Talbot effect of a grating with different kinds of flaws

The term "polarization-dependent Talbot effect" means that the Talbot self-imaging intensity of a high-density grating is different for TE and TM polarization modes. Numerical simulations with the finite-difference timedomain method show that the polarization dependence of the Talbot images is obvious for gratings with period d between 2 and 3. Such a polarization-dependent difference for TE and TM polarization of a high-density grating of 630 lines/ mm (corresponding to d / = 2.5) is verified through experiments with the scanning nearfield optical microscopy technique, in which a He-Ne laser is used as its polarization is changed from the TE mode to the TM mode. The polarization-dependent Talbot effect should help us to understand more clearly the diffraction behavior of a high-density grating in nano-optics and contribute to wide application of the Talbot effect.

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“…The convergence of the solution has been verified in Ref. 17. In addition, we have compared our numerical results with those in Refs.…”

Section: Numerical Simulationsupporting

confidence: 55%

“…20 It has previously been applied to evaluations of high-density grating. 17,20 A schematic illustration of the experimental system of the Talbot SNOM method for observation of the polarization-dependent Talbot effect in a high-density grating is shown in Fig. 4.…”

Section: Methodsmentioning

confidence: 99%

Polarization-dependent Talbot effect

Zhou

Wang

et al. 2006

J. Opt. Soc. Am. A

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“…Associated effects such as the quasi-Talbot effect [17] or the fractional and fractal Talbot effects [18] were equally investigated. Also, rigorous studies were done using, e.g., electromagnetic theory [19], the finite-difference timedomain (FDTD) method [20] and the Rayleigh-Sommerfeld formula to understand the impact of aberrations on the self-imaging process [21]. In physical optics, researchers discussed such effects down to the quantum mechanical level, i.e., the quantum Talbot effect [22,23].…”

Section: Introductionmentioning

confidence: 99%

Phase anomalies in Talbot light carpets of self-images

Kim¹,

Scharf²,

Menzel³

et al. 2013

Opt. Express

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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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“…However, this assumption is not always right. Flaws or defects can be produced, such as lost strips, during the fabrication process [17][18][19][20][21]. Other non-ideal behaviour is owing to roughness on the surface of the gratings, as it happens for steel tape gratings.…”

Section: /mentioning

confidence: 99%

Diffraction of gratings with rough edges

Torcal-Milla¹,

Sanchez‐Brea²,

Bernabéu³

2008

Opt. Express

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Abstract:We analyze the far field and near field diffraction pattern produced by an amplitude grating whose strips present rough edges. Due to the stochastic nature of the edges a statistical approach is performed. The grating with rough edges is not purely periodic, although it still divides the incident beam in diffracted orders. The intensity of each diffraction order is modified by the statistical properties of the irregular edges and it strongly decreases when roughness increases except for the zero-th diffraction order. This decreasing firstly affects to the higher orders. Then, it is possible to obtain an amplitude binary grating with only diffraction orders -1, 0 and +1. On the other hand, numerical simulations based on Rayleigh-Sommerfeld approach have been used for the case of near field. They show that the edges of the self-images are smoother than the edges of the grating. Finally, we fabricate gratings with rough edges and an experimental verification of the results is performed. Opt. Soc. Am. A 11, 1874-1885 (1994

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Talbot effect of a grating with different kinds of flaws

Cited by 22 publications

References 22 publications

Polarization-dependent Talbot effect

Polarization-dependent Talbot effect

Phase anomalies in Talbot light carpets of self-images

Diffraction of gratings with rough edges

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