Complex numbers/phasors and amplitudes There was a question last time: since the Re part of a complex field is the physical one, why do we need the full phasor length as the physical field magnitude? The physical field is the Re part of E any time. But the real part of the phasor as usually drawn is the physical field only at t = 0. The maximum physical field strength (amplitude) won’t generally be seen t= 0, but instead whenever the phasor rotates across the real axis, given by the phase angle). So the phasor magnitude is the physical field amplitude.

Announcements HW 3 on Tues includes a lab L1.10. Just write up your work as one of the HW problems. See text under problems (1.10), and intro video at physics dept website then courses/optics, etc. Lab will be ready today at noon. I will ask them to leave the hallway door unlocked until 7pm, but I suggest you do it before 5 pm Tues to be sure. Optics lab S415 ESC, which you get to from S420. Combination 88542 (e0 digits)

Reading Quiz A disadvantage of using real functions to model the motion of oscillators is you can’t model phase shifts you have to use two functions and their derivatives the amplitude depends on frequency

Reading Quiz Q1. In the simple Lorentz model of a dielectric material, the restoring force on the electron cloud depends on the displacement r as: a) -r b) -r2 c) -1/r d) -1/r2 e) -1/r3

Index of refraction from polarization (know the following derivation of n from the wave equation) Assumption of a linear medium A Assumption of single-frequency wave

Index of refraction from polarization

Index of refraction from polarization

Lorentz model of spring-like oscillating dipoles to model polarization

Lorentz model of r spring-like oscillating dipoles wo

Meaning of complex quantities

Lorentz model of spring-like oscillating dipoles P leads E P lags E wo P with E

The index has a form similar to displacement

Change of wave speed is due to phase shift of P vs E

Effect of damping g

Meaning of complex index

Complex index, dielectric constant, k

Complex index, dielectric constant, k P. Near a resonance frequency, materials with atomic dipoles might have for example n = 2 and k = 3 When the wave has moved into the material by a distance of one vacuum wavelength, by what factor is the wave amplitude reduced? a) exp(-2p) b) exp(-3p) b) exp(-4p) d) exp(-6p) P4. What is the phase change of the wave after traveling this distance? A

What “spring=like“ resonances do electrons in atoms have?

P2. Clear, colorless glass has no resonances and no resonances in the visible, but does have them in the UV, which is at a higher w. Hence in clear glass, index n has ______ curvature vs w for visible light. positive negative

Common optical glass indices vs wavelength

Hint: what would these curves look like in the limit of N  0? P3. If we increase the density of a gas (N), index n a) increases for all w b) decreases for all w c) increases with density below resonance, decreases above d) decreases with density below resonance, increases above Hint: what would these curves look like in the limit of N  0?

P4. In a glass that absorbs green light the index , imaginary index k is greatest for ______ red yellow green blue violet P5. In the same glass, real index n is probably greatest for ______ light. (same choices)

nk nk kk kk Glass: changes in the IR n, k due to vibrating atoms Organic semiconductor for solar cell: visible n,k