L10 Flashcards
1
Q
Helmholtz Equation
duplicate
A
Describes the propagation of a wave. U: complex value function, related to the amplitude of E and light intensity.
2
Q
Wavefront
A
- A 2-D surface of constant complex phase, ϕ(r) = arg[U(r)].
- Planes of constant phase at any moment in time.
- Solves Helmholtz Equation
3
Q
Linear System
What is it characterised by?
A
- Characterised by impulse-response or transfer function.
- Transfer function is the Fourier transform of impulse-response function.
4
Q
Paraxial Approximation
What does it simplify and what is it important for?
A
- Simplifies the Helmholtz equation for small angles.
- Important for Gaussian beams and wavefronts.
5
Q
Gaussian Beam
A
- Solution to the paraxial Helmholtz equation
- Intensity distribution is Gaussian
- Minimal width at beam waist
6
Q
Transfer Function
A
Factor by which an input spatial harmonic function is multiplied to yield an output spatial harmonic function.
7
Q
Fresnel Approximation
A
- Simplifies wave transmission through apertures.
- Uses Taylor expansion for low spatial frequencies.
- Apporximates spherical wavefronts as parabolas.
8
Q
Fresnel Number
A
- Dimensionless number
- N_F = a^2 / (λz)
- Characterises the wave propagation regime (near or far field).
9
Q
Impulse Response Function
A
- Response of a system to a point input.
- Inverse Fourier transform of the transfer function.
10
Q
Fraunhofer Diffraction
A
- Interference pattern of light in the far field.
- Observed many wavelengths away from the object.
11
Q
Rayleigh Range
A
- Distance over which a Gaussian beam’s cross-sectional area doubles.
- zR = π w02 / λ
12
Q
Gouy Phase Shift
A
- Phase delay of a Gaussian beam compared to a plane wave.
- Excess delay corresponds to the beam’s curvature.
13
Q
Huygens-Fresnel Principle
A
Every point on a wavefront is a source of spherical wavelets. Explains wave propagation and diffraction.
14
Q
Plane Wave
A
Wave with constant phase surfaces. Described by the Helmholtz equation.
