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An easy method is put forward to estimate the optical bandwidth and the wavelength of maximum transmission of Lyot optical filter by measuring the change in phase retardation of birefringent plates as function of thickness. The objective is to demonstrate the experiment with common undergraduate laboratory equipment and thereby provide with an educational aid. The filter is fabricated with cellotape using its birefringence property. The accuracy of measurement is cross-checked with precision spectroradiometric measurements. Some simplification is suggested in the theoretical derivation of the transmitted intensity and a possibility of realizing tunable filter by changing the angle of incidence is indicated.

Colored light can be obtained from white light by passing it through selectively absorbing materials like glass filter, by dispersion through prism and by diffraction through grating. Another method of producing monochromatic light is to use the birefringence property of materials [

The present work supports the above idea and puts forward a befitting measuring technique for such filter. Some simplification in the theoretical derivation is also suggested and the possibility of realizing tunable filter by changing the angle of incidence is indicated. A Lyot optical filter is fabricated using pieces of mobile phone screen as polarizers. The birefringent plates of different thicknesses are prepared by fixing counted layers of cellotape on glass slides. A method is suggested to estimate the full width half maximum (FWHM) of the filter by measuring the change in phase shift between the orthogonally polarized waves introduced by the birefringent plates of varying thickness. The proposed method worked well with reasonable accuracy, as cross-checked with precision spectroradiometric measurements.

This filter is comprised of a series of polarizers with pass axes in the same direction and having a birefringent plate of variable thickness inserted between each two polarizer. The plate thickness varies as

where

is the phase difference between the orthogonally polarized waves, henceforth termed as ‘phase retardation’, introduced by the birefringent plate of thickness t and Δn is the difference in refractive index of the plate for the two wave components.

The maximum transmittance through the filter occurs when Γ = 2kπ, where _{m}) assessed from Equation (2) is expressed as

The bandwidth of the filter, estimated in terms of full width half maximum (FWHM) is determined by bandwidth of the thickest plate, multiplied by the factor 0.886 due to presence of other stages.

which indicates that the bandwidth decreases and the filter becomes sharper, as the number of plates (N) increases. However, a compromise is required because increased number of polarizers and retarders also diminishes the transmitted light intensity.

The following methodology is proposed for determining the parameter Δn for Equation (4) using Equation (2). The electric field vector of the monochromatic polarized light transmitted normally through a retarder can be represented as

where E_{0} is the initial amplitude, z is the direction of light propagation, xʹ is the direction of polarizer transmission axis so that

When this electric vector passes through the analyzer making angle θ with the xʹ-direction, the x and y components make angle (θ − φ) and (90˚ + φ − θ), respectively with analyzer pass axis. The emergent electric field has magnitude

so that the intensity (I) of the emergent light can be expressed, in terms of E_{1} and its complex conjugate (

where

It may be noted that Equation (8) is derived by algebraic simplification only, which is much easier. The same expression was derived earlier by Jones matrix method [_{0}/2)cosΓ and I-axis intercept of I_{0}/2 and the value of Γ can be determined for any arbitrary thickness (t) of the birefringent plate.

The birefringent plates were fabricated by fixing commercial cellotape on thin glass slides. The thickness of a single film of cellotape was determined mechanically by measuring the average thickness of the full pack with micrometer of least count 10 μm and then exfoliating it layer by layer and counting the number of layers. The average thickness (t) of a single layer was found to be 38 μm. The thickness of the glass slide was immaterial because glass has no birefringence and the same glass was used everywhere so that its transmittance always acted as a constant term. Sodium vapor lamp was used as monochromatic source for determining Γ from Equation (8). The transmitted light intensity was measured with Metravi 1330 digital light intensity meter calibrated in lux. Standard polarizer and analyzer graduated up to 2˚ angular resolution were employed. It was verified that

the blank glass slide did not introduce any polarization effect.

For fabricating the Lyot filter, N = 3 was maintained. The architecture of the device is sketched in _{m}) was determined with conventional spectrometer and grating arrangement, as mentioned in

Equation (2) indicates that Γ?t graph for any arbitrary thickness of retarder should be straight line with slope of (2π/λ)Δn. The number of cellotape layers was increased from 1 to 10 so that the thickness of the retarder increased as multiples of t, the thickness of a single layer. In each case, Γ was determined from Equation (8). The experimental variation of Γ with thickness of cellotape layers is shown in _{m} and t, FWHM was determined using Equation (4) and compiled in _{m} calculated from Equation (3) using experimental value of Δn. Accurate determination of t is essential because even 5% deviation can lead to wide change in λ_{m}, as mentioned in

Parameter | Present Method | Spectroradiometric data |
---|---|---|

λ_{m} (nm) | (i) measured with spectrometer & grating: 529 - 532 (ii) Calculated from Equation (3) with experimental t and Δn and using k = 2: (a) 525 with exact value of t (b) 498 assuming 5% increase in t (c) 551 assuming 5% decrease in t | 532 - 534 |

FWHM (nm) | 28 (calculated from Equation (3) with experimental Δn) | 30 |

In order to check the accuracy of the above method, the spectrum of the transmitted light of the tungsten- halogen source passing through the filter was directly measured with accurate Analytical Spectral Devices spectroradiometer, which can record the relative intensities of radiation at almost 1 nm resolution. The parameters λ_{m}and FWHM were directly measured and compared with the above results, as mentioned in

Theoretical variation of transmittance with wavelength for the Lyot filter was generated, as shown in _{m} and FWHM determined by the present method and from spectroradiometer data are in good agreement and also match the predicted value, as compared in

The relative transmission of the filter was also studied with four different light sources of distinct wavelengths, namely sodium lamp and semiconductor lasers of red, green and blue colours. The transmission percentages compiled in

The present work demonstrates an experiment comprising the fabrication of Lyot birefringence filter and measurement of its wavelength selectivity; all carried out within common undergraduate laboratory environment. The Lyot birefringent filter is fabricated with mobile phone screens as polarizers and cellotape layers on glass

Source | Blue laser | Green laser | Sodium light | Red laser |
---|---|---|---|---|

Transmission (%) | 0.36 | 22.0 | 8.0 | 0.20 |

slides as birefringent plates. The basic theory of birefringence is discussed and an equation relating the transmitted intensity to the analyzer and plate orientations is derived by algebraic method. An easy method is put forward to estimate the full width half maximum (FWHM) of the filter by measuring the change in phase retardation introduced by the birefringent plates of varying thickness. The correctness of the results obtained by the proposed method is assured by comparing with those obtained from precision measurements with spectroradiometer. The expression for the transmitted intensity is derived only by algebraic simplification. Also the possibility of realizing tunable filter by changing the angle of incidence is suggested.

The authors acknowledge the facilities of using the equipment and other infrastructural conveniences obtained from the laboratories of the Department of Physics, Presidency University.

Ayantika Khanra,Barun Raychaudhuri, (2016) Cellotape Birefringent Filter: Some New Demonstrations. Optics and Photonics Journal,06,139-145. doi: 10.4236/opj.2016.67016