Patent Application
20110194120
The present invention relates to the field of phase measurement, particularly optical phase measurement.
In one form, the invention relates to a method of measuring the phase between distinct signals by converting phase variations between the signals into amplitude variations.
In another form, the invention relates to a photonic crystal for converting phase variations between distinct signals into amplitude variations and devices incorporating said photonic crystal.
In one particular aspect the present invention is suitable for use as a photonic crystal phase detector in optical communications, optical measurement and optical sensing.
It will be convenient to hereinafter describe the invention in relation to optical communications and the use of optical phase detectors, however it should be appreciated that the present invention is not so limited and has a wide range of application to many fields and many different devices. Furthermore, while the invention is described with particular reference to the use of gallium arsenide (GaAs) photonic crystals, the invention is not so limited and can be used in relation to a wide range of dielectric materials.
It is to be appreciated that any discussion of documents, devices, acts or knowledge in this specification is included to explain the context of the present invention. Further, the discussion throughout this specification comes about due to the realisation of the inventor and/or the identification of certain related art problems by the inventor. Moreover, any discussion of material such as documents, devices, acts or knowledge in this specification is included to explain the context of the invention in terms of the inventor's knowledge and experience and, accordingly, any such discussion should not be taken as an admission that any of the material forms part of the prior art base or the common general knowledge in the relevant art in Australia, or elsewhere, on or before the priority date of the disclosure and claims herein.
A phase detector generates a voltage signal that represents the difference in phase between two signal inputs. Detection of phase differences is used in many applications including motor control, radar systems, telecommunications systems, servo mechanisms and demodulators.
Phase detectors are typically either electronic or optical. Optical phase detectors are basically interferometers—devices that diagnose the properties of two or more lasers or waves by studying the pattern of interference created when they are superimposed. For pulsed (amplitude modulated) light, it can be used to measure the phase between carriers. It is also possible to measure the delay between the envelopes of two short optical pulses by means of cross correlation in a nonlinear crystal. And it is possible to measure the phase between the envelope and the carrier of an optical pulse, by sending a pulse into a nonlinear crystal. There the spectrum gets wider and at the edges the shape depends significantly on the phase.
Development of the Technology
Optical phase detectors are used in a wide range of applications that rely on optical signals and the phase information for detection or encryption such as communication, measurement or sensing systems.
The development of optical phase detector technology can be conveniently described using optical fibre communication as an example. The first optical fibre communication systems used on-off shift-keying modulation techniques. At the transmission end, the current of the light source (initially an incoherent light source such as a light emitting diode and later on laser diodes) was directly modulated, generating streams of optical pulses that were transmitted through optical fibres.
Improvements in the coherence of laser diodes allowed the generation of light with much more stability: single frequency, high power and stable phase optical beams could now be generated. This opened up the possibility of modulating the phase of the optical carrier and to transmit information by using modulation schemes such as differential phase shift keying and phase shift keying.
In order to recover the information contained in the phase of the carrier, there is a need to employ phase detectors in the receiver end. Typical phase detectors convert variations in phase of a given waveform into variations in amplitude. Variations in amplitude can be detected much more easily.
In recent years, techniques such as on-off shift keying modulation of the optical carrier has been replaced by advanced modulation techniques such as differential phase shift keying (DPSK) and orthogonal frequency division multiplexing (OFDM). DPSK data format is particularly favoured because of its improved receiver sensitivity and higher tolerance to fiber nonlinearities. These advanced modulation techniques in modern optical communication systems are dependent on accurate phase detection of optical signals. At present, phase detection in these systems is performed using a combination of a number of pieces of equipment.
Typical phase detectors that are currently in use include those based on Mach Zehnder or Michelson interferometers. Basically, the incoming modulated light is split into two arms of the interferometers. In case of DPSK, the signal in one of the arms is delayed and recombined with the signal in the other arm, converting variations in phase into variations in amplitude.
Another type of phase detector currently in use is based upon micro-ring resonators. It is a variation of the Mach Zehnder interferometer and converts variations in phase into variations in amplitude. However, the carrier frequency is also shifted in this approach.
A very recently developed phase detector utilises dark and bright states. In this new approach, light is split into two arms and delayed in one of the arms. The light from both arms are coupled into an array of resonators, exciting their dark and bright states.
U.S. Pat. No. 6,147,755 relates to a dynamic optical phase state detector and method for using optical interference with an optical frequency shifter (by radio frequency (RF) modulation technique) that changes frequency up or down by an amount corresponding to the modulation frequency. Specifically, the method includes splitting the signal using a 3 dB splitter which feeds into two beams. One beam is applied to a photonic structure which changes the phase of that beam. The beams are then combined using a phase interference method (i.e. two beams are allowed to interfere with each other and combine into a single beam). An optical beat frequency is generated which corresponds to the frequency of the RF modulator. The phase of the detected beat frequency relative to the original RF modulation signal contains the phase information created by the photonic device. The RF beat frequency and the RF modulation signal is converted to digital waveforms that are digitally divided by an equal number such that the resultant outputs are square waves. The divided waves are applied to an exclusion device or gate that produces a pulse wave with the period correspond to the phase difference of the original RF frequencies.
This method has the disadvantage of requiring a large number of components and pieces of equipment such as 3 dB splitters, photonic structures, interferometers, frequency generators, signal converters and logic gates which makes the final set up bulky. Furthermore all the supporting equipment needs external power.
U.S. Pat. No. 5,392,116 relates to phase interference measurement using profile heights and displacements in the nanometer range. The optical measurements are made using the phase differences generated due to the height differences or displacements. In use, the detector initially uses a beam splitter to split differently polarized light beams into several beams. These beams are passed through a lens to provide laterally displaced parallel light beams which impinge on light sensors. A phase shifter and a polarizer are placed between the lens and sensors. The phase shifter shifts the phase of the beams depending on the position and polarization and the polarizer causes a change in the intensity of the beam. Differences in intensity measured by the sensor are related to the phase difference between the beams and these differences are then converted to the height or displacement measurement.
U.S. Pat. No. 6,891,149 and International patent application WO 00/17613 disclose phase detectors comprising a voltage-tunable electro-optic phase modulator, optical waveguide on an integrated optic substrate, polarization modulator and photodetectors. The device combines two optical signals using a coupler. The two outputs are converted into two corresponding electrical signals. The two electric signals are combined to generate a signal which corresponds to the relative phase difference between the combined optical inputs.
One of the disadvantages of this invention, and many other modern optical phase detectors is that most of the components used are electrically driven and therefore need external power.
Another disadvantage of many modern optical phase detectors is their lack of compactness. Integrated optical devices and systems are essential for harnessing the full potential of photonics including transmission and manipulation of data at very high speeds. In order to fabricate these integrated optical devices, light must be confined in very, very small regions by either using total internal reflection or periodic bandgap effect. The current size of optical phase detectors is adequate for the communications industry, but not sufficiently small for a range of industries including computing, defence and biology. Furthermore, current optical phase detectors are too large to be used in computer chip-scale applications.
An object of at least one embodiment of the present invention is to provide a more compact device, such as a phase detector that enables the range of applications for the device to be extended, optimally from the communications sphere to the computing, defence, food science and biology spheres.
A further object of at least one embodiment of the present invention is to provide a device such as a phase detector that can be applied across the electromagnetic spectrum including optical and microwave applications, radio-frequency identification (RFID) and microwave signal modulation and demodulation.
A further object of at least one embodiment of the present invention is to alleviate at least one disadvantage associated with the related art.
It is an object of the embodiments described herein to overcome or alleviate at least one of the above noted drawbacks of related art systems or to at least provide a useful alternative to related art systems.
It is known that it is possible to create dark and bright states in photonic crystal micro-cavity arrays, the creation of these states depended upon the relative phase between the sources. It has now been found that these arrays can be modified for use as phase detectors to enable detection of the relative phase between two optical signals.
In a first aspect of embodiments described herein there is provided a method of arranging the structure of a crystal to measure the phase between signals, comprising the steps of (i) providing a respective waveguide for each signal and (ii) providing a micro-cavity array arranged to provide a resonance output in response to the phase of the signals.
In a second aspect of embodiments described herein there is provided a method of arranging the structure of a crystal to measure the phase between a pair of signals comprising the steps of;
In a third aspect of embodiments described herein there is provided a method of, and crystal adapted for, measuring the phase between two or more signals, comprising the steps of passing the signals through at least two respective waveguides and at least one micro-cavity array in a crystal structure and measuring the resonance output in response to the phase of the signals.
In a fourth aspect of embodiments described herein there is provided a method of, and crystal adapted for, measuring the phase between two signals, comprising the step of passing each signal through respective input waveguides, a micro-cavity array and an output waveguide, the amplitude of the power passing through the output waveguide being dependent on the relative phase difference between the signals.
Preferably the crystal is a photonic crystal. Where used herein the term ‘photonic crystal’ refers to structures in which the index of refraction is periodic, the periodicity of the structure typically being in the order of the wavelength of the incoming signal. Typically a photonic crystal consists of transparent materials having a different refractive indexes. Micro-cavities are formed by point defects, and waveguides are formed by line defects in the photonic crystal structure.
The present invention is based on passing a single signal through each input waveguide. Input characteristics of a pair of signals pass to the micro-cavity where ‘whispering gallery like modes’ are created if the input waveguides have the same, or very similar frequencies.
The crystal structures suitable for use in the invention are preferably designed to operate on a single frequency with a narrow bandwidth. All other frequencies are suppressed or will decay exponentially in these structures.
Therefore existence of other frequencies, outside the designed bandwidth is not supported. Hence all frequencies not in the designed bandwidth will be suppressed (and will decay exponentially). Noise in optical signals has a low amplitude distribution over a wide frequency range. Therefore optical noise components that are not in the designed bandwidth will be suppressed. This leads to an enhanced signal-to-noise ratio (SNR) in the system. In optical communication systems, this will reduce the bit error ratio (BER) thus enhancing the signal quality.
The structure of the crystal of the present invention may be designed and scaled to operate at the desired frequency with a desired material combination. In particular, the scaling properties inherent in Maxwell's equation may be applied to photonic crystal design.
Typically when the crystal of the present invention is two-dimensional, the structure will have two input waveguides, a single micro-cavity and a single output waveguide. However when the crystal is three-dimensional, the structure may have several pairs of waveguides, each pair having a respective microcavity and an output waveguide.
In a fifth aspect of embodiments described herein there is provided a method of arranging a crystal comprising at least one waveguide and a micro-cavity array, including the step of calculating the structure of the crystal in accordance with Maxwell's equation, wherein the micro-cavity array is arranged to provide a resonance output in response to the phase of signals passed by respective waveguides.
Following from the application of Maxwell's equation fabrication of a suitable crystal structure, preferably a photonic crystal structure, can be carried out using any suitable dielectric material. In a preferred embodiment the crystal comprises elements of any one or more of Group 1 and Groups 5 to 9 of the periodic table. In a particularly preferred embodiment the crystal is fabricated from elements chosen from the group comprising Al, Ga, In, C, Si, Ge, N, P, As, Sb, O, S, Br, I. For example, the crystal may be chosen from the group comprising GaAs, InP, AlGaAs, AlGaAsP, InGaN, ZnO, LiIO3, InAs or Si. However, the person skilled in the art will appreciate that it may be desirable to avoid the selection of a dielectric having an imaginary constant in the dielectric constant, such as ZnO, LiIO3, InAs or Si.
The crystal structure may be two or three dimensional. In a preferred embodiment the crystal is a square lattice photonic crystal of dielectric material. Preferably the square lattice is designed to operate under transverse electric (TE) modes with the main magnetic field component along the y direction. The typical operating frequency is 10 to 15 Hz and the crystal may operate at any part of the electromagnetic spectrum.
For example, the crystal may consist of a GaAs core, an oxidized lower cladding, and a GaAs substrate. The oxidized and air regions confine light in the GaAs core region. The oxidised and air regions confine the signal within the GaAs core region. For example, the thickness of the GaAs core is typically 140 nm, and the oxidized layer is typically 450 nm (prior to oxidation).
Preferably the crystal is built on an epitaxially layered structure, that is, by deposition of a monocrystalline film on a monocrystalline substrate. A GaAs crystal for operation at a wavelength of 1040 may for example consist of square lattice air holes with lattice constant =317 nm and air hole radius of 120 nm. The lattice constant can be changed to suit any operating frequency (wavelength) at which the crystal may operate.
Maxwell's equation can also be adapted to provide a general formulation for the relation between the properties of the crystal material (dielectric constant or refractive index) including the gap between holes and the radius of the holes.
In a sixth aspect of embodiments described herein there is provided a method of arranging a crystal, and the crystal, comprising at least one waveguide and a micro-cavity array, including the step of calculating the structure of the crystal by applying the relationship
wherein
g(φ) describes the column orientation in the unit cell, and
be and ae are dimensions of the rods given by the major and minor axes, wherein the micro-cavity array is arranged to provide a resonance output in response to the phase of signals passed by respective waveguides.
In a seventh aspect of embodiments described herein there is provided a crystal for converting phase variations between distinct signals into amplitude variations, the photonic crystal comprising at least two input waveguides and at least one micro-cavity array,
wherein the crystal is adapted to allow, each signal to pass through respective input waveguides to a micro-cavity array,
and wherein in response to the relative phase between the signals, the micro-cavity array creates low group velocity bright or high group velocity dark states,
and wherein the excited micro-cavity array transmits power to an output waveguide, the amplitude being a function of the relative phase difference between the signals.
Typically, maximum power is transmitted to the output waveguide when the relative phase between the two signals is 180° and minimum power is transmitted to the waveguides when the signals are in-phase. Typically there is a slow change of transmitted power as a function of their relative phase (a rate of about 0.27% of the total input power for each degree change in the relative phase). Also, the phase detector will typically have phase symmetry with respect to 180°, that is, it produces the same amount of transmitted power for angles θ and θ+180°.
With respect to optical signals, coherent detection is sensitive to the phase and amplitude of a signal and it can be used to detect phase-encoded modulation formats like binary phase shift keying (BPSK), quadrature phase shift keying (QPSK) and quadrature amplitude modulation (QAM). Sensitivity is dependent on the power coupling efficiency between the input waveguides and the cavity array of the phase detector, where ‘whispering gallery like modes’ are created. Therefore the invention can be used in coherent detection in optical communication systems by further optimization to achieve a high coupling efficiency in to the cavity array.
In an eighth aspect of embodiments described herein there is a provided a signal from an output waveguide of a crystal, preferably a photonic crystal, the signal comprising amplitude variations corresponding to phase variations between distinct input signals, wherein the input signals pass through an input waveguide to a micro-cavity array, and in response to the relative phase between the signals, the micro-cavity array creates low group velocity bright or high group velocity dark states from the input signals, and the excited cavities transmit the signal to the output waveguide.
Preferably the output signal may be embodied in the form of an optical waveform or, an electrical waveform, or an electrical waveform that has been converted from the optical domain.
The embodiments of the present invention can be used as, or as part of, numerous devices for a wide range of purposes including communication, measurement, detection, sensing and imaging. Relevant devices include, but are not limited to interferometers, logic gates, chips, modulators, demodulators, phase comparators, phase recovery devices, amplifiers, repeaters, and band filters.
In an ninth aspect of embodiments described herein there is a provided an apparatus adapted to measure the phase between two signals, said apparatus including processor means adapted to operate in accordance with a predetermined instruction set, and wherein said apparatus, in conjunction with said instruction set, is adapted to perform any of the methods previously described.
Other aspects and preferred forms are disclosed in the specification and/or defined in the appended claims, forming a part of the description of the invention.
In essence, embodiments of the present invention stem from the realization that the ability to forbid the propagation of light in a certain wavelength range (periodic bandgap effect) can be used to engineer the flow of light in many different ways. Specifically, introduction of defects to these structures enable one to inject or extract light in a controlled way. Thus, by introducing defects, it is possible to create optical waveguides and cavities in micro-scale and nano-scale ranges and couple these structures to conventional optical devices.
Advantages provided by the present invention comprise the following:
As mentioned above embodiments of the present invention can potentially be applied to a wide range of new (and existing) applications including, but not limited to the following:
a. Communication, including,
b. Measuring devices, including,
c. Sensors, principally in,
For example, the present invention could be applied to the following:
Further scope of applicability of embodiments of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the disclosure herein will become apparent to those skilled in the art from this detailed description.
Further disclosure, objects, advantages and aspects of preferred and other embodiments of the present application may be better understood by those skilled in the relevant art by reference to the following description of embodiments taken in conjunction with the accompanying drawings, which are given by way of illustration only, and thus are not limitative of the disclosure herein, and in which:
In a recent article (P. Chak, J. K. S. Poon, and A. Yariv, Optical bright and dark states in side-coupled resonator structures, Opt. Letters 32, 1785-1787 (2007)) Chak and co-workers showed that it was possible to create dark and bright states in photonic crystal micro-cavity arrays. These arrays could create low group velocity bright and high group velocity dark states. The creation of these states depended upon the relative phase between the sources. It has now been found that these arrays can be used as phase detectors by modifying the multi-cavity array to enable it to detect the relative phase between two optical sources. The modification of the multi-cavity array enables detection of the relative phase between two optical sources, with potential applications to the demodulation of DPSK signals.
The system illustrated in
In order to confine light in the vertical direction, the epitaxially layered structure shown in
The photonic crystal in which the phase detector is built consists of a square lattice of air holes with lattice constant =317 nm. The air holes have a radius of 120 nm. In order to assess the performance of this phase detector, two sources were placed in the same x-position but in different input waveguides (A and B). These input waveguides transported the optical fields to the single-defect cavity array as shown in
In the dark state, the coupled resonators are not excited by the two input waveguides, while in the bright states, these coupled cavities are excited. Since the excitation of these states depend upon the relative phase of the input signals, this property is key to operation of the phase detectors.
Two small slots are provided close to the bends of the input waveguides to optimize the transmission of light through the bends. If light is not coupled into the cavities, they will continue to propagate into the bent waveguides without suffering much reflection. Moreover, it may indirectly contribute to the coupling of light into micro-cavities.
A single-defect micro-cavity in a square lattice of air holes has just a whispering gallery mode in its bandgap region. This mode has odd symmetry with respect to the x-axis, i.e., the four lobes of this mode have opposite phases with respect to the center of the cavity and to the x-axis. Hence it can be expected that if the sources are in-phase, they will not strongly excite these cavities, but if they have opposite phases, the cavities will be strongly excited and will carry power into the output waveguide (E). This is observed for the phase detector shown in
Where P180
The relative power transmitted into the output waveguide as a function of the relative phase between the sources is shown
In some situations, the power divider in
The number of cavities in the phase detector also influences its performance. For example, if there is just a single cavity in the phase detector, power can be directly coupled into the waveguide and not via the single-defect PhC micro-cavity. In this case, the extinction ratio is just 2.7 because of parasitic coupling into the waveguide.
The number of holes between distinct micro-cavities in the array (Ncav) defines the spacing and coupling strength between the different cavities. Ncav affects the quality factor (Q) of the peak around λ=1040 nm and the number of peaks in the phase detector. Q increases with the number of holes between the cavities until the point when the cavities are weakly coupled and act as nearly independent resonators, leading to a saturation of Q. This can be clearly observed in
ER is also affected by the number of holes between adjacent micro-cavities. In case of 1 hole between adjacent cavities, light can be easily coupled into the waveguide, either for a dark or a bright state, resulting in low value of ER. ER increases when the number of holes between adjacent cavities increases, reaching a maximum value for Ncav=2. When Ncav is greater than two, less power is coupled into the waveguide in the bright state, leading to lower values of ER. This can be clearly observed in
Analysis of the effects of having different number of holes between the input cavities and the first micro-cavity in the array (Ncg). Ncg determines the coupling strength into the micro-cavity array. If the coupling is strong, light will be easily coupled into the micro-cavities array, otherwise light will prefer to propagate through the bent input waveguides (C and D).
Based upon the results described above, it is apparent that the device can operate as a phase detector and can be used in DPSK demodulators.
The structure of the photonic crystal of the present invention may be designed and scaled to operate at the desired frequency with a desired material combination. In particular, the scaling properties inherent in Maxwell's equation may be applied to photonic crystal design, as has been illustrated by the prior art work of Joannopoulos et al, in Photonic Crystals: Molding the Flow of Light, 2nd edition, (2008).
As mentioned in Joannopoulos et al, with respect to electromagnetism in dielectric media, there is no fundamental length scale other than the assumption that the system is macroscopic. The spatial scale of the potential function is generally set by the fundamental length scale of the Bohr radius and means that configurations of material that differ only in their overall spatial scale can have very different physical properties. Photonic crystals do not have a fundamental constant with the dimensions of length and therefore the master equation is scale invariant. Accordingly relationships between electromagnetic problems are simple and differ only by a contraction or expansion of all distances.
For example, for an electromagnetic eigenmode H(r) of frequency ω in a dielectric configuration ∈(r) the master equation is as follows:
When the dielectric configuration is
Given that ∈(
Equation (4) is the same equation as equation (3), but with mode profile
By applying the principle described above a photonic crystal suitable for use in the present invention may be designed. For example, a photonic crystal can be designed for use in a phase detector intended to operate at a frequency of ω1. If the design parameters of the photonic crystal are r1 and a1 (where r2 is the radius of an air hole and a2 is the length between the central points of two air holes).
If a photonic crystal of the same material is required, but having a different operational wavelength, ω2, then the scaling parameter required to scale the design parameters is as follows,
ω2=Sω1 equation (5)
and the new scaled design parameters (r2, a2) will be,
r2=Sr1
a2=Sal equation (6)
The design parameters must be scaled with the constant where the frequency was scaled. By doing so the fundamental ratio (a1/r1=a2/r2) does not change.
This scaling can be performed for the structure to operate at any frequency. Accordingly it is possible to test the structure for the microwave frequency and fabricate in optical frequency or the inverse.
In addition to changing the operating frequency from ω1 to ω2, the material used for fabrication may also be changed. In doing so, the operating frequency of the original structure will be shifted by a constant that can be calculated as described in equation (2).
If a structure is operating at frequency ω1 with the dielectric constant of ∈1 and the new dielectric constant is ∈2 then the expected frequency shift can be calculated as follows,
where γ is a constant. Therefore, the new frequency, ωi (where ωi is an intermediate frequency) can be calculated from,
where k is an arbitrary constant.
Since the structure is required to operate at the frequency ω2, it is also necessary to change the structural parameters (a, r) from frequency ωi to ω2. Then,
Therefore the structural parameters must be changed such that,
r2=Γr
a2=Γa equation (10)
Using this method, first a frequency shift is calculated by introducing a new dielectric and then the frequency is shifted to the desired frequency by changing the structural parameters. By doing so, it is possible to design a new structure with new material to operate in any frequency that is required.
The fabrication of a suitable photonic crystal structure can be carried out using any dielectric material. However, the person skilled in the art will appreciate that it may be desirable to avoid the selection of a dielectric having an imaginary constant in the dielectric constant. Table 1 sets out a few examples of commonly used dielectrics with their refractive index for a single frequency close to λ=1040 nm.
The lattice constant can be changed to suit any operating frequency (wavelength) at which the crystal may operate.
For example, with reference to a GaAs crystal operating at a wavelength of 1040 with lattice constant =317 nm and air hole radius of 120 nm, lattice constants and radius of holes can be calculated for other operating wavelengths by scaling using a scaling factor of 1 (ω2/ω1=1). Exemplary values are set out in Table 2. The
/r ratio is the kept the same after scaling to the new frequency.
=
*S
* 0.3785
Prior art document Hillebrand et al, ‘Band gap studies of triangular 2D photonic crystals with varying pore roundness’, Solid State Communications, Volume 115, Issue 5, 19 Jun. 2000, pages 227-232 describes studies of photonic crystals which is background to the present invention.
The master equation (2) can be derived by solving Maxwell's equation for the magnetic field H(r). Where ω is the frequency of light and c is the speed of light.
For the analysis of the air hole distribution in the photonic crystal an analytical solution have been derived for the Fourier transformation (∈−1) for elliptical columns, ∈s the dielectric constant of the columns and ∈b is the background dielectric constant. In this formulation n is the refractive index in the material (n=√∈). The elliptical columns may show different orientations with respect to the lattice. The dimensions of the rods are given by the major and minor axes (be, ae) resulting in an eccentricity of e=ae/be. In the case of circular cylindrical air holes, as in our case, e=1 (that is, be=ae). For the objective of forming a general formulation for the relation between the material properties (dielectric constant or refractive index), the Fourier transform ∈−1 (G) for the real structure can be can be written as;
Here J1 is a Bessel function of the first kind and the factor γe is the filling factor. It related all the dimensions of the structure to the material properties.
γe=2πaebe/(a2√{square root over (3)}) equation (12)
The factor γe describes the ratio of the area of the column to the area of the total unit cell. Function g(φ) describes the orientation of the column in the unit cell.
The dispersion properties of 2D photonic crystals are basically determined by the dielectric contract, the lattice type, for example square or triangular, and the lattice filling ratio.
While this invention has been described in connection with specific embodiments thereof, it will be understood that it is capable of further modification(s). This application is intended to cover any variations uses or adaptations of the invention following in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains and as may be applied to the essential features hereinbefore set forth.
As the present invention may be embodied in several forms without departing from the spirit of the essential characteristics of the invention, it should be understood that the above described embodiments are not to limit the present invention unless otherwise specified, but rather should be construed broadly within the spirit and scope of the invention as defined in the appended claims. The described embodiments are to be considered in all respects as illustrative only and not restrictive.
Various modifications and equivalent arrangements are intended to be included within the spirit and scope of the invention and appended claims. Therefore, the specific embodiments are to be understood to be illustrative of the many ways in which the principles of the present invention may be practiced. In the following claims, means-plus-function clauses are intended to cover structures as performing the defined function and not only structural equivalents, but also equivalent structures.
It should be noted that where the terms “detector”, “optical detector” or similar terms are used herein, a communication device is described that may be used in a communication system, unless the context otherwise requires, and should not be construed to limit the present invention to any particular communication device type. Thus, a communication device may include, without limitation logic gates, sensors and band filters.
It should also be noted that where a flowchart or equivalent illustration of processes or systems is used herein to demonstrate various aspects of the invention, it should not be construed to limit the present invention to any particular logic flow or logic implementation. The described logic may be partitioned into different logic blocks without changing the overall results or otherwise departing from the true scope of the invention. Often, logic elements may be added, modified, omitted, performed in a different order, or implemented using different logic constructs without changing the overall results or otherwise departing from the true scope of the invention.
Hardware logic (comprising programmable logic for use with a programmable logic device) implementing all or part of the functionality where described herein may be designed using traditional manual methods, or may be designed, captured, simulated, or documented electronically using various tools, such as Computer Aided Design (CAD), a hardware description language (e.g., VHDL or AHDL), or a PLD programming language (e.g., PALASM, ABEL, or CUPL).
Programmable logic may be fixed either permanently or transitorily in a tangible storage medium, such as a semiconductor memory device (e.g., a RAM, ROM, PROM, EEPROM, or Flash-Programmable RAM), a magnetic memory device (e.g., a diskette or fixed disk), an optical memory device (e.g., a CD-ROM or DVD-ROM), or other memory device. The programmable logic may be fixed in a signal that is transmittable to a computer using any of various communication technologies, including, but in no way limited to, analog technologies, digital technologies, optical technologies, wireless technologies (e.g., Bluetooth), networking technologies, and internetworking technologies. The programmable logic may be distributed as a removable storage medium with accompanying printed or electronic documentation (e.g., shrink wrapped software), preloaded with a computer system (e.g., on system ROM or fixed disk), or distributed from a server or electronic bulletin board over the communication system (e.g., the Internet or World Wide Web).
‘Comprises/comprising’ and Includes/including' when used in this specification is taken to specify the presence of stated features, integers, steps or components but does not preclude the presence or addition of one or more other features, integers, steps, components or groups thereof. Thus, unless the context clearly requires otherwise, throughout the description and the claims, the words ‘comprise’, ‘comprising’, ‘includes’, ‘including’ and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”.
