According to this article, Microsoft and Facebook have completed a 160 terabits cross-Atlantic cable. Based on my calculations, this doesn't seem probable, so what did I miss in my calculation?
The maximum frequency that a mono-mode fiber can reach is roughly:
$F_{max}=(1/\lambda)*\sqrt{\frac{c}{DL}}$ $(1)$
$D$ is the dispersion parameter. $L$ its length. $\lambda$ is the central wavelength.
For $\lambda$=1500 nm , $D$ = 100 ps/nm/km and $L$ = 10 km.
I find: 10 GHz
Assuming 400 wavelength channels, 2 polarizations, 8 fibers, without relays under the ocean and a bit of magic I cannot reach 160 THz. What am I missing?
$(1)$ is obtained with the definition of $D$ assuming that the dispersion of a pulse of angular frequency $\omega_0$ , angular line-width width $\delta \omega_0$, duration $\delta \tau_0=2\pi/\delta \omega_0$ is $\delta \tau_1=L(1/Vg(\omega_0+\delta \omega_0 /2)- 1/Vg(\omega_0-\delta \omega_0 /2)=LD\lambda^2/(\delta \tau_0)$. $Vg$ is the group velocity.
The maximum frequency is such that:
$F_{max}=1/\delta \tau_0$
and
$F_{max}=1/\delta \tau_1=\frac{\delta \tau_0}{LD\lambda^2}$
