![]() There are 3 and 11 diffraction orders for the transmission and the reflection, respectively. The results are consistent with those presented above. The following images show the transmitted and reflected orders at 0.85 \(\mu m\). This can be best visualized by representing each supported order as a point in the far-field semi-sphere. It is also insightful to learn about the behavior of the whole grating orders for a specific wavelength. The focus so far has been on how the number of diffraction orders, diffraction efficiencies and diffraction angles change in terms of the wavelength. As the wavelength gets shorter, its propagation direction moves towards the polar axis (z-axis in this example.)ĭiffraction efficiencies and angles at a specific wavelength This specific order starts to appear at 0.9 \(\mu m\) and propagates almost parallel to the substrate. The following plot shows the diffraction angle of the transmitted (0,1) order in terms of the wavelength. The only exception is the (0,0) order, which is fixed by the angle of the incident beam (theta=0 and phi=0 in this example). The diffraction angle of the grating is also dependent on the operating wavelength and exhibits different values for different orders. These are to do withĪnd can be noticeable at the wavelengths where the number of grating orders changes.ĭiffraction angle for a specific diffraction order vs. There appear to be some discontinuities near 0.9 \(\mu m\). The differences between the T_Total and the T(0,0) can be attributed to the transmission into higher diffraction orders since there is no absorption in the material used.įor the reflection, the transmission to (0,0) order is negligible over the whole wavelength range, meaning most of the reflected power is converted to a higher order. This is because the grating supports only a single transmission order at this wavelength range as shown in the previous plot. The transmission to (0,0) order, T(0,0), is the same as the total transmission for wavelengths over 0.9 \(\mu m\). It can be observed from the following plot that In many cases, it might be necessary to calculate how much of the transmitted/reflected power is converted into a specific diffraction order: This is consistent with the above observation.īoth the transmission and reflection show abrupt changes in the number of grating orders at 0.9 um, below which new grating orders start to appear.įractional power into a specific diffraction order vs. This is because the index of the substrate (1.45) is larger than that of the air, meaning a shorter effective wavelength in the substrate. The reflection shows larger number grating order than the transmission. The grating supports a larger number of diffraction orders at a shorter wavelength. The following plot shows the number of transmitted/reflected orders the grating supports in terms of the wavelength. Instructions for running the model and discussion of key results The above results are returned as a function of wavelength and can be directly used in your grating design or further processed to yield the figure of merit of your interest. Grating efficiency for each grating orderĭirection cosine of each grating order (Equivalently, theta and phi values in the far-field half-sphere) Returns a comprehensive list of results necessary for general characterization of grating: A broadband (0.85-1 \(\mu m\)) planewave is normally incident on the surface grating from the substrate, resulting in multiple diffraction orders in the transmission and the reflection regions. The diffraction grating in this example is a 2D array of half-ellipsoids on a planar surface. Understand the simulation workflow and key results Lumerical provides a set of grating scripts for the DGTD solver, making it easy to calculate common results such as the number of grating orders, diffraction angles and grating efficiencies at different wavelengths. Characterize a diffraction grating in response to a broadband planewave at normal incidence. ![]()
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