Useful Calculations

(click to expand)

• Laser Intensity
This script computes the peak intensity of a continuous-wave Gaussian laser beam.
---
Power [W]:
Beam waist (1/e²) [mm]:
---
Peak power density [W/mm²]: —
Peak power density [mW/cm²]: —
Peak power density [kW/cm²]: —
• Convert between W, dBm, Vpp, and Vrms
This script converts between:
• W: 1 Watt = 30 dBm = 20 Vpp = 7.07 Vrms
• dBm: dB relative to 1 mW. ± 10 dBm = order of magnitude change in Watts; ± 3 dBm ~ factor of 2 change in Watts
• Vpp: Volts peak-to-peak of a sine wave
• Vrms: Root mean square voltage (effective DC voltage with the same power as the AC signal)
---
Load [Ohm]:
---
Input unit: W dBm Vpp Vrms
Input value:
---
Power [W]: —
Power [dBm]: —
Voltage [Vpp]: —
Voltage [Vrms]: —
• Gaussian Beam Propagation
This script computes the Rayleigh range and beam waist of a Gaussian beam.
---
Wavelength [nm]:
Waist (w₀) [mm]:
Propagation (z) [mm]:
---
Rayleigh range [mm]: —
Beam waist w(z) [mm]: —
Factor w(z)/w₀: —
• Objective Imaging
[link to image]
This script computes the required imaging lens focal length given the objective entrance pupil diameter (EPD) and effective focal length (EFL); as well as the camera properties.
---
Wavelength [nm]:
Objective EPD [mm]:
Objective EFL [mm]:
Pixel size [μm]:
Pixels per spot (n_px) [mm]:
---
Objective resolution [μm]: —
Imaging focal length [mm]: —
• Fiber Coupling
This script computes the focal lengh of the lens required to mode-match a free-space Gaussian beam with an optical fiber. The focal length is given by f = π D⋅MFD/4λ. The optical fiber has fixed NA; therefore, a larger beam requires a longer focal length lens compared to a smaller beam.
---
Wavelength [nm]:
Beam diameter (2w₀) [mm]:
Mode field diameter [μm]:
---
f [mm]: —

Miscellany

• Red-detuned magneto-optical trap [pdf]
• Tap and drill reference [pdf]
• Simulated Annealing [html]
• Chi-Squared [pdf]
• Catenary [pdf] [py]
• Ray transfer matrix analysis [py]
• Bloch's theorem and toy models [pdf]
• Polarization (in progress) [mp4][ipynb]
• Vernier scale [jpg]
• Signal generator impedance [pdf]
• Matplotlib Cheat Sheet [github]
• Thorlabs screw size chart [pdf]
• dB [pdf]
• Notes:
• Physics 112 (Statistical and Thermal Physics) [pdf]