3D FFT. initialization

%% -- propagation Variable(z) --
L        = 30;                      % length of space
step_num = 300;                     % represented z steps
dz       = L/step_num;              % Step size in z = 0.1                               

%% %% -- t, x, and y Arrays -- 

nt       = 500;         
tmax     = 50 ;                                  % FFT point and window size                           
t2       = (0:dt:tmax);                          % Temporal Grid
t        = t2(1:nt);                                
ktt      = (2*pi/tmax)*[0:nt/2 -nt/2:-2];        % Frequency Grid
dt       = tmax/nt;                              % Step size in t

N        = 500;                                  % No. of Fourier modes(sample points)
gridsize = 10;
                
x        = (gridsize/N)*(-N/2:N/2-1);            % Grid point along x
y        = (gridsize/N)*(-N/2:N/2-1);            % Grid point along y
[X,Y]    = meshgrid(x,y); 

% -- wave numbers
kx       = [0:N/2 -N/2+1:-1];
ky       = [0:N/2 -N/2+1:-1];
[kxx,kyy]= meshgrid(kx,ky);                       % Wave number along both direction
kxx      = (2*pi/gridsize)*kxx;                   % scaling
kyy      = (2*pi/gridsize)*kyy;

im solving a 3D wave eqaution using split step FM. the wave is moving along z, i have an extra propgation Vector K in time "ktt". im wondering if my initializtion is correct. or shoiuld i do a 3d mesh grid [T,X,Y]?