FDTD Soft sources, hard sources, added sources in a waveguide

[peponas]

I would like to simulate a waveguide.
First of all I haven't implement a pml layer, so reflections at pec walls (Transverse Planes of the Waveguide) are expected to be observed. I manually set the tangential Electric field at z=0 (which is not calculated using FDTD update equations) according to a drive function (sinusoidal or pulsed) in time and a specific mode distribution in space.I've already told that this approach equals to a sinusoidal boundary condition, and not source implementation (at z=0 I have an explicitly value of the field where at z=L field is zero) so I get the steady state, if I observe the time signal near the PEC wall at the end of the waveguide. I have also excite only with the tangential electric field components. Another approach is to add the desired field value to the already calculated one (soft source) and eliminate the problem of two different boundary conditions (PEC and sinusoidal). But, in both ways, I don't see an "explosion" in time signal amplitude. I assume that amplitude should have increased due to reflections on both ends because waveguide is essentially a cavity. I import power by setting the field values both ways (hard and soft source) but I don't get an amplitude rise at all, but rather a "steady state" of the system. So my question is...

How can I import power in fdtd scheme, using an excitation source, in a closed cavity, and see the physical expected value?

 

[wavenology]

Real cavity is fed with either a pin connected with coaxial cable or a small waveport on one side of the wall. In such way, you can calculate the input power and survived power in cavity and Q factor, blablabla.

However in numerical FDTD, you can also put values (hard of soft) at a single point or on a surface, but keep in mind that excitation this way will not have a physical meaning in real life. Thus you can not expect a reasonable input/reflected results, this is b/c if you excite at a point or a surface, you do not know the reflected energy to the source since they are fake sources, but you can still observe the resonant mode as well as Q-factor in such case.

 

[peponas]

Thanks for the answer, but once again, how can I import energy-power in a waveguide? I know that the question is so general but I can't find, even in literature, a convincing answer.
Moreover, added sources act like hard sources, except for the reflections I guess