Diffraction grating
Optical lattices, also called diffraction grating or multiple slit, are periodic structures of diffraction of light. Everyday examples are CDs and fine combs. The grating constant is the period of the grating, typical values are 0.5 microns to 10 microns. All types of grids consist of parallel, line-like structures:
- Column in non-transparent material or opaque webs on a transparent plate ( wire, slit or grating )
- Ridges or furrows on a reflective surface ( reflection grating )
Lattice work by diffraction of coherent light: The interfering light of the single column, forming an interference pattern. Monochromatic light is in a few different directions (exactly: in maxima of different orders ) distracted. The angle of deflection depends on the lattice constant and the wavelength, larger deflection angles corresponding to higher orders. Polychromatic (e.g. white light), in its spectrum spread out similar to a prism. Very close to the grating, the light interferes to copies of the grating structure ( Talbot - effect).
Grids were invented in 1785 by David Rittenhouse, also built in 1821 Joseph von Fraunhofer grating.
- 2.2.1 Ruled blazed grating
- 2.2.2 Holographic gratings
- 2.2.3 Imaging gratings
- 3.1 grating equation
- 3.2 intensity calculation with Fourier optics
- 3.3 resolution
Application
Optical gratings are used in optical measurement systems for monochromatisation of radiation ( monochromator ) and for the analysis of spectra ( optical spectrometer ). So as to be frequency stabilized laser (see Bragg reflector DFB ) laser, a high power short laser pulses amplified and generates dot pattern in laser shows. Another field of application is the channel separation and reunification in optical data transmission.
Lattice types
Distinguishing characteristics of grid types are:
- Method of production: A distinction ( optically generated =) between grids mechanically produced (for example, with diamond styluses divided ) and holographic. A method is rarely used in the imaging of a mask in photoresist.
- How it works: There is a distinction between transmission and reflection gratings.
- Transparency: It is between amplitude gratings ( absorbing gratings ) and phase gratings differed (forming the wavefront )
A more recent development imaging grating, which is also both a holographic - within limits - can be prepared by mechanical subdivision.
X-ray grid are a special case in which the (X-ray ) diffraction by the periodic structure of the crystal lattice occurs. Because here are the lattice constants of the order of an atomic diameter, these are suitable for very short wavelengths.
Transmission grating
Transmission gratings are amplitude grating. They consist of a sequence of permeable and impermeable areas (gaps and ridges ). They therefore have the inherent disadvantage that the webs, part of the incident light is reflected or absorbed, and thus does not contribute to the intensity of the resulting spectrum. In a web - gap ratio of 1:1 or 50 %.
Wire mesh
Used 1820 Joseph von Fraunhofer wires that he harnessed side by side. Likewise, fine fabrics act (eg umbrella as an example of a 2D lattice).
A wire grid is also the X-ray diffraction grating shown above.
Wire mesh can also be used in microwave, millimeter-wave, terahertz radiation, and in the mid / far-infrared, they then have correspondingly large lattice constants.
Laminargitter
Laminargitter be used where there are substrate materials that are transparent to the field of application of wavelengths. Accordingly, they consist of strips made of metal or an absorbent material, which are applied to the substrate or formed on the latter. The lattice structures, that is, by interference of two coherent laser beams directly on a photoresist-coated glass or plastic substrate are created by way of holography. You can create with this technique furrows densities up to several 1000 lines per millimeter.
Reflection grating
Reflection grating is a phase grating. They work so that, for certain angles and wavelengths elementary waves in adjacent areas (eg bridge and gap of a box section ) have a path difference of a whole number multiple of the wavelength, leading to constructive interference. Reflection gratings are generally effective as a transmission grid because ideally all of the radiation power - less the reflection loss and possible shadowing - contributes to the diffracted power.
Ruled blazed grating
In monochromators and spectrometers so-called sawtooth or blaze gratings are frequently used. These are lattice with a sawtooth -like profile, the Blaze surfaces used for constructive interference corresponds to the long leg of the ramp. The blaze angle between surface and substrate ( the blaze angle ) can be chosen so that as much light of a particular wavelength into a particular diffraction order falls. This is achieved if the same applies to the reflection condition with respect to the blaze area for incident and emergent radiation. Ideally, such a diffraction efficiency reaches 100%.
In the mechanical division of the blaze angle can be varied within wide ranges, which is why, despite their drawbacks like the technique used for the production of blazed gratings. The mechanical division parallel grooves are produced with a suitably polished diamond stylus in a metal surface. Here, the material is to be divided (often gold) plastically deformed. When set correctly, the stylus angle and suitable diamond cut is reached that a Aufwurf created with clean saw-tooth profile. The physicist Henry Augustus Rowland improved 1882 production of mechanically split grille crucial by significantly improved the precision of the method; it is therefore also called Rowland grating. In addition, the division succeeded him as the first on concave substrates.
Holographic gratings
Reflection gratings may also be produced photolithographically or holographically. These two coherent partial beams of a laser are placed in the photoresist a substrate for interference. The interference pattern generated areas with strong and weaker exposure. In the subsequent development of the two areas is preferred removed ( depending on the nature of the developer). It is immediately apparent, that in this way laminar can be produced. However, it is within narrower limits also possible to produce Blaze profiles holographic.
An important advantage of the photolithographic process is that gratings can be formed even on highly curved substrate surfaces. Another advantage may be the fact that potentially a large number of originals in a relatively short time can be made if the structure is only once and the laser operates in a stable.
Imaging gratings
The combination of a grid having a concave surface which thus forms a concave mirror, has the advantage that the diffracted radiation is equal focused without additional optical elements are necessary. However, this focus is still stamped with the typical aberrations of a concave mirror. However, one can modify the grating design so as to correct these errors.
A broader example is the so-called flat -field grating. In the case described above, the focuses of the different wavelengths do not lie on a plane but on a curved surface. Modern detector arrays, as they are often used in compact spectrometers, however, usually are. Therefore, the parameters of the Holografieaufbaus be corrected so that the focuses of all wavelengths of a region of interest located in one plane. In such grids, the diffracting structures are neither straight nor parallel nor equidistant. It already is relatively complex holograms.
Also mechanically divided grids can an imaging effect can be given. In so-called chirped gratings, the lattice constant is varied in accordance with setting by the grating surface. Can thereby be made perpendicular to the grating grooves, for example, a focus in the plane.
Replica
For the production of larger numbers resorting to Replikatechniken.
A replica has, interestingly, a better quality (scattered light and higher orders is reduced ) than the original. In manufacturing a diamond stylus the furrows produced are very precise in shape, but the edges with neighboring furrows have a slight burr inevitable result of the imprint will eliminate the problem. Now there are copies of the disturbing ridges in the " bottom " and the precise furrows form the tips of the grid. The footprints are cemented to a glass plate and steamed for reflection grating was from metal. The grid quality is so good that it is only surpassed by holographically produced gratings. The production is similar to that of a CD- ROM, however, takes place because of the significantly smaller numbers on factory level off. Due to the replication technique is not dependent on the mechanical division process or the holographic production, both of which require considerable time and expense and are subject to high credit risk.
Function
Grating equation
Generating a series of grating lines of constructive interference, when irradiated with light of a certain wavelength and coherence. In these transmission gratings on either side of the direction of the incident beam ( " zero order " ) are. The angle of these directions arise at normal incidence from the relation for the phase difference:
With:
Light incident on a diffraction grating, diffracted comparable to the double slit experiment, the unit thus formed waves interfere to form a grating spectrum.
For the main maxima holds:
When participating in the diffraction grating elements arise between two main peaks each minima and dark directions. Therefore, the main maxima with increasing sharply; the secondary maxima are indeed numerous, but weaker. Thus, the resolution increases.
Even with non -normal incidence angle continues to comply with the zeroth order the behavior of a pane of glass ( transmission grating ) or a mirror ( reflection grating ), this light remains unchanged and thus reduces the effect of the grating (remedy by blaze grating ). More is the path difference
Intensity calculation with Fourier optics
Hereinafter, it is assumed that the grid is irradiated with monochromatic light. To calculate the precise intensity distribution in the far field of the grating, it uses the methods of Fourier optics. The aperture function of the grid is made up as follows:
- A single slit of width b can be described by the rectangular function.
- In order to obtain infinitely many first column with the same distance a, the convolution of the single slit with a Dirac comb.
- The spatial boundary of the grid is described by the multiplication of the folded Dirac comb with a rectangular function in x - space. B is the total width of the grating.
The full aperture function is:
By Kirchhoff's Beugunsintegral it can be shown that the diffraction pattern of the Fourier transform of the autocorrelation function of the aperture corresponds.
The modular design and the convolution theorem can be the Fourier transform of the aperture function of the Fourier transform of the individual components put together.
The Fourier transform of the delta- comb shows that a smaller pitch of the grid column in the x - space leads to a larger distance between the minima and maxima in the k-space - and vice versa.
Thus results for the intensity distribution, as the square of the amplitude distribution:
In many cases, the finite width of the grid, causing the folding in k-space, can be neglected. This method is, however, preferable to that which describes the boundary of the grid with a finite sum instead of the infinitely long delta comb.
- Image and diffraction pattern of a line grid
Diffraction pattern of a line grid
Resolution
The resolving power of a grating is given by the Rayleigh criterion thus
Where the order of the maximum and the number is illuminated lines.
Multiple slit
If the light through gaps with distance from one another, it is called an N -way split or multiple slit.
The main peaks can be found at the same angles as in the grid. Between two main maxima are always secondary minima and secondary maxima. Therefore, the main maxima with increasing sharply; the secondary maxima are indeed numerous, but weaker. Thus, the resolution increases.
The intensity distribution for narrow gap width is given by
In consideration of the gap width, the formula supplemented to
Manufacturer specifications
Manufacturers give for grid always offered the mechanical dimensions of, whereby the usable beam diameter is determined, as well as the lattice constant, which is, however, typically specified in " lines / mm ". For blazed gratings, the angle is indicated as well as the one wavelength for which the grating is optimized by the lattice constant and the blaze angle. In holographic gratings, however, always a whole wavelength range is specified, for which the grating is arranged.
Everyday example
CDs have track spacing to 1.6 microns, so that they are directly suitable as a grid for the visible part of the electromagnetic spectrum ( wavelengths 400-700 nm). Accordingly, one sees a clear fanned color spectrum, if you can reflect white light from a CD. DVDs have virtually the same effect as CDs.
A CD split light into individual colors / wavelengths.
A disc reflects the light beam of a laser pointer, and shows a plurality of major peaks.