**2. Experimental arrangement for holographic elements**

Holographic recording of diffractive optical elements involves careful spatial overlapping of two or more coherent beams so that the interference pattern they produce, once recorded into the material, will create a photonic structure capable of diffracting light in the desired way. For a simple diffractive device such as a two‐way beam splitting element, the desired pho‐ tonic structure may be a simple grating. For example, two coherent, collimated beams would be arranged to meet at the recording plane at a specific angle, producing a simple sinusoidal variation in intensity across, say, the horizontal axis of the recording medium. Once this is recorded in the material, a sinusoidal grating is produced which will act as a two‐way beam splitter for a beam of the appropriate wavelength and incident angle.

The next step up in complexity is a shaped beam, such as a diverging beam, which when combined with the collimated reference beam produces an interference pattern consisting of a series of concentric rings. Once recorded, this pattern will produce a diffractive element with a similar variation in the refractive index, which, when illuminated correctly, produces a diverging beam. There are many types and variations of diffractive elements that can be produced in this way, especially when we consider recording with multiple beams, converg‐ ing and diverging wavefronts, different inter‐beam angles and different wavelengths. In this chapter, we discuss basic gratings and focusing/diverging elements with an angular offset.

The basic set‐up for recording is shown in **Figure 1**; however, different adaptations are neces‐ sary for the work in each of the sections below. In order to make cylindrical lens elements, for example, a cylindrical lens is introduced into one of the interfering beams and for single‐beam recording (Section 5) one beam is blocked completely during the second step. These altera‐ tions are mentioned in the relevant sections. Here, we show the standard optical arrangement for recording using the interference between two coherent beams.

The beam from a coherent laser source is spatially filtered, collimated and split in two and, after reflection of one of the beams of a plane mirror, the two beams are made to overlap at the photopolymer plate. The angle at which the beams meet can be altered by reposition‐ ing the mirror, allowing variation of the spatial frequency of the interference pattern and therefore the fringe period of the recorded grating. A grating has a single spatial frequency throughout, because two collimated beams are interfering so the inter‐beam angle is constant across the polymer. The interference pattern at the photopolymer is recorded as a variation Holographically Recorded Low Spatial Frequency Volume Bragg Gratings and Holographic Optical Elements http://dx.doi.org/10.5772/67296 77

**Figure 1.** Basic optical arrangement for the recording of a holographic grating.

where *d* is the thickness of the grating, *n*<sup>1</sup>

76 Holographic Materials and Optical Systems

is the refractive index modulation, *λ* is the

wavelength of the reconstructing beam, *Δθ* is the deviation from the Bragg angle and *k* is interference fringe vector, normal to the fringes with a magnitude *K* = 2*π*/spatial period. It can be seen from Eq. (4) that increasing the spatial period (reducing spatial frequency) is effective in controlling the angular selectivity. In materials where the refractive index modulation is small, significant thickness is required for high efficiency. Decreasing the spatial frequency (increasing the period) can be the better approach to control the angular

Holographic recording of diffractive optical elements involves careful spatial overlapping of two or more coherent beams so that the interference pattern they produce, once recorded into the material, will create a photonic structure capable of diffracting light in the desired way. For a simple diffractive device such as a two‐way beam splitting element, the desired pho‐ tonic structure may be a simple grating. For example, two coherent, collimated beams would be arranged to meet at the recording plane at a specific angle, producing a simple sinusoidal variation in intensity across, say, the horizontal axis of the recording medium. Once this is recorded in the material, a sinusoidal grating is produced which will act as a two‐way beam

The next step up in complexity is a shaped beam, such as a diverging beam, which when combined with the collimated reference beam produces an interference pattern consisting of a series of concentric rings. Once recorded, this pattern will produce a diffractive element with a similar variation in the refractive index, which, when illuminated correctly, produces a diverging beam. There are many types and variations of diffractive elements that can be produced in this way, especially when we consider recording with multiple beams, converg‐ ing and diverging wavefronts, different inter‐beam angles and different wavelengths. In this chapter, we discuss basic gratings and focusing/diverging elements with an angular offset.

The basic set‐up for recording is shown in **Figure 1**; however, different adaptations are neces‐ sary for the work in each of the sections below. In order to make cylindrical lens elements, for example, a cylindrical lens is introduced into one of the interfering beams and for single‐beam recording (Section 5) one beam is blocked completely during the second step. These altera‐ tions are mentioned in the relevant sections. Here, we show the standard optical arrangement

The beam from a coherent laser source is spatially filtered, collimated and split in two and, after reflection of one of the beams of a plane mirror, the two beams are made to overlap at the photopolymer plate. The angle at which the beams meet can be altered by reposition‐ ing the mirror, allowing variation of the spatial frequency of the interference pattern and therefore the fringe period of the recorded grating. A grating has a single spatial frequency throughout, because two collimated beams are interfering so the inter‐beam angle is constant across the polymer. The interference pattern at the photopolymer is recorded as a variation

selectivity as long as the gratings still behave as thick volume gratings [7].

**2. Experimental arrangement for holographic elements**

splitter for a beam of the appropriate wavelength and incident angle.

for recording using the interference between two coherent beams.

in the local refractive index inside the volume of the photosensitive material. The recording set‐up includes a green laser of 532 nm wavelength, spatial filter, collimating lens, polarizing beam splitter, plane mirror, and for focusing elements, a conventional cylindrical lens (focal length 5 cm, ThorLabs, LJ182L2‐A). The recording medium is the standard photopolymer used by researchers at the Centre for Industrial and Engineering Optics (IEO). It is an acryl‐ amide‐based formulation using acrylamide and bisacrylamide monomers, triethanolamine as the electron donor and polyvinylalchohol as the binder, as described elsewhere [7]. Layer thickness is controlled by the volume of liquid coating solution deposited on a known area of glass substrate.
