Study Of Fabrication Technique Of Photonic Crystals With Controlled Defects By Holographic Lithography And Two-photon Polymerization And Their Propagation Properties

The conception of photonic crystal was first proposed by E.Yablonovitch and S.John at the same time in 1987. Photonic crystals are structures made of dielectric materials with their dielectric constants verified periodically, and the periods are about the same order of magnitude as optical wavelength. Photonic crystal is also called photonic bandgap materials and electromagnetic crystals.There are two important characters of photonic crystals which made them have a huge application foreground: photonic band gap and photon localization. For example, lots of devices like Photonic crystal fibers, waveguides and photonic crystal lasers with low threshold etc, can be fabricated by inducing defects into perfect photonic crystals. My dissertation is aimed to give a systematic and comprehensive analysis in this field theoretically and experimentally, with emphases on following four respects:1. Experimental demonstration of holographic fabrication of photonic crystalsFor demonstrate the fabrication of photonic crystals experimentally, we mainly focus the research on two important parts in this section: first fabricating perfect photonic crystals for a large area without any defects in one step using holographic lithography; the second inducing defects into photonic crystals by combination of holographic lithography and two-photon polymerization.Since photonic crystals have demonstrated attractive potential applications in many areas, their fabrication has always been of great interest. Hence there are many available methods of making photonic microstructures include semiconductor microfabrication, colloidal crystallization, tightly focused laser beam scanning and two-photon polymerization etc. Holographic lithography(HL) method is one of them, which means that fabrication of 1D, 2D and 3D periodical microstructures by interference of two beams, three or four noncoplanar beams, multiple mutually coherent laser beams are made to intersect and interfere, producing period patterns of light and dark areas repeated on a scale proportional to the wavelength of the beams used. Projecting these interference patterns onto some proper optical recording materials, thus many 2- and 3-D crystalline structures can be formed by holographic lithography method. Compared with all previous methods, the technique of holographic lithography has obvious advantages such as high spatial resolutions, easiness of controlling the pattern form by adjusting wave design, one-step recording, and the ability to obtain photonic crystals with high refractive index contrast by using polymeric templates.Two-photon polymerization(TPP) method for fabrication photonic crystals means using doubled-frequency laser beams from a Ti:sapphire femto-second laser focused on the sample which made of photon polymerization materials, then moving the sample precisely point by point to form the structures as we designed with a computer controlled machine, at last the sample is developed and only polymerized areas left. This method is always used to fabricate very precise structures, but not available for massive production, since TPP is a serial pinpoint writing process that takes lots of money and times.In this work, we proposed a new method for fabricating photonic crystals with controlled defects by combination of holographic lithography (HL) and two-photon polymerization (TPP). First, the large-area photonic crystal lattice is patterned in photopolymer by holographic interference quickly and easily in one-step recording with wavelength at 532 nm, which is visible and more propitious for arranging optical setup in experiments compared with 355nm and 325nm used before. In the second step, the defects in the lattice to implement the functional devices are introduced by two-photon absorption with a femtosecond laser. Since the two-photo absorption probability depends quadratically on intensity, the polymerization of material is localized only in a small vicinity of orderλ~3 (where X is the laser wavelength) near the focus point, and thus the form of defects can be exactly controlled. Using such a process we can introduce point defects to create 3D or 2D nanocavities, or line defects to create a linear waveguide or fiber, as well as any other desired pattern in principle. Consequently this hybrid approach has an advantage in terms of fabrication time and cost compared with other methods for the patterning of large-scale photonic crystal-based integrated systems.A comprehensive study of the optical setup and the experimental processes of fabricating 1D, 2D and 3D photonic crystals using holographic lithography were given in chapter 2. And in the second part of this chapter, we discussed the preparation of the material, the optical setup and the preliminary experimental results for making photonic crystals with controlled defects by combination of HL and TPP.2. Photonic bandgap properties of holographic photonic crystalsThe most important property of photonic crystals is band gap, which means the existence of a frequency gap in the electromagnetic wave spectrum. Whether the band gaps appear or not, defended on the distribution of dielectric materials, and the contrasts between dielectric constants. Generally, the dispersion of incident waves would be much stronger as the contrasts between dielectric constants getting bigger, thus there are more chances for band gaps to appear in these situations. The shapes of photonic crystal atoms can also influence the appearance of photonic band gaps, since band gaps usually come from the boundary of Brillouin zone, theoretically complete band gaps are more likely to exist in structures with almost circular Brillouin zones (complete band gap means that electromagnetic waves in the band gap can not transmit in any direction inside the photonic crystals.). The spectrum range that could be properly controlled or manipulated is totally decided by the size of bandgap, so how to increase the bandgaps of photonic crystals by designing the lattices and sizes of photonic crystals has been of great interest..In the previous work, we have made 2D triangular photonic crystals which have photonic bandgap (PBG) for both TE and TM polarization modes, by the interference of three beams coming through a DBS(diffractive beam splitter) with symmetric umbrella geometry. In chapter 3 of this work, we made some improvement on the base of original work and proposed a double exposure multi-beam interference method to fabricate a hexagonal lattice with irregular columns.The first exposure process is made to form regular triangular photonic crystals with circular columns, and in the second exposure, three beams have the same symmetry as in the first exposure only rotated for 60°, results showing that this hexagonal lattice can yield a complete PBG as large as△ω/ω= 24.0 %.3. Propagation properties of photonic crystals-negative refraction and superlensThe dielectric constants (ε) and magnetic permeability (μ) of usual materials are both positive, so is the refractive index, and the directions of electric fields (E), magnetic fields (H), and the propagation vectors (K) follow the right handed rule. Thus Left-handed-materials (LHM) are materials with simultaneously negative dielectric permittivity (ε) and negative magnetic permeability (μ). The phase velocity of the light wave propagating inside this material is pointed in the opposite direction of the energy flow. So the Poynting vector and wave vector are antiparallel, consequently, the light is refracted negatively, and also there are many other unusual behaviors in LHM like reverse Cerenkov radiation, contrary Doppler effect etc.In 2002, left handed properties such as negative refraction and superlens were found in photonic crystals either, when the frequency of incident wave and incident angle were appropriate. So in chapter 4 we first give an elaborate introduction of the principle how left handed effects happen in photonic crystals, analyze these situations that appropriate for negative refraction and superlens effects using wave vector program, and simulate these effects appeared in photonic crystals with Finite Difference in Time Domain method (FDTD).Since holographic structures usually have irregular atoms or columns, and the light propagation properties of PhCs are closely related to their specific structures. We may expect some difference in propagation behavior between regular and holographic structures. Considering that two-dimensional (2D) holographic structures can be more easily made and have wide potential use, it is of interest and importance to extend the study of negative refraction to 2D HL structures. In the second part of this chapter, we take a 2D square structure with circular columns connected by veins as an example to investigate this effect compared with regular PCs, and the results show that left handed properties are more likely to exist in structures with high-epsilon, filling ratios or in connected lattices. For some certain frequencies, negative refraction happens with the incident angle changes in a large area, and propagation waves converge behind the photonic crystals. Sometimes a perfect imaging could appear, which means that the effective refractive index is almost -1, and we call this effect as superlens.4. Properties and Quality factors of Defect Microcavities in 2D photonic crystal slabsDefect modes would appear among the band gaps if we induce some defects into perfect photonic crystals, and electromagnetic waves with the same frequencies as defect modes can be localized in the defects strongly, thus the defect cavities which is of the order of optical wavelength have very high state densities and quality factors, and are very important for a variety of scientific and engineering applications.A comprehensive study of defect microcavities in 2D photonic crystal slabs is given in chapter 5, the band map for photonic crystal slabs with finite thickness, the eigenfrequencies of defect cavities, and quality factors (Q) are calculated with plane wave expansion method (PWM) and finite difference in time domain method (FDTD). We have also researched on the properties of defect microcavities in photonic crystals made by holographic lithography combined with our previous work.