the concentration and refractive index of the CaCl2 solution, and where n2 = 1.33 is the refractive index of the distilled water.

In this model, the flow rates of distilled water is varied from 0.6 to 3.0 μl·min-1 while the flow rate of the CaCl2 solution is kept constant at 3.0 μl·min-1.

Results and Discussion

The laminar fluid flow provides an optically smooth fluidic interface. Figure 2 and Figure 3 respectively shows the concentration of CaCl2 in the channel and the effect of the concentration profile on the mixture’s refractive index.

The curvature of the fluidic interface and, therefore, the focus point of the fluidic lens can be conveniently adjusted by simply changing the flow rates of the distilled water. Figure 4 shows the ray trajectories for a water flow rate of 3.0 μl·min-1.

Displaying Figure 4 for different flow rates shows that higher water flow rates result in larger refractive index contrast, which causes light to bend toward the lens axis more significantly and leads to the decreased focal distance.

Figure 5 shows the light intensity profiles for different flow rates as they reach the end of the channel. The maximum and smaller half-width maximum of the intensity is observed for a water flow rate of 2.4 μl·min-1.

Figure 2: Concentration of CaCl2 for a water flow rate of 3 μm/min.

Figure 3: Refractive Index of the mixture for a water flow rate of 3 μm/min.

Figure 4: Ray trajectories for a water flow rate of 3 μm/min.

Figure 5: Intensity profiles at the end of the microfluidic channel for different water flow rates.

Reference

1. X. Mao and others, “Tunable Liquid Gradient Refractive Index (L-GRIN) lens with two degrees of freedom,” Lab Chip, vol. 9, no. 14, pp. 2050–2058, 2009.

Ray_Optics_Module/Lenses_Cameras_and_Telescopes/tunable_liquid_gradient_refractive_index_lens

Modeling Instructions

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Global Definitions

Parameters 1

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Browse to the model’s Application Libraries folder and double-click the file tunable_liquid_gradient_refractive_index_lens_parameters.txt.

Definitions

Variables 1

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Browse to the model’s Application Libraries folder and double-click the file tunable_liquid_gradient_refractive_index_lens_variables.txt.

Geometry 1

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ex	x
ey	y

Add an accumulator at the end of the channel in order to estimate the intenisty profiles at this location.

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Materials

Water, liquid (mat1)

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In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Refractive index, real part	n_iso ; nii = n_iso, nij = 0	n	1	Refractive index
Refractive index, imaginary part	ki_iso ; kiii = ki_iso, kiij = 0	0	1	Refractive index

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Parameter name	Parameter value list	Parameter unit
fr2 (Flow rate of distilled water)		ul/min

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Refractive Index

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Surface 1

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button in the toolbar. The plot should look like Figure 3. Select a different parameter value to see the effect of the water flow rate on the refractive index of the lens.

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Ray Trajectories 1

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Color Expression 1

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button in the toolbar. The plot should look like Figure 4. Select a different parameter value to see the effect of the water flow rate on the focal length of the lens.

Intensity Profiles

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