One-dimensional gratings

The thermal healing has been studied most extensively for one-dimensional gratings. Above roughening, the gratings acquire, for small amplitude to wavelength ratios, a sinusoidal form, as predicted by the classical continuum theory of Mullins and confirmed by experimenf-s and Monte Carlo simulations. - The decay of the amplitude is, asymptotically, exponential in time. This is true for both evaporation dynamics and (experimentally more relevant) surface diffusion. 

Sahaf, H., Masson, L., Leandri, C., Aufiay, B., Le Lay, G., Rond, F. (2007). Formation of a one-dimensional grating at the molecular scale by self-assembly of straight silicon nanowires. Appl. Phys. Lett. 90,263110(3). 

With the capability to fabricate replica molds from hard master molds, complex two-dimensional geometries that would be otherwise difficult to fabricate from conventional lithography techniques can be created. An example of this was described by Lucas et who were able to fabricate two-dimensional NIL molds through subsequent imprinting of a one-dimensional grating stmcture at various orientations parallel to the substrate. 

Figure 9. Cross-section of a refractive index sensor based on a quasi one-dimensional photonic crystal with grating period A = 190 nm. The top cladding over the grating is formed by a fluid contained in a cuvette that is sealed to the sensor chip.

To develop such a model, a further simplification can be made. In a reference frame attached to the grate, the process can be regarded as a one-dimensional sys-... 

All these problems can be avoided, if the writing laser beams are not switched on and off but the phase of the interference grating is modulated instead according to Eq. (9), while keeping the average intensity distribution within the laser spot constant. Under these conditions, it can be justified to employ Eq. (12) in its one-dimensional form [27,28,45] ... 

Concentration grating Due to the Ludwig-Soret effect, the temperature grating is the driving force for a secondary concentration grating, which starts to build up and is superimposed upon the thermal one. Its temporal and spatial evolution is obtained from the one-dimensional form of the extended diffusion equation... 

Chan CY, Li J, Xu JB, Ong HC (2009) The dependence of surface enhanced Raman scattering on the groove size of one-dimensional metallic gratings. MRS Spring Meeting, San Francisco... 

In order to study the optical properties of microstructures it is helpful to crmsider periodic structures (Fig. 1). Periodic surface-relief structures are called diffraction gratings in an optical context. By regularly repeating a surface-relief in one or two directions one-dimensional (ID) or two-dimensi(Mial (2D) surface-relief gratings are formed. The spacing between the repeated structures is called period A. Because of the periodic structure the incident radiation is diffracted into diffraction orders... 

Figure 3 One-dimensional spectrographs used for Raman spectroscopy. Several variations on these designs are available. FP, spectrograph exit focal plane ES, entrance slit CM, concave mirror TG, transmission diffraction grating L, multielement lens XG, convex diffraction grating CG, concave diffraction grating.

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