Polarisation, Anisotropy - PDF document

Polarisation, Anisotropy - total electric vector is a straight line at an anglegiven by tan) - linearly polarised(2m+1) = E - circularly polarisedAnything else - elliptically polarised lightAll described by the locus of the vector + EOr in complex notation exp i + Eexp i( + Eexp i Some Common Polarisations But You Can Only Measure EnergyOK so we must characterise things in terms of energyquantities = E + E = s Total energy = E = sDifference inenergy = 2 E) = s = 2 E) = sStokes Parameters - after Lord Stokes. = s + s + sThe angles 2 form the latitude and longitudeon the sphereAll polarisations of a single beam are points on thesurfaces of the sphereEg poles are circular polarisationEg equator is linear polarisation See a sum of lots of little “wavelets” (except lasers!)Stokes parameters are energy-like quantities and canbe added up for the sum of a set of “wavelets” = = s = = s 2 = 2 )= s 2 = 2 )= s s2 Natural light does not follow the restrictions onfrequency and phase as previous discussionNatural light considered as random superposition ofwavelets of random phasing + s + sFor light from a thermal source� , s = s = s = 0For white light from a linear polariser = ±s� , s = s = 0 Anisotropy = Without doing too much math. The permittivity andrefractive index in the right co-ordinates can bewritten as a diagonal matrix (three values)If two diagonal elements are the same -� unixialIf theyre all different -� biaxialThat means that we can propagate E at differentvelocities and the phase relationship will depend uponthe distance from the ref. pointNOTE 1: The axes are controlled by the dielectric(crystal) axes - they are no longer arbitraryNOTE 2: Need to orient the crystal in the system to getall the axes right EExy
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 Convenient to write E as a columnvectorHere are some Jones vectors LinearCircularJones Vectors can be added BUT only if everythingrefers to the same (exactly the same) frequency(defined phase relationship) An optical element can be configured as a 2x2 matrixwhich multiplies the Jones vector to give a new vectorOptical elements can be stacked to find the effect of asystem on polarisation Linear PolariserscossincossincossinPhase Changer0exp() Start with anythingLinearly polarise it - generates an axis setAdd a phase retarder where = Called a quarter wave plate because the relativeretardation is 1/4 of a wavelengthGot circularly polarised light! Optical ActivitySubstances can rotate the plane of polarisationAmount of rotation per unit length = specific rotarypower eg 3.7Can be explained as a different propagation speed(refractive index) for RH and LH circular polarisationHow does this happen?Effect of a magnetic field on propagation Optical ActivityNotice that this is a static external field, not the fieldfrom the wave itselfUsing our SHM model of the dielectric = -e - e d/dt x (µBut the polarisation = neSo can solve the above for a wave solution + K ) = Ne + i x Which can be written in the form of a tensorxxxyxyxxWhere all the are functions of the field HWe can solve for the dispersion relation for the twopolarisations... + = - + i + = - + Which has solutions for = ±i EAnd k = (( 1+ ± Which leads to = ( 1+ + = ( 1+ Optical Activity - NaturalBirefringence - multiple refractive indices (linear)Optical activity - multiple refractive indices (circular) Optical Activity - InducedFaraday rotationApply a magnetic fieldBecomes optically activeVoigt EffectApply a magnetic fieldBecomes birefringentPockels Effect - material has no centre of inversion(crystal)Apply an electric fieldBecomes (changes) birefringenceKerr Effect - material does have a centre of inversionApply an electric fieldBecomes birefringentAbove are used routinely to manipulate (switch) laserbeams - high frequency operation Typical Kerr CellLinearly polarise light going inWhen Kerr cell off (no field) nothing happensKerr cell axis at 45 to x,yApply field to apply relative phase shift between EThen polarisation is still linear but rotates 180Use a second polariser at 90 to firstBlocks off, Passes on....