28-02-2013, 12:32 PM
TOTAL INTERNAL REFLECTION
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INTRODUCTION
Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is greater than the critical angle, no light can pass through and all of the light is reflected. The critical angle is the angle of incidence above which the total internal reflectance occurs.
When a light beam crosses a boundary between materials with different kinds of refractive indices, the light beam will be partially refracted at the boundary surface, and partially reflected. However, if the angle of incidence is greater (i.e. the ray is closer to being parallel to the boundary) than the critical angle – the angle of incidence at which light is refracted such that it travels along the boundary – then the light will stop crossing the boundary altogether and instead be totally reflected back internally. This can only occur where light travels from a medium with a higher [n1=higher refractive index] to one with a lower refractive index [n2=lower refractive index]. For example, it will occur when passing from glass to air, but not when passing from air to glass.
Optical description
Total internal reflection can be demonstrated using a semi-circular block of glass or plastic. A "ray box" shines a narrow beam of light (a "ray") onto the glass. The semi-circular shape ensures that a ray pointing towards the centre of the flat face will hit the curved surface at a right angle; this will prevent refraction at the air/glass boundary of the curved surface. At the glass/air boundary of the flat surface, what happens will depend on the angle.
Critical Angle
The critical angle is the angle of incidence above which total internal reflection occurs. The angle of incidence is measured with respect to the normal at the refractive boundary (see diagram illustrating Snell's law). Consider a light ray passing from glass into air. The light emanating from the interface is bent towards the glass. When the incident angle is increased sufficiently, the transmitted angle (in air) reaches 90 degrees. It is at this point no light is transmitted into air. The critical angle is given by Snell's law.
Frustrated Total Internal Reflection
Under "ordinary conditions" it is true that the creation of an evanescent wave does not affect the conservation of energy, i.e. the evanescent wave transmits zero net energy. However, if a third medium with a higher refractive index than the low-index second medium is placed within less than several wavelengths distance from the interface between the first medium and the second medium, the evanescent wave will be different from the one under "ordinary conditions" and it will pass energy across the second into the third medium. (See evanescent wave coupling.) This process is called "frustrated" total internal reflection (FTIR) and is very similar to quantum tunnelling. The quantum tunnelling model is mathematically analogous if one thinks of the electromagnetic field as being the wave function of the photon. The low index medium can be thought of as a potential barrier through which photons can tunnel.
The transmission coefficient for FTIR is highly sensitive to the spacing between the high index media (the function is approximately exponential until the gap is almost closed), so this effect has often been used to modulate optical transmission and reflection with a large dynamic range. An example application of this principle is the multi-touch sensing technology for displays as developed at the New York University’s Media Research Lab.
Phase Shift Upon Total Internal Reflection
A lesser-known aspect of total internal reflection is that the reflected light has an angle dependent phase shift between the reflected and incident light. Mathematically this means that the Fresnel reflection coefficient becomes a complex rather than a real number. This phase shift is polarization dependent and grows as the incidence angle deviates further from the critical angle toward grazing incidence.
The polarization dependent phase shift is long known and was used by Fresnel to design the Fresnel rhomb which allows to transform circular polarization to linear polarization and vice versa for a wide range of wavelengths (colours), in contrast to the quarter wave plate. The polarization dependent phase shift is also the reason why TE and TM guided modes have different dispersion relations.