Fabrication

Phase profiles can be recorded in the surface topography of an optical element [14], or in controlled variations in a dielectric's index of refraction [5]. Liquid crystal displays also have been used as phase-modulating elements [15], and dynamically reconfigurable patterns of beams suitable for forming optical tweezer arrays have been demonstrated [16], although not yet used to make three-dimensional traps. Some photorefractive elements such as those being explored as optical memory devices also can be reconfigured, but must be programmed optically. Few, if any, are available as commercial optical elements. Photorefractive holograms created with photographic techniques [5] promise the greatest flexibility for creating static tweezer arrays at very low cost, but do not appear to have advanced beyond the research stage.

Figure 6: Encoding phase in surface profile. A plane wave incident upon the flat side of a transparent dielectric material acquires a spatially modulated phase upon passing through its textured surface.

Surface patterning takes advantage of well-established photolithographic techniques and can be implemented easily and inexpensively. We have taken this approach in creating our own holographic optical tweezer arrays. Fig. 6 shows the principle. Light propagates more slowly in a dielectric material than in air. When a wavefront first enters the material, it is uniformly slowed to a speed $c/n$, where $c$ is the speed of light in vacuum and $n$ is the material's index of refraction. Parts of the wavefront emerging first from the textured surface propagate at speed $c$, while sections remaining in the material fall behind, picking up a phase delay proportional to the extra thickness of material. Consequently, the relative phase at $\vec r$ is proportional to the surface's relief, $d(\vec r)$:

$$\Phi^{in}(\vec r) = 2 \pi (n-1) \frac{d(\vec r)}{\lambda}.$$ (18)

A similar principle applies when imposing a pattern of phase delays through the relief on a reflective surface, but with the factor $n-1$ replaced by 2.

The pattern of hills and valleys needed to create a desired phase profile can be formed in photoelastic polymer gels. Such materials provide the recording medium for commercial holographic printers. These are not so common as photolithographic facilities for surface etching, however, so we digress in the next Section to describe the details of our fabrication process.