Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator

Abstract

We propose a simple and straightforward method to generate a spatially variant lattice structures by optical interference lithography method. Using this method, it is possible to independently vary the orientation and period of the two-dimensional lattice. The method consists of two steps which are: numerical synthesis of corresponding phase mask by employing a two-dimensional integrated gradient calculations and experimental implementation of synthesized phase mask by making use of a phase only spatial light modulator in an optical 4f Fourier filtering setup. As a working example, we provide the experimental fabrication of a spatially variant square lattice structure which has the possibility to guide a Gaussian beam through a 90° bend by photonic crystal self-collimation phenomena. The method is digitally reconfigurable, is completely scalable and could be extended to other kind of lattices as well.Photonic crystals are the ultimate structured materials with the ability to control the flow of light 1 which leads to so many applications. But perfectly periodic photonic crystals have limited functionality and it becomes essential to have more degrees of freedom in photonic crystal design to make way for more devices. More degrees of freedom could be added by spatially varying some of the properties of photonic crystal i.e. lattice orientation, lattice spacing and fill-factor 2-4 etc. A single step, low cost, large area fabrication of periodic (or quasi periodic) photonic crystal structures is possible by the method of interference lithography 5,6 and few recent advances with phase only spatial light modulator (SLM) assisted interference lithography has enabled the fabrication of some unconventional photonic crystal structures. These structures include embedding of defect sites 7-9 , creation of line defects 10 , dual lattice structures 11 and gradient structures 12,13 .

Spatial light modulator based holographic fabrication of 3D spatially varying photonic crystal templates

“…In Ref. 42, the calculated phase function was used with a SLM to generate a 2D spatially variant wave field. We further expand on this method by introducing spatially variant defect structures within a uniform lattice.…”

“…40 and used in Ref. 42. By utilizing these different approaches to engineer the phase pattern displayed on the SLM, a greater variety of photonic structures can be produced.…”

“…41 This method was also very recently used with a SLM to holographically produce a spatially variant 2D photonic crystal with a 90° bend. 42 In this paper, we describe the results of three different methods of fabricating spatially varying photonic crystal templates. The first incorporates a simple angularly varying phase into the 0th order diffraction to produce an angularly graded photonic crystal template.…”

Registering functional defects into periodic holographic structures

“…The index of refraction in holographic structures can be achieved by the local filling fraction of the dielectric material in the structure [13,17]. As an alternative approach to the coordinate transformation method in transformation optics, a synthesis algorithm method [14,18,19] has been used to generate spatially variant lattices. An example of a variant lattice was designed and used to flow a light beam around a 90 deg bend [14,18,19].…”

“…As an alternative approach to the coordinate transformation method in transformation optics, a synthesis algorithm method [14,18,19] has been used to generate spatially variant lattices. An example of a variant lattice was designed and used to flow a light beam around a 90 deg bend [14,18,19]. But the designed variant lattices have not yet been registered into a periodic lattice [14,18,19].…”