Optimal coupling of entangled photons into
single-mode optical fibers
Department of Physics, Faculty of Agriculture and Natural Sciences, The University of the West Indies, St.
Augustine, Republic of Trinidad and Tobago, W.I..
E. R. Pike and Sarben Sarkar
Department of Physics, King’s College London, Strand, London WC2R 2LS, UK.
We present a consistent multimode theory that describes the coupling of
single photons generated by collinear Type-I parametric down-conversion
into single-mode optical fibers. We have calculated an analytic expression
for the fiber diameter which maximizes the pair photon count rate. For a
given focal length and wavelength, a lower limit of the fiber diameter for
satisfactory coupling is obtained.
2004 Optical Society of America
OCIS codes: (190.0190) Nonlinear optics; (190.4410) Parametric processes
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bandwidth of the down-converted light reaching the fibers. To obtain the count rate we take
the modulus square of the integral in Eq. (12). Typical photon detectors have resolving times
much larger than the coherence time of the down-converted photons. The limits in the
integration with respect to may then be taken as effectively from
The integration gives a delta function which reduces a double integral to a single x-integral.
After performing the x-integral and using the approximation
rads-1, we obtain, to a good approximation,
for a typical
where C is the pair count rate and
. This approaches a maximum when
4 . 4
. This gives the fiber radius
5 . 1w0
for optimal coupling where is the
wavelength in the fiber. For a fiber diameter equal to the Rayleigh width of the diffraction
of the maximum.
pattern of the aperture, i.e.,
, the two-photon count rate in the fiber is only 56%
We have presented, from a first-principles calculation, a fully quantized multimode theory to
describe the coupling of single photons generated by collinear Type-I SPDC into single-mode
optical fibers. We have thus produced a practical recipe to maximize the coupling of single
photons into optical fibers. As pointed out earlier this is important for quantum cryptography
and quantum communication applications. For the type-I collinear down-conversion studied
here, we find no significant dependence of the coupling on the transverse width of the pump
beam and crystal length which have been obtained for non-collinear geometries. The
important parameters for the collinear case are simply the photon wavelength, the focal length
of the lens and the fiber diameter.