Physics 116 Session 24 Interference in gratings and thin films Nov - - PowerPoint PPT Presentation

• R. J. Wilkes

Email: ph116@u.washington.edu

Physics 116

Session 24

Interference in gratings and thin films

Nov 8, 2011

• 2 clickers have quiz data logged, but no

registration:

• 649314
• 614235

If one of these is yours, see me pls

• Exam 2 results
• Avg 84
• Std dev 15
• Median 88

Grades should be on Webassign gradebook later today

3

Lecture Schedule

(up to exam 3)

Today

10

Interference: reflected waves

• Phase shift on reflection

– Recall behavior of wave on a rope:

• If end of rope is rigidly secured, reflected wave gets inverted (180 deg

phase change)

• If end of rope can move up and down freely, no inversion

– Similar behavior for reflection of EM waves if reflecting surface is on a medium with higher index of refraction (slower light propagation speed)

• SO phase flip going from air to water, but no flip from water to air
• Phase shift means interference can occur between incident and

reflected waves

n2 = 1.5 n1 = 1.0 B n’1 = 1.5 n’2 = 1.0 A A’

C=180deg out of phase with A C’

B’

C’ = in phase with A’

11

Interference in a thin layer of air

Tshim

t Not to scale! Glass is much thicker than air layer

• Air gap between flat glass plates

– Make a layer of air between 2 glass plates by inserting a shim (fine wire, or hair) at both ends

• Thickness of air layer is constant: t = Tshim
• Ray reflected from top surface (air to glass): phase flip
• Ray reflected from 2nd surface (glass to air): no flip (Ray 1)
• Ray reflected from 3rd surface (air to glass): phase flip again (Ray 2)
• Suppose angle of incidence is nearly vertical

– so neglect the angle shown in drawing: Ray 2 travels 2t further than ray 1

• Rays 1 and 2 show destructive or constructive interference if 2t is some

multiple of wavelength

2 1

2 1 = 2t = m / 2

( )

Constr : m = 0,2,4… Destr : m = 1,3,5…

2 1 = 2t + 2

• = m

2

• 2t

+ 1 2

• = m

2 , Constr if : m = 2,4,6… Destr : m = 1,3,5…

If there were no phase flip for ray 2, would be Constructive if m= even (so full wavelength difference) Destructive if m= odd (so half-wavelength difference) Phase flip of ray 2 in effect adds another half-wavelength:

12

Interference in reflected waves

• Example: wedge of air between flat glass plates

– Make a wedge of air between 2 glass plates by inserting a shim (fine wire, or hair) in one end

• Thickness of air layer is proportional to x: t(x) = Tshim x

– We see fringes as t increases: dark fringe when m is odd, bright when m is even

• Requirements:

– Illuminate with monochromatic light, or fringes will be smeared in a rainbow! – Plates have to be very flat (“optical quality”) or ripples will make interference pattern impossible to see

• Flat to within wavelength: this is a very sensitive flatness test!

– Light source and observer are “distant”

• Meaning: ~ parallel light rays

x=0 x=1

Tshim

2 1 = 2t + 2

• = m

2

• 2t

+ 1 2

• = m

2 , Constr if : m = 2,4,6… Destr : m = 1,3,5…

www.oldham-optical.co.uk

13

Newton’s rings

• Air gap between a convex lens and a flat glass plate

– Another air layer of variable thickness – This setup is used to test lenses – again, we can immediately see flaws at the scale of wavelength

r R t

• If you enjoy geometry and algebra,

here’s how to determine radius r of the mth ring, for a given lens radius of curvature R and wavelength of light

• Usually need a microscope to see

rings for a typical lens

14

Thin films

• Reverse the air gaps we’ve just discussed

– Make a thin film of some substance with n>nair

• Soap bubble (water layer, held together by surface tension)
• Oil slick on a puddle of water
• Film of plastic material specifically designed for coating optical parts

– Now ray 1 has a phase flip, and ray 2 does not – Otherwise, exactly the same analysis – except

• Path difference occurs in medium with n>1

n = air n , effective 1 = air 2

(just the phase flip), 2 = 2t (path length in film)

= 2 1, measure in units of wavelength to get phase relations

interference if 2

n

• 1

air

• =

2t n

• 1

2

• = m

2

• 2t

n 1 2

• = m

2 ,

• 2nt

air 1 2

• = m

2 , Constr if : m = 0,2,4,6… Destr : m = 1, +1, 3,5…

t 2 1

• We have to take into account the wavelength in the

medium (but we measure wavelengths in air

(nair ~ nvacuum =1.0)

• Notice: if t is nearly 0, we still get destructive interference due to the phase flip

for ray 1, so we need to add that case to our list – that’s why the -1 is in there

15

Antireflection coatings

• Application of thin films: arrange for destructive interference of

reflected rays

– Then film = non-reflective coating for lenses, glasses, etc

• Example: glass (n=1.5 coated with magnesium fluoride (n=1.38)

What is the thickness of MgF layer needed?

– Now both ray 1 and ray 2 have a phase flip, but ray 2 also has path 2t – Choose wavelength in center of human-visible range: 555 nm – For destructive interference, we want m=1 (m=-1 means t=0) MgF = air 1.38 , effective 1 = air 2

(just the phase flip), 2 = 2t + n

2

(path length in MgF film plus phase flip)

= 2 1, measure in units of wavelength to get phase relations

interference if 2

n

• 1

air

• =

2t n + 1 2

• 1

2

• = m

2 2nt air

• = m

2 , Constr if : m = 0,2,4,6… Destr : m = 1, +1, 3,5… so t = 1 2 air 2n = 1 4 air n

• = 555nm

4(1.38) = 100.5nm

MgF t 2 1 glass