New Classical Optics | Components • Devices • Systems

## DIFFRACTIVE OPTICS, HOLOGRAMS

#### Contact: Henrik C. Pedersen, Carsten Dam-Hansen

Just like regular refractive optics (e.g. lenses) or reflective optics (e.g. mirrors), diffractive optics can be used to shape light. Look at this example:

Here, collimated laser light is launched from below on the left towards a polymer chip. In the top surface of the polymer, a periodic grating structure is engraved and metal coated to increase the reflection of the light. Because of the periodic nature of the grating, the light will diffract in a direction θ given by

$$\sin (\theta ) = {\lambda _c}/\Lambda$$

-where λC is the effective wavelength of the light in the polymer chip (= the vacuum wavelength divided by the refractive index of the polymer) and Λ is the period of the grating.

In the specific case above, the grating period varies gradually (so-called chirp), so that the diffraction angle θ decreases from the edge of the polymer chip towards the center of the chip, i.e. θ1 > θ2. Hence, by carefully controlling the chirp it is possible to have the light form a focus right at the top of the polymer chip. (Note that right after being diffracted, the light is internally reflected at the bottom surface of the chip).

In the specific case above, the grating period decreases from 440nm down to 415nm across a surface area of 5 X 15 mm. Such a large pattern with so small features is not easily generated by standard direct writing technology, e.g. laser or E-beam writing. We therefore use holography:

Above is shown a setup for recording a holographic grating with a chirp. A glass plate with a thin layer of photoresist applied, typically 2 µm thick, is exposed by two laser beams from a Helium Cadmium laser. The beams form a sinusoidal interference pattern (= lines of light) with the following period:

$$\Lambda = {{{\lambda _R}} \over {\sin ({\theta _1}) + sin({\theta _2})}},$$

-where λR is the laser wavelength and θ1,2 are the local angles of incidence of the two beams at the surface. By choosing the right convergence and divergence properties of the two laser beams (i.e. placing their focal points carefully) we can make the interference pattern match the desired polymer grating pattern described above, i.e.

$${{{\lambda _R}} \over {\sin ({\theta _1}) + sin({\theta _2})}} = {{{\lambda _c}} \over {\sin (\theta )}}.$$

After laser exposing the photoresist, a chemical liquid removes the exposed material leaving a surface relief grating behind in the photoresist. This surface relief grating is then transferred to a nickel shim using a galvanic growth technique. This shim is then placed in a polymer injection mold from which the polymer chips are replicated.

#### The holographic chip is inserted into a biosensor device

The example described above was part of a collaboration project with the Danish company, Vir A/S, who used the polymer chip for a so-called surface plasmon resonance biosensor.

### LITERATURE

Many more details can be found in these papers:

1. H. C. Pedersen, W. Zong, M. H. Sorensen, Carsten Thirstrup, "Integrated holographic grating chip for surface plasmon resonance sensing," Opt. Eng. 43(11) (2004).

2. Pedersen, H.C.; Thirstrup, C. “Design of near-field holographic optical elements by grating matching”, Appl. Opt., Vol. 43, 2004, p. 1209-1215.