Is the link gain the gain of the whole system or just over the diode? And why does the threshold current of a diode laser have no impact on link gain whereas increases in slope efficiency have a major impact?
Definition of link gain for an optical system
communicationdigital-communicationsoptics
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"Typical" fiber for communication is 9, 50, or 62.5 um diameter in the core, but there is a 125 um cladding that is also necessary for the fiber to work. There is also 900 um core plastic optical fiber. What is out there for illumination, I'm not sure. Clearly you're not working with one of the types that I'm familiar with.
But, the key point is that the core is smaller than the cladding. And the light coupled into the fiber will be (best-case) what falls on the core. With .87 NA you'll probably get pretty close to this ideal. So I'll just make up some numbers. Say you have a 30 um core in a 60 um cladding. Overall the maximum coupling efficiency you could expect from uniformly illuminating the end of the fiber bundle is 302/602 or 25%.
Then there's a factor for the packing density of round objects into a an area (the gaps between the fibers in the bundle) which I believe is about 78% best-case.
And a reflection loss of about 4% for light entering the glass from air.
Add all these up, (.25) x (.78) x (.96), and you have about 19% best-case coupling efficiency. (You'll need to re-calculate this knowing the correct factor for the first term)
If you are getting near this, I'd say you are actually doing pretty well.
Of course it wouldn't hurt to find an LED that emits in a narrowish cone instead of over half of all space, or even to add some kind of lens to focus the light on the area of the fiber bundle. But generally your best case coupling is still not going to be all that great.
First, just to pick nits, an LED is not a laser, and vice-versa.
That said, you might try eBay, searching for "laser module TTL", and you can get quite powerful lasers which can be digitally modulated, usually in excess of 10 kHz - that's why you need to specify TTL. Beware of the small cylindrical units - they typically cannot run for more than 60 seconds without overheating unless you provide extra heatsinking. And the bigger ones will have problems with eye safety, but you can get around that by defocussing them. However, you really need to start learning about the ins and outs of eye safety, since more or less by definition you're going to be pointing lasers at people's eyes. Nowadays folks tend to really freak out if they find themselves looking down the beam of a laser (the wussies).
While you're on eBay, consider finding very narrowband optical filters at the wavelength you're planning to use. When you're operating in the great outdoors, Mr. Sun is not your friend.
Putting a detector in an old headlight is a decent idea in principle, but the details of actually making a robust mount will be more of a challenge than you think. Plus, the better your system gets at concentrating your incoming light, the narrower its field of view and the more difficult aiming it gets. Maintaining alignment also gets iffier, too.
As an aiming guide, you might consider sending a constant stream of null data, as close to alternating ones and zeros as you can, and producing an audio output from the receiver. This will let you aim your system by listening to the tone, and such fast audio feedback will be enormously useful.
I'm not bringing this up to discourage you, just to let you know that you're in for a tussle.
Best Answer
It depends on what you define to be your "link".
In general it would only make sense to define a gain over a part of your system that is linear. So it would not include a digitally modulated laser driver or a digital-output decision circuit following the receiver.
It might refer to just the transmission path: optical fiber, connectors, and possibly coupling efficiency effects at the receiver.
Or it could refer to the laser, transmission path, and possibly the receiver.
In many cases, you will find the "gain" of the system to be less than 1, sometimes much less than 1.
The threshold current only changes how you have to bias the laser to avoid nonlinearity in the modulation (clipping). The slope efficiency is \$\dfrac{\mathrm{d}P}{\mathrm{d}I}\$ describing the gain of the laser from input (current) to output (optical power). As such, if your link is defined to include the laser, the slope efficiency will be one of the multiplicative factors whose product is the link gain.