Optics 430530 week VI Fabry Perot Introduction to

Optics 430/530, week VI • Fabry Perot • Introduction to anisotropic media This class notes freely use material from http: //optics. byu. edu/BYUOptics. Book_2015. pdf P. Piot, PHYS 430 -530, NIU FA 2018 1

Fabry-Perot (F-P) Instrument • An example of instrument is the F-P interferometer : two parallel surface with adjustable spacing • If spacing fixed F-P etalon • Transmittance through a double boundary is • With P. Piot, PHYS 430 -530, NIU FA 2018 2

Role of Finesse • Large finesse results in better sensitivity to the phase • Finesse is maximized with maximum reflectance • Also note P. Piot, PHYS 430 -530, NIU FA 2018 3

F-P configuration • Ignore this is a constant P. Piot, PHYS 430 -530, NIU FA 2018 4

Example of application of FP: distinguishing nearby wavelengths • F-P instrument can be used to detect a change in wavelength. The change needs to be not too large P. Piot, PHYS 430 -530, NIU FA 2018 5

Free-spectral range • P. Piot, PHYS 430 -530, NIU FA 2018 6

Finesse • Consider the smaller change in wavelength we can resolve it is given by the full-width half max defined as • Solving yields or Define the finesse as P. Piot, PHYS 430 -530, NIU FA 2018 7

Resolving power RP • Note that FWHM • The resolving power (RP) is defined as P. Piot, PHYS 430 -530, NIU FA 2018 8

Multilayer coatings (Advanced) • a P. Piot, PHYS 430 -530, NIU FA 2018 9

Matching conditions I • At interface 0 • At any interface j in the middle P. Piot, PHYS 430 -530, NIU FA 2018 10

Matching conditions II • At the final interface N P. Piot, PHYS 430 -530, NIU FA 2018 11

Matching conditions: Matrix formulation I • Equation on slide 10 can be written as the recurrent relation • Inverting give the field 1 1 P. Piot, PHYS 430 -530, NIU FA 2018 12

Matching conditions: Matrix formulation II • So we can combine to get • where • and P. Piot, PHYS 430 -530, NIU FA 2018 13

Computing overall transmission and reflection coefficient P. Piot, PHYS 430 -530, NIU FA 2018 14

Comments • Done with chapter 1 -4 • Please review pp. 115 -119 as these are the type of questions you should expect on the mid term and final. P. Piot, PHYS 430 -530, NIU FA 2018 15

Anisotropic Media I • We introduce the polarization where • The relation between E and D (or E and P) is called a constitutive relation (and it captures the electromagnetic properties of a medium (same applies to B, H and M). P. Piot, PHYS 430 -530, NIU FA 2018 16

Anisotropic Media II • Susceptibility tensor P. Piot, PHYS 430 -530, NIU FA 2018 17

Plane wave in crystals • Consider • Gauss’s law for D and B in charge-free medium yields so that, generally, • We conclude that the Poynting vector. anymore P. Piot, PHYS 430 -530, NIU FA 2018 is not parallel to k 18