OPTICS SUMMARY (Intro Level)

OPTICS SUMMARY (Intro Level)

Electromagnetic Waves

- Wave Equations:

- Speed of Light:

- Index of Refraction:

- Maxwell’s Equations:ME1: ME2:

ME3: ME4:

- 1-D Waves: or

- Plane Waves:

- Polarized Waves:

- Laser Beam Approx.:

- Spherical Waves:

- Photons:

- Wave Eqn w/ Polarization:for

Intensity & Irradiance

- The Poynting Vector:[W/m²]

- Irradiance/Flux:[W/m²]

- Intensity per Solid Angle:

- Blackbody:

- Irradiance/Flux/Intensity:

- Total Values:forA = Q, I

- Further BB Laws:

- Note – many different definitions exist of the terms above; please use caution

Interference of Waves

- Same Phase:

- Opposite Direction:  Standing Wave

- Different Frequency:  Beats

- Group/Phase Velocity:

Reflection & Refraction

- Reflection:

- Refraction (Snell’s Law):

- Dispersion:an increasing function, except in “anomalous” regions

- Prisms, Diffraction Gratings, Interferometers

- Diffraction Grating:for integerm

- Huygens’ Principle

- Lens Focal Length:

- Lens Law:

Polarization

- Plane of Incidence ( || to the table) – XZ-Plane

- General (Elliptical) Polarization:

- Linear Polarizations:- S-Polarized: to plane of incidence,

- P-Polarized: || to plane of incidence,

- Arbitrary Linear Polarization:(still in phase)

- Circular Polarization:

- Birefringence:depends on polarization too

- Polarizers:- transmit one component (ie 100% P) while reflecting the other (ie 80% S)

- ie calcite (2 prisms), dielectric (layered)

- Waveplates:- delaycomponent of wave by fractionqof a wavelength

- Quarter Waveplate: , ie 450 lin left circ

- Half Waveplate: , ie 450 lin  -450 lin

- Pockels Effect:- applied electric field can induce birefringence & control polarization

where r63 = electro-optic constant

- Kerr Effect:where K = Kerr constant

- Faraday Effect:- applied magnetic field (solenoid) can induce optical activity (chirality)

Vwhere V = Verdet constant

- Jones Vector: or

- Jones Matrices: changing polarization

Reflection & Transmission

- Reflection & Transmission Coefficients (Fresnel Equations):

- S-Polarized:

- P-Polarized:

- Brewster Angle: when ie for

- Critical Angle: when

- Anti-Reflective (AR) Coating:

- Transmittance/Transmissivity:

- Reflectance/Reflectivity:

- iefor air  glass, @, ,

Fourier Transform, Convolution & Correlation

- Fourier Transform:

- Light:At ,

F

- Pulse Widths:, ,

- Uncertainty Principle: (depending on width definition)

- Parseval’s Theorem:(energy equality)

- Convolution:F FF

- Autoconvolution:

- Autocorrelation:

- Autocorrelation Thm:F

More Interference & Diffraction

- Interference Intensity:where (2 interfering waves)

- Different Polarization:

- Same Polarization:(cross term)

- Diffraction:- tendency of light to bend around object edges

- far field is the F.T. of the aperture fieldie slit (rect) sinc

- X-Ray Crystallography:- crystal structure given by diffraction of X-rays

Lasers

- Gain: -in one pass,- will lase when (threshold)

- Process:- pumping, population inversion, stimulated emission, lasing

- Divergence Angle of Beam:

- Types:- ruby, HeNe, Nd:YAG, Ti:sapphire, Dye, Diode, etc

- Temporal AKA Longitudinal Modes – laser’s frequencies

- Spatial AKA Transverse Modes

Non-linear Optics

- Non-linear Materials:or

- Second Harmonic Generation:- two photons excite atom twice, and one energetic photon emitted

- Doubling Crystal:

- Non-linear Refractive Index: where

- Self-Phase Modulation:

-- Ryan Newson, S2004