**3. Holographic low spatial frequency lens elements for light collection**

The purpose of a diffractive solar collector is to gather sunlight from a large area and direct it onto a smaller area, where it can be converted to electric or thermal energy by, for example, using PV cells or thermal conversion. The advantage is that the light can be harvested cheaply from a larger area and the energy per unit area on the converter can be increased. As discussed previ‐ ously, diffraction gratings can be used to change the direction of a light beam very efficiently, but they are only efficient over a small range of angles close to the Bragg angle, so they need to be used in combination if they are to be useful in collecting sunlight over most of the day.

Holographic optical elements (HOEs) have potential as solar concentrators because of their ability to diffract light at large offset angle and the potential for multiplexing a number of opti‐ cal components in the same layer. Recent research has demonstrated different holographic elements in a variety of arrangements for solar applications to make diffractive elements that will re‐direct and focus incoming light to the desired line using (cylindrical HOE) or spot (spherical HOE) for conversion [8–12].

A large number of researchers have demonstrated novel designs, for example, a planar con‐ centrator using a low‐cost holographic film that selects the most useful bands of the solar spec‐ trum and concentrates them onto the surface of the photovoltaic cell, has been demonstrated by Kostuk et al. [13], and Sreebha et al. [14] have reported results on transmission holographic optical elements recorded in a silver halide material. Bianco et al. have recently reported suc‐ cessful concentration of solar light using an array of three spherical lenses recorded in a sol‐ gel photopolymer [15].

Photopolymers are excellent materials for producing such diffractive elements, being thin, lightweight, inexpensive and highly efficient, but challenges remain in reducing the angular selectivity of these relatively thick layers and in applying the technology to natural light in real‐world applications.

High‐efficiency diffractive optical elements have been recorded and multiplexed in photo‐ polymer materials previously for this and other applications [16, 17]. Previous work by the authors addressed the issue of increasing the angular working range in photopolymers and demonstrated photopolymer spherical and cylindrical focusing elements that had very high efficiency when measured with monochromatic, linearly polarized laser sources [18]. In this section, the combination of pairs of elements with the same focus is demonstrated in photo‐ polymer and tested with a solar simulator.

For these experiments, the electrical characterisation was carried out by measuring the cur‐ rent‐voltage (*I‐V*) characteristics of c‐Si solar cells (Solar capture Technologies) with and with‐ out the DOE placed in front of the cell in such a way as to re‐direct and focus additional light onto the solar cell. *I‐V* measurements were performed using an Keithley 2400 SMU (source meter unit) with a LabVIEW interface, using the set‐up shown in **Figure 2**. The light source used was a metal halide discharge lamp (Griven, GR0262).

The distance between the HOE and the silicon cells was the same as the focal length of the HOEs which in this case was 5 ± 0.1 cm. This arrangement tests the effect of two DOE elements; however applications could involve arrays of such elements surrounding the cell, each con‐ tributing additional light.

**Figure 2.** Diagram of the experimental setup for electrical measurements.

#### **3.1. Recording high efficiency diffractive optical elements at low spatial frequency**

optical elements recorded in a silver halide material. Bianco et al. have recently reported suc‐ cessful concentration of solar light using an array of three spherical lenses recorded in a sol‐

Photopolymers are excellent materials for producing such diffractive elements, being thin, lightweight, inexpensive and highly efficient, but challenges remain in reducing the angular selectivity of these relatively thick layers and in applying the technology to natural light in

High‐efficiency diffractive optical elements have been recorded and multiplexed in photo‐ polymer materials previously for this and other applications [16, 17]. Previous work by the authors addressed the issue of increasing the angular working range in photopolymers and demonstrated photopolymer spherical and cylindrical focusing elements that had very high efficiency when measured with monochromatic, linearly polarized laser sources [18]. In this section, the combination of pairs of elements with the same focus is demonstrated in photo‐

For these experiments, the electrical characterisation was carried out by measuring the cur‐ rent‐voltage (*I‐V*) characteristics of c‐Si solar cells (Solar capture Technologies) with and with‐ out the DOE placed in front of the cell in such a way as to re‐direct and focus additional light onto the solar cell. *I‐V* measurements were performed using an Keithley 2400 SMU (source meter unit) with a LabVIEW interface, using the set‐up shown in **Figure 2**. The light source

The distance between the HOE and the silicon cells was the same as the focal length of the HOEs which in this case was 5 ± 0.1 cm. This arrangement tests the effect of two DOE elements; however applications could involve arrays of such elements surrounding the cell, each con‐

gel photopolymer [15].

78 Holographic Materials and Optical Systems

real‐world applications.

tributing additional light.

polymer and tested with a solar simulator.

used was a metal halide discharge lamp (Griven, GR0262).

**Figure 2.** Diagram of the experimental setup for electrical measurements.

Focusing HOEs were made by interfering a beam focused by a cylindrical lens beam with a collimated reference beam and placing the photopolymer layer at the area of overlap using the basic holographic set‐up described in the experimental section. In such off‐axis focusing DOEs, the spatial frequency of the grating planes will vary across the DOE, as will be dis‐ cussed in the next section. In this example, the minimum and maximum spatial frequencies were 112 and 485 lines/mm, respectively.

A range of HOEs with an off‐axis focusing effect was recorded in order to demonstrate that high efficiency could be achieved with low spatial frequency elements. Diffraction efficiency at Bragg incidence is over 95% (corrected for reflection at front and back surfaces). **Figure 3** shows how the diffraction efficiency changes with the angle of incidence. The full‐width half‐ maximum (FWHM) is approximately 4°, which is a significant improvement on the working range for higher spatial frequencies [18]. The data were obtained by mounting the grating on a rotation stage keeping the laser and detector fixed.

**Figure 3.** Diffraction efficiency versus angle for a cylindrical DOE at central spatial frequency of 300 lines/mm and recording intensity of 1 mW/cm2 . The dotted line shows the measured values and the smooth line is the theoretical curve for a 300 lines/mm volume grating of this diffraction efficiency in a 50 micron thick photopolymer layer.

#### **3.2. Investigating the potential for multiplexing by stacking: three gratings with different slant angles**

Photopolymer gratings were recorded with three different slant angles. **Figure 4** shows plots of the percentage of light falling on the fixed detector as the angle of incidence of the light is varied for the three individual gratings before stacking them together. In each case, the grat‐ ing is fixed relative to the detector and only the angle of incidence is varied. This mimics the function of a passive (non‐tracking) solar cell. The detector collects the light that would fall on

**Figure 4.** The variation of the percentage of light falling on the detector with angle of incidence for three individual gratings recorded at different slant angles with a spatial frequency of 300 lines/mm in layers with thickness of about 50 µm; the recording intensity was 1 mW/cm<sup>2</sup> . A photopolymer layer with no grating is included for comparison.

the cell with and without the gratings in place. The 'photopolymer' line shows the variation in intensity at the detector without the presence of any grating (just a layer of clear photopoly‐ mer) for comparison. From these results, redirection of the incident beam by the gratings can clearly be observed at the appropriate angles. Light incident at over 25°, which would have otherwise missed the detector (or solar cell in a real application) is very efficiently captured using the gratings. However, a key issue is highlighted here. As well as directing the light from higher angles to a lower angle, each grating will also do the reverse. This is caused by the fact that each grating has two angles for which the light is 'on Bragg' for diffraction (cor‐ responding to the two beams with which the grating was recorded).

The angular selectivity of the stack of the three gratings laminated together was then mea‐ sured using the same method. The results are shown in **Figure 5**. The same effect was observed for the stacked device as in **Figure 4**. The results confirm that this method has improved the angular working range of the device. However, efficiency is reduced at the lower angles so that there is no net gain. Diffraction from higher angles would appear to be most useful in circumstances where the grating is offset from the main path to the solar cell, such as off‐axis DOEs, in this way the direct light is unaffected, but the grating can usefully divert light from higher angles onto the solar cell.

#### **3.3. Use of a combined device to increase the concentration ratio of solar cells**

An alternative arrangement is to use off‐axis elements to increase the area from which light is collected and focused onto the solar cell, thereby increasing the energy at the cell. For maxi‐ mum concentration, the DOEs should be recorded so that their focal points overlap. Low

Holographically Recorded Low Spatial Frequency Volume Bragg Gratings and Holographic Optical Elements http://dx.doi.org/10.5772/67296 81

**Figure 5.** The variation of the percentage of light falling on the detector with angle of incidence for a stack of three laminated gratings (from **Figure 4**) and a clear photopolymer layer with no grating.

the cell with and without the gratings in place. The 'photopolymer' line shows the variation in intensity at the detector without the presence of any grating (just a layer of clear photopoly‐ mer) for comparison. From these results, redirection of the incident beam by the gratings can clearly be observed at the appropriate angles. Light incident at over 25°, which would have otherwise missed the detector (or solar cell in a real application) is very efficiently captured using the gratings. However, a key issue is highlighted here. As well as directing the light from higher angles to a lower angle, each grating will also do the reverse. This is caused by the fact that each grating has two angles for which the light is 'on Bragg' for diffraction (cor‐

**Figure 4.** The variation of the percentage of light falling on the detector with angle of incidence for three individual gratings recorded at different slant angles with a spatial frequency of 300 lines/mm in layers with thickness of about 50

. A photopolymer layer with no grating is included for comparison.

The angular selectivity of the stack of the three gratings laminated together was then mea‐ sured using the same method. The results are shown in **Figure 5**. The same effect was observed for the stacked device as in **Figure 4**. The results confirm that this method has improved the angular working range of the device. However, efficiency is reduced at the lower angles so that there is no net gain. Diffraction from higher angles would appear to be most useful in circumstances where the grating is offset from the main path to the solar cell, such as off‐axis DOEs, in this way the direct light is unaffected, but the grating can usefully divert light from

An alternative arrangement is to use off‐axis elements to increase the area from which light is collected and focused onto the solar cell, thereby increasing the energy at the cell. For maxi‐ mum concentration, the DOEs should be recorded so that their focal points overlap. Low

responding to the two beams with which the grating was recorded).

**3.3. Use of a combined device to increase the concentration ratio of solar cells**

higher angles onto the solar cell.

µm; the recording intensity was 1 mW/cm<sup>2</sup>

80 Holographic Materials and Optical Systems

spatial frequency elements are used so that the wavelength selectivity is low and the elements can focus the full spectrum of white light onto the same solar cell. Tests were carried out using a solar simulator and a Si solar cell.

The current *I*, as a function of voltage applied, *V*, across the c‐Si solar cell, was measured and the *I‐V* curve was obtained (**Figure 6**). In this experiment, the area of the DOE was kept con‐ stant at 113 mm<sup>2</sup> . In **Table 1**, *I*sc represents the short circuit current for the solar cell, which is the maximum possible, produced when the cell impedance is low and is calculated when the voltage equals zero, i.e. at *V* = 0, *I* = *I* sc. The short circuit current is due to the generation and collection of light‐generated carriers within the cell. For an ideal solar cell, the short circuit current and the light‐generated current are identical for moderate resistive loss. Therefore, an increase in the short circuit current is a reliable indicator of an increase in the light‐generated current. *J* sc is the short circuit current density, defined as *J* sc = *I*sc/area of the cell.

The short circuit current (*I*sc) output of the reference cell, without the DOE in place, was approximately 3.7 ± 0.1 mA. When a single cylindrical DOE was included, an increase in *I* sc of 16% was observed.

This measurement was then carried out for an array of two cylindrical DOEs, which resulted in an increase in the *I* sc of 40%. These results suggest that the use of larger arrays of cylindri‐ cal and/or spherical DOEs can achieve higher relative increase in *I* sc for smaller areas of solar cells. The value for the short circuit current density (*J*sc) of the Si solar cell was estimated using the *I‐V* data for a single cylindrical DOE and a pair of DOEs for a solar cell of area 60 mm2 . The results are presented in **Table 1**.

**Figure 6.** *I‐V* curves for a c‐Si solar cell (area = 60 mm2 ) with and without a cylindrical DOE in place.


**Table 1.** Calculated *J* sc of the Si solar cell with a range of DOEs. *I* sc is the short‐circuit current and *J*sc is the short circuit current density.

**Figure 7** presents the relative increase in the *I* sc for the c‐Si solar cells versus the area of the solar cells. The illuminated area of the DOE remained constant at 113 mm<sup>2</sup> throughout the experiment while the solar cell area was varied between 9 and 100 mm2 . In order to optimize the concentration ratio, the preference is to use solar cells significantly smaller than the DOEs. These results show that there is a significant improvement in the output current obtained when using the holographic focusing elements.

It has been observed that for solar cells with an area of 9 mm<sup>2</sup> , a 34% increase in the output current is achieved with a single DOE compared to 10% for a 100 mm2 solar cell. This is because the smaller cell area makes better use of the focusing effect.

The relative increase for an array of two cylindrical DOEs was nearly double that of single cylindrical DOE. The device is capable of collecting light from a large incident angle and redirecting it onto the centre of the solar cell. Photographs of the light spots diffracted from holographically recorded diffractive lenses are shown in **Figure 8**. The first photograph shows a collimated green laser beam (circular spot) which is brought to a line focus by the DOE on the left of the picture. Additional beams to the left and right of these are also observed in the photograph; however, in reality they are very weak. Experimentally, for off‐axis focusing DOE lenses, more than 90% of the incident light is typically measured in the focused beam. The second image in **Figure 8** is a photograph of the transparent diffractive lens viewed in room lighting.

**Figure 7.** The percentage increase of output current of c‐Si solar cells versus area of the c‐Si cells for a single cylindrical DOE and an arrangement of two cylindrical DOEs.

**Figure 7** presents the relative increase in the *I*

**Figure 6.** *I‐V* curves for a c‐Si solar cell (area = 60 mm2

82 Holographic Materials and Optical Systems

*I***sc mA/cm2**

Array of two cylindrical DOE

**Table 1.** Calculated *J*

current density.

when using the holographic focusing elements.

solar cells. The illuminated area of the DOE remained constant at 113 mm<sup>2</sup>

Si cell 3.7 0.061 With cylindrical DOE 4.3 0.6 16 0.071

the concentration ratio, the preference is to use solar cells significantly smaller than the DOEs. These results show that there is a significant improvement in the output current obtained

**Δ** *I***sc Δ** *I***sc %**

5.2 1.5 40 0.086

The relative increase for an array of two cylindrical DOEs was nearly double that of single cylindrical DOE. The device is capable of collecting light from a large incident angle and

experiment while the solar cell area was varied between 9 and 100 mm2

sc of the Si solar cell with a range of DOEs. *I*

current is achieved with a single DOE compared to 10% for a 100 mm2

It has been observed that for solar cells with an area of 9 mm<sup>2</sup>

because the smaller cell area makes better use of the focusing effect.

sc for the c‐Si solar cells versus the area of the

sc is the short‐circuit current and *J*sc is the short circuit

*J* **sc mA/cm2**

) with and without a cylindrical DOE in place.

**±0.03**

throughout the

. In order to optimize

solar cell. This is

, a 34% increase in the output

**Figure 8.** Photographs of the light diffracted by holographic lenses recorded in acrylamide photopolymer (a) illuminated with an expanded laser beam and (b) in room light.
