Attenuation constant is obtained from the slope of the line of best fit to the natural logarithm of the field (calculated by HFSS), using the least square technique.

For more details, have a look at: 

[1] J. Liu, D. R. Jackson, and Y. Long, “substrate integrated waveguide (SIW) leaky-wave antenna with transverse slots,” IEEE Trans. Antennas Propag., vol.60, Jan. 2012.

thanks Mr Mirzavand for answer

I used too this approach but my result is different of the results in the cheng & Ke Wu's paper.

[1] Y. J. Cheng, W. Hong, KeWu

Y. Fan, "Millimeter-Wave Substrate Integrated Waveguide Long Slot Leaky-Wave Antennas and Two-Dimensional Multibeam Applications," IEEE Trans. ON Antennas and Propagation, Vol. 59, no. 1, January 2011.

If you are trying to estimate the propagation constant from the field distribution, the presence of higher order modes should also be included in your consideration. Treating a multi-mode field distribution as a mono-mode one will of course introduce errorness results, unless you are sure that the "other modes" can be ignored.

Thanks Mr Jeng-Hau Lu

How to treat a multi-mode field distribution and observe the results in HFSS?

The most convenient approach is to "avoid observing" the higher order modes and make sure you are observing the one you are interested in.

Choose the sampling points far away enough (some books tell you a quarter wave length, as a rule of thumb) from the "feeding discontinuity" will help. Meanwhile, you will also not want to observe the field too far away from the excitation since the field (especially leaky wave modes) will decay.

Moreover, if the structure is symmetric, you can try introducing PEC or PMC boundary condition on the symmetry plane if you are sure that does not alter the modal field distribution. By doing so, you can avoid some "other modes" to increase the accuracy.

If you are interested in further study, check Professor Tapan K. Sarkar's paper for some sophisticated approach.

Thanks Mr Jeng-Hau Lu

method 1:

Radiation Efficiency= 1-exp(-2*alpha*Lr)

Radiation Efficiency = (1-|S11|2-|S12|2)/(1-|S11|2)

also for this approach must tapered the slot (here uniform slot).by tapering S11 has a very small size and ignorable.

another method: Attenuation constant is obtained from the slope of the line of best fit to the natural logarithm of the field and as well as by slot tapering.