Physics
Diffraction Gratings
Diffraction gratings are optical components with a series of closely spaced, parallel slits or grooves that diffract light. When light passes through a diffraction grating, it is dispersed into its component wavelengths, creating a spectrum. This dispersion property makes diffraction gratings useful in spectroscopy and other applications where precise wavelength separation is required.
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5 Key excerpts on "Diffraction Gratings"
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- Douglas B. Murphy, Michael W. Davidson(Authors)
- 2012(Publication Date)
- Wiley-Blackwell(Publisher)
Fig. 5.8 ). If we illuminate the grating with a narrow beam from a monochromatic light source, such as a laser pointer, and project the diffracted light onto a screen 1–2 m distant, a bright, central 0th order spot is observed, flanked by one or more higher order diffraction spots, the 1st, 2nd, 3rd, … order diffraction maxima. The 0th order spot is formed by waves that do not become diffracted during transmission through the grating. The spots are always arranged such that the orientation of an imaginary line containing them is perpendicular to the orientation of rulings in the grating. The diffraction spots identify unique directions (diffraction angles) along which waves emitted from the grating are in the same phase and become reinforced as bright spots due to constructive interference. In the regions between the spots, the waves are out of phase and destructively interfere.Figure 5.8 The action of a diffraction grating. Multiple orders of diffracted light are shown.The diffraction angle θ of a grating is the angle subtended by the 0th and 1st order spots on the screen as seen from the grating (Fig. 5.9 ). The right triangle containing θ at the screen is congruent with another triangle at the grating defined by the wavelength of illumination, λ , and the spacing between rulings in the grating, d . Thus, sin θ = λ /d , and reinforcement of diffraction spots occurs at locations having an integral number of wavelengths—that is, 1λ , 2λ , 3λ , and so on—because diffracted rays arriving at these unique locations are in phase, have optical path lengths that differ by an integral number of wavelengths, and interfere constructively, giving bright diffraction spots. If sin θ is calculated from the distance between diffraction spots on the screen and between the screen and the grating, the spacing d of the rulings in the grating can be determined using the grating equation
eBook - ePub- Richard J. D. Tilley(Author)
- 2019(Publication Date)
- Wiley(Publisher)
A transmission diffraction grating made up of a series of transparent apertures in an opaque material produces its effect by selectively changing the amplitude of the light passing through it and is known as an amplitude object and specifically an amplitude grating. Suppose, instead, that the grating is composed of adjacent strips of material that are transparent but of differing refractive indices. In this case, a phase difference will be selectively introduced between the beams traversing adjacent regions, and the material is known as a phase object or phase grating. Differences in phase are not visible, but can be transformed into visible intensity differences using wave recombination techniques such as interference. Reflection gratings can also alter the amplitude or phase of the interfering beams to form amplitude and phase objects. It is diffraction that often sets a limit to the performance of optical instruments, including the eye, and the topic is therefore of particular practical importance. As well as allowing a quantitative analysis of the performance of optical instruments to be made, the mathematical analysis of diffraction lead to the production of Diffraction Gratings for use in spectroscopy and the understanding of crystal structures, thus providing the foundations of much of modern science. More recently diffraction studies have expanded into areas in which disorder, partial order, or sub-wavelength order, are dominant. These have important consequences – in explaining the transparency of the cornea of the eye, for example. The diffraction patterns formed by diffracting centres are sensitive to the wavelength of the incident light. When white light is involved a multiplicity of such patterns form. When these are spatially separated, intense colours can be observed. Commonplace examples of this abound. Diffraction effects contribute to the shifting colours seen on many multicoloured wrapping paper and bags
eBook - ePubElectromagnetics Explained
A Handbook for Wireless/ RF, EMC, and High-Speed Electronics
- Ron Schmitt(Author)
- 2002(Publication Date)
- Newnes(Publisher)
The law states that the scattered light is proportional to the area of the object multiplied by the fourth power of the electrical dimension of the object. This result is the complement of the transmission of light through small apertures, which I discussed in Chapter 9. In 1944, Nobel Prize-winning physicist Hans Bethe derived the theory of diffraction for small apertures. The equivalent result of the two theories demonstrates the success of Babinet’s principle. FRAUNHOFER AND FRESNEL DIFFRACTION Diffraction is a radiation phenomenon. Fraunhofer diffraction occurs when the wave source and observer are far from the aperture or scattering object. Fresnel diffraction occurs when the source and/or observer are close to the aperture or scattering object. Figure 14.5 shows Fresnel diffraction patterns for apertures of various cross-sections. Figure 14.6 shows Fresnel diffraction patterns for opaque (perfectly absorbing) objects with different size cross-sections. In other words, Figure 14.6 shows the Babinet complements to those objects in Figure 14.5. In each case, the source frequency is 100 MHz (λ × 3 m), and the source antenna is assumed to be very far away from the objects. The electric field is measured at a distance of 10m from the object. For electrically large objects, the shadow is in proportion to the object. The shadows cast by ordinary everyday objects under illumination by visible light fall into this category. For electrically small objects, the shadow becomes almost impossible to discern. The shadows cast by ordinary everyday objects when illuminated by radio waves fall into this category. Figure 14.5 Simulated diffraction patterns for apertures of various widths, with incident radiation of 100 MHz (3m wavelength). Patterns “measured” 10m from aperture. The figures graph the intensity of the radiation pattern. Figure 14.6 Simulated diffraction patterns for objects of various widths, with incident radiation of 100 MHz (3m wavelength)
eBook - ePubSilicon Photonics
Fundamentals and Devices
- M. Jamal Deen, Prasanta Kumar Basu(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
Diffractions gratings have been in use over decades to separate light into its different component wavelengths. In principle, gratings can be used as demultiplexers in WDM systems. A reflection grating has been used for demultiplexing WDM signals.Due to difficulty in fabricating planar Diffraction Gratings, AWGs have so far enjoyed a monopoly in the WDM demultiplexing scenario. Three fundamental challenges in the fabrication of planar Diffraction Gratings must be overcome before these devices could be employed on a large scale in present DWDM communications systems. These are (1) fabrication of vertical grating facets in a waveguide structure, (2) reduction of polarization dependence of the grating diffraction efficiency, and (3) elimination or compensation of the birefringence of the device.Blaze is a tilt on the grooves of a reflection grating to concentrate the light at a higher angle, and therefore in orders M > 0. Thus light is concentrated in the dispersed orders. An echelle grating is an extreme example of a blazed grating. The blaze angle is set very high (to the order of 65̊), where i and d are, respectively, the angles of incidence and diffraction.In recent years, echelle gratings (EGs) have proven to be promising devices for demultiplexing DWDM light and potential competitors to the more advanced AWG devices. The EGs have some inherent advantages 13.The AWGs are usually realized with shallow-etched ridge waveguides. Grating-based devices, on the other hand, require deeply etched grating facets. The size of the phased array, however, is much larger than the grating demultiplexers. The number of waveguides in the AWG is much smaller than the number of teeth in the grating, and therefore the finesse is much smaller in AWGs. This limits the number of channels available over its free spectral range. The EC grating shown in Figure 12.12 has a folded beam path and does not need an array. Its size is several times smaller than the AWG for the same number of channels 13.ProblemsFigure 12.12 Schematic diagram of an Echelle grating.12.1 Derive an expression for the free spectral range in terms of frequency from Eq. (12.6)
eBook - ePub- Alexander McPherson(Author)
- 2011(Publication Date)
- Wiley-Blackwell(Publisher)
Figure 1.8 of Chapter 1. In principle, this means that if we can formulate an expression for the Fourier transform of a single unit cell, and if we can do the same for a lattice, then if we multiply them together, we will have a mathematical statement for how a crystal diffracts waves, its Fourier transform.The reader probably has it branded indelibly upon his/her mind by now that Fourier transform and diffraction pattern are mathematical and physical correlates. Hence the point will be belabored no more, and only one or the other will be used. The questions now become specific. How does a collection of atoms diffract X-rays, and how does a point lattice diffract X-rays?DIFFRACTION PATTERN OF AN ARBITRARY ARRAY OF POINTS IN SPACEIn Figure 5.1 , if waves arriving along a direction0(defined according to some coordinate system) encounter scattering points, each point will scatter the waves as if it was itself the originator of a spherical wave emitted in all directions. These scattered waves, it is important to note, give rise to diffraction effects only when distances between the points are close to the wavelength of the radiation. The points we are dealing with here will always be assumed to have that property. For any direction in space we can define a vector originating at each scattering point and traveling in that direction in space to where we wish to observe the diffracted radiation. The vectors are normal to the wavefronts of the spherical waves they represent.Figure 5.1 shows an incident wave0illuminating two points P 0 and P 1 and an arbitrary direction , along which we seek the consequences of the scattered waves. That is, we want to know what is the amplitude and phase of the resultant wave at any point along the direction created by the interference of the two scattered waves. Because is general, we can ask this question for any direction and the analysis will be the same. For simplicity, let us assume that the points at x 0 , y 0 , z 0 and x 1 , y 1 , z 1 scatter X rays equally, meaning they have the same number of electrons. Hence the amplitudes of the two scattered waves will be the same. The crucial question in combining the two scattered waves is: What are their relative phases? As we saw earlier, we can choose the phase of the first wave, from P 0 , at x0, y0, z0to be zero (remember, we get the first one free when we establish our reference system for the waves). Then what is the relative phase of the wave scattered by P 1 , at x 1 , y 1 , z 1
