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PubMed1999

Radial dose distribution, dose to water and dose rate constant for monoenergetic photon point sources from 10 keV to 2 MeV:EGS4 Monte Carlo model calculation.

A comprehensive set of dose distributions from monoenergetic photon-emitting isotropic point sources in a medium can be used as a reference database for the dosimetry of photon emitter sources in that medium. Data of this type for water over the photon energy range from 15 keV to 2 MeV have been published based on calculations using a one-dimensional photon transport model. The present work, based on a previously published EGS4 Monte Carlo code, updates the classic data set of Berger and provides more extensive calculations than previously available. Air kerma strength per unit photon emission rate from an isotropic point emitter is obtained as a function of energy using published data for mass energy absorption coefficients. The TG-43 dose rate constant for water as a function of energy is calculated for monoenergetic photon emitters as the ratio of dose rate to water at 1 cm to air kerma strength for unit photon emission rate. Results for the radial dose distribution agree well with the data of Berger between 40 and 400 keV. For energies > or =500 keV, a previously undescribed buildup region for the radial dose function is identified. Thickness of the buildup region ranges from 1 mm at 500 keV to 8 mm at 2 MeV. Between 15 and 30 keV, the radial dose function within a few millimeters of the emitter is calculated to be 4%-5% higher than values derived from Berger's data. The maximum dose rate constant for monoenergetic photon emitters occurs at an energy of 60 keV, and has the value 1.355 cGy h(-1)U(-1), where U is the unit of air kerma strength, 1 microGy m2 h(-1). This would correspond to the maximum hypothetical dose rate constant for a brachytherapy photon source emitting photons of energy < or =2 MeV.

Dose-Response Relationship, Radiation↗
PubMed1995

Monte Carlo study of electron spectra and dose from backscattered radiation in the vicinity of media interfaces for monoenergetic photons of 50-1250 keV.

In the present paper electron fluence spectra and backscatter dose factors for monoenergetic photons (50, 100, 250 and 1250 keV) are presented. The influence of the atomic number of the backscatter materials glass, bone, steel and titanium is studied. For all radiations increases in dose were found in the immediate vicinity of the interface in a region extending over a distance determined by the photon energy. In a thin layer extending several tens of micrometers from the interface, a large increase in dose was found for 50 and 100 keV photons. The largest backscatter dose factor (3.5) was found for 50 keV photons and a steel interface. This large effect was found to be due largely to backscattered photoelectrons. K-shell fluorescent photons from titanium and steel were also included but were found to have almost no effect on backscatter dose factors or electron spectra. With both K-shell fluorescence and sampling of the photoelectron angular distribution switched off, much smaller backscatter factors were obtained. Beyond the thin region near the interface where the dose is increased, significant dose depressions were found for photons of these energies in a region extending several centimeters from the interface. The effect was maximum for 50 keV photons, for which dose depressions of about 35% for steel and titanium and 15% for glass and bone were obtained. For 250 and 1250 keV photons a more modest dose enhancement was found close to the interface (40-50%) but extending over a larger region (e.g. 5 mm for 1250 keV photons). Small differences in radiation quality nearer to the interface were found as expressed by track-averaged and dose-averaged restricted linear energy transfer, LET100,T and LET100,D, with a maximum effect for the 100 keV photons. For this radiation quality a decrease of 50% in LET100,T was found close to the interface.

Dose-Response Relationship, Radiation↗
PubMed1993

Artificial sunlight irradiation induces ultraweak photon emission in human skin fibroblasts.

Photons participate in many atomic and molecular interactions and changes in the physical universe. In recent years sophisticated detection procedures for the measurement of ultraweak photons in a variety of different cells have been performed leading to the conclusion that plant, animal and human cells emit ultraweak photons. Using an extremely low-noise, high-sensitive photon-counting system, which allows maximal exploitation of the potential capabilities of a photomultiplier tube, ultraweak photons were quantitated in human skin fibroblasts. It was found that light from an artificial sunlight source induces ultraweak photon emission in these cells. However, the results demonstrate that this induction is significantly lower in normal fibroblasts compared with those obtained from a donor suffering from xeroderma pigmentosum disease group A, a disease characterized by deficient repair of DNA. The largest increase in ultraweak photon emission after UV exposure was measured in mitomycin-C-induced post-mitotic xeroderma pigmentosum cells which showed 10-20 times higher ultraweak photon intensities than mitotic UV-irradiated normal cells. These data suggest that xeroderma pigmentosum cells tend to lose the capacity of efficient storage of ultraweak photons, indicating the existence of an efficient intracellular photon trapping system within human cells.

Cell Line↗
PubMed2005

Photon blockade in an optical cavity with one trapped atom.

At low temperatures, sufficiently small metallic and semiconductor devices exhibit the 'Coulomb blockade' effect, in which charge transport through the device occurs on an electron-by-electron basis. For example, a single electron on a metallic island can block the flow of another electron if the charging energy of the island greatly exceeds the thermal energy. The analogous effect of 'photon blockade' has been proposed for the transport of light through an optical system; this involves photon-photon interactions in a nonlinear optical cavity. Here we report observations of photon blockade for the light transmitted by an optical cavity containing one trapped atom, in the regime of strong atom-cavity coupling. Excitation of the atom-cavity system by a first photon blocks the transmission of a second photon, thereby converting an incident poissonian stream of photons into a sub-poissonian, anti-bunched stream. This is confirmed by measurements of the photon statistics of the transmitted field. Our observations of photon blockade represent an advance over traditional nonlinear optics and laser physics, into a regime with dynamical processes involving atoms and photons taken one-by-one.

Journal Article↗
PubMed2001

On the quantum physical relation between photon tunnelling and near-field optics.

The standard theory of optical tunnelling based on a mathematical analogy between the time-independent one-particle Schrödinger equation describing electron tunnelling and the Helmholtz equation for the macroscopic electric field is criticized. In a classical perspective photons are related to the dynamics of the transverse part of the electromagnetic field, and with the assumption that the electrons in a coupled photon-atom system are driven in a linear fashion by the field, a rigorous integro-differential equation for the transverse field is established. In the near-field zone of matter a transverse self-field exists and this may cause the appearance of superluminality in optical tunnelling. In the wake of a brief review of the space-time dynamics of free photons, a first-quantized description of the birth process of a single polychromatic photon in the near-field region of an active atom (molecule, mesoscopic particle) is presented, and afterwards the link between photon localizability, Einstein causality and near-field photon tunnelling is discussed. On the basis of a new one-photon quantum theory of near-field scattering from a microscopic (or mesoscopic) object, it is shown that photon tunnelling always appears in photon-atom scattering. A first-order Born approximation cannot capture the phenomenon, however. The emergence of the energy wave function of the scattered photon is followed in space and time.

Journal Article↗
PubMed2005

A feasibility study of Dynamic Phantom scanner for quality assurance of photon beam profiles at various gantry angles.

The effect of gantry rotation on beam profiles of photon and electron beams is an important issue in quality assurance for radiotherapy. To address variations in the profiles of photon and electron beams at different gantry angles, a Dynamic Phantom scanner composed of a 20 x 12 x 6 cm3 scanning Lucite block was designed as a cross-beam-profile scanner. To our knowledge, differences between scanned profiles acquired at different gantry angles with a small size Lucite block and those acquired a full-size (60 x 60 x 50 cm3) water phantom have not been previously investigated. We therefore performed a feasibility study for a first prototype Dynamic Phantom scanner without a gantry attachment mount. Radiation beams from a Varian LINAC 21EX and 2100C were used. Photon beams (6 MV and 18 MV) were shaped by either collimator jaws or a Varian 120 Multileaf (MLC) collimator, and electron beams (6 MeV, 12 MeV, and 20 MeV) were shaped by a treatment cone. To investigate the effect on profiles by using a Lucite block, a quantitative comparison of scanned profiles with the Dynamic Phantom and a full-size water phantom was first performed at a 0 degrees gantry angle for both photon and electron beams. For photon beam profiles defined by jaws at 1.0 cm and 5.0 cm depths of Lucite (i.e., at 1.1 cm and 5.7 cm depth of water), a good agreement (less than 1% variation) inside the field edge was observed between profiles scanned with the Dynamic Phantom and with a water phantom. The use of Lucite in the Dynamic Phantom resulted in reduced penumbra width (about 0.5 mm out of 5 mm to 8mm) and reduced (1% to 2%) scatter dose beyond the field edges for both 6 MV and 18 MV beams, compared with the water phantom scanner. For profiles of the MLC-shaped 6 MV photon beam, a similar agreement was observed. For profiles of electron beams scanned at 2.9 cm depth of Lucite (i.e., at 3.3 cm depth of water), larger disagreements in profiles (3% to 4%) and penumbra width (3 mm to 4 mm out of 12 mm) were observed. Additional profiles with the gantry at 90 degrees and 270 degrees were performed for both MLC- and jaw-shaped photon beams and electron beams to evaluate the effect of gantry rotation. General good agreement is seen (less than 1 % variation) at all field sizes for collimator-shaped 6 MV and 18 MV photon beams. Similar variations observed for MLC-shaped photon beams indicate that the uncertainty in MLC position is similar to that for the collimator jaws. We conclude that the Dynamic Phantom scanner is a useful device for the routine quality assurance on beam profiles of photon beams and for constancy check on electron beams at various gantry angles. Caution should be taken when using this device to acquire basic electron dosimetry data.

Equipment Design↗
PubMed2004

Live cell ultraviolet microscopy: a comparison between two- and three-photon excitation.

We compare conventional infrared laser based three-photon excitation with a visible laser based two-photon excitation scheme for imaging the ultraviolet fluorophore serotonin in solution and in live cells. To obtain a signal level of 1000 photons per second per mM serotonin solution, we need a back aperture power of 5 mW at 550 nm (for two-photon excitation) and 33 mW at 740 nm (for three-photon excitation). The detectivity of serotonin (defined as the concentration of serotonin that yields a signal equivalent to three times the standard deviation of the signal obtained from the buffer alone) is 12 microM for two-photon, and 220 microM for three-photon excitation. Surprisingly, for live cell imaging of vesicular serotonin in serotonergic cells, three-photon excitation appears to provide better image contrast than two-photon excitation. The origin of this is traced to the concentration-dependent shift of the serotonin emission spectrum.

Animals↗
PubMed2006

Probing nucleocytoplasmic transport by two-photon activation of PA-GFP.

Two-photon activation of photoactivatable green fluorescent protein (PA-GFP) provides a unique tool for probing cellular transport processes, because activation is strictly limited to the sub-femtoliter optical volume of the two-photon spot. We demonstrate two-photon activation of PA-GFP immobilized in a gel and freely diffusing within cells and recover a quadratic power dependence. Illumination at 820 nm allows simultaneous activation and fluorescence monitoring by two-photon excitation. Alternatively, we activate PA-GFP using two-photon excitation and monitor the fluorescence of the photoconverted product with one-photon excitation. We probe nucleocytoplasmic transport through the nuclear pore complex of COS-1 cells, by observing the time-dependent fluorescence at various locations within the cell after two-photon activation of PA-GFP in the nucleus and in the cytoplasm. Two-photon activation of a tandem construct of two PA-GFPs showed a markedly slower rate of crossing through the nuclear pore. Analysis based on a restricted diffusion model yields a nuclear pore radius of 4.5 nm, which is in good agreement with previously reported values. This application demonstrates the attractive features of two-photon photoactivation over traditional techniques, such as photobleaching, for studying transport processes in cells.

Active Transport, Cell Nucleus↗
PubMed1997

Hyper-Rayleigh and hyper-Raman scattering background of liquid water in two-photon excited fluorescence detection.

The detection of two-photon excited fluorescence is practically free from background caused by linear scattering because two-photon excited fluorescence occurs at a much shorter wavelength region than the excitation light. This property can be used to achieve ultrasensitive fluorescence detection. However, similar to linear scattering in the detection of one-photon excited fluorescence, the question arises whether background caused by non-linear scattering may limit the detection sensitivity of two-photon excited fluorescence. In this work, quantitative comparisons between two-photon induced scattering of liquid water and two-photon excited dye fluorescence in a standard epifluorescence geometry show that the relative scattering background is typically reduced by orders of magnitude in two-photon excitation as compared to single-photon excitation with confocal detection. Hyper-Rayleigh and hyper-Raman (3400 cm-1) cross sections of liquid water have been measured to be 8 x 10(-62) and 7 x 10(-63) cm4.s/photon, respectively, at 840 nm incident wavelength, with absolute values calibrated with respect to the known two-photon fluorescence excitation cross section of fluorescein.

Fluorescence↗
PubMed2006

Two-photon vibrational spectroscopy for biosciences based on surface-enhanced hyper-Raman scattering.

Two-photon excitation is gaining rapidly in interest and significance in spectroscopy and microscopy. Here we introduce a new approach that suggests versatile optical labels suitable for both one- and two-photon excitation and also two-photon-excited ultrasensitive, nondestructive chemical probing. The underlying spectroscopic effect is the incoherent inelastic scattering of two photons on the vibrational quantum states called hyper-Raman scattering (HRS). The rather weak effect can be strengthened greatly if HRS takes place in the local optical fields of gold and silver nanostructures. This so-called surface-enhanced HRS (SEHRS) is the two-photon analogue to surface-enhanced Raman scattering (SERS). SEHRS provides structurally sensitive vibrational information complementary to those obtained by SERS. SEHRS combines the advantages of two-photon spectroscopy with the structural information of vibrational spectroscopy and the high-sensitivity and nanometer-scale local confinement of plasmonics-based spectroscopy. We infer effective two-photon cross-sections for SEHRS on the order of 10(-46) to 10(-45) cm4 x s, similar to or higher than the best "action" cross-sections (product of the two-photon absorption cross-section and fluorescence quantum yield) for two-photon fluorescence, and we demonstrate HRS on biological structures such as single cells after incubation with gold nanoparticles.

Animals↗
PubMed2003

Treatment planning intercomparison for spinal chordomas using intensity-modulated photon radiation therapy (IMRT) and carbon ions.

Spinal chordomas cannot be treated with an effective dose using conventional radiation therapy (RT) without exceeding the tolerance dose of the spinal cord while ensuring sufficient target coverage at the same time. In this study we investigate the potential physical advantages of combined photon intensity-modulated radiation therapy (IMRT) and raster-scanned carbon ion RT over photon IMRT alone. For a representative patient we generated a carbon ion RT plan and a photon IMRT plan. Additionally, combined plans consisting of both carbon ions and photon IMRT were calculated using ratios of 20:40 GyE, 30:30 GyE and 40:20 GyE. The best target coverage was obtained using carbon ions alone. Using a combination of photon IMRT and carbon ions, the target coverage was better than with photon IMRT alone. Due to the applied dose constraints, the sparing of the spinal cord was comparable for all plans. Using carbon ions alone, the non-target tissue volume irradiated to at least 30 GyE/50.4 GyE was reduced by 72%/84% compared to photon IMRT alone. These advantages were evident even with combined techniques. The actually delivered dose distribution is expected to be more dependent on patient misalignment with carbon ions compared with photon IMRT. A combination of carbon ions and photon IMRT might be preferable in order to profit by the physical advantages of carbon ions while ensuring a safe treatment.

Carbon Radioisotopes↗
PubMed2004

Optimization of combined electron and photon beams for breast cancer.

Recently, intensity-modulated radiation therapy and modulated electron radiotherapy have gathered a growing interest for the treatment of breast and head and neck tumours. In this work, we carried out a study to combine electron and photon beams to achieve differential dose distributions for multiple target volumes simultaneously. A Monte Carlo based treatment planning system was investigated, which consists of a set of software tools to perform accurate dose calculation, treatment optimization, leaf sequencing and plan analysis. We compared breast treatment plans generated using this home-grown optimization and dose calculation software for different treatment techniques. Five different planning techniques have been developed for this study based on a standard photon beam whole breast treatment and an electron beam tumour bed cone down. Technique 1 includes two 6 MV tangential wedged photon beams followed by an anterior boost electron field. Technique 2 includes two 6 MV tangential intensity-modulated photon beams and the same boost electron field. Technique 3 optimizes two intensity-modulated photon beams based on a boost electron field. Technique 4 optimizes two intensity-modulated photon beams and the weight of the boost electron field. Technique 5 combines two intensity-modulated photon beams with an intensity-modulated electron field. Our results show that technique 2 can reduce hot spots both in the breast and the tumour bed compared to technique 1 (dose inhomogeneity is reduced from 34% to 28% for the target). Techniques 3, 4 and 5 can deliver a more homogeneous dose distribution to the target (with dose inhomogeneities for the target of 22%, 20% and 9%, respectively). In many cases techniques 3, 4 and 5 can reduce the dose to the lung and heart. It is concluded that combined photon and electron beam therapy may be advantageous for treating breast cancer compared to conventional treatment techniques using tangential wedged photon beams followed by a boost electron field.

Breast↗
PubMed2006

Study of scattered photons from the collimator system of Leksell Gamma Knife using the EGS4 Monte Carlo code.

In the algorithm of Leksell GAMMAPLAN (the treatment planning software of Leksell Gamma Knife), scattered photons from the collimator system are presumed to have negligible effects on the Gamma Knife dosimetry. In this study, we used the EGS4 Monte Carlo (MC) technique to study the scattered photons coming out of the single beam channel of Leksell Gamma Knife. The PRESTA (Parameter Reduced Electron-Step Transport Algorithm) version of the EGS4 (Electron Gamma Shower version 4) MC computer code was employed. We simulated the single beam channel of Leksell Gamma Knife with the full geometry. Primary photons were sampled from within the 60Co source and radiated isotropically in a solid angle of 4pi. The percentages of scattered photons within all photons reaching the phantom space using different collimators were calculated with an average value of 15%. However, this significant amount of scattered photons contributes negligible effects to single beam dose profiles for different collimators. Output spectra were calculated for the four different collimators. To increase the efficiency of simulation by decreasing the semiaperture angle of the beam channel or the solid angle of the initial directions of primary photons will underestimate the scattered component of the photon fluence. The generated backscattered photons from within the 60Co source and the beam channel also contribute to the output spectra.

Computer Simulation↗
PubMed2002

Assessment of fluorochromes for two-photon laser scanning microscopy of biofilms.

A major limitation for the use of two-proton laser scanning microscopy (2P-LSM) in biofilm and other studies is the lack of a thorough understanding of the excitation-emission responses of potential fluorochromes. In order to use 2P-LSM, the utility of various fluorochromes and probes specific for a range of biofilm constituents must be evaluated. The fluorochromes tested in this study included classical nucleic acid-specific stains, such as acridine orange (AO) and 4",6"-diamidino-2-phenylindole (DAPI), as well as recently developed stains. In addition, stains specific for biofilm extracellular polymeric substances (EPS matrix components) were tested. Two-photon excitation with a Ti/Sapphire laser was carried out at wavelengths from 760 to 900 nm in 10-nm steps. It was found that autofluorescence of phototrophic organisms (cyanobacteria and green algae) resulted in strong signals for the entire excitation range. In addition, the coenzyme F(420)-related autofluorescence of methanogenic bacteria could be used to obtain images of dense aggregates (excitation wavelength, 780 nm). The intensities of the emission signals for the nucleic acid-specific fluorochromes varied. For example, the intensities were similar for excitation wavelengths ranging from 780 to 900 nm for AO but were higher for a narrower range, 780 to 810 nm, for DAPI. In selective excitation, fading, multiple staining, and combined single-photon-two-photon studies, the recently developed nucleic acid-specific fluorochromes proved to be more suitable regardless of whether they are intended for living or fixed samples. Probes specific for proteins and glycoconjugates allowed two-photon imaging of polymeric biofilm constituents. Selective excitation-emission was observed for Calcofluor White M2R (780 to 800 nm) and SyproOrange (880 to 900 nm). In addition, fluor-conjugated concanavalin A lectins were examined and provided acceptable two-photon emission signals at wavelengths ranging from 780 to 800 nm. Finally, CellTracker, a fluorochrome suitable for long-term labeling of microbial eucaryote cells, was found to give strong emission at wavelengths ranging from 770 to 810 nm. If fluorochromes have the same two-photon excitation cross section, they are suitable for multiple staining and multichannel recording. Generally, if an appropriate excitation wavelength and fluorochrome were used, it was possible to obtain more highly resolved images for thick biofilm samples with two-photon laser microscopy than with conventional single-photon laser microscopy. Due to its potential for higher resolution in light-scattering tissue-like material, such as biofilms, and extremely localized excitation, 2P-LSM is a valuable addition to conventional confocal laser scanning microscopy with single-photon excitation. However, further development of the method and basic research are necessary to take full advantage of nonlinear excitation in studies of interfacial microbial ecology.

Biofilms↗
PubMed2000

A custom confocal and two-photon digital laser scanning microscope.

We describe a custom one-photon (confocal) and two-photon all-digital (photon counting) laser scanning microscope. The confocal component uses two avalanche photodiodes (APDs) as the fluorescence detector to achieve high sensitivity and to overcome the limited photon counting rate of a single APD ( approximately 5 MHz). The confocal component is approximately nine times more efficient than our commercial confocal microscope (fluorophore fluo 4). Switching from one-photon to two-photon excitation mode (Ti:sapphire laser) is accomplished by moving a single mirror beneath the objective lens. The pulse from the Ti:sapphire laser is 109 fs in duration at the specimen plane, and average power is approximately 5 mW. Two-photon excited fluorescence is detected by a fast photomultiplier tube. With a x63 1.4 NA oil-immersion objective, the resolution of the confocal system is 0.25 microm laterally and 0.52 microm axially. For the two-photon system, the corresponding values are 0.28 and 0.82 microm. The system is advantageous when excitation intensity must be limited, when fluorescence is low, or when thick, scattering specimens are being studied (with two-photon excitation).

Animals↗
PubMed1988

Neutron vs photon irradiation of inoperable salivary gland tumors: results of an RTOG-MRC Cooperative Randomized Study.

A total of 32 patients with inoperable, recurrent or unresectable malignant salivary gland tumors were entered on a randomized RTOG/MRC study comparing fast neutron radiotherapy with conventional photon radiotherapy. Twenty-five patients were entered from the United States and 7 patients were entered from Scotland. Seventeen patients were randomized to receive neutrons and 15 patients were randomized to receive photons. Sixty-one percent of the neutron-treated patients and 75% of the photon-treated patients presented with inoperable or unresectable tumors, while 39% of the neutron-treated and 25% of the photon-treated patients had recurrent disease. Twenty-five patients were study-eligible and analyzable. The minimum follow-up time is 2 years. The complete tumor clearance rates at the primary site were 85% (11/13) for neutrons and 33% (4/12) for photons following protocol treatment (p = 0.01). The complete tumor clearance rates in the cervical lymph nodes were 86% (6/7) for neutrons and 25% (1/4) for photons. The overall loco/regional complete tumor response rates were 85% and 33% for neutrons and photons respectively. The loco/regional control rates at 2 years for the 2 groups are 67% for neutrons and 17% for photons (p less than 0.005). The 2-year survival rates are 62% and 25% for neutrons and photons respectively (p = 0.10). These findings are consistent with previously published uncontrolled series.

Adenocarcinoma↗
PubMed2006

Quantum interference between two single photons emitted by independently trapped atoms.

When two indistinguishable single photons are fed into the two input ports of a beam splitter, the photons will coalesce and leave together from the same output port. This is a quantum interference effect, which occurs because two possible paths-in which the photons leave by different output ports-interfere destructively. This effect was first observed in parametric downconversion (in which a nonlinear crystal splits a single photon into two photons of lower energy), then from two separate downconversion crystals, as well as with single photons produced one after the other by the same quantum emitter. With the recent developments in quantum information research, much attention has been devoted to this interference effect as a resource for quantum data processing using linear optics techniques. To ensure the scalability of schemes based on these ideas, it is crucial that indistinguishable photons are emitted by a collection of synchronized, but otherwise independent sources. Here we demonstrate the quantum interference of two single photons emitted by two independently trapped single atoms, bridging the gap towards the simultaneous emission of many indistinguishable single photons by different emitters. Our data analysis shows that the observed coalescence is mainly limited by wavefront matching of the light emitted by the two atoms, and to a lesser extent by the motion of each atom in its own trap.

Journal Article↗
PubMed2003

Degeneracy analysis for a supercell of a photonic crystal and its application to the creation of band gaps.

A method is introduced to analyze the degeneracy properties of the band structure of a photonic crystal by making use of supercells. The band structure associated with a supercell of a photonic crystal has degeneracies at the edge of the Brillouin zone if the photonic crystal has some kind of point group symmetry. The E-polarization and H-polarization cases have the same degeneracies for a two-dimensional (2D) photonic crystal. Two theorems on degeneracies in the band structure associated with the supercell are given and proved. These degeneracies can be lifted to create photonic band gaps by changing the translation group symmetry of the photonic crystal (the point group symmetry of the photonic crystal may remain unchanged), which consequently changes the transform matrix between the supercell and the smallest unit cell. The existence of photonic band gaps for many known 2D photonic crystals is explained through the degeneracy analysis. Some structures with large band gaps are also found through the present degeneracy analysis.

Journal Article↗