Phase anomalies in Talbot light carpets of self-images

Abstract

An interesting feature of light fields is a phase anomaly, which occurs on the optical axis when light is converging as in a focal spot. Since in Talbot images the light is periodically confined in both transverse and axial directions, it remains an open question whether at all and to which extent the phase in the Talbot images sustains an analogous phase anomaly. Here, we investigate experimentally and theoretically the anomalous phase behavior of Talbot images that emerge from a 1D amplitude grating with a period only slightly larger than the illumination wavelength. Talbot light carpets are observed close to the grating. We concisely show that the phase in each of the Talbot images possesses an anomalous axial shift. We show that this phase shift is analogous to a Gouy phase of a converging wave and occurs due to the periodic light confinement caused by the interference of various diffraction orders. Longitudinal-differential interferometry is used to directly demonstrate the axial phase shifts by comparing Talbot images phase maps to a plane wave. Supporting simulations based on rigorous diffraction theory are used to explore the effect numerically. Numerical and experimental results are in excellent agreement. We discover that the phase anomaly, i.e., the difference of the phase of the field behind the grating to the phase of a referential plane wave, is an increasing function with respect to the propagation distance. We also observe within one Talbot length an irregular wavefront spacing that causes a deviation from the linear slope of the phase anomaly. We complement our work by providing an analytical model that explains these features of the axial phase shift. References and links1. F. Talbot, "Facts relating to optical science. No. IV," Philos. Mag. 9, 401-407 (1836). 2. L. Rayleigh, "On copying diffraction gratings and some phenomena connected therewith," Philos. Mag. 11(67), 196-205 (1881). 3. J. C. Bhattacharya, "Measurement of the refractive index using the Talbot effect and a moire technique," Appl.Opt. 28(13), 2600-2604 (1989). 4. G. Spagnolo, D. Ambrosini, and D. Paoletti, "Displacement measurement using the Talbot effect with a Ronchi grating," J. Opt. Soc. A 4(6), S376-S380 (2002). 5. J. R. Leger, M. L. Scott, and W. B. Veldkamp, "Coherent addition of AlGaAs lasers using microlenses and diffractive coupling," Appl. Phys. Lett. 52(21), 1771-1773 (1988). 6. J. R. Leger, "Lateral mode control of an AlGaAs laser array in a Talbot cavity," Appl. Phys. Lett. 55(4), 334-336 (1989 416-419 (1973). 11. E. Bonet, J. Ojeda-Castañeda, and A. Pons, "Imagesynthesis using the Laueffect," Opt. Commun. 81(5), 285-290 (1991). 12. J. C. Barreiro, P. Andrés, J. Ojeda-Castañeda, and J. Lancis, "Multiple incoherent 2D optical correlator," Opt.Commun. 84(5-6), 237-241 (1991). 13. R. F. Edgar, "The Fresnel diffraction images of periodic structures," J. Mod. Opt. 16, 281-287 (1969). 14. J. T. Winthrop and C. R. Worthington, "Theory of Fresnel images. I. Plane periodic objects in monochromatic light," J. Opt...

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