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Optical ranging and vibration sensing based on the lagging propagation phase of structured beams

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Recently, studies have shown that the spatial confinement on waves or photons with beam shaping techniques would modify the propagation speed of optical fields including both group and phase velocities. Particularly, for the monochromatic spatially structured beams, the reduced longitudinal wave vector enables the phase velocity to be superluminal, causing a lagging propagation phase. In this Letter, we propose a novel, to the best of our knowledge, scheme for optical ranging and vibration sensing with the lagging propagation phase of structured beams. We experimentally demonstrate the extraction of displacement from the rotating angles of interfering fringes of superposed Gaussian and higher-order Bessel beams with lagging propagation phase difference. The measuring range is 0.2 m with the limitation of the tested moving stage, but it can be extended to tens of meters in principle. The measuring resolution can reach sub-millimeters, which can be further improved by carefully designing the probe beam and using a finer camera. The results may provide potential applications in position sensing and monitoring.

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Data availability

Data underlying the results presented in this paper may be obtained from the authors upon reasonable request, and the MATLAB codes for data collection and processing are available in Ref. [39].

39. Z. Wan and Z. Tang, “StructuredBeamMonitoring,” GitHub (2023), https://github.com/ZWan1/StructuredBeamMonitoring.

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Figures (4)

Fig. 1.
Fig. 1. Concept and principle. (a) Comparison of longitudinal wave vector between plane waves and structured beams, where a Bessel beam created by an axicon is an example. (b) Visualization of lagging propagation phase difference. (c) Principle of displacement monitoring from the rotating angles of superposed beams with lagging propagation phase differences.
Fig. 2.
Fig. 2. Experimental configuration. BE, beam expander; HWP, half-wave plate; SLM, spatial light modulator; M1–M3, mirror; BS1, BS2, beam splitter; L1–L4, lens; CCD, charge-coupled device.
Fig. 3.
Fig. 3. Experimental demonstration for optical ranging. (a)–(c) Observed beam intensity patterns of superposed Gaussian and higher-order Bessel beams with different displacements. (a) Detection of large displacement with measuring range of 0.2 m and step of 20 mm using small α (α = 0.00135); (b) detection of small displacement with measuring range of 20 mm and step of 2 mm using moderate α (α = 0.004); (c) detection of tiny displacement with measuring range of 2 mm and step of 200 µm using large α (α = 0.008); the OAM index remains 2 in all measurements. (d)–(f) Extracted rotating angles of petal spots from (a) to (c).
Fig. 4.
Fig. 4. Experimental demonstration for vibration sensing. (a)–(c) Detection of simple-harmonic vibrations with amplitudes of (a) 0.2, (b) 20, and (c) 2 mm. The insets are the beam intensity patterns captured over half a motion period. (d) and (e) Detection of complex harmonic vibrations with two different harmonics. (f) Detection of under-damped vibration. (g) Detection of driving-forced vibration. The points are experimentally measured and the lines are the set motions. Probe beams are with (a), (d), and (e) α = 0.0014, (b), (f), and (g) α = 0.005, and (c) α = 0.009;  = 2. The CCD records at a frame rate of 50 fps.

Equations (2)

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Δ φ B e s s e l = α 2 k 0 2 Δ z .
Δ θ = α 2 k 0 Δ z 2 .
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