It is well established that light beams gradually diverge during propagation due to diffraction effects, imposing limitations on their practical applications. Extensive research has been conducted to develop methods for generating non-diffraction beams. While significant progress has been achieved, substantial challenges remain. For example, propagation distance and efficiency are highly sensitive to beam parameters. Precise control and stable generation of high-quality non-diffraction beams in experimental settings thus remain a focal point of current research. Recent advancements in micro-nano optical devices have enabled optical field manipulation through structural parameter tuning. For instance, metasurface-based approaches have been used to engineer non-diffraction properties; however, these complex metasurface structures often pose significant fabrication challenges. In this paper, we study the diffraction field generated by the picometer misplacement combined grating (PMCG) with the property of non-diffraction. The PMCG is prepared by the double holographic exposure technique. By adjusting the angle between the two beams and the parameters of the exposure period, the period difference between the two exposures is set at a picometer scale. This new method of generating a non-diffraction field by adjusting the holographic exposure period is expected to be applied in the field of three-dimensional measurement and precision measurement.

The PMCG is a diffraction optical element generated by two exposures of a holographic interference field with a controllable period at the picometer scale. In the holographic exposure field, an angle θ exists between two interfering beams. By adjusting θ to θ+Δθ, the period of the exposure field changes from d to d+Δd, resulting in a period difference (Δd) between the two exposures. A scanning reference grating (SRG) system is employed for precise measurement of the interference field, enabling long-travel online measurement of the lithographic interference field. By measuring the period of the interference light field, the difference between the two exposure periods is accurately controlled at the picometer scale. The holographic interference field is used to expose a quartz substrate coated with photoresist. The first exposure records an interference field with a period of d. After the expected period change of the holographic interference field is determined using the SRG system, a second holographic exposure is performed, recording the superposed interference field from both exposures on the quartz substrate.

In this study, the PMCG with dimensions of 30 mm×50 mm×10 mm is fabricated. The first holographic exposure has a period of 4096 nm, and the period difference Δd between the second and first exposures is 400 pm. The PMCG is characterized using an atomic force microscope (AFM). As shown in Fig. 7, variations in exposure intensity at different positions are observed, with adjacent grating periods exhibiting cumulative or subtractive states. These results confirm that the PMCG accurately records the superposed interference field from the two holographic exposures. Physical analysis of the diffraction field generated by the PMCG reveals that two interfering beams within the field maintain a constant field structure regardless of propagation distance, which is the mechanism underlying its non-diffraction property. A laser collimating and beam-expanding system is constructed to analyze the non-diffraction field produced by the PMCG, as shown in Fig. 9. During field propagation, the diffraction field structure remains essentially unchanged, with a divergence angle of only 0.001 rad. This experimental result verifies that the diffraction field exhibits propagation invariance, confirming the non-diffraction characteristic of the PMCG.

In this study, a novel non-diffraction optical element is proposed, whose diffraction field exhibits propagation invariance. The PMCG is fabricated using the double holographic exposure technique. By measuring the period of the exposure interference field with the SRG system, the periods of the two exposures are set as d and d+Δd, achieving period differences between the two exposures at the picometer scale. Through analysis of the physical principles governing the superposed interference fields from the two holographic exposures, the underlying mechanism for generating the diffraction field by the PMCG is identified. The mutual interference of two coherent beams within the diffraction field ensures that the diffraction field structure remains unchanged regardless of propagation distance. To validate the theoretical analysis, a laser collimating and beam-expanding system is constructed to characterize the propagation properties of the picometer optical comb in free space. By examining the diffracted field intensity patterns at different propagation distances, the non-diffraction characteristic of the PMCG is experimentally confirmed. This work introduces a new paradigm for non-diffraction optical elements, paving the way for potential applications in optical manipulation, optical imaging, optical measurement, and other precision-related fields.