Reflective losses quickly become significant Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

Antireflective Coatings Melles Griot Catalogue  = 1  = 1.38  = 1.5  =  = Total  = 2.7% compared to  ( ) = 3.5% without coating

Melles Griot Catalogue Film thickness further reduces reflections

Melles Griot Catalogue Observed  for MgF 2 coated optic

If incident beam is not at 90 º use Fresnel’s complete equation  component component Ingle and Crouch, Spectrochemical Analysis

For an air-glass interface Ingle and Crouch, Spectrochemical Analysis For unpolarized light,  increases as  1 increases  component component

Eugene Hecht, Optics, Addison-Wesley, Reading, MA, Example of high  at high  1

Ingle and Crouch, Spectrochemical Analysis Brewster’s Angle  1 where  of polarized light is zero For an air-glass transition  p = 58 ° 40’

Are you getting the concept? Suppose light in a quartz crystal (n = 1.55) strikes a boundary with air (n = 1.00) at a 50-degree angle to the normal. At what angle does the light emerge? Why?

Total Internal Reflection  1 sin  1 =  2 sin  2 Snell’s Law: If  2 = 90 º At any  1   c T( )  0      

For a glass-air transition  c = 42 º Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

Fiber Optics Defining Characteristics: Numerical Aperture Spectral Transmission Diameter

Are you getting the concept? Light of vacuum wavelength 0 = nm enters the end of an optical fiber from air at an angle of 20.5 o with respect to the normal. Its wavelength inside the fiber is nm. A. What is the index of refraction inside the fiber? B. What is the angle between the light ray and the normal inside the fiber? C. Assuming the end of the fiber is perpendicular to its upper edge, what is the angle between the light ray and the surface when the light reaches the upper edge? 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 it exits the upper edge?

Numerical Aperture (NA) NA: A dimensionless number that characterizes the range of angles over which the system can accept or emit light  outside Cut-off Angle: This maximum value for the angle of incidence on the fiber that experiences TIR is called the cut-off angle.

Are you getting the concept? Consider an optical fiber having a core index of 1.46 and a cladding index of What is the critical angle for this core- cladding interface? For what range of angles inside the fiber at the entrance to the fiber (  2 ) will light be totally internally reflected at the upper edge of the fiber? To what range of incidence angles (  1 ) does this correspond? What is the numerical aperture of this fiber?

Evanescent Waves in Fiber Optics /

Evanescent Waves for TIR Microscopy