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I need to show the function I created "LinearOpticalElement.m" file into the GUI I created with axes in it. How should I go about it?

I have implemented cases just in case I need to add in more functions later on. How should I do it?

I have trouble with the GUI function calling another function which is LinearOpticalElementsGUI.m

function varargout = GUITest(varargin)
% GUITEST MATLAB code for GUITest.fig
% GUITEST, by itself, creates a new GUITEST or raises the existing
% singleton*.
%
% H = GUITEST returns the handle to a new GUITEST or the handle to
% the existing singleton*.
%
% GUITEST('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in GUITEST.M with the given input arguments.
%
% GUITEST('Property','Value',...) creates a new GUITEST or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before GUITest_OpeningFcn gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to GUITest_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES

% Edit the above text to modify the response to help GUITest

% Last Modified by GUIDE v2.5 26-Oct-2018 18:51:49

% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
 'gui_Singleton', gui_Singleton, ...
 'gui_OpeningFcn', @GUITest_OpeningFcn, ...
 'gui_OutputFcn', @GUITest_OutputFcn, ...
 'gui_LayoutFcn', , ...
 'gui_Callback', );
if nargin && ischar(varargin1)
 gui_State.gui_Callback = str2func(varargin1);
end

if nargout
 [varargout1:nargout] = gui_mainfcn(gui_State, varargin:);
else
 gui_mainfcn(gui_State, varargin:);
end
% End initialization code - DO NOT EDIT

% --- Executes just before GUITest is made visible.
function GUITest_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to GUITest (see VARARGIN)

% Choose default command line output for GUITest
handles.output = hObject;

% Update handles structure
guidata(hObject, handles);

% This sets up the initial plot - only do when we are invisible
% so window can get raised using GUITest.
if strcmp(get(hObject,'Visible'),'off')
 %plot(rand(5));
end

% UIWAIT makes GUITest wait for user response (see UIRESUME)
% uiwait(handles.figure1);


% --- Outputs from this function are returned to the command line.
function varargout = GUITest_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure
varargout1 = handles.output;

% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
axes(handles.axes1);
cla;

popup_sel_index = get(handles.popupmenu1, 'Value');
switch popup_sel_index
 case 1

 axes(LinearOpticalElementsGUI);


end


% ----------------------------------------------------------------- ---
function FileMenu_Callback(hObject, eventdata, handles)
% hObject handle to FileMenu (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)


% --------------------------------------------------------------------
function OpenMenuItem_Callback(hObject, eventdata, handles)
% hObject handle to OpenMenuItem (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
file = uigetfile('*.fig');
if ~isequal(file, 0)
 open(file);
end

% --------------------------------------------------------------------
function PrintMenuItem_Callback(hObject, eventdata, handles)
% hObject handle to PrintMenuItem (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
printdlg(handles.figure1)

% --------------------------------------------------------------------
function CloseMenuItem_Callback(hObject, eventdata, handles)
% hObject handle to CloseMenuItem (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
selection = questdlg(['Close ' get(handles.figure1,'Name') '?'],...
 ['Close ' get(handles.figure1,'Name') '...'],...
 'Yes','No','Yes');
if strcmp(selection,'No')
 return;
end

delete(handles.figure1)


% --- Executes on selection change in popupmenu1.
function popupmenu1_Callback(hObject, eventdata, handles)
% hObject handle to popupmenu1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)

% Hints: contents = get(hObject,'String') returns popupmenu1 contents as cell array
% contentsget(hObject,'Value') returns selected item from popupmenu1


% --- Executes during object creation, after setting all properties.
function popupmenu1_CreateFcn(hObject, eventdata, handles)
% hObject handle to popupmenu1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called

% Hint: popupmenu controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
 set(hObject,'BackgroundColor','white');
end

set(hObject, 'String', 'RH Circular');

And this is the LinearOpticalElementsGUI.m file

clear
clc
theta=0:2*pi/1000:2*pi;
x=cos(theta);
y=sin(theta);
x1(1)=0;
y1(1)=0;
xaxx=[-1;1];
xaxy=[0;0];
yaxx=[0;0];
yaxy=[-1;1];
figure('color','white');
for i=1:1:size(x')
 x1(2)=x(i);
 y1(2)=y(i);
 xcompx(1)=x(i);
 xcompy(1)=y(i);
 xcompy(2)=0;
 xcompx(2)=sqrt(x(i)^2+y(i)^2)*cos(theta(i));
 ycompx(1)=x(i);
 ycompy(1)=y(i);
 ycompx(2)=0;
 ycompy(2)=sqrt(x(i)^2+y(i)^2)*sin(theta(i));
 plot(xaxx,xaxy,'b',yaxx,yaxy,'g',x,y,'r',xcompx,xcompy,'- b',ycompx,ycompy,'-g',x1,y1,'-ro')
 axis square;
 title('Right-Handed Circular polarization')
 getframe();

end

The problem seems to be, that "LinearOpticalElementsGUI" is a script not a function. Scripts do not have a return value. So you could try to simply call the script instead of passing its non-existent return value to a function.

% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
axes(handles.axes1);
cla;

popup_sel_index = get(handles.popupmenu1, 'Value');
switch popup_sel_index
 case 1

 LinearOpticalElementsGUI;


end

This might show a new axes. So you could also try to call the plot function within your script like this: plot(gca(), xaxx, ...)

But it would actually be a better style to convert the script "LinearOpticalElementsGUI" to a function that has the axes handle as an argument.

function LinearOpticalElementsGUI(ax)

% "clc" and "clear" not useful
% ...
% "figure(...)" is not needed anymore
% ...

 plot(ax, xaxx, ...)

% ...
end