Step 1: The Simple Circuit Diagram of Joule Thief.

You may find this diagram every where throughout internet.The working principal is also as same as explained by others.

The basic requirement is any NPN transistor, a Laser Diode, a Ferrite ring,a resistance,A 3 V battery,Bread Board , Wires.etc.
The pin Configuration of BD139 is Front Facing E-C-B. However any NPN transistor can be used.

It is the combination of Joule thief which will make a pulsed Current to flow Via laser Diode. In other words it is a Pulsed Laser.

We can burn things specially black or dark colored stuff by simple 3V battery but this will heat up the diode after intensive use. In case we need to make a Laser engraver which needs to operate over long time, Requires assembly to cool the diode down. How ever by using Joule Thief we can increase its brightness and eventually draw the heat away from diode to the transistor used

Step 2: The Ferrite Ring , the Heart of the Circuit.

This toroid was found from a CFL driver. 3 Turns each for each Winding. If the figure does not work out. Reverse the wire. i.e interchange the Blue and Violate wires.

Please try to understand the winding. If understood correctly, we can use any toroidal ring for the same purpose. Please Note that Torroidal Ring used in good SMPS have good performance against high frequency.

Step 3: The IR Laser Diode From Old DVD Burner

This is specifically a Infra-Red Laser found inside a DVD Burner. I removed all optics and finally wanted to fix with the focusing lens. We can use any lens depending upon requirement and focusing length.

Step 4: Transistor the Brain

The pin Configuration of BD139 is Front Facing E-C-B. More detais can be found on its data sheet.

However any NPN transistor can be used depending upon power requirements. Its I max is 1A

Step 5: WoW! Its Roasting My Mice....

See the White Smoke. Its very handy circuit for your home made laser Engraver. Excess use will tear the tranistor but your laser will survive.

Here's an instructable on dissembling a DVD burner.
https://www.instructables.com/id/Disassembling-a-CD... There are others that are older, but typically, they are pretty much the same. Here's an instructable for building a laser cutter with a laser purchased off of ebay. https://www.instructables.com/id/Disassembling-a-CD... Just do a search for laser cutters, cnc laser cutter ect.

Step 6: More Details About the Concept

The operational mechanism by why this works could probably be explained a bit better, a so called "joule thief" is actually a very simple switch mode power supply. To be precise its a very simple boost converter, minus the voltage or current regulation that is. Now this is why it actually works very well to limit the heating of the laser diode, but more about that later.

Since I presume most people here are not very familiar with electronics I'll give the simple explanation (a technically correct one can be found on enough websites): When the circuit switches on a DC voltage is applied over the coil and transistor, but the voltage is too low to drive the diode. As a result the current starts to flow through both sides of the transformer into the transistor base and collector. The coil prohibits a very large change in current so it might take a few microseconds, or even milliseconds before magnetic field saturates the ferrite core. (There are a few more things going on here, but that'll only make it harder to understand.) Once this saturation occurs the current to the transistor base will be squeezed off, reducing the current through the collector and lowering the current flow through the transistor. At this point the inductive behaviour of the coil tries to keep the current flowing and starts to increase the voltage to the point where the current starts flowing again, but this time the voltage is high enough to force the diode to conduct. This energy was stored in the magnetic field, once this energy is depleted the voltage starts dropping again and the transistor will start to conduct again. I hope that explains the Joule thief part accurately enough. Now the laser diode will act as a pulsed diode because of this! Pulsed lasers have a few advantages, you fire it in short bursts which gives the diode time to cool down between pulses. This also allows the momentary light intensity to exceed that which you could normally be achieved. This means there is less time for the delivered energy to dissipate through heat conduction, so the material gets hotter and will start to ablate a lot quicker than without pulses.

Thank you