Beam deflection sensitivity of quadrant detector using a Bessel beam

A quadrant detector is a device that measures a displacement of a beam from the center. It relies on the difference between the detected intensity in its four semiconductor cells. It has been used in determining deflection of Gaussian beams and recently, of Laguerre-Gaussian beams. It is known that the sensitivity to beam displacement S of the quadrant detector is a function of the waist of the impinging beam while with LG beams, S diminishes as the orbital mode number l is increased. Since the S increases with decreasing waist w0, would a first-order Bessel beam whose most intense region can have much lower beam diameter, have a greater sensitivity? In this presentation, the sensitivity of a quadrant detector to a deflected Bessel beam is calculated. We show that the beam displacement sensitivity is increased when using BB's when the transverse wavevector kr is greater that (2/π)^(1/2) w0^(-1). However, the working displacement is reduced and should be much shorter that (6)^(1/2)/kr. Immediate application includes the increased sensitivity of devices such as atomic force microscopes.