Week 10 – More E&M theory, attenuation, color

Dispersion model for Dielectric

Dispersion-model.xmcd

Resonant frequencies at 1012 and 5*1012 radians/sec

damping frequencies at 1012/10 and 5*1012 /10 radians/sec

Oscillator strengths equal for both.

22

2 20

( ) j

je oj j

fNqn

m i

Dispersion model for Dielectric

Dispersion-model.xmcd

damping frequencies at 1012/10 and 5*1012 /10 radians/sec

How does refractive index change with damping frequency?

damping frequencies at 1012/2 and 5*1012 /10 radians/sec

Dispersion model for Dielectric

Dispersion-model.xmcd

Equal oscillator strengths

How does refractive index change with oscillator strength?

Oscillator strength of high frequency 3 times low frequency

Dispersion model for Metal

Metal-Dispersion-model.xmcd

Note: for Electromagnetic frequencies below plasma frequencies,And imaginary refractive index LARGE.

For frequencies above plasma frequency,

And real refractive index approaches UNITY.

Plasma frequency set to be 1012 radians/sec

0/ 0

/ ~ 1o

Negative Refractive Index Materials

Snell’s Law with negative refractive index… so called ‘Left Handed Materials’

‘Cloaking’ devices

Focusing and Absorbing example

You can also design metamaterials which are perfect absorbing material (in a spectral range) …. Good for stealth technology. Energy from radar absorbed rather than reflected.

Negative Refractive Index MaterialsTime Averaged Poynting Vector is ANTIPARALLEL to phase velocity.

E, B, and k follow a LEFT HANDED rule

E

Bk

Right-handed ‘NORMAL’ wave

Negative Refactive Index wave

E

B

k

What do metamaterials look like?

Microwave range – combination of metallic split rings (for magnetic permeability control) and metallic lines (for permittivity E field controll)

Size of individual structures SMALLER than wavelength of electromagnetic radiation

Subwavelength Structures – Photonic Crystal

Pillars of GaAs

Light in

Light out

wavelength

Other methods of ‘cloaking’

Color from ScatteringOpal structures – (interference from scattered light from small structures)

Primary ColorsRed Green Blue - RGB

What is this due to?

Primary color set NOT unique. Typically use RGB since these are the phosphors used to generate colors in TV sets/ monitors. RGB also correspond (roughly) to the photoreceptors in the human eye

James Clerk Maxwell

ADDITIVE combinations of RGB

Human Detection of Light• Two types of color receptors in the human eye– Rods (best for dim light)– Cones (best for bright light)

Normalized responsivity spectra of human cone cells, S (short), M (medium), and L (long) types

Wavelength (nm)

Resp

onsi

vity

Rod sensitivity compared to Cones

SUBTRACTIVE combinations (ie. Transmission)

STARTING with WHITE light, REMOVE the blue color (by absorbing blue) and the resulting color appears as yellow (combination of Red and Green)

Additive vs Subtractive Colors

RGB cyan, magenta and yellow (CMY)

Complimentary colors – Absence (subtraction or absorption) of green light from ‘white’ light gives purple (magenta).

Eg. Amount of printed magenta ink determines how much green light is absorbed (not reflected) from page

Transmission colors

Overall transmission is the MULTIPLICATION or product of individual multiplications