TRIVIA QUESTION! Under President Ronald Reagan, what was the nickname of the science initiative to develop, among other things, a ‘photon torpedo’. (a) The Bourne Initiative (b) Avatar Missile System (c) The 2001 Initiative (d) Star Wars Initiative (e) Star Trek Initiative

Diffraction: Light does not like to be confined

Examples of Diffraction Light passing by a sharp edge Knife edge

Examples of Diffraction Waves passing through a small hole Huygen’s Construction

Examples of Diffraction Focusing light with a lens wo Geometric Optics – Wavelength small compared to other dimensions. No Diffraction. Light focuses to a point. Wave Optics – Wavelength can be comparable to other dimensions. Diffraction MUST be considered. Light focuses to a minimum spot size.

Huygen’s Principle

Huygen’s Principle - Reflection

Huygen’s Principle - Reflection

Huygen’s Principle (formulated by Fresnel) Model each point m in wavefront as a spherical wave (point source of wave). Phase change due to propagation of wave. E scales as 1/R as it should for point source producing spherical wave Principle of Superposition – TOTAL wave is sum of all the spherical waves. As one increases the number of points along wavefront to infinity, the SUM becomes an INTEGRAL

Huygen’s Principle (formulated by Fresnel) Model each point (x’, y’, 0) in wavefront at aperture as a spherical wave. Principle of Superposition – TOTAL wave is sum (integral) of all the spherical waves which originate from the aperture. Justification for i/λ in Section 10.3 and 10.A

Aperture Shape?

Fresnel Approximation NOTE: this is generally HARD to evaluate analytically

Fraunhoffer Diffraction (far-field) Increasing Distance Fresnel Diffraction (near-field)

Solution for Rectangular Aperture NOTE: the light SPREAD MORE (diffracts more) in the direction corresponding to the SMALLER opening.

Circular Aperture Fraunhofer limit Convert to POLAR coordinates since aperture is circularly symmetric