This invention relates to photonic band gap materials and more particularly to 2-pattern photonic crystals that have a large, complete photonic band gap (PBG) [1, 2]. Numbers in brackets refer to the list of references included herewith. The contents of these references are incorporated herein by reference.
Two-dimensional (2D) photonic crystal devices have wide applications in slow light devices [3-5], optical chip components [6, 7], spontaneous emission control devices [8, 9], quantum information devices [10], waveguides [11-14], lasers [15-17], light emitting diodes [18-22] and optical communications [23-25]. For the above applications, the optical wave is classified to two modes according to its polarization: transverse electronic (TE) and transverse magnetic (TM). To date, one of the challenges for photonics is that there is no general method to integrate multiple optical wave control devices for different polarizations onto the same plane at the scale of the wavelength. To solve this problem, we invented a novel set of PBG structures with large, complete PBG and an approach to design on chip devices. The PBG structures, called 2-pattern photonic crystals, do not belong to any know photonic crystal category and have the largest complete PBG reported so far. They come from the superposition of two sub-photonic crystals: one contributes the TM PGB and the other contributes the TE PBG. We demonstrate the unique advantages of the 2-pattern crystals to efficiently and freely mold both TM and TE waves for polarization specific waveguides, crossed waveguide, a wavelength scale polarizer, and a high quality resonator for both polarizations. The 2-pattern photonic crystal and the associated device design are general liable and intuitive. They have the potential to be standard tools for future optical chip devices.
The 2-pattern photonic crystal with a large, complete PBG according to the invention includes a TM sub-structure having discrete dielectric features providing a large TM PBG superimposed on a TE sub-structure having expanded dielectric features providing a large TE PBG. The sub-structures may be periodic or aperiodic. In a preferred embodiment, the TM sub-structure comprises rods on a triangular lattice. In yet another embodiment, the TM sub-structure comprises an eight-fold quasicrystal of dielectric rods. The TE sub-structure may be a connected honeycomb structure or circular rings on a triangular lattice. A suitable material for the sub-structures is GaAs or silicon.
It is preferred that the sub-structures include defects suited to optical devices of particular polarizations. Because the TM/TE PBGs of the 2-pattern photonic crystals each arise from one of the two patterns, by purposely introducing defects into the sub-structures, photonic devices for different polarizations can be integrated. They can bend, split, couple, and filter TM/TE waves simultaneously on the scale of wavelength. Those devices can be used for general wave molding purposes (wave-guiding, resonator, integrated circuit, filtering, etc).
In a particularly preferred embodiment, features are removed from the TE sub-structure without modifying the TM sub-structure to create a waveguide for propagating TE waves and stopping propagation of TM waves. In another embodiment, features are removed from the TM sub-structure without modifying the TE sub-structure to create a waveguide for propagating TM waves and stopping propagation of TE waves. Integrated optical circuits, such as a wavelength-scale polarizer, a crossed waveguide, and a high-Q resonator, are also demonstrated here.
a, b, c are schematic illustrations of sub-structures having large TM PBG along with the corresponding PBG's calculations shown below the sub-structures,
d, e are schematic illustrations of sub-structures having large TE PBG along with the corresponding PBG's calculations shown below the sub-structures.
a is a schematic illustration of a 2-pattern photonic crystal made from R-p4mm plus CR-p6mm sub-structures.
b is a plot of PBG calculated via density of states (DOS) for a(TM)/a(TE)=0.559.
c is a plot of PBG calculated via DOS for a(TM)/a(TE)=0.656.
a is a schematic illustration of a 2-pattern photonic crystal made from the superposition of the R-p6mm plus HC-p6mm,
b is a plot of TE PBG and TM PBG of a 2-pattern photonic crystal for different filling ratios of the TE sub-structure.
c is PBG calculation for a TE sub-structure filling ratio of f(TE)=0.058.
d is PBG calculation for f(TE)=0.086.
e is PBG calculation for f(TE)=0.114.
a is a schematic illustration of four 2-pattern photonic crystals corresponding to different relative positions of the sub-structures.
b is PBG calculation showing the small impact on complete PBG of relative positions of the sub-structures in
a is a schematic illustration of six 2-pattern photonic crystals corresponding to different relative orientations of the sub-structures.
b is PBG calculation showing the small impact on complete PBG of relative orientation of the sub-structures in
a is a schematic illustration of a champion structure based on the R-p6mm plus HC-p6mm sub-structures with the filling ratio of the TE sub-structure: f(TE)=0.086, the filling ratio of the TM sub-structure: f(TM)=0.086, and the periodicity ratio of the TM/TE sub-structures: a(TM)/a(TE)=0.7157. The discrete Fourier transform (DFT) calculation of the 2-pattern photonic crystal and corresponding PBG calculation are shown below.
b is a schematic illustration of a 2-pattern photonic crystal from the R-p4mm plus HC-p6mm sub-structure with f(TE)=0.08, f(TM)=0.14 and a(TM)/a(TE)=0.67.
c is a schematic illustration of a 2-pattern photonic crystal from the QC-8mm plus HC-p6mm suc-structures with f(TE)=0.11 and f(TM)˜0.14.
d is a schematic illustration of a 2-pattern photonic crystal from the R-6mm plus CR-p6mm sub-structures with f(TE)=0.121, f(TM)=0.102 and a(TM)/a(TE)=0.7258.
e is a schematic illustration of a 2-pattern photonic crystal from the R-p4mm plus CR-p6mm sub-structures with f(TE)=0.108, f(TM)=0.149 and a (TM)/a(TE)=0.6563.
f is a schematic illustration of a 2-pattern photonic crystal from the QC-8mm plus CR-p6mm sub-structures with f(TE)=0.084 and f(TM)˜0.14.
a is a schematic illustration of a periodic 2-pattern photonic crystal comprising honeycomb and rods of a triangular lattice.
b is a graph illustrating the PBG calculation of the structure of
c is a graph showing the PBG properties of the 2-pattern structure as the TM sub-structure filling ratio is tuned while keeping the TE sub-structure filling ratio at 0.088.
d is a graph showing the PBG properties of the 2-pattern structure as the TE sub-structure filling ratio is tuned while keeping the TM sub-structure filling ratio at 0.089.
a is a schematic illustration of a TE waveguide.
b is a schematic illustration of a TM waveguide.
c is a graph showing optical wave transmission spectra for TE wave inside the TE waveguide.
d is a graph showing the optical wave transmission spectra for TM wave inside the TM waveguide.
e is an illustration of a TE wave of working frequency propagating inside the TE waveguide.
f is an illustration of a TM wave of working frequency propagating inside the TM waveguide.
a is a schematic illustration of a crossed waveguide in which the transverse channel allows the propagation of TM waves and the vertical channel allows the propagation of TE waves.
b is an illustration of TE wave light intensity distribution in the waveguide of
c is an illustration of TM wave light intensity distribution in the waveguide of
a is a schematic illustration of a wavelength-scale T-shape polarizer. Both TM wave and TE wave are introduced into region 3 and are separated into region 2 and region 1,
b is an illustration of TE wave light intensity distribution in the structure of
c is an illustration of TM wave light intensity distribution in the structure of
a is a schematic illustration of a resonator for both TM and TE waves.
b is a graph showing energy dissipation for the two resonance peaks. The upper lines are for TM waves and lower lines are for TE waves.
In our approach, we create a superior 2-pattern photonic crystal by combining a TM sub-structure having discrete dielectric features that provide a large TM PBG with a TE sub-structure having expanded dielectric features chosen to provide a large TE PBG. The sub-structures can be periodic or aperiodic. Our concept is based on the rationale that the TE sub-structure of the 2-pattern photonic crystal can be assumed to be a type of geometrical perturbation to the TM sub-structure and vice versa. If the TE sub-structure filling ratio is not high, the ordered geometrical perturbation does not strongly modify the TM PBG of the 2-pattern photonic crystal. Further, the small or zero TM PBG of the TE sub-structure brings trivial impact on the TM PBG of the 2-pattern photonic crystal which arises predominately from the TM sub-structure. The reverse situation holds for the TE PBG of the 2-pattern photonic crystal arising predominately from the TE sub-structure. One 2-pattern photonic crystal is comprised of two superposed patterns, while previously reported photonic crystals are based on a single pattern. The TE and TM PBGs of 2-pattern photonic crystals are much less interdependent than the PBGs of conventional photonic crystals. Importantly, by selectively creating defects in the different sub-structures, we can design photonic devices for particular polarizations (TM, TE, or both) and integrate them together.
To analyze the PBG, we calculate the normalized density of states (DOS) via finite-difference time-domain (FDTD) [26, 27]. We assign a radiating dipole near the middle of a large portion of the structure and provide a perfectly matched layer (PML) on the boundaries. Four hundred detectors are distributed near the boundary of the simulated area to collect the transmission spectra, which represents the DOS. The calculation results are tested for different radiating dipole positions and radiating sources of a group of random distributed dipoles.
In 2D, the following factors define the 2-pattern photonic crystal: the morphology, the filling ratios, and the relative scale, position and orientation of the sub-structures. The first design factor is the morphology of the sub-structures. Here it is desirable to select one structure with a large TE PBG but trivial TM PBG and another structure with a large TM PBG but trivial TE PBG. Throughout, we assume that the dielectric material is GaAs with a permittivity of 11.4. We pick three candidates for the TM PBG sub-structure: rods on a triangular lattice (R-p6mm), (see
The second design factor is the relative length scale of the two sub-structures. If we tune the scale of the TE(TM) sub-structure, the position of the TE (TM) PBG is shifted accordingly. The central frequency of the TE (TM) PBG is proportional to 1/a, here a is the characteristic scale of the sub-structure [30]. For the TM sub-structure consisting of rods, the TM gap mainly comes from Mie resonance. As we increase the scale of the sub-structure, the radius of the rods increases, which leads to a lower Mie resonance frequency and lower central gap frequency. An example is shown in
The third design factor is the individual sub-structure filling ratio. The filling ratio of each type of sub-structure controls the respective TE or TM gap but also modifies the strength of the ordered geometrical perturbation on the PBG of the other sub-structure. Therefore, altering the TE sub-structure can in general shrink the size of the TM PBG and the shrinkage will increase with the filling ratio of TE sub-structure while the reverse situation holds for varying the filling ratio of the TM sub-structure. The above effect has also been observed in a disordered system [31]. An example of the effect of filling ratio on the band gap is evident from the superposition of the R-p6mm and HC-p6mm crystals shown in
The fourth and the fifth design factors are the relative position and orientation of the sub-structures. Interestingly, it turns out these factors have essentially no influence on the PBG since the changes in the relative location of the TE pattern, as an ordered geometrical perturbation to TM pattern, should not substantially vary the TM PBG of the 2-pattern photonic crystal with the same reasoning for the behavior of the TE PBG by the presence of the TM pattern. Therefore, the relative position and orientation of the TE/TM sub-structures only bring minor impact on the complete PBG, as confirmed in
Controlling electromagnetic waves at terahertz (THz) and gigahertz (GHz) frequencies is important and fabrication of 2-pattern photonic crystals at the associated length scales (microns and mm) is easy. Experimental techniques that can be used to fabricate “2-pattern photonic crystals” for the visible and near IR frequency regimes include nanoimprint lithography [32], electron beam lithography (EBL) [33], and focused ion beam lithography (FIBL). The 2-pattern photonic crystals are reasonably tolerant to possible experimental errors, including the variations of air gaps between dielectric regions. For example, for the structure shown in
For the three selected TE sub-structures and the two TM sub-structures shown in
In the above discussion, the 2-pattern photonic crystals are aperiodic, 2-pattern photonic crystal can also be periodic with a super unit cell. Periodic 2-pattern photonic crystal consists of two sub-structures superposing on the same plane with commensurate periodicity ratio. An exemplary periodic 2-pattern photonic crystal is shown in
Because the TM/TE PBGs of the 2-pattern photonic crystals each arise from one of the two patterns, by purposely introducing defects into the sub-structures, novel types of photonic devices for different polarizations (TE, TM or both) can be readily designed. Four exemplary devices are given: polarization specific waveguides, crossed waveguide, T-shape polarizer, and a resonator for both polarizations. Two photonic crystal waveguides are shown in
The 2-pattern photonic crystal also offers a platform to integrate the polarization specific waveguides to optical circuits. For example, a crossed waveguide is shown in
By creating defects in both patterns, we can create a cavity which resonates for both TM and TE waves at the same frequency, which is shown in
In summary, a novel set of PBG structures named “2-pattern photonic crystals” consisting of two sub-structures are described here. They exhibit large, complete PBGs, and they open a wide range of future opportunities. Firstly, a rich variety of different 2-pattern photonic crystals can be developed using the large inventory of existing photonic crystals with sizeable TM or TE gaps. We anticipate that our method will become a useful tool to design photonic crystals with large, complete PBGs, which is essential for the associated photonic devices. Secondly, we demonstrate that the TE and TM PBGs of a 2-pattern photonic crystal can be tuned much more independently than conventional photonic crystals. By introducing defects into the sub-structures, photonic devices for TM/TE polarizations can be realized to achieve functionality not possible or highly challenging for conventional photonic crystal devices. Lastly, we demonstrate the intuitive, generalizable design process of several interesting optical devices. Given the diverse set of other sub-structures and various photonic crystal device designs, more integrated optical devices based on 2-pattern photonic crystals arc expected to be designed in the near future.
The contents of all of the references appended hereto are incorporated herein by reference.
This application claims priority to provisional application No. 61/512,038 filed Jul. 27, 2011, the contents of which, are incorporated herein by reference in their entirety.
This invention was made with government support under Grant No. W911NF-07-D-0004, awarded by the Army Research Office. The government has certain rights in this invention.
Number | Date | Country | |
---|---|---|---|
61512038 | Jul 2011 | US |