Wave Nature Of Light Flashcards
Light
Electromagnetic wave. Time varying electric (Ex) and magnetic (By) fields. Ex and By are perpendicular
Augustine Jean Fresnel
French physicist and civil engr. proponent of the wave theory of light
Propagation constant
AKA wave number. 2pi/lambda
Simplest traveling wave with propagation along z.
A sinusoid! Ex=E0Cos(wt-kz+phi0)
Monochromatic plane wave
Described by Ex=E0Cos(wt-kz+phi0). It is a PLANE wave of infinite extent. The one above travels in the positive z direction
Wavefront
A surface over which the phase of a wave is constant. Also called phase planes A plane that intersects the EM wave perpendicularly; so if the wave is traveling in the z direction the wavefront is in the x-y plane.
Electric Field
A vector field generated by electric charges of time varying magnetic fields
Faraday’s Law
Time varying magnetic fields result in time varying electric fields and viceversa. A time varying E fields sets up a time varying B field with the same frequency. in a monochromatic plane wave, By and Ex accompany each other and have the same freq, and propagation constant. However their direction is orthogonal.
Optical Field refers to…
Electric Field
Wave vector
K(vector) indicates the direction of propagation. Magnitude of propagation constant is 2pi/lambda
Ex equation using field vector:
Ex=E0Cos(wt-k . r+phi0). r and k are both vectors. r is a point on plane. The dot product is the product of k and projection of r onto k.
Using the wave vector, if propagation is along z, the dot product of k.r becomes
k.r=(kx)(x)+(ky)(y)+(kz)(z) since x=y=0, k.r=(kz)(z)=kz
Equation for phase velocoty
V=dz/dt=w/k=(v)lambda w=2(pi)v
Phase difference can be expressed as
2pi((delta z)/lambda)= k(delta z)
Waves are in phase if:
Phase difference is 0 or multiple of 2pi.
Maxwell’s Equations (in words)
Describe how B and E fields are generated. All EM waves obey this Describes the time and space dependence of the E-field
Describe a perfect wave plane
Wavefronts are separated by 2pi or lambda (Generally). Direction of wave propagation (Kvector) is normal to the wavefront surface. So here, propagation vectors are all parallel. This plane wave has no divergence -> 0 degrees of optical divergence. The amplitude, E0, does not depend on the distance from a reference point. it is the same at all points on a given perpendicular plane to K. So it is also independent of x and y. Extends to infinity and there is infinite energy. An infinitely large EM source with infinite power is needed to generate a perfect plane wave. Light beam’s area and power depend on the extent of the e and b fields.
Isotropic
Uniform
Maxwell’s EM wave equation
has partial derivatives.
Describe a spherical wave
A point source is needed. A traveling field emerges from this point and amplitude decays with distance r form the source. Wavefronts are spheres centered at source point O. since direction of propagation is normal to the wavefronts, K diverges outward Has 360 degrees of optical divergence.
Optical Divergence
the angular separation of wave vectors on a given wavefront.
Gaussian Beams
Many light beams are described like so. Beam has an expj(wt-kz) dependence (still) Amplitude varies spatial away from the beam axis and also along the beam axis. Light intensity distribution is Gaussian.
Beam diameter
Only on Gaussian beams? 2w… defined so that the cross sectional area pi(w^2) at that point contains 85% the beam power. beam diameter increases as the beam travels along z.
waist/waist radius/spot size
the finite width 2w0, where the wavefronts are parallel w0 is the waist radius 2w0 is the spot size.
Beam divergence
2theta. increase in beam diameter with distance is linear, and makes an angle 2theta at O. eq on pg 6.
What slows down an EM field wave?
The interaction between the field and the dipoles. The stronger the interaction, the slower the propagation of a wave. (since energy gets transferred when field polarizes molecules in the medium it is traveling. )
Relative permitivity, what does it do, symbol?
Measures the ease with which the medium become polarized. Or you can say that: Indicates the extent of interaction between the field and induced poles. symbol: epsilon_r
phase vel. for EM wave traveling in medium with relative permitivity epsilon_r
V=1/sqrt(epsilonr epsilon µ0)
epsilon_r in free space
1
phase velosity in vacuum V=
V=1/sqrt(epsilon0 X µ0)= c
C, speed of light in vaccum (numerical)
3X108ms-1
refractive index
(definiton and equation)
def: the ratio of the speed of light it its speed in a medium
eq: n=c/v=sqrt(epsilonr)
when light progapagets to another medium, what happens to the speed, and the frequency?
the speed changes, slows down if the medium is more dense.
the frequency **remains the same **
wave vector and wavelength in a medium (equations)
kmedium=nk
lambdamedium=lambda/n
*n=refractive index
In which materials does the refractive index stay the same in all directions? ( ie. is isotropic? )
non-crystaline materials
(glasses, liquids)
which materials have anisotropic properties?
Crystals .
depending on the structure, the relative permitivity is different along different crystal directions.
optically isotropic means
the refractive index remains the same in a material for all directions.
when two perfectly harmonic waves with diferent frequencies, and wave vectors travel along the same direction the form….
A wave paket
group velocity is…
a wave paket’s velocity
Vg=dw/dk
Vg(vacuum)= dw/dk=c=phase vel.
group vel on a medium
n is a function of wavelength: n(lambda)
Vg(medium)=c/Ng
Ng=n-lambda(dn/dlambda)
Ng= group index
group index of medium
Ng=n-lambda(dn/dlambda)
is epsilonr frequency dependent?
YES
Dispersive medium
when both the phase velocity and group velocity depend on hte wavelength
S used to represent
S=v2epsilln0epsilonr (E X B)
Energy flow per unit area
total internal reflection
everything gets reflected. When thetac reaches 90.
thetac=n2/n1
Poyting vector
S. represents thenergy flow per unit time per unit area in a direction determined by E X B
irradiance
Poynting vector’s magnitude.
Power flow per nit area.
intensity is sometimes used to mean
Irradiance!
refracted light
when light is traveling through one medium, then reaches the boundary and gets transmitted on to medium 2. this transmited light is also known as refracted light,
the magnitudes of Kr and Ki are the same beause
they are on the same medium
Kr=Ki
if Ai and Bi are both incident rays parallel to each other and are in phase, the only way that the light can be reflected qith equal intensity for both rays is if:
thetai = thetar
this way, Ar and Br are in phase and don’t destructively interfere with one another.
A t and Bt have diferent velocities than Ai and Bi because….
they are on a different mediium
