I used a collimator to couple a 670nm Gaussian laser into a Plastic Optical Fiber (POF). If the other tail of the fiber is open ended, the light will come out of the fiber and will propagate into free space.
My question is "What is the distribution of the free space light?" Is it Gaussian, Lambertian or etc?
Hi Mojtaba,
The answer depends on the fiber. A POF has no fundamental difference, i think, with a glass optical fiber. The guiding is made thanks to total internal reflection (i.e. refractive index difference). The intensity distribution then corresponds to the modal structure of the fiber. Usually, POF are highly multimode, i suppose it is the case of your fiber. In a highly multimode fiber, the intensity profile is often "top hat", i.e. close to : 1 inside the core and 0 outside.
Then when the light is coupled out of the fiber, it should propagate as the diffraction of this spatially incoherent (because multimode) top-hat profile. In the far field, i suppose it should be the squared Fourier transform of the top-hat profile... Bessel function ?
Am I right ?
Michaël
Hi Michaël,
Thanks for your reply. Interesting suggestion!
Meanwhile I talked to my supervisor. He said the beam will have a pattern like Lambertian distribution. I did some measurements and I came to believe he is right.
The POF is a step index fiber, with NA = 0.5 and diameter of 2.2 mm.
Considering the results from the measurement and taking account the following equation:
I = I0 * (cos(T))^m
For a green laser, I obtained m = 20.
Any way I am looking for some valid reference to confirm the idea and if I find it, I'll let you know.
However If there is no reference, I will use your suggestion and try to derive some expression for that.
The light intensity distribution at the multimode fiber end will be ~ top-hat, if fiber length is large, when mode energy distribution become almost uniform. According my experience, 3 meter length of 1 mm core diameter fiber is not sufficient to obtain top-hat (supposing that maximum to average intensity ratio over fiber end area is less than 1.2)
But angular distribution definitely is not Lambertian for real fiber with length~2-3 m. It will depent on launching geometry, fiber bending, etc. Check yourselves beam spot at ~10 cm from the end. Bend the fiber and you will see different pictures : circle, or o-ring,or multiple o-ring.
If you see uniform spot, the possible reason, to my mind, is bad surface quality of the fiber end - not polished (like diffuser after fiber).
Thanks Mr. Aleksandr Tarasov,
Nice advice. Could you please address me some reference for it? I am not so familiar with this subject.
May be this book can be useful:
Donald J. Sterling, Jr., Leo Chartrand, Technician`s Guide to Fiber Optics, 4 Ed., 2003
Thanks a lot Mr. Aleksandr Tarasov,
I did an experiment in which I tried to collimate the output fiber beam. After exposing the collimated beam on a screen I realized that you were absolutely right. I saw multiple rings in the spot. At first I thought it was a Coma effect and I tried to fix it by moving the fiber and the lens. However the rings moved but they did not disappear.
I will check the book you suggested. Thank you again.
Another way to look at this is in terms of numerical aperture of the fiber. If light is not propagated in the cladding layer, you can measure the size of the spot, two distances away from the fiber tip. For fibers with different core/cladding refractive indexes you will see that the angle of the cone of light will be different. Numerical aperture = nsin(theta) = squareroot( Coreindex squared minus Cladding index squared). Matching the numerical aperture is a good way to improve the efficiency of coupling light into the fiber, if it is a laser or a point source.
As mentioned above if the light is coherent you will see speckle, or multimode interference, and that interference can also have structure. It can be very sensitive to the launch conditions, bending the fiber etc.