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This article, published in the Physics Teacher journal, discusses the phenomenon of diffraction of light through the wings of a hummingbird. The author explains that diffraction occurs when light interacts with objects that have features close to the wavelength of light. In the case of hummingbird wings, the wing structure acts as a diffraction grating, causing the light to spread and create colorful patterns. The article also mentions photographer Christian Spencer, who has captured this diffraction effect in stunning photographs. [Extracted from the article]

We analyze the far-field diffraction pattern produced by linear spatial chirped gratings. An intuitive analytical interpretation of the generated diffraction orders is proposed for gratings with linear variation of the period and linear variation of the spatial frequency. Also, experiments using Gaussian beams and plane wave illumination are performed. The analytical expressions are compared to numerical and experimental results, showing a high agreement. Chirped gratings can be implemented in interesting applications: we analyze how they can be used as a deflector, since tunable direction of diffracted orders can be achieved by displacing laterally the grating with respect to the incident light beam. Also the angular width of diffraction orders can be controlled and chirped gratings can be used to generate uniform illumination over a controlled angular range. These two applications have also been experimentally shown. [ABSTRACT FROM AUTHOR]

An accurate and simple technique for determining the focal length of a lens is presented. It consists of measuring the period of the fringes produced by a diffraction grating at the near field when it is illuminated with a beam focused by the unknown lens. In paraxial approximation, the period of the fringes varies linearly with the distance. After some calculations, a simple extrapolation of data is performed to obtain the locations of the principal plane and the focal plane of the lens. Thus, the focal length is obtained as the distance between the two mentioned planes. The accuracy of the method is limited by the collimation degree of the incident beam and by the algorithm used to obtain the period of the fringes. We have checked the technique with two commercial lenses, one convergent and one divergent, with nominal focal lengths (+100±1) mm and (−100±1) mm respectively. We have experimentally obtained the focal lengths resulting into the interval given by the manufacturer but with an uncertainty of 0.1%, one order of magnitude lesser than the uncertainty given by the manufacturer. [ABSTRACT FROM AUTHOR]

In this work, a reflective beam-splitter based on a metallic Ronchi diffraction grating normally illuminated is designed and analysed. This kind of beam-splitter could have potential applications in photonics and optical technologies in which robustness is necessary since it may be manufactured over malleable metallic substrates. The main idea under the design is as simple as obligating the zero-th diffraction order to be null. Firstly, scalar approach is performed, showing an approximation to the parameters of the grating necessary to cancel zero-th diffraction order. After that, a more rigorous approach such as Rigorous Coupled Waves Analysis (TE and TM polarization) is used to evaluate the proposed diffraction gratings as reflective beam-splitters. Beam-splitting is demonstrated for TE and TM polarization with slightly different dimensional parameters of the diffraction grating. Besides, we show how physical height of the grating grooves that allows cancelling zero-th diffraction order for a certain illumination wavelength depends on the metals used to manufacture the grating and its period. The dependence of the grooves height on the period is exponentially decreasing. To complete the analysis, we demonstrate how for a given grating period, the grooves height also depends on the illumination wavelength. [ABSTRACT FROM AUTHOR]

Steel tape gratings are diffraction gratings engraved on a steel substrate, whose slits are commonly manufactured by laser ablation. They behave as amplitude diffraction gratings, since the engraved slits act as strong scatters. Here, we extend previous works to the case of finite-size illumination sources, as they are used in applications such as optical encoders, where LEDs are commonly used as illumination sources. We obtain an analytical formulation for the near field behavior of this kind of gratings. When the light source increases its size, a decreasing in the contrast of the self-images is added to the effect of the surficial roughness. The agreement between analytical and numerical results is high, validating the obtained formulation. Besides, these results could be crucial in metrological applications in which steel tape gratings or other diffractive optical elements engraved on steel substrates are used, providing with a theoretical formalism to analyze the near field propagation of light after reflecting in them. [ABSTRACT FROM AUTHOR]

Abstract: In previous works, the authors have analyzed diffraction gratings with surface roughness on their strips. Appl. Opt. 46 (2007) 3668 determined the near field of a grating whose strips present two kinds of roughness, one of them so rough that the grating acts as an amplitude grating. On the other hand, in J. Opt. Soc. Am. A 25 (2008) 2390, a grating with roughness only in one of the grating levels is studied. In the present work, we extend our analysis to the general case where the strips of the grating present two finite roughness levels. As a consequence, the periodic modulation is only generated by random micro-topography of the strips. A statistical analysis is developed to obtain equations that predict the average intensity distribution after the grating. This general case presents differences with the previous works. For example, the maximum contrast of the self-images is given at a certain distance from the grating, that is, the contrast of the self images firstly increases with the distance of the observation plane and after, it decreases. Numerical simulations, based on Rayleigh–Sommerfeld approach, are performed which confirm the theoretical predictions. [Copyright &y& Elsevier]

Diffraction gratings are used in measurement devices for scientific and industrial applications. As it is well known, self-images appear in the near field when diffraction gratings are illuminated with a coherent beam, such as a plane wave. This effect has been analyzed in depth and its behavior is well known under ideal grating and illumination conditions. Usually, the illumination beam is not perfectly collimated but it presents a certain degree of aberration. In this work we analyze the behavior of the self-images of an ideal amplitude grating when it is illuminated by an aberrated beam. As it is expected the contrast of the self-images decrease when the order of them increases and also when the aberration degree increases. In some cases, contrast inversion is also produced for high degree aberrations. [ABSTRACT FROM PUBLISHER]

Abstract: Steel tape is used in optical applications due to its mechanical properties. However, roughness of steel surfaces affects to wave propagation. The effect can be observed using diffraction gratings with low periods. In such a case, self-images of the grating appear at certain periodic distances from the grating (Talbot planes). When standard steel is used, the contrast of Talbot self-images strongly decreases with the distance from the grating. In this work, we prove that controlling the surface quality of steel, it is possible to improve its optical behavior and, as a consequence, high quality surface steel represents a good choice for diffractive optics when the use of chrome-on-glass masks is not indicated. As an example, we have manufactured a diffraction grating over a high quality steel surface by means of an ablation process with a nanosecond pulsed laser. The contrast of the self-images for these gratings decreases very slowly with the distance, in comparison with the self-images obtained with standard steel tape gratings. [ABSTRACT FROM AUTHOR]

Abstract: We analyze the near field behavior of binary amplitude gratings which present a curved profile. This configuration has an important application in rotary optical encoders. This kind of encoders is used to measure the angular displacement between two different parts of the devices. To our knowledge, its behavior in the near field has not been analyzed yet. We have found that Talbot effect is produced but the period of the self-images and Talbot distances change as we separate from the grating. We have fabricated a curved grating and have performed the experiment to corroborate the behavior theoretically found. This fact could be useful in systems that use Talbot effect to measure displacements, since the mechanical tolerances grow. [ABSTRACT FROM AUTHOR]

The Gibbs phenomenon is a well-known effect that is produced at discontinuities of a function represented by the Fourier expansion when it is truncated to perform numerical calculations. This phenomenon appears because it is not possible to fit a discontinuous function as the summation of continuous functions, such as it is done with the Fourier expansion. Only considering infinite terms of the summation, the Fourier expansion fits the real signal. From a general point of view, it will affect to the final results since the representation of the signal does not include higher frequencies. It is true that the higher is the truncation, the better are the results, but an error is always committed. The Gibbs phenomenon has been studied in electric signal and diffractive optics, where the Fourier expansion is commonly used. In this work, we drop complex mathematics to show the effect of the Gibbs phenomenon on the near field propagation of diffraction gratings (self-imaging phenomenon) and also possible implementations of some corrections which allow diminishing the analytical or numerical errors in comparison with less accurate approaches. Anyway, the conclusions of this work would be applicable to other numerically solved diffractive problems which include sharp edges apertures. Simulations are compared with experiments giving interesting results. [ABSTRACT FROM AUTHOR]

Abstract: Steel tape gratings are used in different metrology applications. As the period of these gratings was large (around 100μm,), its analytical study has been performed, up to date, using a geometrical approach. Nowadays, steel tape gratings can be manufactured with lower periods, around 20–40μm, and diffractive effects must be taken into account. Also, due to the roughness of the surface, statistical techniques need to be considered to analyze their behavior. In this work, an analysis of the pseudo-imaging formation in a double grating system including one steel tape grating is performed. In particular Moiré and Lau configurations are analyzed. We have found that roughness significantly affects to Moiré configuration. However, its effect is negligible in Lau configuration. Generalized grating imaging configuration is also studied in depth. It is shown that roughness does not affect to the contrast of pseudoimages, but it modifies their depth of focus. [Copyright &y& Elsevier]

Abstract: Metallic gratings can be found in applications such as optical metrology. Due to their fabrication process, the surface presents a certain roughness. In this work, the effect of roughness on Talbot effect has been analyzed when the grating is illuminated with a Gaussian beam. A model based on Fresnel regime is used in order to determine the intensity distribution in the near field. Contrast of the self-images is obtained and it is found that it decreases in terms of the distance between the grating and the observation plane. When the autocorrelation function of roughness presents a Gaussian behaviour, the diffracted beams are still Gaussian although some of their properties change. For example, the width of the diffracted beams increases with respect to the case of the standard chrome on glass gratings. On the other hand, the power of each diffracted beam is independent on the roughness properties of the surface. [Copyright &y& Elsevier]

Abstract: We obtain a general analytical formulation for determining the near field produced by N diffraction gratings disposed in stack using a scalar approximation. Parameters of the gratings such as type-amplitude/phase-, fill factors, periods and relative positions between gratings along the x and y axes are considered. The obtained formulation is useful for analyzing problems which involve several diffraction gratings, such as optical encoders since it is computationally faster than integral formulations. Finally, analytical results are compared with numerical simulations based on the Rayleigh–Sommerfeld equation. [Copyright &y& Elsevier]