Efficiencies of Coupling Light into a Fiber I am in AMO Physics and work a lot with optics. I just wanted to get an idea of what coupling efficiencies one "should" get in a "reasonable time"* by coupling light into a fiber using different couplers, like collimators, mounting plates, mounted lens systems, etc. I understand that this dependents on a lot of factors, so I will narrow it down for my specific case but would appreciate if ppl report some numbers with a short info about their setups.
We use a cage system system with a 5 mm lens and a FC/APC (Angled Physical Contact) fiber plate to couple 633 nm laser light into an APC single mode fiber. Pretty much everything of the optical equipment is from Thorlabs.
The reason for my question: My PI told me I should get efficiencies up 80% percent with our coupling scheme but I can only get 30%. I hope to get a better feeling for coupling efficiencies with this answer. 
Thanks for your input, 
n3rd
*With "should" and "reasonable time" I refer to coupling efficiencies one can achieve at time scales on the order of tens of minutes rather than hours, days, weeks. 
 A: How much light couples into the fiber depends on the NA (numerical aperture) of the fiber, the diameter of the beam of light entering the collimating lens, and the focal length of the lens.  Typical fibers accept light only from a limited angle about the axis of the fiber.  This is referred to as the NA of the fiber.  If the NA is large (e.g. 0.7) the fiber can accept light at up to about 44 degrees from the axis.  For an optical fiber this would be a remarkable NA.  Most fibers are in the 0.2 range and can accept light only within about 10-12 degrees from the axis.
Assuming that you have collimated light to start with, the diameter of the beam and the focal length of the lens then determine the effective NA of the light converging on the fiber.  The NA is the ratio of the radius of the beam to the focal length of the lens (this is a little approximate since NA is defined as the sin of the half angle, but for normal NA's it is very close).  If the converging beam of light has too great an angle, the outer parts of the beam will fail to couple into the core of the fiber.
Finally, if the beam is not collimated, i.e. it doesn't focus to a small spot on the core of the fiber, then the part of the beam that misses the core will not couple into the fiber.
A: Some more practical tips: 


*

*After having finished fiber coupling, i.e. positioning the tip of the fiber as precisely as possible in the beam path, beam walking (usually performed with two mirrors that lead the beam to the fiber-coupling stage) can also help in elevating the efficiency and can be performed in a matter of minutes. 

*This one is time-consuming but if the project is very efficiency-hungry, then it's worth a try. Assuming you have chosen the correct lens and incoming spot-size of the beam (matched to the NA of the fiber i.e.) but a high efficiency still eludes you, then: 


*

*mount a 1:1 telescope on an optical rail before the fiber-coupling stage,

*change this ratio in tiny amounts and optimize the coupling every time,

*Perform the optimization mentioned in point 1 above.



Perform them iteratively and, with luck, you may get higher values. 
A: With the setup you describe I would expect to get 60% without too much effort.  Optimizing the mode matching to the fiber as described by @jayann should get you up to 80%.  An experienced person could do all of this in a day, but if you are new to alignment of optics then it will take longer.  
If you are only getting 30%, then either your fiber is bad or your mode matching solution is wrong.  You can check to see if the fiber is bad by looking at the transmitted light on a CCD.  If the beam doesn't look like a nice Gaussian beam, then your fiber is not single mode and you have a problem.  
More than likely it is a mode matching issue.  Start by looking up the mode coming out of the laser (or measuring it with a beamscan) and the mode accepted by the fiber.  You need to use ABCD matrices to choose the proper lenses to put in between.  If you don't want to put all of this effort in, then use the solution discussed by @jayann where you add a 1 to 1 telescope (equal focal lengths placed 2 focal lengths apart) in the beam upstream of the fiber coupler.  Mount one of the lenses on a movable stage and use this to optimize the mode matching to the fiber.  
A: I realise this is an old question, but this is something that most newcomers to fibre optics struggle with, so I thought some more practical tips might be useful to others stumbling across this question.
Coupling into a fibre is something that becomes a lot easier with experience/practice. The first couple of times it can be hugely time consuming. Here's a couple of things I would check/do:


*

*Check whether your fibre entry is angled appropriately (the fibre end of the fibre connector you mentioned is angle-cleaved, the angle plate has to be mounted such that the angle of incidence with respect to the fibre end facet increases, rather than decreases), see image below (input beam should be along the beam path labelled 'output beam'):

Image from https://www.thorlabs.com/images/TabImages/FC-APC_Coupling_dwg_780.gif.

*Because you will never be able to align your coupling setup absolutely perfectly, optimising the coupling efficiency is not an optimisation with a single maximum. A good strategy is usually to maximise the coupling for a given z-position (along axis through fibre length-wise) using the x-y-position adjustments of your fibre dock (plane perpendicular to fibre axis). Note the maximum achieved throughput and move the z-position a little bit. Repeat. If the achieved maximum is smaller, move z the other direction. If it's larger, you're moving in the right direction.

*A good tip mentioned already in one of the comments above is to connect a fibre-coupled source to the other end of the fibre, and do the inital alignment 'backwards', collimating the output beam. This will result in a focussing lens position that is already pretty close to where it needs to be.

*Make sure you align your beam nice and parallel to the fibre axis. This is particulary important if the acceptance angle of your fibre is quite small. This is best done with an iris that is set to a height in the middle of the range of your 3-axis stage, and if you're using a top plate with a groove where your fibre mount slides into, you can use an iris that uses the same groove to align your beam along the z-axis.

*Check your fibre end facet with a fibrescope or under a microscope. If it's damaged or dirty you will never achieve good coupling efficiency.
A: When you are using APC facet of your receiving fiber, you should set a proper angle for that fiber due to misaligment between laser beam (it can be considered to be plane wave) and the fiber. Once you realign the APC fiber with a small angle (let's say 8 degree) then attach to the laser beam path, you will increase the coupling efficency.
