Reflective losses quickly become significantReflective losses quickly become significant

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.

Antireflective CoatingsAntireflective Coatings

Melles Griot CatalogueMelles Griot Catalogue

= 1= 1 = 1.38= 1.38 = 1.5= 1.5

= 0.025

= 0.002

Total Total = 2.7% = 2.7%compared to compared to (() = 3.5% ) = 3.5%

without coatingwithout coating

Melles Griot CatalogueMelles Griot Catalogue

Film thickness further reduces reflectionsFilm thickness further reduces reflections

Melles Griot CatalogueMelles Griot Catalogue

Observed Observed for MgF for MgF22 coated optic coated optic

If incident beam is not at 90If incident beam is not at 90ºº use Fresnel’s use Fresnel’s complete equationcomplete equation

componentcomponent componentcomponent

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

For an air-glass interfaceFor an air-glass interface

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

For unpolarized light, For unpolarized light, increases increases as as 11 increases increases

componentcomponent componentcomponent

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.

Example of highExample of high at high at high 11

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

Brewster’s AngleBrewster’s Angle

11 where where of polarized light of polarized light

is zerois zero

1

21-p tan

1

21-p tan

For an air-glass transition For an air-glass transition pp

= 58= 58° ° 40’40’

Are you getting the concept?Are you getting the concept?

Suppose light in a quartz crystal (n = 1.55) strikes a boundarySuppose light in a quartz crystal (n = 1.55) strikes a boundarywith air (n = 1.00) at a 50-degree angle to the normal. At whatwith air (n = 1.00) at a 50-degree angle to the normal. At whatangle does the light emerge?angle does the light emerge?

Why?

http://www.rpi.edu/dept/phys/Dept2/APPhys1/optics/optics/node15.htmlhttp://www.rpi.edu/dept/phys/Dept2/APPhys1/optics/optics/node15.html

Total Internal ReflectionTotal Internal Reflection

11sinsin11 = = 22sinsin22

Snell’s Law:Snell’s Law:

If If 22 = 90 = 90ºº

1

21-c1 sin

1

21-c1 sin

At any At any 11 cc T( T() ) 0 0

For a glass-air transition For a glass-air transition cc = 42 = 42ºº

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.

Fiber OpticsFiber Optics

http://www.us.schott.com/fiberoptics/english/company/index.html#http://www.us.schott.com/fiberoptics/english/company/index.html#..

Defining Characteristics:

• Numerical Aperture• Spectral Transmission• Diameter

Are you getting the concept?Are you getting the concept?Light of vacuum wavelength Light of vacuum wavelength 00= 850.0 nm enters the end of an optical= 850.0 nm enters the end of an optical

fiber from air at an angle of 20.5fiber from air at an angle of 20.5oo with respect to the normal. with respect to the normal.Its wavelength inside the fiber is 574.3 nm. Its wavelength inside the fiber is 574.3 nm. A. What is the index of refraction inside the fiber? A. What is the index of refraction inside the fiber? B. What is the angle between the light ray and the normal inside the B. What is the angle between the light ray and the normal inside the fiber? fiber? C. Assuming the end of the fiber is perpendicular to its upper edge, whatC. Assuming the end of the fiber is perpendicular to its upper edge, whatis the angle between the light ray and the surface when the light reachesis the angle between the light ray and the surface when the light reachesthe upper edge? the upper edge? D. If the index of refraction outside the upper edge of the fiber is 1.44,D. If the index of refraction outside the upper edge of the fiber is 1.44,what is the angle between the light and the normal to the surface as itwhat is the angle between the light and the normal to the surface as itexits the upper edge?exits the upper edge?

Numerical Aperture (NA)Numerical Aperture (NA)

http://www.us.schott.com/fiberoptics/english/company/index.html#http://www.us.schott.com/fiberoptics/english/company/index.html#..

NA: A dimensionless number that characterizes the range ofangles over which the system can accept or emit light

offcutoutsideNA sin offcutoutsideNA sin

outside

Cut-off Angle: This maximum value for the angle of incidence onthe fiber that experiences TIR is called the cut-off angle.

Are you getting the concept?Are you getting the concept?

Consider an optical fiber having a core index of 1.46 and acladding index of 1.45. What is the critical angle for this core-

cladding interface? For what range of angles inside the fiber atthe entrance to the fiber (2) will light be totally internally reflectedat the upper edge of the fiber? To what range of incidenceangles (1) does this correspond? What is the numerical apertureof this fiber?

Evanescent Waves in Fiber OpticsEvanescent Waves in Fiber Optics

http://www.olympusmicro.com/primer/java/tirf/evaintensityhttp://www.olympusmicro.com/primer/java/tirf/evaintensity // http://www.photonics.cusat.edu/

d

z

eIzI

0)( d

z

eIzI

0)(

Evanescent Waves for TIR MicroscopyEvanescent Waves for TIR Microscopy

http://www.olympusmicro.com/primer/java/tirf/penetration/index.htmlhttp://www.olympusmicro.com/primer/java/tirf/penetration/index.html

2123

22

0

sin4 cf

p

nnd

2123

22

0

sin4 cf

p

nnd