Light Propagation Equations Research Articles

Direct generation of a 635 nm red random laser based on praseodymium (Pr)-doped ZBLAN fiber.

Visible random fiber lasers have garnered significant attention due to their unique emission properties and potential applications in various fields. We first, to the best of our knowledge, demonstrateda compact all-fiber structure, red wavelength, and random fiber laser (RFL) based on a double-clad Pr-doped ZBLAN fiber. The simple half-open cavity consists of a high-reflectivity fiber pigtail mirror and the Pr-doped ZBLAN fiber. The Pr-doped ZBLAN fiber not only served as a gain medium but also offered random backward scattering. We investigated the effects of different lengths on output power and slope efficiency of the RFL. For 21 m Pr-doped fiber, the RFL emitted a maximum output power of 208.50 mW with a slope efficiency of 11.09%. For 15 m Pr-doped fiber, the maximum power decreased to 120.18 mW with the slope efficiency of 7.27%. We are also numerically simulating the output power versus the pump power at different fiber lengths based on power steady-state light propagation equations. This novel RFL has the potential for broad applications in fields such as display technology, spectroscopy, biomedical imaging, and optical sensing due to its unique properties and simple all-fiber structure.

Spherical harmonics representation of the gravitational phase shift

We investigate the general relativistic phase of an electromagnetic wave as it propagates in the gravitational field of the Earth, which is modeled as an isolated, weakly aspherical gravitating body. We introduce coordinate systems to describe light propagation in the Earth's vicinity along with the relevant coordinate transformations, and discuss the transformations between proper and coordinate times. We represent the Earth's gravitational field using Cartesian symmetric trace-free (STF) mass multipole moments. The light propagation equation is solvable along the trajectory of a light ray to all STF orders $\ensuremath{\ell}$. Although we focus primarily on the quadrupole ($\ensuremath{\ell}=2$), octupole ($\ensuremath{\ell}=3$), and hexadecapole ($\ensuremath{\ell}=4$) cases, our approach is valid to all orders. We express the STF moments via spherical harmonic coefficients of various degree and order, ${C}_{\ensuremath{\ell}k},{S}_{\ensuremath{\ell}k}$. The result is the gravitational phase shift expressed in terms of the spherical harmonics. These results are new. We also consider contributions due to tides and the Earth's rotation. We estimate the characteristic magnitudes of each term of the resulting overall gravitational phase shift. The terms assessed are either large enough to impact current-generation clocks or will become significant as future-generation clocks offer greater sensitivity. Our formulation is useful for many practical and scientific applications, including space-based time and frequency transfers, relativistic geodesy and navigation, as well as quantum communication links and space-based tests of fundamental physics.

First-principles method for nonlinear light propagation at oblique incidence.

We have developed a computational method to describe the nonlinear light propagation of an intense and ultrashort pulse at oblique incidence on a flat surface. In the method, coupled equations of macroscopic light propagation and microscopic electron dynamics are simultaneously solved using a multiscale modeling. The microscopic electronic motion is described by first-principles time-dependent density functional theory. The macroscopic Maxwell equations that describe oblique light propagation are transformed into one-dimensional wave equations. As an illustration of the method, light propagation at oblique incidence on a silicon thin film is presented.

Dispersive detection of atomic ensembles in the presence of strong lensing

We experimentally and theoretically investigate in-medium propagation effects of off-resonant light in dense, spatially inhomogeneous ultracold atomic gases. Focussing on frequency modulation spectroscopy as the dispersive detection tool of atoms, we observe that the refractive gradient-index lenses presented by localised atomic ensembles can significantly modify the interpretation of the dispersive signal even for large probe detuning, owing to the collective response of the atoms. We identify criteria for distinguishing between thin and thick atomic lenses, leading to either diffraction-dominated and lensing dominated regimes for the outgoing probe beams. Our findings are consistent with experimental data and solutions of paraxial wave equation for light propagation. Our study provides important practical insights for dispersive, minimally intrusive optical detection and imaging schemes of ultracold atoms and will be valuable for choosing optimal parameter regimes in numerous applications.

A first-principles simulation method for ultra-fast nano-optics

We develop a computational approach for ultrafast nano-optics based on first-principles time-dependent density functional theory. Solving Maxwell equations for light propagation and time-dependent Kohn-Sham equation for electron dynamics simultaneously, intense and ultrashort laser pulse interaction with a dielectric nano-structure is described taking full account of nonlinear effects. As an illustrative example, irradiation of a pulsed light on silicon nano-sphere system is presented.

Resonant-state expansion of light propagation in nonuniform waveguides

A new rigorous approach for precise and efficient calculation of light propagation along non-uniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoing-wave boundary conditions, form a natural basis for expansion of the local electromagnetic field. Using such an expansion at fixed frequency, we convert the wave equation for light propagation in a non-uniform waveguide into an ordinary second-order matrix differential equation for the expansion coefficients depending on the coordinate along the waveguide. We illustrate the method on several examples of non-uniform planar waveguides and evaluate its efficiency compared to the aperiodic Fourier modal method and the finite element method, showing improvements of one to four orders of magnitude. A similar improvement can be expected also for applications in other fields of physics showing wave phenomena, such as acoustics and quantum mechanics.

Tapered fiber based high power random laser.

We propose a novel high power random fiber laser (RFL) based on tapered fiber. It can overcome the power scaling limitation of RFL while maintaining good beam quality to a certain extent. An output power of 26.5 W has been achieved in a half-open cavity with one kilometer long tapered fiber whose core diameter gradually changes from 8 μm to 20 μm. The steady-state light propagation equations have been modified by taking into account the effective core area to demonstrate the tapered RFL through numerical calculations. The numerical model effectively describes the power characteristics of the tapered fiber based RFL, and both the calculating and experimental results show higher power exporting potential compared with the conventional single mode RFL.

Hybrid simplified spherical harmonics with diffusion equation for light propagation in tissues

Aiming at the limitations of the simplified spherical harmonics approximation (SPN) and diffusion equation (DE) in describing the light propagation in tissues, a hybrid simplified spherical harmonics with diffusion equation (HSDE) based diffuse light transport model is proposed. In the HSDE model, the living body is first segmented into several major organs, and then the organs are divided into high scattering tissues and other tissues. DE and SPN are employed to describe the light propagation in these two kinds of tissues respectively, which are finally coupled using the established boundary coupling condition. The HSDE model makes full use of the advantages of SPN and DE, and abandons their disadvantages, so that it can provide a perfect balance between accuracy and computation time. Using the finite element method, the HSDE is solved for light flux density map on body surface. The accuracy and efficiency of the HSDE are validated with both regular geometries and digital mouse model based simulations. Corresponding results reveal that a comparable accuracy and much less computation time are achieved compared with the SPN model as well as a much better accuracy compared with the DE one.

Enhanced 1.53 μm radiative transition in Er3+/Ce3+ co-doped tellurite glass modified by B2O3 oxide

Er3+/Ce3+ co-doped and B2O3 modified tellurite glasses with initial composition of TeO2–GeO2–Li2O–Nb2O5 were prepared using melt-quenching technique for potential applications in Er3+-doped fiber amplifiers (EDFAs) and lasers. The absorption spectra, fluorescence spectra, up-conversion spectra, Raman spectra and differential scanning calorimeter (DSC) curves of glass samples were measured to evaluate the effect of B2O3 modification on the 1.53μm band spectroscopic properties of Er3+, structural nature and thermal stability of glass hosts. It was shown that the introduction of an appropriate amount of B2O3 oxide can further improve the 1.53μm band fluorescence emission through an enhanced phonon-assisted energy transfer (ET) from Er3+ to Ce3+ ions under the excitation of 980nm, and the quantitative studies were carried out to elucidate the ET mechanism via calculating the microscopic parameters and phonon contribution ratios. Meanwhile, the thermal stability of glass hosts increases slightly with the introduction of B2O3 oxide. Furthermore, the 1.53μm band optical signal amplification was simulated based on the rare-earth ion rate and light power propagation equations. An increment in signal gain by about 1.4dB at 1532nm was observed in the Er3+/Ce3+ co-doped tellurite glass fiber containing 6mol% amount of B2O3 oxide, and the maximum signal gain reaches to 31dB on a 50cm fiber pumped at 980nm with power 200mW. The present results indicate that the prepared Er3+/Ce3+ co-doped tellurite glass modified by an appropriate amount of B2O3 oxide has good prospect as a gain medium applied for 1.53μm band EDFAs and lasers.

A numerical method for solving gain characteristics of Er3+/Yb3+ codoped waveguide amplifiers

By means of the interpolation and iteration methods to deal with the rate equations and the light propagation equations for the Er3+/Yb3+ codoped waveguide amplifier (EYCDWA), the gain characteristics in the forward, backward, and bidirectional pumped styles are analyzed. In order to obtain high gain, some parameters such as waveguide length, dopant concentration, pump power, and signal power are optimized. The results show that the pump power and signal power are about 50mW and 1mW, respectively, the gain is about 6.5dB for the 2.0cm-long EYCDWA with an Er3+ ion concentration of 1.5×1026m–3 and Yb3+ ion concentration of 1.9×1027m–3. Moreover, the upconversion is investigated for the designed device.

Light propagation in the averaged universe

Cosmic structures determine how light propagates through the Universe and consequently must be taken into account in the interpretation of observations. In the standard cosmological model at the largest scales, such structures are either ignored or treated as small perturbations to an isotropic and homogeneous Universe. This isotropic and homogeneous model is commonly assumed to emerge from some averaging process at the largest scales. We assume that there exists an averaging procedure that preserves the causal structure of space-time. Based on that assumption, we study the effects of averaging the geometry of space-time and derive an averaged version of the null geodesic equation of motion. For the averaged geometry we then assume a flat Friedmann-Lemaître (FL) model and find that light propagation in this averaged FL model is not given by null geodesics of that model, but rather by a modified light propagation equation that contains an effective Hubble expansion rate, which differs from the Hubble rate of the averaged space-time.

An all-optical switch/photodetection at 1550 nm, based on a micro-ring resonator array

In this paper, a photodetector based on InGaAs micro-ring resonator array with 5μm radius, in telecommunication wavelength region has been investigated. Then for the first time to our knowledge, with the change of refractive index due to optical nonlinear effects (such as: Kerr effect, two photon absorption, free carrier dispersion and free carrier absorption), an all-optical switch, based on pump-probe configuration using this photodetector have been proposed. So, the suggested device, will introduce a dual functionality that is important from view point of economically purposes and in term of integration. By numerically solving the light propagation equations, with FDTD and Crank–Nicolson methods, in addition to steady state and transient response, also we have found the frequency response, in both configurations. With increasing reverse bias voltage, and optimizing the free carrier transportation from absorption region, switching frequency can be increased up to 200GHz. Also by optimal choosing of parameters such as the number of rings and spaces between two adjacent rings and so on, the box-like spectral response of photodetector with high efficiency is achievable.

Performance of Er3+-doped chalcogenide glass MOF amplifier applied for 1.53 μm band

A model of Er3+-doped chalcogenide glass (Ga5Ge20Sb10S65) microstructured optical fiber (MOF) amplifier under the excitation of 980 nm is presented to demonstrate the feasibility of it applied for 1.53 μm band optical communications. By solving the Er3+ population rate equations and light power propagation equations, the amplifying performance of 1.53 μm band signals for Er3+-doped chalcogenide glass MOF amplifier is investigated theoretically. The results show that the Er3+-doped chalcogenide glass MOF exhibits a high signal gain and broad gain spectrum, and its maximum gain for small-signal input (−40 dBm) exceeds 22 dB on the 300 cm MOF under the excitation of 200 mW pump power. Moreover, the relations of 1.53 μm signal gain with fiber length, input signal power and pump power are analyzed. The results indicate that the Er3+-doped Ga5Ge20Sb10S65 MOF is a promising gain medium which can be applied to broadband amplifiers operating in the third communication window.

Multiparameter-dependent spontaneous emission in PbSe quantum dot-doped liquid-core multi-mode fiber

A theoretical model was established in this paper to analyze the properties of 3.50 and 4.39 nm PbSe quantum dot-doped liquid-core multi-mode fiber. This model was applicable to both single- and multi-mode fiber. The three-level system-based light-propagation equations and rate equations were used to calculate the guided spontaneous emission spectra. Considering the multi-mode in the fiber, the normalized intensity distribution of transversal model was improved and simplified. The detailed calculating results were thus obtained and explained using the above-mentioned model. The redshift of the peak position and the evolution of the emission power were observed and analyzed considering the influence of the fiber length, fiber diameter, doping concentration, and the pump power. The redshift increased with the increases of fiber length, fiber diameter, and doping concentration. The optimal fiber length, fiber diameter, and doping concentration were analyzed and confirmed, and the related spontaneous emission power was obtained. Besides, the normalized emission intensity increased with the increase of pump power in a nearly linear way. The calculating results fitted well to the experimental data.

Theoretical studies on mid-infrared amplification in Ho3+-doped chalcogenide glass fibers

This paper investigated the MIR emission of Ho3+-doped Ge20Ga5Sb10S65 chalcogenide glasses upon excitation of 900nm laser diode. The spontaneous emission probability, absorption cross-section, and emission cross-section were calculated using the Judd-Ofelt theory and the Fuchbauer–Ladenburg equation. Theoretical studies of the Ho3+-doped chalcogenide glass fiber amplifier operating in the MIR wavelength range, specifically around the 2.86μm wavelength, were performed based on the rate and light propagation equations. The results indicate that the chalcogenide glass fiber presented a larger signal MIR gain and wider MIR gain spectrum. The maximum signal gain was 36dB and the gain width was 20dB.

Celestial ephemerides in an expanding universe

Post-Newtonian theory was instrumental in conducting the critical experimental tests of general relativity and in building the astronomical ephemerides of celestial bodies in the solar system with an unparalleled precision. The cornerstone of the theory is the postulate that the solar system is gravitationally isolated from the rest of the universe and the background spacetime is asymptotically flat. The present article extends this theoretical concept and formulates the principles of celestial dynamics of particles and light moving in gravitational field of a localized astronomical system embedded to the expanding Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. We formulate the precise mathematical concept of the Newtonian limit of Einstein's field equations in the conformally-flat FLRW spacetime and analyze the geodesic motion of massive particles and light in this limit. We prove that by doing conformal spacetime transformations, one can reduce the equations of motion of particles and light to the classical form of the Newtonian theory. However, the time arguments in the equations of motion of particles and light differ from each other in terms being proportional to the Hubble constant, H. This leads to the important conclusion that the equations of light propagation used currently by Space Navigation Centers for fitting range and Doppler-tracking observations of celestial bodies are missing some terms of the cosmological origin that are proportional to the Hubble constant, H. We also prove that the Hubble expansion does not affect the atomic time scale used in creation of astronomical ephemerides. We derive the cosmological correction to the light travel time equation and argue that their measurement opens an exciting opportunity to determine the local value of the Hubble constant, H, in the solar system independently of cosmological observations.

Suppression of ASE by Using Pulsed-Pumped Technique in Fiber Amplifier

Implementation of pulsed-pump technique in fiber amplifier is highly useful in the situation of low repetition rate and high energy pulses operation. In this paper, the ASE (Amplified Spontaneous Emission) dynamics simulation in a pulsed-pumped ytterbium-doped double-clad fiber amplifier is presented for the first time, which provides important guidance about optimizing the pulsed-pump mode. The simulations of ASE dynamics are carried out by solving the rate equations and light power propagation equations in fiber using the finite elements analysis method, including variations of ASE output power at two terminals of the fiber in the time span from 0 ~ 740μs after pump light injection. Furthermore, a way of optimizing signal injection time is discussed.

Light Propagation in the Second post-Newtonian Approximation of Scalar-Tensor Theory of Gravity

In this paper, we use the metric coefficients and the equation of motion obtained in the second post-Newtonian approximation of scalar-tensor theory to derive the second-order light propagation equation and the light deflection angle and compare it with previous works. These results are useful for precision astrometry missions like ASTROD, GAIA, Darwin and SIM which aim at astrometry with micro-arcsecond and nano-arcsecond accuracies, and need for the second post-Newtonian framework and ephemeris for observations to determine the stellar and spacecraft positions.

Effect of Ce 3+ codoping on Er 3+-doped bismuth-germanate glass and fiber under 980 nm excitation

Er 3+/Ce 3+ codoped bismuth-germanate glasses with the composition of Bi 2O 3-GeO 2-Ga 2O 3-Na 2O were prepared by the conventional melt-quenching method. The absorption spectra, fluorescence spectra, upconversion emission and lifetimes of Er 3+ ions were measured, and the effects of Ce 3+-doping on the spectroscopic properties of 1.53 μm band fluorescence of Er 3+ ion were investigated based on the analysis of energy transfer between Er 3+ and Ce 3+ ions. The results indicate that the 1.53 μm band fluorescence intensity can be improved evidently with the Ce 3+-doped concentration under the excitation of 980 nm. Meanwhile, the theoretical simulation based on the population rate equation and light power propagation equation indicates that the C + L band signal gain can also be improved dramatically by introducing Ce 3+ ions into the Er 3+-doped bismuth-germanate glass fiber. Therefore, it is necessary to introduce Ce 3+ ions when Er 3+-doped bismuth-germanate glass with low phonon energy is applied to the 1.53 μm band broad Er 3+-doped fiber amplifier (EDFA).

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.