2D photonic crystal

The DFB grating concept was extended to higher dimensions. Two-dimensional (2D) gratings can be made in a variety of forms, from the simple overlapping of two orthogonal gratings up to concentric rings, or more complicated structures. In modern theory, they can be treated as 2D photonic crystals. 

The interest in optical properties of periodic structures, based on silicon, originates from the perspectives to use such structures as optical processing elements which can be implemented into the same chip with electronic devices. It is known that macroporous silicon with a regular pattern of deep chaimels forms two-dimensional (2D) photonic crystal (PC) [1]. Grooved silicon with the periodic "lattice" of Si ribs forms ID PC [2,3]. 

Fig. 35 Fabrication of a two-dimensional (2D) photonic crystal for sensing applications. (1, 2) PS particles self-assembled into a 2D close-packed array, (3) A hydrogel film is polymerized around the 2D array, (4) The swollen hydrogel with the embedded 2D array is peeled from the glass substrate. (5) Diffraction from the 2D array/hydrogel sandwich is monitored visually. Reproduced with permission from [112]...

A difficulty arises because the photonic crystal structures for the visible region are not easy to fabricate. However, in this chapter we describe a facile extrusion method for fabricating polymers with a ID structure like that shown in Figure 2. The nanolayered polymeric structures can consist of many thousands of layers and have a modulation in the nonlinear refractive index in the direction normal to the surface of the layers. Such materials are the nonlinear analogue of polymeric multilayer interference mirrors. (10,11,12) They are also the ID analogue of the 2D photonic crystals studied by Lin et. al. (13) The latter workers demonstrated that photonic crystals do indeed provide an effective method for converting an intensity dependent refractive index into an intensity dependent transmission. 

To fabricate 2D photonic crystal cavities, expensive e-beam lithography should be used. In addition, a bulky and complicated detection setup is required to catch the lasing signals. In spite of all the disadvantages, photonic crystal lasing units show a sub-l-nm resolution, which is required for single-molecule-level detection of analytes [15]. 

Nanoscale Optofluidic Characterization Techniques, Fig. 4 Nanoscale characterization in a 2D photonic crystal cavity, (a) Resonance mode of a 2D photonic crystal... 

A number of prototype active devices based on 2D PBG heterostructures have been designed and tested. For example, 2D photonic crystal microlasers already rival the best available microcavity lasers in size and performance. For a 2D PBG the localization of light and control of spontaneous emission from excited two-level systems is incomplete. Nevertheless, low-threshold lasing from ultracompact devices has been demonstrated (Painter et al, 1999 Imada et al., 1999). 

Astrova EV, Borovinskaya TN, Tolmachev VA, Perova TS (2004) Technique for patterning macroporous silicon and the fabrication of bars of 2D photonic crystals with vertical walls. Semiconductors 38(9) 1088-1091... 

The Ottow technique was used to fabricate 2D photonic crystal bars of macroporous Si with a precision of less than one pore lattice constant (Muller et al. 2000 see Fig. 8a). 

Another approach to fabrication of structures with vertical walls is by simultaneous electrochemical etching of pores and trenches first introduced by Geppert et al. (2006). Forming a closed contour, the trenches define the sacrificial parts of the structure, which fall out from a sample after the substrate is removed. Figure 9 shows a schematic of the method and a bar of a 2D photonic crystal, produced by removal of sacrificial parts of the sample. 

Astrova EV, Tolmachev VA, Zharova YA, Fedulova GV, Baldycheva AV, Perova TS (2010a) Silicon periodic structures and their liquid crystal composites. Solid State Phenom 156-158 547-554 Astrova EV, Fedulova GV, Guschina EV (2010b) Formation of 2D photonic crystal bars by simultaneous photoelectrochemical etching of trenches and macropores in silicon. Semiconductors 44 1617-1623... 

Zharova YA, Fedulova GV, Astrova EV, Baldycheva AV, Tolmachev VA, Perova TS (2011) Fabrication technology of heterojunctions in the lattice of a 2D photonic crystal based on macroporous silicon. Semiconductors 45 1103-1110... 

Figure 13-2. (a) Schematic illustration of a 2D photonic crystal consisting of dielectric columns arrayed in a square lattice with a lattice constant of a, and (b) a photonic band structure calculatedfor a square array of dielectric columns (with e = 8.9 for example AI2O3) with r = 0.2a (Joannopoulos, 1995). 

Figure 13-16 shows optical reflection spectra obtained for three 2D photonic crystals consisting of PLZT ceramic pillars with different values of r and , sample A... 

Figure 13-16. Reflection spectra for 2D photonic crystals consisting ofhexagonal arrays of PLZT pillars with three different r and a values (A) r = 120 nm, a = 600 nm (B) r= 100 nm, a = 700 nm and (C)r= 100 nm, a — 800 nm.

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