Tight focusing properties of a circular partially coherent Gaussian beam

Tight focusing properties of a circular partially coherent Gaussian (CPCG) beam with linear polarization have been studied based on vectorial Debye theory. Expressions for the intensity distribution and degree of coherence near the focus are derived. Numerical calculations are performed to show the intensity distribution and degree of coherence of the CPCG beam in the focal region. It is interesting to find that after focusing the CPCG beam through a high numerical-aperture objective we can obtain a super-length optical needle (>12λ) with homogeneous intensity along the propagation axis and wavelength beam size (∼λ). Moreover, the numerical calculations of coherence illustrate that, in the range of full width at half-maximum of the optical needle, for any two of the parallel electric field components of the optical needle the coherence is close to 1, but for any two of orthometric electric field components the value of coherence is between 0.4 and 0.9. Such a non-diffracting optical needle may have potential applications in atom optical experiments, such as in atom traps and atom switches.