In Young's double slit experiment I put a convex lens after double slit and direct interference pattern on to a fibre. Then I expose the other end of fibre to a screen. What will I observe - the interference pattern (slightly jumbled) or a dot? Will photons behave as wave or particle?
This is not a particularly clean experiment. Be careful.
First, study up on Fourier Optics: http://www.amazon.com/Introduction-Fourier-Optics-Joseph-Goodman/dp/0974707724 . This tells you that you can't just put an arbitrary lens in front of the double slit.
I assume you are putting the fiber at the back focal plane of the lens. This is essentially the Fourier transform of the double slit and the fiber samples this irradiance pattern.
Next, is this a SMF (Single Mode Fiber) or a MMF (Multimode Fiber)? See http://www.amazon.com/Fundamentals-Optoelectronics-Clifford-R-Pollock/dp/0256101043/ref=sr_sp-atf_title_1_1?s=books&ie=UTF8&qid=1400043557&sr=1-1&keywords=pollock+optoelectronics. I assume based upon your question it is a SMF. In which case, it only captures light that matches the mode of the fiber. In other words, only a diffraction limited focused spot (roughly 8 um in diameter depending upon the fiber).
Finally, this is done all the time without any fun quantum effects. Everything from AWG's to non-diffraction limited coupling optics, to guided wave to fiber coupling encounters something like this. The confinement of a SMF is not sufficient to be relevant in a quantum mechanical sense. There are many quantum states and many photons involved.
If you used a photonic crystal or single photon emitter, you might be able to see something interesting. However, I doubt you'll see any particle / wave duality at home or in a standard research lab; it'll be all wave optics.
I believe you will observe a dot. The reason for this is that you interfered way too much with the photon's wavefunction, and essentially forced it to behave classically. This phenomenon is known as Quantum Decoherence.