Foundations — Photonic and optical interconnects

Before you can read the parent note, you need to own every symbol it throws at you. Below, each one gets: plain words → the picture → why the topic needs it, ordered so each rests on the one above.

1. Bits, electrons, and photons — the three "things" being moved

Why the topic needs this: the entire chapter is a contest between "bits ride on electrons" (copper) and "bits ride on photons" (photonics). You cannot judge the winner without knowing the two contestants. See Copper interconnects and RC delay.

2. Length $L$ and the idea of "per-length" quantities

Many electrical properties are quoted per metre and then multiplied by $L$:

Why "per-length"? A long wire is just many short wires in a line. Each short piece adds its own resistance (they stack in series, $R$ grows) and its own bit of surface to store charge ($C$ grows). So both $R$ and $C$ grow with $L$ — remember this, it is the seed of the $L^2$ wall.

3. Multiplication as "$\times$" and the symbol $\tau$

Substituting the per-length forms: $\tau =RC=(rL)(cL)=rc{L}^2$

Why the square matters: one $L$ came from $R$, one $L$ came from $C$. Two things that each grow with length, multiplied, give length-squared. Double the wire → four times the delay. That is the wall photonics dodges.

4. Speed of light $c$, refractive index $n$, and $v=c/n$

The transit time of light down a waveguide of length $L$ is then $t=\frac{L}{v}=\frac{nL}{c}.$

Why the topic needs this: notice $t$ grows with $L$ to the first power — linear, not squared. This single fact, contrasted with copper's $L^2$, is the physics heart of the whole topic. Full detail lives in Refractive index and speed of light in media.

5. Wavelength $\lambda$ and "colours" of light

6. Bit rate $B$, channel count $N$, and the sum $B_{\text{total}}=NB$

Because independent colours add without stealing from each other: $B_{\text{total}}=N\times B.$

Why a sum and not a max? In a shared electrical bus, streams take turns (they divide time), so more streams do not add up. Independent colours run simultaneously, so their rates add. Example: $N=40$ colours at $B=25\text{Gb/s}$ give $B_{\text{total}}=1000\text{Gb/s}=1\text{Tb/s}$ on one line.

7. Fields, phase $\Delta \varphi$, and the symbol $e^{i\theta }$

These three unlock the modulator maths in the parent.

8. Power $P$, energy-per-bit $E_{\text{bit}}$, and current $I=R_{\lambda }P$

How these foundations feed the topic

Equipment checklist

Hide the right side and test yourself — if any line stumps you, reread its section above.