What kind of far field pattern or intensity distribution do you expect to see?

The mode field of a single mode fibre is only approximately Gaussian, and in general there will be multiple diffraction rings around the central spot.  Their intensity depends on the mode profile of the fibre, which in turn depends on the operating wavelength and the core and cladding refractive index profiles.

Thanks Alan. It was pretty intense in the outer rings (by eye at least). It wasn't a dim halo. 

When multiple modes are present, they interfere at the output.  The pattern depends on the exact phase difference between modes.  If the pattern is stable as you manipulate the fibre, then you are unlikely to have cladding or higher order modes present.

If you project the beam onto a card or other screen, Is the pattern consistent as you move from close to the collimating lens towards the wall?  With multiple rings in the fibre far field distribution, evolution of the beam profile is expected, and may account for an increase in ring brightness.

If you have an iris diaphragm to hand and can afford a small loss of power, place it near to the collimating lens, and close the aperture until it matches the diameter of the first dark ring.  A fixed aperture is fine if you have one of suitable diameter.  The vignetted central spot should better approximate a Gaussian beam, and ought to retain a clean profile for some distance from the lens.  This can also help if there is residual spherical aberration in the lens, though this should not be a major problem with a decent quality aspherized achromat.

Hope this helps.

Thanks again, Alan. Your answer was extremely insightful, and I'll give this a try. 

Have you tried using another type of collimation lens? The ring pattern you described could also relate to the surface form deviation caused by polishing the aspheric surface. 

How long is you fiber? Remember that higher modes and cladding modes may propagate, with loss, along a short length of fiber (up to 2-3m, perhaps more). Are you sure that you're launching a single mode only (spot size and converging radiance angle)?

A long, long time ago, I was tasked with couple an visible argon laser into a multi-mode 50/125 fiber with considerable power. To ensure proper input alignment, I created an microscope/imager with very good rejection for 500nm and shorter wavelengths. This allowed me to inspect the fluorescence produced at the fiber tip to precisely center the spot. If your application lends itself to inspecting irradiance profiles at the fiber tips, it may give more insight. But be very careful regarding eye-safety and keep your laser safety officer involved.

Two phenomena described by corresponding laws should be taken into account to answer this question of diffraction of light getting out of the tip of the fiber:

a) Huygens principle of the reflected light (constituted from the secondary wavelets generated de to interaction of the EM–waves with the atoms of the matter and

b) Interaction of light with matter during the transmitting, reflection mode, including the interaction on the obstacles or walls of the fiber while leaving the tip of the fiber.

 Remember , the incident light ( of frequency  ω0) to the atoms  of the walls of the fiber induce polarization and wavelets ( secondary) of frequency ω, and the multi beam interference determine  the direction of propagation leaving the obstacle ( the tip of the fiber). The preferred direction of these multi beam interference create the interferometric rings interconnected with the shape of the opening of the tip of the fiber.  

The diffraction pattern (which is multi –beam interference) appearing in your experiment will be more or less emphasized according to the relationship of the wavelength of the light and smoothness or distance of the atoms of the matter interacting with the light, and relationship of the  diameter of the opening of the fiber  with the size of the light aperture.

You don't say much about the fiber or its face-finish. This is a first place to be concerned: if the fiber faces are not anti-reflective coated, you can be building interference within the fiber. APC (angled physical contact) connector ends deflect the reflection (which can be as much as 4% of incident light) into the cladding, rather than back down the core. Anti-reflective coatings are even better, but beware, they can be damaged by some cleaning methods. Additionally, if your method of cleaning fibers is the quick-n-dirty-good-ol' stick tape on it and rip it off, you can be damaging the face of the core, which will affect the shape of the output wave considerably. A first step would be to inspect the face of the core on both sides of the fiber, just to be sure you are working with a clean, scratch/pit/dig/oil-or-other-contamination surface.

Is your lens anti-reflective coated for the wavelength and angle-of-incidence of the output of the fiber? If you're operating without an anti-reflective coating, you can get a reflection from the inside of the output surface of the lens (as much as 4%), reflected by the input-side of the lens (again, as much as 4%) which then can overlay and interfere with the collimated output. Using a convex first-surface mirror eliminates this situation, and makes a fairly quick way to verify whether the lens is contributing to your interference pattern. Again, it is important that the surfaces be clean (although dust and scratches on lens/mirror surfaces are pretty easy to see in the resulting spot.)

Likewise, is the fiber-launch apparatus clean, properly aligned and free of blemishes? 

You don't mention which wavelength you are working with, nor the diameter of the fiber. 'Standard' communications SMF aims at 1550nm (or 1310nm), while Argon lasers can produce wavelengths from 1090nm to 229nm (gas with frequency-doubling via crystal). SMF is not SMF if the wavelength of the laser light is significantly smaller than the wavelength the fiber is designed to be single-mode for. The wavelength of single mode operation requires calculation which involves, for step fiber, the index of the glass on each side of the step, and the radius of the core. For index-profile fiber, an additional factor is applied to the square of the same calculation (using the indexes at the extremes of the profile), plus a factor which involves the profile factor. If you aren't sure of the wavelength that the fiber is meant to be single-mode for, it is best to consult the fiber manufacturer, or use a fiber which is designed to be single-mode for the wavelength you are using.

It is good to look at vendors' specs to get a feel for this. A good instance is the Thor Labs Single Mode Fiber page (https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=949). For each wavelength range SMF fiber listed, you can click on the "Specs" tab to see important parameters. As an example, they have a single mode fiber designed for wavelengths from 320-430nm, and provide the calculated mode field diameter for 350nm: 2.0 to 2.4um. They also give the core index for different wavelengths in the intended range, 320 nm: 1.48770, 375 nm: 1.47809 and 430 nm: 1.47214; with cladding indexes for those wavelengths in the next column. 

Obviously, if you are using one of the lower wavelengths (UV) of a frequency-doubled wavelength Argon-Ion laser in communications SMF 28 (with a fairly-standard 9um core, intended for mode diameters of 9.2um to 10.4um for 1310nm and 1550nm, respectively) you'll have room for many modes of 291nm coherent laser light to form. However, even with a higher wavelength, it is possible to form modes above the first if the core is too large to support singlemode operation.

You may have more than one spatial mode in the beam. Focus it tightly, and block everything except he central beam (with an iris). This is called spatial filtering.

Matthew Farrar, I ran into the same problem. Did you manage to solve your problem? If so, how did you do it?

I try to collimate NA=0.22 fiber output by simple lens with 75mm focal, and my beam is awful. A lens from ''laser pointer" with focal near 11 mm resolved my probleme. I think there is something as diffraction on the end off fiber and it needs some distance to appear. Now the question, which focal is optimal?