Trivia Question Which “Big Bang Theory” character is from New Jersey? (a) Raj Koothrappali (b) Bernadette Rostenkowski (c) Howard Wolowitz (d) Sheldon Cooper (e) Amy Farrah Fowler (f) Leonard Hofstadter (g) Penny d c a e b f g

The grand overview of Optics/Photonics Historical Development: Ray Optics → Wave Optics → EM Optics → Quantum Optics. Ray Optics is an approximation of Wave Optics in which wavelength short compared to other dimensions (focal lengths, diameter of optical components, etc.) so that Diffraction can be ignored. Wave Optics – Is needed to describe phenomena such as INTERFERENCE, DIFFRACTION, Phase and Group velocities

The Electromagnetic Spectrum

Postulates of Wave Optics Light travels as waves with a speed of light in a vacuum given by c o. Speed of light in a medium determined by refractive index n Optical wave is expressed mathematically as a wavefunction  (r,t) which satisfies the wave equation: Principle of superposition: Refractive index n(r) can vary with position as long as variations occur of distances long compared to wavelength.

Postulates of Wave Optics Optical Intensity (optical power/ unit area) [W/cm 2 ] is proportional to average of square of waveform. Average over times much longer then duration of optical cycle 1/ν. Optical power (Watts) calculated as power flowing through area perpendicular to direction of propagating wave. Optical energy: Integrate optical power over some period of time. (Energy/ time=Watts)

Animation of transverse waves: string/wave-on-a-string_en.html USE IE as browser.

V→V→ General Wave Function X position S t0t0 t1t1 t2t2 t3t3 t4t4 Shape the same at some later time. x’x Wave Function

When waves collide Animation of transverse waves: string/wave-on-a-string_en.html USE IE as browser. Perform animation with low tension (so speed of waves is low) and put too pulses of wave separated by some time. What happens when waves overlap after reflection?

In phase, out of phase, partially out of phase waves In phase Out of phase Partially out of Phase

Electric fields as Phasors (similar to E field as phasors in Phys 121)

When waves collide – Superposition of waves Animation of transverse waves: string/wave-on-a-string_en.html USE IE as browser. Perform animation with normal tension, but oscillate the one end. Reflected waves form a standing wave with incoming wave.

Illustrates principle of Superposition Illustrates standing waves Illustrates “beats” Illustrates effect of phase difference between the waves Illustrates effect of waves of different amplitudes Illustrates concept of # of wavelengths in optical path length. When waves collide – Superposition of waves

Beat Wave

Group Velocity versus Phase velocity For animation below, GREEN dot follows position of GROUP of waves. Note: follows speed at which the envelope of wave motion travels. RED dot follows constant PHASE within the wave. Note that PHASE and GROUP velocity in general are DIFFERENT. Which speed determines Velocity at which INFORMATION can be transmitted? Which velocity can be LARGER than speed of light? 15

Group Velocity