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Introduction to Optics ME46300 Silvania Pereira Paul Urbach Optics Group, Faculty of Applied Sciences

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Polarisation Consider If both E 0 and H 0 are constant and real then the wave is called linearly polarised wave The direction of polarisation follows the direction of oscillation of the electric field 0 0 E( , ) E exp[ ( . r )] H( , ) H exp[ ( . r )] z t i k t z t i k t
Linear polarisation Here, the electric field oscillates in the vertical direction, thus that wave is called “vertically polarized

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Polarisation Natural light: polarisation fluctuates rapidly, random way (unpolarised light) Linear polarisation can be obtained by letting natural light through a device called polariser E , incident E 2 E 1 , transmitted Transmission axis of the polariser
Polarisation E 1 = E cos The transmitted intensity is : I 1 = I . cos 2 , with I being the intensity of the incident beam Transmission axis of the polariser E , incident E 2 E 1 , transmitted

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Polarisation - Unpolarised light: transmission through a polariser is ½ of the incident intensity (average of the cosine squared) - Partially polarised light: where I max and I min are the maximum and minimum transmission through a rotating polariser max min max min degree of polarisation = pol pol unpol I P I I I I P I I
Scattering and polarisation

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Scattering and polarisation Scattering of molecules: radiation pattern of an oscillating dipole is “directional”
Circular and elliptic polarisation Consider the case of two linearly polarised waves, perpendicular to each other, same amplitude, but with a phase shift of /2 The total electric field is given by 0 0 ˆ i cos( ) ˆ j sin( ) E kz t E kz t 0 ˆ ˆ E = [icos( ) jsin( )] E kz t kz t

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Circular and elliptic polarisation 0 1/2 ˆ ˆ E = [i cos( ) jsin( )] Amplitude of the wave |E.E| E kz t kz t
Circular and elliptic polarisation 0 ˆ ˆ E = [icos( ) jsin( )] E kz t kz t wave of constant magnitude What about the direction of the field as it propagates?

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Circular and elliptic polarisation 0 ˆ ˆ E = [icos( ) jsin( )] E kz t kz t By fixing a point on the axis, say z 0 , at time t=0, the field lies along a certain reference axis
Circular and elliptic polarisation 0 0 0 ˆ ˆ E = [i cos( ) jsin( )] E kz t kz t At time t=kz 0 / , then the sine term vanishes

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Circular and elliptic polarisation 0 ˆ ˆ E = [icos( ) jsin( )] E kz t kz t right circular polarisation (right handed spirals)
Circular and elliptic polarisation 0 ˆ ˆ E = [icos( ) jsin( )] E kz t kz t Reversing the sign of the second term left circular polarisation

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Circular and elliptic polarisation 0 0 ˆ ˆ E = icos( ) ' jsin( )] E kz t E kz t If the amplitudes of the two waves are not the same then we have elliptic polarisation
Circular and elliptic polarisation 0 0 0 0 ˆ ˆ E = i ' j E = E exp[ ( )] E iE i kz t Using the notation of the complex vector amplitude the corresponding wave function is: If E 0 is real -> linear polarisation, if it is complex, it implies circular (if Re ( E 0 )= Im ( E 0 )) or elliptic polarisation

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• Fall '19
• Polarization, Snell's Law, Total internal reflection, Geometrical optics

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