Characteristics of Laser Grade Substrates – (see pages 24-28)
• ω: angular frequency
• n: refractive index
• c: speed of light in a vacuum (2.998 × 108 m/s)
• nD, nF and nC: refractive indices at the wavelengths of the
Fraunhofer D- (589.3nm), F- (486.1nm), and C- (656.3nm) spectral lines
• k: wavenumber (2π/λ)
Relating wavelength and angular frequency to refractive index:
Sellmeier formula with material constants B1, B2, B3, C1, C2, and C3:
Abbe number:
Optical Coatings – (see pages 32-37)
• OD: optical density
• T: % transmission
Relating OD to transmission:
Ultrafast Dispersion – (see pages 40-41)
Group velocity:
Group velocity dispersion:
Group delay dispersion:
Laser Induced Damage Threshold (LIDT) – (see pages 44-51)
• τ: pulse duration
• ∅: laser beam diameter
Continuous wave lasers:
Pulsed lasers:
Fluence:
Approximation for scaling LIDT:
Gaussian Beam Propagation – (see pages 8-11)
• I0: peak irradiance
• r : radial distance from propagation axis
• w(z): radius of laser beam
• z: propagation distance
• P: power of the beam
• w0: beam waist
• λ: wavelength
• θ: divergence angle
• zR: Rayleigh range
• s: distance from lens to input beam waist
• s' : distance from lens to output beam waist
• f: lens focal length
• α: system magnification
Irradiance profile of Gaussian beam:
Relating beam waist to wavelength and divergence angle:
Rayleigh range:
Thin lens equations for a Gaussian beam:
Magnification:
Beam Shape, Beam Quality, and Strehl Ratio – (see pages 13-15)
M2 ratio:
Beam parameter product:
Power in the bucket:
Beam Expanders – (see pages 20-21)
• m: beam expander magnification
• θI: input beam divergence
• θO: output beam divergence
• DI: input beam diameter
• DO: output beam diameter
• DL: diameter at distance L
• Φ: spot size
Magnifying power:
Beam diameter scaling:
Focused spot size:
Reference Equations