This paper reports on a simple approach of determining the ability of a transparent material, such as cellophane to rotate the direction of polarization of a light beam. In order to determine the birefringence of such a material, a Mach-Zehnder interferometer is used to generate interference patterns when the cellophane sheet is mounted on one arm such as to intercept a portion of the laser beam. The recorded interferograms show a phase shift which is calculated to be 0.98π radians. By rotating the cellophane sheet on the object beam, the fringe separation is measured for different angles and the values used to calculate the ordinary and extraordinary refractive indices as 1.4721 ± 0.0002 and 1.4680 ± 0.0002 respectively at 632.8 nm wavelength. A surface error of approximately λ/16 (peak to valley) is measured from the recorded interferograms. Because of its sufficient birefringence and small thickness of 24 μm, cellophane can be used to fabricate special polarization pupil masks by cutting and aligning different cellophane structures appropriately.
Cellophane is a thin, flexible, transparent material made from wood pulp and used as a moisture proof wrapping. Its impermeability to air, oils, greases, and bacteria makes it useful for food packaging. It is still used today for packaging a variety of food items as well as in industrial applications like a base for self-adhesive tapes. There has been some resurgence of interest on cellophane sheet due to its behavior as a half-wave plate [
During its manufacturing process, an alkaline solution of cellulose fibers (usually wood or cotton) known as viscose is extended through a narrow slit of an acid bath. The acid regenerates the cellulose, forming a film. Further treatment, such as washing and bleaching, yields cellophane. Due to the unidirectional stress during the extrusion process, the cellophane is an anisotropic material and behaves like a calcite crystal. The refractive index ny of the cellophane along the longer dimension of the rolled cellophane is different from the refractive index nx in the direction of the shorter dimension (x-direction). As a result, a light wave component polarized in the x-direction propagates through the medium faster than the component polarized in the y-direction. After transmission through such a medium, a phase difference arises between these two light wave components. This behavior exhibited by the cellophane sheet strongly points to the fact that it can be used as a half-wave plate. The sheet shows superior behavior when used for rotating the direction of polarization and as a result has been used to convert a laptop computer screen into a three dimensional display [
where is wavelength of the incident light, nx and ny are the refractive indices of the fast and slow axes respectively and d is the thickness of the wave plate [6-8]. If such a phase difference is equivalent to π radians, the material is a half-wave plate (HWP). Such a material will rotate an incident beam to twice the angle between the incident beam and the optical axis [9-11].
In the next sections, it will be demonstrated that, the ability of a transparent material to rotate polarization of an incident beam can be deduced by measuring the optical power modulation of the sand p-polarized components. Further, a Mach-Zehnder interferometer is used to measure the birefringence due to a transparent sheet such as cellophane.
A simple optical system is designed to measure the modulated light beam as the cellophane sheet is being rotated. A comparison with a commercial HWP is done. Further, a Mach-Zehnder Interferometer is used to study the birefringence of a cellophane sheet.
The schematic set-up used for this study is shown in
To further investigate the birefringence properties of the
cellophane sheet, a Mach-Zehnder interferometer set-up was used as shown in
The patterns were projected on the CCD-Camera interfaced to a computer for the display and recording of the inteferograms. The results of this experiment are presented in
The refractive indices were determined by measuring the spacing between adjacent fringes and for two sets of interference patterns recorded at different angles of the mounted cellophane sheet. Equation (2) was used for evaluating the extraordinary and ordinary refractive indices nx and ny respectively.
where n is the refractive index and is the incident angle [
A series of experiments were performed to investigate the ability of a cellophane sheet to perform as a purpose built half-wave plate (HWP). The graph presented in
The graph shows power in milliwatts at each of the data points corresponding to an angular position of the cellophane sample and HWP. The cellophane sample compares very well to an ideal HWP in rotating the direction of polarization of the laser beam. The power is maximum when the polarization direction of the beam emerging from the cellophane sheet is parallel to the direction of an s-polarized wave of the PBS and minimum
when orthogonal. It is also clear from the graph in
For fast and slow axis the direction of polarization is only altered in such a way that the two beams remain parallel to each other and therefore make maximum contribution to interference. When mounted 450 from the fast axis the polarizations of the object and reference beams are orthogonal to each other. Their contribution to interference is zero.
polarizations of the interfering beams are parallel and orthogonal respectively. The cellophane sheet showed maximum fringe contrast along the length axis and along the width axis (
In order to determine the fast and slow axis, interferograms were recorded for angles of incidence adjacent to the two axes. The recorded interferograms were further analyzed to obtain the fringe separation in each case. Using the measured values and applying Equation (2) for the fringes recorded at different angles of incidence adjacent to both axes yields refractive index values of 1.4680 ± 0.0002 and 1.4721 ± 0.0002. The fast axis has the lower value of refractive index and is along the length of the cellophane sheet. The slow axis is along the width of the sheet and has the higher value of the refractive index. Therefore the ordinary and extraordinary refractive indices for the cellophane sample at 632.8 nm wavelength are given as 1.4680 ± 0.0002 and 1.4721 ± 0.0002 respectively. From the refractive index obtained and thickness of 24 µm, it becomes possible to calculate the phase difference. Applying Equation (1) results to a phase difference of 0.977031 radians. A peak to valley surface quality error of 0.063λ (approximately λ/16) was calculated using the Atmosfringe optical software.
Interferometry analysis of a cellophane sample has been accomplished using a Mach-Zehnder interferometer (MZI) setup. Using the setup, it was established that a right choice of cellophane sheet possessed sufficient birefringence to perform as a half wave retarder. The fast and the slow axis of the sample were determined to be along the length and width of the sample respectively. The calculated values of the ordinary and extraordinary refractive indices were 1.4680 ± 0.0002 and 1.4721 ± 0.0002 respectively which gave a birefringence value of 0.0041 ± 0.0003 with the error being calculated as the square root of the sum of the squares of the errors.
A phase shift of 0.98π radians was evaluated from interferograms recorded when mounting the cellophane sample on one arm of the MZI as to intercept a portion of the laser beam. The measured phase shift value compares very well with that of a purpose built half wave plate. Its retardation is 98% that of an ideal half wave retarder; hence a correct choice of cellophane is good enough to perform as a half wave retarder. A surface quality error of approximately λ/16 (peak to valley) was measured by analyzing the recorded interferograms. Consequently, the cellophane sheet provides an alternative to commercial half wave plates especially in applications that are not critical to surface aberrations or the beam can be spatially filtered after passing through the sample. Because of its sufficient birefringence and small thickness, cellophane can be used to fabricate special polarization pupil masks by cutting and aligning cellophane structures appropriately. Such a mask has been proposed in a theoretical paper on super resolution [
This research was conducted at Jomo Kenyatta University of Agriculture and Technology, Optics and Lasers Research Laboratory and supported by Kenyatta University.