SUPERPOSITION OF WAVES Waves of different k vector, same frequency Counter-propagating waves Intersecting waves Waves mixing (AOM) Co-propagating, random phase Waves of the same k vector, same frequency Waves of the same k vector direction, different frequencies Beat note Creation of an arbitrary Group velocity

Constructive and destructive Superposition is just like adding two vectors, Waves of the same k vector, same frequency constructive destructive

Waves of the same k vector, same frequency Energy conservation If the energy is lost by destructive interference, it has to reappear somewhere else by constructive interference and a complex transmission coefficient Incident intensity Energy conservation: Reflected intensity Transmitted intensity A beam splitter is an element with a complex reflection coefficient

Waves of the same k vector, same frequency Energy conservation If the energy is lost by destructive interference, it has to reappear somewhere else by constructive interference and a complex transmission coefficient Energy conservation: A beam splitter is an element with a complex reflection coefficient

Waves of the same k vector, same frequency Energy conservation Mach Zehnder: Michelson

Waves of the same k vector, same frequency Energy conservation Antiresonant ring

Random and Coherent source

APPLICATIONS Mach Zehnder: measurement of small absorption, index of refraction Michelson Wavemeter Antiresonant: extracting light from a cavity

SUPERPOSITION OF WAVES Waves of (nearly) the same k vector, same frequency: Fresnel biprism Given the angle, what is the fringe spacing? How to determine the angle of the biprism?

P S1S1 S2S2 SUPERPOSITION OF WAVES Waves of (nearly) the same k vector, same frequency: Youngs double-slit experiment

Interference of two circular waves – Wavelength (decreasing bottom to top) and wave centers distance (increasing to the right) Waves of different k vector, same frequency

SUPERPOSITION OF WAVES Waves of different k vector, same frequency Counter-propagating waves Intersecting waves Waves mixing (AOM) Co-propagating, random phase Waves of the same k vector, same frequency Waves of the same k vector direction, different frequencies Beat note Creation of an arbitrary Group velocity

Waves mixing: not necessarily optical waves Example: AOM

FABRY-PEROT