PHYS 408 Applied Optics (Lecture 7) Jan-April 2016 Edition Jeff Young AMPEL Rm 113

Quiz #3 1) If a planar dielectric/air interface has a normal vector in the z direction, the z component of a plane wave’s wavevector is conserved when it transmits through the interface (T/F). 2) The normal component of the electric field is continuous across a planar dielectric boundary (T/F). 3) The reflection and transmission properties of a thin dielectric film excited by an harmonic plane wave can be obtained by summing an infinite series of interfering waves at the boundaries of the thin film (T/F). 4) The normal incidence reflectivity of a lossless dielectric film can be made zero for some specified visible wavelength of light if the thickness of the layer can be varied over a range larger than the wavelength of the light inside the material (T/F).

Quick review of key points from last lecture When plane waves interact with a planar interface, the in-plane component of the k vector (momentum) is preserved since there are no terms in the equation of motion that depend on the in-plane coordinates. This requirement for all waves in the problem (incident, reflected, and transmitted) to share the same in-plane wavevector can be thought of as “phase matching”. It can also be understood if you think of the polarization density excited by the incident wave, and how that has to act as the source for both the reflected and transmitted waves. Transmitted light is refracted (bent) due to the difference in wave speed, and hence wavelength in the material for a given frequency field. Multiple reflections are crucial to include when solving for the full reflected and transmitted field amplitudes, and the phase of the field at each pass through the film is crucial to keep track of.

Multiple reflections: superposition of many waves with well-defined relative phase and amplitudes z x Spent time on this, get them to try to roughly get the amplitudes right for a specific r and t, similar to matlab sims Ask groups to sketch results on board Sketch the situation at z=0 for all of the leftward propagating fields (amplitude and phase).

First steps… Add more waves with roughly the right amplitude progression, for different relative phases.

Simulation

How to solve? Infinite series (homework, very intuitive) More powerful approach Remind them of what they did last week at this stage for the single interface problem Write down expressions for the total E field in each region.

Equations Wait for them to get this Four unknowns: what are the four equations you need to solve for the unknowns?

The solution (see Lecture 7.pdf) Show pdf of handwritten algebra

The solution Condition (equation) for zero reflection? d=600 nm d=600 nm r and t from notes? No, |r|^2 and |t|^2What do you note about these results? 2 pi/lambdo_0 x n x 2d = m (integer) 2 pi, so 1/lambda_0=m/(2 n d), m= 1, 2 Because first reflection has a negative sign, and all remaining ones have positive phase at interfaces Condition (equation) for zero reflection?

Vary e for fixed d=600 nm d=600 nm e=13 d=600 nm e=4 d=600 nm e=2.4