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Showing papers on "Spontaneous emission published in 2005"


Journal Article
TL;DR: This work examined the competing dynamical processes involved in optical amplification and lasing in nanocrystal quantum dots and found that, despite a highly efficient intrinsic nonradiative Auger recombination, large optical gain can be developed at the wavelength of the emitting transition for close-packed solids of these dots.
Abstract: The development of optical gain in chemically synthesized semiconductor nanoparticles (nanocrystal quantum dots) has been intensely studied as the first step toward nanocrystal quantum dot lasers. We examined the competing dynamical processes involved in optical amplification and lasing in nanocrystal quantum dots and found that, despite a highly efficient intrinsic nonradiative Auger recombination, large optical gain can be developed at the wavelength of the emitting transition for close-packed solids of these dots. Narrowband stimulated emission with a pronounced gain threshold at wavelengths tunable with the size of the nanocrystal was observed, as expected from quantum confinement effects. These results unambiguously demonstrate the feasibility of nanocrystal quantum dot lasers.

2,098 citations


Journal ArticleDOI
TL;DR: It is demonstrated that the structure represents an on-demand single photon source with a pulse duration from 210 ps to 8 ns, and the suppression of QD emission rate is explained using finite difference time domain simulations and finds good agreement with experiment.
Abstract: We observe large spontaneous emission rate modification of individual InAs quantum dots (QDs) in a 2D photonic crystal with a modified, high-$Q$ single-defect cavity. Compared to QDs in a bulk semiconductor, QDs that are resonant with the cavity show an emission rate increase of up to a factor of 8. In contrast, off-resonant QDs indicate up to fivefold rate quenching as the local density of optical states is diminished in the photonic crystal. In both cases, we demonstrate photon antibunching, showing that the structure represents an on-demand single photon source with a pulse duration from 210 ps to 8 ns. We explain the suppression of QD emission rate using finite difference time domain simulations and find good agreement with experiment.

840 citations


Journal ArticleDOI
TL;DR: The chemical process used to terminate the surfaces of the silicon quantum dots changes the internal electronic structure and thus plays an important role in the resultant emission wavelength and radiative lifetime, and ultimately determines the solubility.
Abstract: For silicon quantum dots to be used in biomedical applications it is essential that they have a substantial photoluminescence quantum yield in the visible region, have a fast radiative recombination rate, and are water soluble and hydrophilic to prevent aggregation and precipitation in a biological environment. The chemical process used to terminate the surfaces of the silicon quantum dots changes the internal electronic structure and thus plays an important role in the resultant emission wavelength and radiative lifetime, and ultimately determines the solubility. [18] Silicon quantum dots with an oxide surface passivation typically display a dipole-forbidden yellow-red emission with radiative lifetimes of 10 3 –10 6 s. [18, 26] This slow rate of recombination limits the use of oxide-passivated silicon quantum dots in biological imaging. However, silicon quantum dots with a hydrogen or carbon surface passivation have electric-dipole-allowed direct band gap transitions that lead to blue photoluminescence with fast recombination rates of 10 8 –10 9 s. [18, 20]

515 citations


Journal ArticleDOI
27 May 2005-Science
TL;DR: This work demonstrates both the “inhibition” and “redistribution” of spontaneous light emission by using two-dimensional photonic crystals, in which the refractive index is changed two-dimensionally.
Abstract: Inhibiting spontaneous light emission and redistributing the energy into useful forms are desirable objectives for advances in various fields, including photonics, illuminations, displays, solar cells, and even quantum-information systems. We demonstrate both the "inhibition" and "redistribution" of spontaneous light emission by using two-dimensional (2D) photonic crystals, in which the refractive index is changed two-dimensionally. The overall spontaneous emission rate is found to be reduced by a factor of 5 as a result of the 2D photonic bandgap effect. Simultaneously, the light energy is redistributed from the 2D plane to the direction normal to the photonic crystal.

485 citations


Journal ArticleDOI
TL;DR: It is shown that spontaneous emission can coherently interfere with the continuum modes and gives interesting transport properties and analytical solutions are given.
Abstract: A two-level system coupled to a one-dimensional continuum is investigated By using a real-space model Hamiltonian, we show that spontaneous emission can coherently interfere with the continuum modes and gives interesting transport properties The technique is applied to various related problems with different configurations, and analytical solutions are given

458 citations


Journal ArticleDOI
TL;DR: In this paper, a 32-fold increase in spontaneous emission rate of InGaN/GaN quantum well at 440 nm was observed by employing surface plasmons (SPs) probed by time-resolved photoluminescence spectroscopy.
Abstract: We observed a 32-fold increase in the spontaneous emission rate of InGaN/GaN quantum well (QW) at 440 nm by employing surface plasmons (SPs) probed by time-resolved photoluminescence spectroscopy. We explore this remarkable enhancement of the emission rates and intensities resulting from the efficient energy transfer from electron-hole pair recombination in the QW to electron vibrations of SPs at the metal-coated surface of the semiconductor heterostructure. This QW-SP coupling is expected to lead to a new class of super bright and high-speed light-emitting diodes (LEDs) that offer realistic alternatives to conventional fluorescent tubes.

346 citations


Journal ArticleDOI
TL;DR: The controlled nanoscale silicon engineering, combined with the low material loss in this sub-bandgap spectral range and the long electron lifetime in such A-type trapping centres, gives rise to the measured optical gain and stimulated emission and provides a new pathway to enhance light emission from silicon.
Abstract: Persistent efforts have been made to achieve efficient light emission from silicon1,2,3,4,5,6,7 in the hope of extending the reach of silicon technology into fully integrated optoelectronic circuits, meeting the needs for high-bandwidth intrachip and interchip connects8. Enhanced light emission from silicon is known to be theoretically possible9,10, enabled mostly through quantum-confinement effects2,3,4. Furthermore, Raman-laser conversion was demonstrated in silicon waveguides11,12. Here we report on optical gain and stimulated emission in uniaxially nanopatterned silicon-on-insulator using a nanopore array as an etching mask13. In edge-emission measurements, we observed threshold behaviour, optical gain, longitudinal cavity modes and linewidth narrowing, along with a collimated far-field pattern, all indicative of amplification and stimulated emission14,15,16,17. The sub-bandgap 1,278 nm emission peak is attributed to A-centre mediated phononless direct recombination between trapped electrons and free holes18,19,20. The controlled nanoscale silicon engineering, combined with the low material loss in this sub-bandgap spectral range and the long electron lifetime in such A-type trapping centres, gives rise to the measured optical gain and stimulated emission and provides a new pathway to enhance light emission from silicon.

312 citations


Journal ArticleDOI
TL;DR: The broadband infrared luminescent characteristics of the glasses indicate that they are promising for broadband optical fiber amplifiers and tunable lasers.
Abstract: Near infrared broadband emission characteristics of bismuth-doped aluminophosphate glass have been investigated. Broad infrared emissions peaking at 1210nm, 1173nm and 1300nm were observed when the glass was pumped by 405nm laser diode (LD), 514nm Ar+ laser and 808nm LD, respectively. The full widths at half maximum (FWHMs) are 235nm, 207nm and 300nm for the emissions at 1210nm, 1173nm and 1300nm, respectively. Based on the energy matching conditions, it is suggested that the infrared emission may be ascribed to 3P1→ 3P0 transition of Bi+. The broadband infrared luminescent characteristics of the glasses indicate that they are promising for broadband optical fiber amplifiers and tunable lasers.

308 citations


Journal ArticleDOI
TL;DR: In this article, the spontaneous emission of a cesium atom in the vicinity of a subwavelength-diameter fiber was studied and it was shown that the confinement of the guided modes and the degeneracy of the excited and ground states substantially affect spontaneous emission process.
Abstract: We study the spontaneous emission of a cesium atom in the vicinity of a subwavelength-diameter fiber. We show that the confinement of the guided modes and the degeneracy of the excited and ground states substantially affect the spontaneous emission process. We demonstrate that different magnetic sublevels have different decay rates. When the fiber radius is about $200\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, a significant fraction (up to 28%) of spontaneous emission by the atom can be channeled into guided modes. Our results may find applications for developing nanoprobes for atoms and efficient couplers for subwavelength-diameter fibers.

233 citations


Journal ArticleDOI
TL;DR: This work considers a two-photon correlated emission laser as a source of an entangled radiation with a large number of photons in each mode, and concludes that the creation of entangled states with photon numbers up to tens of thousands seems achievable.
Abstract: We consider a two-photon correlated emission laser as a source of an entangled radiation with a large number of photons in each mode. The system consists of three-level atomic schemes inside a doubly resonant cavity. We study the dynamics of this system in the presence of cavity losses, concluding that the creation of entangled states with photon numbers up to tens of thousands seems achievable.

195 citations


Journal ArticleDOI
TL;DR: It is suggested that surface states are the controlling factor of dark-exciton radiative recombination in currently synthesized colloidal CdSe nanocrystals.
Abstract: Using atomistic, semiempirical pseudopotential calculations, we show that if one assumes the simplest form of a surface state in a CdSe nanocrystal--an unpassivated surface anion site--one can explain theoretically several puzzling aspects regarding the observed temperature dependence of the radiative decay of excitons. In particular, our calculations show that the presence of surface states leads to a mixing of the dark and bright exciton states, resulting in a decrease of 3 orders of magnitude of the dark-exciton radiative lifetime. This result explains the persistence of the zero-phonon emission line at low temperature, for which thermal population of higher-energy bright-exciton states is negligible. Thus, we suggest that surface states are the controlling factor of dark-exciton radiative recombination in currently synthesized colloidal CdSe nanocrystals.

Journal ArticleDOI
TL;DR: The rate of spontaneous emission from colloidal CdSe and CdTe nanocrystals at room temperature is studied and the decay rate, obtained from luminescence decay curves, increases with the emission frequency in a supralinear way.
Abstract: We studied the rate of spontaneous emission from colloidal CdSe and CdTe nanocrystals at room temperature. The decay rate, obtained from luminescence decay curves, increases with the emission frequency in a supralinear way. This dependence is explained by the thermal occupation of dark exciton states at room temperature, giving rise to a strong attenuation of the rate of emission. The supralinear dependence is in agreement with the results of tight-binding calculations.

Journal ArticleDOI
TL;DR: In this article, the effects of metal coating on the near-band-edge emission of ZnO thin films have been studied by photoluminescence and atomic force microscopy.
Abstract: The effects of metal coating on the near-band-edge emission of ZnO thin films have been studied by photoluminescence and atomic force microscopy. Large enhancement in emission intensity has been observed from ZnO films when they are capped by Ag while negligible effect is seen on Au-coated films. In addition, the enhancement is found to increase with Ag thickness and the intensity eventually saturates at thickness of 200nm. By introducing MgO as a spacer between the metal coating and ZnO, the enhancement is shown to decrease with increasing the spacer thickness, which suggests the presence of the local fields induced by surface plasmons. As the emission energy of ZnO matches closely with the surface plasmon of Ag, it is speculated that the resonant coupling of the spontaneous emission in ZnO into the surface plasmons enhances the emission efficiency.

Journal ArticleDOI
TL;DR: In this paper, a scheme for sub-half-wavelength localization of an atom conditioned upon the absorption of a weak probe field at a particular frequency was proposed, where one of the drive fields is a standing-wave field of a cavity.
Abstract: We propose a scheme for subwavelength localization of an atom conditioned upon the absorption of a weak probe field at a particular frequency. Manipulating atom-field interaction on a certain transition by applying drive fields on nearby coupled transitions leads to interesting effects in the absorption spectrum of the weak probe field. We exploit this fact and employ a four-level system with three driving fields and a weak probe field, where one of the drive fields is a standing-wave field of a cavity. We show that the position of an atom along this standing wave is determined when probe-field absorption is measured. We find that absorption of the weak probe field at a certain frequency leads to subwavelength localization of the atom in either of the two half-wavelength regions of the cavity field by appropriate choice of the system parameters. We term this result as sub-half-wavelength localization to contrast it with the usual atom localization result of four peaks spread over one wavelength of the standing wave. We observe two localization peaks in either of the two half-wavelength regions along the cavity axis.

Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate the ability to control the spontaneous emission dynamics of self-assembled quantum dots via the local density of optical modes in two-dimensional s2Dd photonic crystals.
Abstract: We demonstrate the ability to control the spontaneous emission dynamics of self-assembled quantum dots via the local density of optical modes in two-dimensional s2Dd photonic crystals. We show that an incomplete 2D photonic band gap is sufficient to significantly lengthen the spontaneous emission lifetimes.2 3 d over a wide bandwidth sDl o40 nmd. For dots that are both spectrally and spatially coupled to strongly localized fVmodes, 1.5sl / nd 3 g, high Q, 2700 optical modes, we have directly measured a strong Purcell-enhanced shortening of the emission lifetime o5.63, limited only by our temporal resolution. Analysis of the spectral dependence of the recombination dynamics shows a maximum lifetime shortening of 19± 4. From the directly measured enhancement and suppression we show that the single-mode coupling efficiency for quantum dots in such structures is at least b = 92% and is estimated to be as large as ,97%.

Journal ArticleDOI
TL;DR: By patterning the silver layer, it is estimated that the plasmon frequency can be tuned to match dye doped polymer emission frequencies and even larger emission enhancements as well as extraction efficiencies are expected.
Abstract: We have experimentally verified that the emission of visible light from dye doped polymers can be enhanced with the use of surface plasmon coupling. By matching the plasmon frequency of a thin unpatterned silver film to the emission of a dye doped polymer deposited onto this metal surface, we have observed a eleven-fold enhancement of light emission. By patterning the silver layer, we estimate that the plasmon frequency can be tuned to match dye doped polymer emission frequencies and even larger emission enhancements as well as extraction efficiencies are expected.

Journal ArticleDOI
TL;DR: In this paper, the absorption and emission spectroscopic behavior of cyclometalated fac -tris(2-phenylpyridine) iridium(III) [Ir(ppy) 3 ] is studied at room temperature.

Journal ArticleDOI
TL;DR: The peak stimulated emission cross sections rank among the highest found for oxide glasses in the ultraviolet-visible-near-infrared (UV-VIS-NIR) region.
Abstract: Glasses of composition (x - 1)PbO(100 - x)GeO21Ln2O3, with x= 30 mol% (Ln = Nd, Eu, Er), 40 mol% (Ln = Pr, Nd, Sm, Eu, Dy, Ho, Er, Tm), and 50 mol% (Ln = Eu, Er), have been prepared by quenching the oxidic melts. From the optical absorption and emission spectra in the ultraviolet-visible-near-infrared (UV-VIS-NIR) region, the intensity parameters, spontaneous emission probabilities, branching ratios, radiative lifetimes, and, for selected NIR transitions, peak stimulated emission cross sections have been obtained. The trends observed in the intensity parameters have been discussed, as a function of the number of f electrons as well as a function of the lead content. As the amount of lead increases, the covalency of the Ln-O bond increases, the symmetry of the rare-earth site increases, and the dopant site distribution narrows. The peak stimulated emission cross sections rank among the highest found for oxide glasses.

Journal ArticleDOI
TL;DR: In this paper, the spontaneous emission of a single-quantum dot embedded in a two-dimensional photonic crystal cavity was investigated, and the resonant coupling between the dot and the strongly localized optical mode significantly shortened the spontaneous emissions lifetime, so that the emitted photons are indistinguishable.
Abstract: We report on the spontaneous emission of a single-quantum dot embedded in a two-dimensional photonic crystal cavity. The resonant coupling between the dot and the strongly localized optical mode significantly shortens the spontaneous emission lifetime, so that the coherence time of the emitted photons is dominated by radiative effects: The emitted photons are indistinguishable, with a mean wave-packet overlap as high as 72%.

Journal ArticleDOI
TL;DR: In this article, the authors reported room-temperature ultraviolet stimulated emission and lasing from optically pumped high-quality ZnO nanowires and attributed the mechanism of laser emission to coherent multiple scattering among the random-growth oriented nanowsires.
Abstract: We report room-temperature ultraviolet stimulated emission and lasing from optically pumped high-quality ZnO nanowires. Emission due to the exciton-exciton scattering process shows apparent stimulated-emission behavior. Several sharp peaks associated with random laser action are seen under high pumping intensity. The mechanism of laser emission is attributed to coherent multiple scattering among the random-growth oriented nanowires. The characteristic cavity length is determined by the Fourier transform of the lasing spectrum.

Journal ArticleDOI
A. Gover1
TL;DR: In this paper, a formulation for the characterization of superradiant and stimulated-superradiant radiative emission from bunched electron beams is presented, where the radiation is characterized in terms of power and spectral power per radiation mode.
Abstract: A formulation for the characterization of superradiant and stimulated-superradiant radiative emission from bunched electron beams is presented. The radiation is characterized in terms of power and spectral power per radiation mode, which provide a measure of the useful spatially coherent radiation power and spectral power emitted by a radiation source. When the bunched electron beam emits superradiantly, these parameters scale like the square of the number of electrons, orders of magnitude more than spontaneous emission. The formulation applies to emission from single bunches, a finite number of bunches in a macropulse, or periodic bunching. It can be employed on any kind of $e$-beam radiation scheme. Specific analytic expressions are derived for coherent synchrotron radiation and prebunched free-electron laser, providing a basis for comparing and understanding their connection.

Journal ArticleDOI
TL;DR: In this article, the authors demonstrated that charge carrier retrapping processes can delay radiative recombination at the luminescence centers in an extended time scale, which makes a substantial part of generated scintillation light technically unexploitable.
Abstract: Luminescence and scintillation dynamics can be extensively influenced by the energy transfer processes, which is demonstrated at three selected scintillator materials: PbWO 4 , Ce-doped aluminium garnets and PrF 3 :Ce single crystals. Charge carrier retrapping processes can delay radiative recombination at the luminescence centers in an extended time scale, which makes a substantial part of generated scintillation light technically unexploitable. Correlated measurements based on time-resolved emission spectroscopy and thermoluminescence are of great help to evaluate these phenomena and to understand their microscopic origin.

Journal ArticleDOI
TL;DR: This method is demonstrated here and used to benchmark the Einstein A coefficients in the Meinel system of OH and measure the radiative lifetime of the upper Lamda-doublet component of the Chi2Pi3/2, v=1, J=3/3 level.
Abstract: Infrared absorption and emission spectroscopy has a long and rich history in the development and application of molecular physics. Absorption and emission of infrared radiation is an important diagnostic means in determining the presence and concentration of molecular species in various environments, ranging from plasmas and flames to the Earth’s atmosphere and interstellar space. A quantitative analysis of these observations relies on a detailed knowledge of the Einstein A coefficients that characterize the spontaneous emission rates. These A coefficients can generally be inferred from absorption measurements, pro

Journal ArticleDOI
TL;DR: In this article, the performance of a photonic band-edge laser fabricated from a low molar mass dye-doped chiral nematic liquid crystal is found to have a strong thermal dependence.
Abstract: The performance of a photonic band-edge laser fabricated from a low molar mass dye-doped chiral nematic liquid crystal is found to have a strong thermal dependence. At each temperature the performance of the laser has been characterized by the slope efficiency which was calculated from a plot of the emission energy as a function of excitation energy. This slope efficiency was found to increase by 36% when the dye-doped chiral nematic liquid crystal was cooled from 53to43°C. The increase in slope efficiency is considered to be due to a change in the lasing conditions, in particular, changes in the emission efficiency of the dye and possibly the quality factor of the liquid-crystal resonator, which is dependent upon the linewidth of the resonant mode. The wavelength dependency of the spontaneous emission intensity and the quantum efficiency of the dye were not found to influence the lasing conditions in this case. The order parameters relating to the dye-doped chiral nematic liquid crystal were considered t...

Journal ArticleDOI
TL;DR: In this paper, the XMM−Newton spectrum of the ultraluminous infrared galaxy Arp 220 was used to detect the Fe Kα line emission in the infrared spectrum.
Abstract: Prominent Fe Kα line emission is detected in the XMM‐Newton spectrum of the ultraluminous infrared galaxy Arp 220. The centroid of the line is found at an energy of 6.7 keV and the equivalent width of the line is EW ∼ 1.9 keV (at 3.5σ significance). A few other spectral features are found at various degrees of significance in the lower energy range on a hard 2.5‐ 10 keV continuum (� ∼ 1). The large EW of the Fe K line poses a problem with interpreting the hard X-ray emission as integrated X-ray binary emission. A thermal emission spectrum with a temperature of kT ∼ 7k eV modified by absorption of N H � 3 × 10 22 cm −2 , can describe the 2.5‐10 keV continuum shape and the Fe K emission. A hot bubble that is shocked internally in a starburst region would have a similar temperature and gives a good explanation for the observed X-ray properties with a high star formation rate. An ensemble of radio supernovae in a dense environment, as suggested from VLBI imaging, could be another possibility, if such powerful supernovae are produced continuously at a high rate. However, the apparent lack of emission from X-ray binaries is incompatible with the high supernova rate (∼2 SNe yr −1 ) required by both interpretations. Highly photoionized, low-density gas illuminated by a hidden Compton-thick active galactic nucleus is a possible alternative for the hard X-ray emission, which can be tested by examining whether radiative recombination continua from highly ionized Ca and Fe are present in better quality data from a forthcoming observation. Ke yw ords: galaxies: individual: Arp 220 ‐ X-rays: galaxies.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the generation and evolution of entangled light in a correlated spontaneous emission laser and derived the master equation for the two-mode field in a cavity and solved it analytically.
Abstract: We discuss the generation and evolution of entangled light in a correlated spontaneous emission laser. The master equation for the two-mode field in a cavity is derived and solved analytically. The time-dependent characteristic function in the Wigner representation for the two-mode field is obtained. It shows that the two-mode field in the cavity evolves in a two-mode Gaussian state. The entanglement degree of the two-mode field in the cavity increases initially, then decreases, and finally vanishes as the field evolves from an initial vacuum. The period of the entanglement is extended as the intensity of the driving field is increased. It is found that the entanglement still exists even when the two-mode squeezing disappears. During the entanglement period, the intensity of the field is amplified. The entanglement for the initial field being a two-mode squeezed vacuum and the entanglement of the output field are also discussed.

Journal ArticleDOI
TL;DR: In this paper, the radiative and nonradiative components of the threshold current in 1.3μm, p-doped and undoped quantum-dot semiconductor lasers were studied between 20 and 370K.
Abstract: The radiative and nonradiative components of the threshold current in 1.3μm, p-doped and undoped quantum-dot semiconductor lasers were studied between 20 and 370K. The complex behavior can be explained by simply assuming that the radiative recombination and nonradiative Auger recombination rates are strongly modified by thermal redistribution of carriers between the dots. The large differences between the devices arise due to the trapped holes in the p-doped devices. These both greatly increase Auger recombination involving hole excitation at low temperatures and decrease electron thermal escape due to their Coulombic attraction. The model explains the high T0 values observed near room temperature.

Journal ArticleDOI
TL;DR: In this article, different ZnO nanostructures (tetrapods, shells, rods, and highly faceted rods) were characterized by photoluminescence (PL) and time-resolved PL measurements.
Abstract: Different ZnO nanostructures (tetrapods, shells, rods, and highly faceted rods) were characterized by photoluminescence (PL) and time-resolved PL measurements. It was found that different nanostructures exhibit very different optical properties in terms of defect emission and decay times of the spontaneous emission. No correlation was found between the PL decay times and defect emission intensities and defect emission positions. The short decay times of the UV emission are most likely due to nonradiative defects that are correlated with the crystalline quality and do not contribute to the visible emission. Neither short PL decay times nor intense defect emissions rule out achievement of stimulated emission.

Journal ArticleDOI
TL;DR: The random laser as discussed by the authors is a type of laser that is formed by multiple scattering in a disordered gain medium, and it can be used for a variety of applications, such as medical imaging.
Abstract: The random laser differs from other types of laser in that its cavity is formed not by mirrors but by multiple scattering in a disordered gain medium. The unique characteristics of the technology have encouraged scientists to explore new applications.

Journal ArticleDOI
TL;DR: In this article, the integrated absorption cross section, spontaneous emission probability, and stimulated emission cross section of Yb3+ were determined in silicate, phosphate, borate, germanate, aluminate, gallate and ZBLAN host glasses.
Abstract: The integrated absorption cross section, the spontaneous emission probability, and the stimulated emission cross section of Yb3+ were determined in silicate, phosphate, borate, germanate, aluminate, gallate, and ZBLAN host glasses. The compositional dependence of the stimulated emission cross section of the 2F5/2→2F7/2 transition is determined mainly by the integrated absorption cross section in the glasses. A peak stimulated emission cross section above 1 pm2, which is the highest value in glasses, was obtained in a gallate glass with a composition of 40K2O·20Ta2O5. 40Ga2O3. The factors affecting the integrated absorption cross section are discussed using the Judd-Ofelt parameters of Er3+ calculated in previous studies.