a la mode demonstration

mode matching and beam propagation solutions in MATLAB.

a la mode is a stimple library of gaussian ABCD matrix tools intended to optimize and visualize optical systems.

Contents

simple beam path

In this example, we will design a simple beam path and then define a target beam for modematchin, and choose an optimum configuration from a list of possible lens choices.

% here we design an initial simple beam path
goo = beamPath;
goo.addComponent(component.lens(1.25,.75,'lens1'));
goo.addComponent(component.lens(1.75,3.25,'lens2'));
goo.seedWaist(.2e-3,0);

% plot the results
zplot = -1:.01:6.5;
goo.components
goo.plotSummary(zplot);

 
ans = 
 
    label    z (m)     type    parameters         
    -----    -----     ----    ----------         
    lens1    0.7500    lens    focalLength: 1.2500
    lens2    3.2500    lens    focalLength: 1.7500


 

mode matching optimization

goo.targetWaist(.4e-3,5);

% we create a list of possible lens choices
focalLengthList = [-.75;.5;1.75;-2;-1;2;3;1;2.5;1.25];
lensList = component.lens(focalLengthList);

tic;
[pathList,overlapList] = goo.chooseComponents(...
                'lens1',lensList,[0.5 3],...  % choose lens1 from the list,
                'lens2',lensList.duplicate,[3.5 4],... %duplicate the list, this allows
                ...                                    %  the same component to be chosen more than once
                'target',[4.5,6]... % we can also allow the target waist position to vary while optimizing the overlap
                ,'-vt',.25); % set the minimum initial overlap to 0.25, if a combination of components
                             % has an overlap less than this, it will be skipped without trying to optimize the lens positions
toc

Searching through 100 combinations. Minimum initial overlap: 0.25
current overlap: 0.98623. best so far: 0.98623. 72 more to try.
current overlap: 0.93378. best so far: 0.98623. 70 more to try.
current overlap: 1. best so far: 1. 42 more to try.
current overlap: 1. best so far: 1. 28 more to try.
current overlap: 0.84139. best so far: 1. 22 more to try.
current overlap: 1. best so far: 1. 8 more to try.
current overlap: 0.49143. best so far: 1. 7 more to try.
current overlap: 0.45192. best so far: 1. 4 more to try.
current overlap: 0.37431. best so far: 1. 3 more to try.
current overlap: 0.90433. best so far: 1. 2 more to try.
current overlap: 0.4031. best so far: 1. 1 more to try.
current overlap: 0.64769. best so far: 1. 0 more to try.
Elapsed time is 14.038783 seconds.

select the best solution and plot it

from the list of all solutions, we may choose the one which has good modematching, but also has minimal sensitivity to component location.

pathList = pathList(overlapList >= 0.99);
sensitivityList = pathList.positionSensitivity;
[sensitivityList,sortIndex] = sort(sensitivityList);
pathList = pathList(sortIndex);
bestPath = pathList(1);


% print the component list to the command window
disp(' ')
disp(' Optimized Path Component List:')
display(bestPath.components)

bestPath.plotSummary(zplot);

 
 Optimized Path Component List:
 
 = 
 
    label    z (m)     type    parameters    
    -----    -----     ----    ----------    
    lens1    0.9965    lens    focalLength: 1
    lens2    3.5014    lens    focalLength: 2


 

other features and limitations

Features:

Limitations:

Published with MATLAB® 7.14