I want to connect an LED (940nm signal) to a 0.25mm fiber optic. I have researched some possibilities, which involves using shrink heat tube, which is unfortunatly too large or simply buy couplers. I have been told, that couplers have to be designed specifically for the used components. I aim to 3D print my own coupler, but I don't have any resources, from which I can learn the basis of designing a connection between LED and fiber optic.
For experimentation purposes, one can make allowances for the lack of precision resulting from not using industry standard couplings.
If your purpose of connecting fiber optic to an LED is to transmit signal data by means of modulating the LED, it's critical to have a solid optical match between the surfaces of the two materials. One can find index matching fluid for just that purpose, used when there is a simple mechanical coupling involved.
If your purpose is to provide illumination, the situation is not as critical.
A 940 nm wavelength is typically a laser output. If you cleave and polish the end of the fiber using standard practice for such action, you'll get the best results on that end. The LED should also have an optically flat surface, which may require that you also polish it, but if it's a laser diode with a metal shell, you'll have to take your chances.
Once prepared, a simple coaxial mount will provide for substantial signal transmission. I suggest a cylinder of convenient material, drilled one one end as precisely as possible to accept the laser diode and carefully drilled on the other to accept the jacketed fiber.
A single drop of index matching fluid between the diode and the fiber will be sufficient. Apply pressure while inserting the fiber, forcing as much of the fluid clear of the interface.
There will be reflection on the surface but the fluid will minimize that problem. You can get away without the index matching fluid, but some of the power will be lost to mis-alignment. Reflected power may be a concern as well.