{"title":"2D Gauss Diffraction Gratings","authors":"D. S. Citrin","doi":"10.1002/andp.202400187","DOIUrl":null,"url":null,"abstract":"<p>2D diffraction gratings based on Gauss lattices are a class of nonperiodic lattice in which the sites are located at <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>R</mi>\n <mrow>\n <msub>\n <mi>j</mi>\n <mn>1</mn>\n </msub>\n <mo>,</mo>\n <msub>\n <mi>j</mi>\n <mn>2</mn>\n </msub>\n </mrow>\n </msub>\n <mo>=</mo>\n <msubsup>\n <mi>j</mi>\n <mn>1</mn>\n <mi>n</mi>\n </msubsup>\n <mi>d</mi>\n <mover>\n <mi>x</mi>\n <mo>̂</mo>\n </mover>\n <mo>+</mo>\n <msubsup>\n <mi>j</mi>\n <mn>2</mn>\n <mi>n</mi>\n </msubsup>\n <mi>d</mi>\n <mover>\n <mi>y</mi>\n <mo>̂</mo>\n </mover>\n </mrow>\n <annotation>${\\bf R}_{j_1,j_2}=j_1^nd\\hat{\\bf x} + j_2^nd\\hat{\\bf y}$</annotation>\n </semantics></math> with <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>j</mi>\n <mn>1</mn>\n </msub>\n <mo>,</mo>\n <msub>\n <mi>j</mi>\n <mn>2</mn>\n </msub>\n <mspace></mspace>\n <mo>∈</mo>\n <mspace></mspace>\n <mrow>\n <mo>{</mo>\n <mtext>…</mtext>\n <mo>,</mo>\n <mo>−</mo>\n <mn>1</mn>\n <mo>,</mo>\n <mn>0</mn>\n <mo>,</mo>\n <mn>1</mn>\n <mo>,</mo>\n <mtext>…</mtext>\n <mo>}</mo>\n </mrow>\n </mrow>\n <annotation>$j_1,j_2\\!\\in \\! \\lbrace \\ldots, -1,0,1,\\ldots \\rbrace$</annotation>\n </semantics></math>, <span></span><math>\n <semantics>\n <mrow>\n <mi>n</mi>\n <mspace></mspace>\n <mo>∈</mo>\n <mspace></mspace>\n <mo>{</mo>\n <mn>2</mn>\n <mo>,</mo>\n <mn>3</mn>\n <mo>,</mo>\n <mn>4</mn>\n <mo>,</mo>\n <mtext>…</mtext>\n <mo>}</mo>\n </mrow>\n <annotation>$n\\! \\in \\! \\lbrace 2,3,4, \\ldots \\rbrace$</annotation>\n </semantics></math>, <span></span><math>\n <semantics>\n <mrow>\n <mi>d</mi>\n <mover>\n <mi>x</mi>\n <mo>̂</mo>\n </mover>\n </mrow>\n <annotation>$d\\hat{\\bf x}$</annotation>\n </semantics></math> and <span></span><math>\n <semantics>\n <mrow>\n <mi>d</mi>\n <mover>\n <mi>y</mi>\n <mo>̂</mo>\n </mover>\n </mrow>\n <annotation>$d\\hat{\\bf y}$</annotation>\n </semantics></math> orthogonal primitive vectors in the plane, and <span></span><math>\n <semantics>\n <mi>d</mi>\n <annotation>$d$</annotation>\n </semantics></math> the lattice constant. Gauss lattices are treated for various orders <span></span><math>\n <semantics>\n <mi>n</mi>\n <annotation>$n$</annotation>\n </semantics></math>, and discuss applications for gratings separable in the <span></span><math>\n <semantics>\n <mi>x</mi>\n <annotation>$x$</annotation>\n </semantics></math> and <span></span><math>\n <semantics>\n <mi>y</mi>\n <annotation>$y$</annotation>\n </semantics></math> directions. These gratings, while geometrically very simple, produce complex pseudorandom diffraction patterns, though they exhibit rotational invariance and strong correlations along the <span></span><math>\n <semantics>\n <mi>x</mi>\n <annotation>$x$</annotation>\n </semantics></math> and <span></span><math>\n <semantics>\n <mi>y</mi>\n <annotation>$y$</annotation>\n </semantics></math> directions. Then how to generalize the approach is discussed to attain nonseparable gratings where such features are suppressed. The result is an intensity distribution like that of diffuse light, the effect originating in the breaking of the hidden translational invariance of the Gauss lattice.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 11","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.202400187","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annalen der Physik","FirstCategoryId":"101","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/andp.202400187","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
2D diffraction gratings based on Gauss lattices are a class of nonperiodic lattice in which the sites are located at with , , and orthogonal primitive vectors in the plane, and the lattice constant. Gauss lattices are treated for various orders , and discuss applications for gratings separable in the and directions. These gratings, while geometrically very simple, produce complex pseudorandom diffraction patterns, though they exhibit rotational invariance and strong correlations along the and directions. Then how to generalize the approach is discussed to attain nonseparable gratings where such features are suppressed. The result is an intensity distribution like that of diffuse light, the effect originating in the breaking of the hidden translational invariance of the Gauss lattice.
期刊介绍：
Annalen der Physik (AdP) is one of the world''s most renowned physics journals with an over 225 years'' tradition of excellence. Based on the fame of seminal papers by Einstein, Planck and many others, the journal is now tuned towards today''s most exciting findings including the annual Nobel Lectures. AdP comprises all areas of physics, with particular emphasis on important, significant and highly relevant results. Topics range from fundamental research to forefront applications including dynamic and interdisciplinary fields. The journal covers theory, simulation and experiment, e.g., but not exclusively, in condensed matter, quantum physics, photonics, materials physics, high energy, gravitation and astrophysics. It welcomes Rapid Research Letters, Original Papers, Review and Feature Articles.
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