Amplitude-modulation mechanism for designing long-focal-depth cylindrical microlenses with a uniform axial intensity profile

Abstract

Although the long-focal-depth (LFD) function of cylindrical microlenses was previously realized by the phase modulation method, however, there still has no report of obtaining a uniform axial intensity distribution through the pure phase modulation mechanism. In this paper, the amplitude modulation mechanism is proposed for designing LFD cylindrical microlenses. An apodized window function of the incident light is used to suppress the axial intensity oscillations, so that a uniform axial intensity profile is achieved. Rigorous electromagnetic theory and the boundary element method are applied to analyzing focal performance of the designed cylindrical microlenses. Through replacing the incident plane wave with a two dimensional Bessel beam, numerical results demonstrate that the designed cylindrical microlens not only holds an LFD property, but also maintains a uniform axial intensity distribution as we expected. Moreover, the designed LFD cylindrical microlens has a high diffraction efficiency on the real focal plane. It is believed that the designed LFD cylindrical microlens with a uniform axial intensity profile should have wide application prospects in many micro optics systems.