Polarization and Modern Optics

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Polarization and Modern Optics Polarizing Beam-Splitter Cube Half-wave Plate Quarter-wave Plate Electro-Optic Modulator Charles Bernando Polarization Property of waves that describes the orientation of their oscillations Example: electromagnetic wave (light) = phase difference 1 0 cos( . ) E E k y wt = 2 0 cos( . ) E E k y wt = + Linear Polarization Circular Polarization = 0, , 2, .. = /2, 3/2, .. Elliptical Polarization 1 0 cos( . ) E E k y wt = 2 0 cos( . ) E E k y wt = 1 0 cos( . ) E E k y wt = 1 0 cos( . ) E E k y wt = 2 0 0sin( . ) cos .2E E k y wt E k y wt t| |= = |\ .2 0 cos( . ) E k y wt c = Polarizing Beam-splitter Cube Split randomly polarized beams into 2 orthogonal, linearly, polarized components (s-polarized & p-polarized). S-polarized is reflected at 900 angle, while P-polarized light is transmitted S-wave: electric field perpendicular to plane of incidence P-wave: electric field parallel to plane of incidence AR (antireflection) coating: produce max transmission efficiency Cement: bind 2 prisms BS (beam-splitter) coating or dielectric coating or thin film coating: consists of thin layers of transparent dielectric materials with different refractive indexes, which are deposited on a substrate. It will produce phase shift due to reflections and reinforce certain wavelengths. By controlling the thickness and number of the layers, the reflectivity & transmissivity can be adjusted = vector of beam-splitter interface = vector of incident light = state of polarization of s-wave = state of polarization of p-wave For light incident along z-axis, J. L. Pezzaniti and R. A. Chipman. Angular dependence of polarizing beam-splitter cubes. Appl. Opt. 33(10), pp. 1916-1929. 1994. ( )11, 0, 12n.= ( )0, 0,1 k.=n ksn k. ... .= p s k. . .= ( )0,1, 0 s.= ( )1, 0, 0 p.=nks pHalf-wave Plate Shift the phase between 2 perpendicular components of electric field (the phase shift is rad) Change linear polarized wave into another linear polarized wave Material: quartz, calcite Optical axis = fast axis/extraordinary axis is the axis with the smaller index of refraction Slow axis = ordinary axis (perpendicular to fast axis) is the axis with the higher index of refraction The light component along the fast axis will travel faster than the light component along the slow axis Due to velocity difference, the light component along fast axis and slow axis will be shifted until the outcome phase shift is rad. The phase shift depends on the thickness of a material. = phase shift ne = extraordinary index no = ordinary index L = thickness of material = wavelength 2 .( ).e on n L t|=Quarter-wave Plate Shift the phase between 2 perpendicular components of electric field (the shift phase is /2 rad) Change linear polarized wave into circular polarized wave when the incident light makes 450 angle with the fast axis Electro Optic Modulator A device used for controlling the polarization of a laser beam with an electrical control signal By applying an appropriate voltage to the RF input, a corresponding change in the extraordinary refractive index will occur The voltage required for inducing a phase change of is called the half-wave voltage Jones Matrix Linear horizontal polarizer Linear vertical polarizer Half wave plate Quarter wave plate Example: linearly polarized light 450 (basis ) is incident on a horizontal polarizer. The outcome is horizontally polarized 1 00 0 ( ( 0 00 1 ( ( cos 2 sin2sin2 cos 2u uu u ( ( 2 22 2cos sin (1 )sin cos(1 )sin cos sin cosi ii iu u u uu u u u ( + ( + 1 0 1 10 0 1 0 ( ( (= ( ( ( 11 ( ( For beam splitter, please see: A. L. Fymat. Jones's matrix representation of optical instruments. I: Beam splitters. Appl. Opt. 10(11), pp. 2499-2505. 1971. Conclusion Beam splitter is used to resolve a beam of light into 2 beams by reflecting the s-wave and transmitting the p-wave The wave plates (half and quarter wave plate) are designed to change the state of polarization of incoming light The Electro Optic Modulators use a potential difference to change and adjust the extraordinary refractive index to get the expected phase shift between 2 components of light