Toolbox of Optical Efficiency and Resolution

Store what I learn in code

These are the notes after taking the 'Optical Efficiency and Resolution' course

https://www.coursera.org/learn/optical-efficiency-and-resolution/home/welcome

Gaussian beam

Any one quantity determines all the others: $$$ w_0=\sqrt{\frac{\lambda}{\pi}z_0}=\frac{\lambda}{\pi}\frac{1}{\theta_0} $$$

$$$ \theta_0=\frac{\lambda}{\pi}\frac{1}{w_0}=\sqrt{\frac{\lambda}{\pi}\frac{1}{z_0}} $$$

$$$ z_0=\frac{\lambda}{\pi} \theta_0^{-2}=\frac{\pi}{\lambda}w_0^{2}=\frac{w_0}{\theta_0} $$$

$$$ \lambda \equiv \frac{\lambda_0}{n} $$$

watch out the unit!

• 1nm = 10**(-9) m
• 1mm = 10**(-3) m

Gaussian beam transfer in z

• Beam radius $$$ w(z)=w_0\sqrt{1+(\frac{z}{z_0})^2} $$$

• Radius of curvature $$$ R(z)=z1+(\frac{z_0}{z})^2 $$$

• Gouy phase $$$ \zeta(z)=tan^{-1}(\frac{z}{z_0}) $$$

Gaussian beam intensity

$$$ I(\vec r)= \frac{1}{\pi/2} \frac{1}{w^2(z)}e^{-2\frac{\rho^2 }{w^2(z)}} $$$