Fresnel Equations cont.

Transcription

1 Lecture 11 Chapter 4 Fresnel quations cont. Total internal reflection and evanescent waves Optical properties of metals Familiar aspects of the interaction of light and matter

2 Fresnel quations: phases Case n i < n t (air to glass) external reflection If n t > n i, then r < 0 =0 =0 = = 0r r 0i Amplitude changes to negative, equivalent to 180 o phase shift at surface Keep in mind for later: Component normal to the plane of incidence experiences phase shift upon reflection when n i < n t

3 Fresnel quations: Brewster angle Case n i < n t (air to glass) external reflection =0 For light polarized so that is in the plane of incidence there will be no reflection! (Brewsters angle, or polarization angle) =0 tan 1 n n B t i = = Note: at Brewsters angle reflected and transmitted rays form right angle

4 Total internal reflection Case n i > n t (glass to air) internal reflection n t n i Critical angle C : the incident angle for which t is 90 o (n i <n t ) n i sin( C )= n t sin(90 o ) C total internal reflection n i >n t Critical angle (for total internal reflection) C nt sin 1 n i Since t cannot exceed 90 o, there will be no transmitted beam For i > C light is completely reflected: total internal reflection

5 Fresnel quations: total internal reflection Case n i > n t (glass to air), internal reflection At some incidence angle (critical angle c ) everything is reflected (and nothing transmitted). It can be shown that for any =0 angle larger than c no waves are transmitted into media: total internal reflection. Note: Component normal to the plane of incidence experiences no phase shift upon reflection when n i > n t

6 The vanescent Wave Problem with total internal reflection: with only two waves it is impossible to satisfy the boundary conditions Consequence: There must be transmitted wave even for total internal reflection It cannot, in average, carry energy across the interface Solution: There is an evanescent wave that propagates along the surface whose amplitude drops off as it penetrates the less dense medium evanescent wave beam splitter (frustrated total internal reflection) microscope

7 Total internal reflection: example Can the person standing on the edge of the pool be prevented from seeing the light by total internal reflection? 1) Yes 2) No There are millions of light rays coming from the light. Some of the rays will be totally reflected back into the water, but most of them will not.

8 xercise: right angle prism Idea: Can we use total internal reflection to construct a mirror with 100 % reflecting efficiency? Design: right angle prism Will it work? Solution: 45 o Angle of incidence is 45 o. It must be larger than critical angle n glass = 1.5 n air = 1 C sin 1 n n t i sin o Conclusion: it will work

9 Right angle prism: applications A periscope Binoculars

10 Fiber Optics Optical fibers use TIR to transmit light long distances. They play an ever-increasing role in our lives!

11 Propagation of light in an optical fiber Light travels through the core bouncing from the reflective walls. The walls absorb very little light from the core allowing the light wave to travel large distances. Some signal degradation occurs due to imperfectly constructed glass used in the cable. The best optical fibers show very little light loss -- less than 10%/km at m. Maximum light loss occurs at the points of maximum curvature.

12 Fiber optics: applications Applications: Signal transmission: computers, phones etc. Laser surgery ndoscope

13 Optical properties of metals Metal: sea of free electrons. = 0 cos t lectrons will move under - electric current: J conductivity Ideal conductor: =, and J is infinite. No work is done to move electrons - no absorption Real conductor: = finite. lectrons are moving against force - absorption is a function of.

14 Optical properties of metals Assumption: medium is continuous, J Maxwell eq-ns lead to: t t z y x damping Due to damping term solution leads to complex index of refraction: I n R in n ~ x y metal c ny t ky t / ~ cos cos 0 0 Wave equation: Rewrite using exp: c y n c y n t i c ny t i I R e e / / 0 / ~ 0 split real and imaginary terms c y n t i c y n R I e e / / 0 c y n t e R c y n I / cos / 0

15 Metals: absorption coefficient n e I y / c 0 cos t n y / c amplitude decays exponentially R I Intensity is proportional to 2 : I n I y / c 2 2nI y / c y I e I e I 0 Intensity of light in metal: y I 0 e y 0 absorption coefficient: y metal 2n I / c Intensity will drop e times after beam propagates y=1/: 1/ - skin or penetration depth xample: copper at 100 nm (UV): 1/=0.6 nm at 10,000 nm (IR): 1/=6 nm

16 It can be shown that for metals: Metals: dispersion 2 p n 1 p - plasma frequency For < p n is complex, i.e. light intensity drops exponentially For > p n is real, absorption is small - conductor is transparent 2 xample: Critical wavelengths, p = c/ p Lithium Potassium Rubidium 155 nm 315 nm 340 nm

17 Normal incidence: R Metals: reflection 2 2 nr 1 ni 2 2 n 1 n R n I depends on conductivity. For dielectrics n I is small (no absorption) I

18 Light: wavelength and color Typically light is a mixture of M waves at many frequencies: net i 0i cos it ki r i i i Power of waves of each wavelength forms a spectrum of M radiation I() Sun spectrum: Mixture of all wavelengths is perceived by people as white light. How do we see colors?

19 Scattering and color Water is transparent, vapor is white: diffuse reflection from droplets White paint: suspension of colorless particles (titanium oxide etc.) Scattering depends on difference in n between substances: wet surfaces appear darker - less scattering Oily paper - scatters less

20 The yeball There are four kind of detectors of light. They are built around four kinds of organic molecules that can absorb light of different wavelength Color vision - three kinds of cones, B&W - rods

21 The eye s response to light and color The eye s cones have three receptors, one for red, another for green, and a third for blue.

22 How film and digital cameras work

23 Most digital cameras interleave different-color filters

24 The ye: a digital camera? Brain interprets each combination of three signals from R, G and B receptors (cones) as a unique color There are ~120 million receptors in your eye quivalent to 120 Megapixel digital camera! Signal color R G B red yellow green blue

25 The eye is poor at distinguishing spectra. Because the eye perceives intermediate colors, such as orange and yellow, by comparing relative responses of two or more different receptors, the eye cannot distinguish between many spectra. The various yellow spectra below appear the same (yellow), and the combination of red and green also looks yellow!

26 RGB: additive coloration By mixing three wavelengths we can reproduce any color! Primary colors for additive mixing: Red, Green, Blue Complimentary colors - magenta, cyan, yellow (one of the primaries is missing)

27 Computer monitors LCD display

28 CMY: subtractive coloration Use white light and absorb some spectral components Primary colors for additive mixing: Cyan, Magenta, Yellow Cyan - absorbs red Yellow - absorbs blue Magenta - absorbs green Any picture that is to be seen in ambient white light can be painted using these three colors. Color printer: uses CMYK - last letter stands for Black (for better B&W printing) Dyes: molecules that absorb light at certain wavelengths in visible spectral range (due to electronic transitions)