From 80a2facfcaadc54dc904b55ca49f47c921baf6d5 Mon Sep 17 00:00:00 2001 From: Sean Anderson Date: Mon, 5 Jun 2017 20:00:15 +0200 Subject: [PATCH] updated figure paths in main readme --- README.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/README.md b/README.md index d6375d1..f37564b 100644 --- a/README.md +++ b/README.md @@ -21,7 +21,7 @@ This program has several potential applications and uses: For example, the figure below is an overview of the angular dependence of the reflected SHG Yield from the Si(111)(1x1)H surface. Experimentalists will find this very useful, as they can plan the experiment accordingly in order to optimize the output signal strength and polarization. -![An overview of the angular dependence of the SHG Yield for the Si(111)(1x1)H surface](figures/3D-Si1x1.png) +![An overview of the angular dependence of the SHG Yield for the Si(111)(1x1)H surface](example/figures/3D-Si1x1.png) References @@ -78,21 +78,21 @@ In order to calculate the SHG yield, you must first calculate the linear and non χ determines the nonlinear polarizability of a material and is responsible for second-harmonic generation. This relationship is expressed as - + where a, b, and c are crystallographic directions that depend on how you orient your crystalline structure. We can see that a material can produce a polarization response in direction a from two incident fields (E) in directions b and c, by means of χabc. χ is a third-rank tensor, and thus has 27 possible components (unique combinations of a, b, and c; for instance, aaa, aab, and so on.). Second-harmonic generation implies that the incoming fields are identical (two photons of equal energy in, one photon of double-energy out) so it is also implied that - + for this particular phenomenon. This reduces 9 of the possible combinations, reducing to 18 unique components. It is very convenient to express the crystallographic directions in terms of *x*, *y*, and *z*; therefore, we can express χ with all 18 components as - + Symmetry relations are very important for determining χ. A given crystal symmetry can greatly reduce the complexity of the problem by eliminating many of the components. For instance, for the (001) face of cubic crystals, we have that - + which has only 3 independent components. There are many [articles](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.35.1129) and [books](https://books.google.com/books?id=bdFju3af2FsC) with tables and extensive discussion that describe the form that this tensor should have for a given symmetry. @@ -101,11 +101,11 @@ which has only 3 independent components. There are many [articles](https://journ The case for χab(ω) is considerable simpler. χab(ω) is directly related to the dielectric function of the material - + which is directly related to the index of refraction as - + The χab(ω) spectra should obviously have non-zero regions; otherwise, the problem is not very interesting.