I hope this helps :

import math

def beam_waist(w0, z, zr):

w = w0 * math.sqrt(1 + (z/zr)**2)

return w

def diffraction_loss(R, L):

loss = (1 - R) * L

return loss

def photon_lifetime(L, c, loss):

tau = (L/c) * (1/loss)

return tau

# Example usage

w0 = 1.0 # waist size at the laser's output

z = 2.0 # distance from the center of the cavity

zr = 3.0 # Rayleigh range of the beam

R = 0.9 # reflectivity of the cavity mirrors

L = 4.0 # length of the cavity

c = 3.0e8 # speed of light

beam_waist_result = beam_waist(w0, z, zr)

diffraction_loss_result = diffraction_loss(R, L)

photon_lifetime_result = photon_lifetime(L, c, diffraction_loss_result)

print(beam_waist_result)

print(diffraction_loss_result)

print(photon_lifetime_result)