HE11 mode
HE11 Mode
Parameters
Corrugation Depth
d
\(m\)
Corrugation width
w
\(m\)
Corrugation period
p
\(m\)
radius
a
\(m\)
frequency
f
\(Hz\)
Power
P
\(W\)
Output
anger frequency `omega`
`omega=2pi f`
wave number k
`k=omega/c`
wavelength `lambda`
`k=(2*pi)/lambda`
corrugation depth D
`D=d/(lambda/4)`
Gaussian beam waist `w_0`
`w_0=0.6435 a`
HE mode
root `chi`
`J_{m-1}(chi)=0`
cutoff wave number `k_c`
`k_c a=chi`
propagation constant `k_z`
`k^2=k_c^2+k_z^2`
cutoff frequency `f_c`
`k_c=(2 pi f_c)/c`
surface impedance `Z_z`
`Z_z=E_z/H_phi=j Z_0 tan(kd)`
surface impedance `Z_phi`
`Z_phi=-E_phi/H_z=-j Z_0*cot(kd)`
mode ratio
`d_{pm}=|E_{zm}/H_{zm}|=(m*J_m(chi_{mn}))/(chi_{mn} J'_m(chi_{mn}))`
waveguide wavelength `lambda_g`
`k_c=(2 pi)/lambda_g`
angle `theta`
`k*cos(theta)=k_z`
`|E_{y0}|`
`sqrt(2*P*Z_0/pi) 1/a {J_0(0)}/{J_1(2.405)}`