The LC oscillator is most commonly used to generate radio waves for practical use and the frequency $\omega$ of the LC oscillator equals that of the electromagnetic wave so produced. So, can they in principle be used to emit visible light?
The frequency of visible light is on the order of a few hundred terahertz, and the frequency of an LC oscillator is
$$\omega = \frac{1}{\sqrt{LC}}$$
I admit, the product $LC$ does become very small (on the order of $10^{-30}$) when the numbers are plugged in, but making an inductor and a capacitor with small values isn't difficult, is it?
Best Answer
Small-value inductors and capacitors are possible, but you also need extremely small size else the lumped system approximation your equation relies on becomes invalid. Let's say the wavelength of the light to produce is 700 nm. A distance of half that (350 nm) will cause an inversion (180° phase change). Generally, you want to keep the maximum dimension to $\frac{1}{10}$ the wavelength to consider it a lumped system without having to worry about that further.
Your inductor and capacitor, therefore, have to all fit roughly within a 70 nm dimension. With everything that close to everything else, there will be a lot of parasitic capacitance. Getting a low enough capacitance and still have the deliberate capacitance across the ends of the inductor dominate over all the distributed stray capacitance won't be easy. Even if you could do that, you still have to drive it with a 430 THz signal somehow. Where are you going to get that from?