https://www.livescience.com/65113-fastest-camera-captures-speed-of-light.html

This is what light looks like when captured by a camera at 10 trillion fps. Interesting.  You can find this YouTube video in many other places (Planet Slow Mo). Please pay attention to the section between minute 6, 40 seconds, to minute 7, 25  seconds into the video. It looks like the old Pong game. This is a pulse of laser light (multiple photons), exciting atoms and molecules in a reflection cavity, that generate photons in an orthogonal direction (compared to the direction of the initial laser pulse) , that reach our eye.

And here is  formulation of the question.  You can design a special reflection cavity (an Archimedes spiral maze is just an example, many other designs are possible), so that the pulse spends more time in a very small region. If you have many, many pulses of laser light entering this reflection cavity ( simultaneously,  or properly timed, in an empty cavity), you could have, at a certain moment in time, a lot of pulses concentrated in a very small region. In other words, with high probability,  at a certain moment in time (and not after eons, if the reflection cavity is properly designed ), you could have a region of space with extremely high energy density. You probably know by now what I am leading to, little black holes, or something close. The problem is that with each reflection,  some photons will be lost ( this requires some though, the emitted photons go in the wrong direction  ),  but with proper timing of the pulses (and the right design of the reflection cavity), I think that you can guarantee that a high energy density region will emerge in reasonable time, this is a problem of probability , Markov  chains modeling.

A way of creating small regions of high energy density? A way of creating little black holes? Probably not the latter (and is probably recommended not to create any mezoscale black holes close to Earth anyway ), but I think it's worth some thought, exremely high energy density regions of space could open the way to new phenomena

The question, in a nutshell, is the following.

Is is possible to design such  a system?. Would it be feasible, in principle? Am I missing any facts that would make such a design impossible?

Edit. After receiving an answer, I will reformulate the question, without changing the original question (even if I realise now I am off orders of magnitude ).

What is the maximum energy density achievable with such a design (and current technology ) , keeping in mind the fact that it must depend on the design of the reflection cavity , the power and the timing of the laser pulses?

Edit 2. If one puts a White -Juday warp field interferometer inside the reflection cavity, would it lead to any measurable effects? A proper design should lead to regions of high energy density inside the reflection cavity. This a more down to Earth question , after realizing that the original question was orders of magnitude off reality.