Complex non-diffraction beams generated using binary computational holography

The diffraction of optical fields is a universal phenomenon that can cause beams to spread during propagation in free space. Ideal non-diffracting (spatially stable) structured beams can propagate in free space without changing their initial field distribution at any plane orthogonal to the direction of propagation. Moreover, the non-diffracting structured beams also have the ability for self-recovery after encountering obstacles. Hence generating non-diffracting beams or structured beams is a very important field of research for overcoming the diffraction behavior of beams during propagation in free space. Any non-diffracting structured beams with a certain intensity, phase distribution, and propagation properties have special applications in the field of optics. Lately, some non-diffracting beams with complex structures are introduced one after another, such as Mathieu beams, parabolic beams, Lommel beams, asymmetric Bessel beams, and so on. The complex amplitude modulation is necessary to produce the non-diffracting beams with abundant structures. At present, no commercial optical modulator can modulate the phase and amplitude of light waves simultaneously. Based on binary computer-generated holography that can encode the two-dimensional transmission function distribution, a binary real amplitude computer-generated hologram with complex amplitude modulation functionality is designed and constructed. Binary real amplitude computer-generated holograms, which are a kind of binary optical diffracting element that generate non-diffracting beams with complex optical morphology, are designed and constructed by encoding the complex optical filed information by using the Lohmann-type detour phase coding method. For the Lohmann-type detour phase coding method, the coding principle is mainly that the complex field distribution information is transformed into amplitude and phase information. The complex field distribution is sampled, and one can obtain a matrix of point sources. Here, we extract the amplitude and phase information as input information to generate two 2D real value matrices for detour phase coding. By using the homemade projection imaging lithography system, the silver salt halide plate was exposed, developed and fixed, and then a binary mask is precisely machined. The homemade projection imaging lithography system can machine holograms with an ultrahigh resolution of 79874 × 79874 dpi and a maximum output of 156 mm × 156 mm. Using the mask, the non-diffracting beams with abundant structures can be produced accurately.

Taking the non-diffracting Mathieu beam as an example, two kinds of binary real amplitude computer-generated holograms for generating Mathieu beams are constructed by using the Roman type detour phase coding method. In the process of the machine, the photolithography file is firstly divided into 47 unit patterns of 600 pixel × 600 pixel, where each unit pattern is automatically inputted into a DMD (Digital Micromirror Device) in proper sequence, and then subsequently scanned line-by-line for projection exposure. When the lithography is complete, the silver halide plate is processed to obtain the mask. In this experiment, the calculated CGH is 28000 pixel × 28000 pixel, and the size of a pixel is 318 nm×318 nm. The size of the produced binary masks is 8.9 mm × 8.9 mm. The non-diffracting Mathieu beams with elliptic coefficient q=10 and topological charge number m=0, 1 are generated, which belong to the even type Mathieu beams of the first kind. Undoubtedly, the classes of non-diffracting Mathieu beams, including the even type Mathieu beams of the second kind, odd type Mathieu beams of the first kind, and odd-type Mathieu beams of the second kind can also be generated using the same encoding method and experimental setup. Since one can encode both the amplitude information and the phase information of optical field in sole spatial light modulation, the experimental system is simple in structure. The experimental results show that the coding method of binary computer-generated holography is an accurate, convenient and efficient way to generate high-quality non-diffracting beams with abundant structures.