(HFSS)sign of Dielectric Loss Tangent?

We know at frequency below plasma frequency of metal the Im(permittivity ε) is large, and/or the Re(ε) is large bu negative.

according to the Debye's function:
ε(ω)=ε∞ - (ωp2)/(ω2 +iωγ)

=> ε=ε' +iε''

Now, I wanna simulate accurately metal SRR in the gigahertz region, so I need to key in the right number, but I'm not sure the sign of Dielectric Loss Tangent.

in the "HFSS online Help.pdf" page 15-77, it said
ε=ε' +iε''
can be expressed as
ε=ε'(1-i(ε''/ε'))
where (ε''/ε') is the dielectric loss tangent. then I confused.

for example:
the permittivity of material x, εx
εx=a+ib

then, in the Dielectric Loss Tangent column, what should I enter ?
(b/a) or (-b/a)?


P.S: where can we get the ωp (plasma frequency of metal) and the damping item?

I think it should be plus sign

If you enter a positive value for loss tangent...it is treated as loss. If you enter a negative number, it is treated as gain. If you are going to simulate dispersive metals in the THz...you will need to enter a negative real permittivity and a positive loss tangent. Or rather than a loss tangent you can input a conductivity where sigma = 2*pi*Freq*e0*Im(er)

BTW, if you are just in the GHz, you will not see the effects of Drude metal dispersion. These effects are generally not noticed until one approaches near the plasma frequency...tens of THz.

Usually, loss tangent delta is expressed in positive but it means the negative part of the imaginary part of complex permittivity.