# Optoelectronics and Photonics

• Maxwell’s equation
• Geometrical optics
• Interference
• Diffraction
• Fresnel’s equation
• Group velocity
• Group index
• Quantum mechanical concepts
• Vectors
• Complex numbers
• Partial differentiation
• Fourier transforms
• Wave theory
• Particle theory
• light
• Wave theory: wave => interference, diffraction
• Particle theory: photon

# Wave Nature of Light

## Light Waves in a Homogeneous Medium

### Plane Electromagnetic Wave

• Electric field Ex
• Magnetic field By
• Electromagnetic wave
• traveling wave
• time varying
• perpendicular to each other and the direction of propagation: z
• position z
• time t
• propagation constant, wave number k (2*pi/lambda)
• wavelength lambda
• angular frequency omega
• wave amplitude E0
• Phase constant phi0
• Argument (omega*t – k*z + phi0) => phase phi
• Monochromatic plane wave
• wavefront
• Faraday’s law: time varying magnetic field results in time varying electric fields and vice versa
• optical field
z = a+b\,\mathrm i \\ |z| = \sqrt{a^2 + b^2} \\ z = r \cdot \mathrm{e}^{\mathrm{i}\varphi} = r \cdot (\cos \varphi + \mathrm{i} \cdot \sin \varphi) \\ \phi = \omega t - k z + \phi_0 \\ a^{x+y}=a^x \cdot a^y \\ a^{x\cdot y}=(a^{x})^{y} \\ {\displaystyle a^{-x}={\frac {1}{a^{x}}}=\left({\frac {1}{a}}\right)^{x}} \\ {\displaystyle {\sqrt[{q}]{a^{p}}}=a^{\frac {p}{q}}}