Ask questions about Gabor filter's parameters

I am trying to implement a 2D Gabor filter, but I don't understand several parameters of this filter. For example, I use a general form of 2D Gabor filter like h(x, y, f, theta, sigma_x, sigma_y) = exp(-.5 * ( x_theta^2/sigma_x^2 + y_theta^2/sigma_y^2) * cos(2*pi*f*x_theta), i.e. a even symmetric Gabor filet.

The question is that what sigma_x and sigma_y mean? In most of the papers, what has been presented is just 'standard deviation' of the Gaussian envelope along x and y. OK, this confused me several days.

I read several codes about Gabor, this two parameters didn't directly determine the size of the filter. They are either processed as

        if (isnan(SigmaX)==1) | isempty(SigmaX),
      SigmaX = (3*sqrt(2*log(2)))/(2*pi*CtrFreq);
    end
    if (isnan(SigmaY)==1) | isempty(SigmaY),
      SigmaY=sqrt(2*log(2))/(2*pi*tan(pi/8)*CtrFreq);
    end

xlim=round(nstd*(SigmaX*abs(cos(Angle))+SigmaY*abs(sin(Angle)))); ylim=round(nstd*(SigmaY*abs(cos(Angle))+SigmaX*abs(sin(Angle))));

In this case, nstd is said to be length of impulse response. Don't know that.

or

sigmax = wavelength*kx;
sigmay = wavelength*ky.

Thus, I just wonder that how I can determine the size of the filter. And because of this, I have several other questions about wavelength and bandwidth. (Cause I don't have any background in signal processing)

For the second case I provided above, it use wavelength to multiply kx or ky. Why we cannot use sigma_x or sigma_y directly? What this wavelength mean? Is it the size of Gabor filter? What is that bandwidth mean? Is it the size of Gabor filter?

I implemented a simple program, but it seems not correct, as below

                     function [GR, GI, G] = yGabora(f, sigma_x, sigma_y, theta)

                  the = theta * pi/180;        % Angular to degree.

                  % Rotation matrix
                  Rot = [ cos(the) sin(the);
                         -sin(the) cos(the)];  

                  % Calculate gabor filter
                  for x=-sigma_u:1:sigma_u
                      for y=-sigma_v:1:sigma_v

                          % Calculate rotated position of Gaussian function
                          tmpRet = Rot*[x, y]';
                          xt = tmpRet(1);
                          yt = tmpRet(2);

                          h_even(x+sigma_u+1, y+sigma_v+1) = exp(-0.5* (xt^2/(sigma_u^2) + yt^2/(sigma_v^2))) * cos(2*pi*f*xt);
                          h_odd(x+sigma_u+1, y+sigma_v+1)  = exp(-0.5* (xt^2/(sigma_u^2) + yt^2/(sigma_v^2))) * sin(2*pi*f*xt);

                      end
                  end 

                  % Generate a complex unit.
                  j = sqrt(-1);

                  % Real part of G
                  GR = h_even;

                  % Imaginary part of G
                  GI = h_odd.*j;

                  % Gabor filter
                  G = GR + GI;