Building an optical system using `GaussOpt`

GaussOpt can be used to analyze quasioptical systems using Gaussian beam analysis. In this notebook, we walk through the basics of setting up a Gaussian beam telescope.



In [1]:

    
%matplotlib inline
from gaussopt import *
import matplotlib.pyplot as plt

Gaussian beam telescopes

Gaussian beam telescopes use two parabolic mirrors to couple energy between two horn antennas. If the mirrors have focal lengths $f$, then the mirrors should be separated by $2\,f$ and the distance between each horn's beam waist and its respective mirror should be $f$ (as shown below).

We will now build a quick script to analyze a Gaussian beam telescope.

Define frequency sweep

For this notebook, we will sweep the frequency from 150 GHz to 300 GHz. This is done using using the gaussopt.Frequency class.



In [2]:

    
freq = Frequency(150, 300, units='GHz')









    



Frequency sweep:
	f = 150.0 to 300.0 GHz, 301 pts

Define horn antennas

Horn antennas are defined by their slant length, aperture radius and horn factor. See Chapter 7 of "Quasioptical Systems" by Paul Goldsmith for more information.

We will use the gaussopt.Horn class to generate the transmitting horn (horn_tx) and then copy this horn to generate the receiving horn (horn_rx). We will use a corrugated circular feed horn, which has a horn factor of 0.64.



In [3]:

    
slen = 22.64  # slant length (in mm)
arad = 3.6    # aperture radius (in mm)
hfac = 0.64   # horn factor (see chp. 7 of Quasioptical Systems)

horn_tx = Horn(freq, slen, arad, hfac, units='mm', comment='Trasmitting')
horn_rx = horn_tx.copy(comment='Receiving')









    



Horn: Trasmitting
	slen = 22.64 mm
	arad =  3.60 mm
	hf   =  0.64

Horn: Receiving
	slen = 22.64 mm
	arad =  3.60 mm
	hf   =  0.64

Define optical components

Now it is time to build the rest of the circuit, i.e., everything between the transmitting and receiving horns. We can define empty space using the gaussopt.Freespace class and mirrors using the gaussopt.Mirror class.



In [4]:

    
# 16 cm of freespace (air)
d = Freespace(160)

# Mirrors with a focal length of 16 cm
m1 = Mirror(16, units='cm', radius=8, comment='M1')
m2 = m1.copy(comment='M2')









    



Freespace: 
	d = 160.0 mm

Mirror: M1
	f = 16.0 cm

Mirror: M2
	f = 16.0 cm

The distances between the horns and the mirrors have to be reduced because the actual beam waist is behind the horn aperture.



In [5]:

    
# Offset distance (i.e., distance from beam waist to horn aperture) at 230 GHz
z_offset = horn_tx.z_offset(units='mm')[freq.idx(230, units='GHz')]

# Ideal distance between horn aperture and mirror
d_red = Freespace(160 - z_offset, comment='reduced')









    



Freespace: reduced
	d = 154.5 mm

Build Optical System

We can now combine all of the individual optical components to build our optical system. This is normally done by creating a list of optical components (component_list below), starting from the transmitting horn and then listing each component to the receiving horn (in order).

The component list is then passed to the gaussopt.System class, along with the two horns, to calculate the system properties.



In [6]:

    
component_list = (d_red, m1, d, d, m2, d_red)

system = System(horn_tx, component_list, horn_rx)









    



System: 
[[-1.          0.01096053]
 [ 0.         -1.        ]]

Plot Coupling

The coupling between the two horns can be plotted using the plot_coupling method. There should be perfect coupling at the center frequency.



In [7]:

    
system.plot_coupling()
system.print_best_coupling()









    



Best coupling: 100.0 % at 230.0 GHz

Plot Beam Propagation

The beam waist can be plotted through the entire chain using the plot_system command. This method will also plot the aperture of each component to ensure that there isn't too much edge taper anywhere in the system.



In [8]:

    
fig, ax = plt.subplots(figsize=(8,5))
system.plot_system(ax=ax)

Building an optical system using GaussOpt