Transfer Matrix Formalism Research Articles

Modeling multilayer thin film interference effects in interface-specific coherent nonlinear optical spectroscopies

We develop a generalized model to describe thin film interference in interface-specific nonlinear optical spectroscopies of ideal isotropic stratified systems that enables the separation of this effect from the individual interfacial nonlinear responses. The model utilizes a property of the transfer matrix formalism that allows for simplification of an arbitrary layered system to a single layer with newly defined coefficients of reflection and transmission. In addition to the already well known internal transfer coefficients that relate incident fields to internal fields, we define external transfer coefficients that describe how internally generated fields propagate out of the system. By applying the usual boundary conditions we are able to analytically describe the local and induced fields immediately adjacent to an arbitrary interface, followed by transfer of the generated fields out of the system. The model provides a complete and easily implemented approach to calculating the observables from interface-specific spectroscopies on arbitrary layered thin film systems in a concise way.

Layout optimization of organic wrap through solar cells by combined electrical and optical modeling

In organic wrap through solar cells the current which is collected by poly(3,4-ethylenedioxythiophene) doped with poly(styrenesulfonate) (PEDOT:PSS) at the illuminated front side is transferred through vias which are distributed over the cell to another metal layer on the backside. They feature a low area loss and the possibility of broad cell stripes in modules. A combined optical and electrical model is applied on organic wrap through solar cells to optimize the layout. Calculating the absorption by the transfer matrix formalism allows to identify the optimum layer thickness for the PEDOT:PSS which depends on the transparency and the conductivity. The efficiency turns out to be robust regarding layer thickness variations close to the optimum at a layer thickness of 200nm for the PEDOT:PSS. The via diameter has to be chosen as small as possible for the best performance and the parasitic resistances caused by the PEDOT:PSS and the vias mainly determine the optimum distance between the vias. It is furthermore possible to use the model to estimate the series resistance of the vias and the series resistance which can be attributed to the transport through the photoactive layer and its interfaces which is helpful for further device optimization. Wrap through solar cells on plastic substrates were manufactured with a maximum efficiency of 2.8% on a cell area of 2.25cm2. The investigations revealed that there is further optimization potential by optimizing the processing of the active layer.

Electronic transmission in non-linear potential profile of GaAs/AlxGa1−xAs biased quantum well structure

We study the effect of the nonlinearity on electrons transmission properties in a double barriers structure GaAs/AlxGa1−xAs superlattices. The nonlinearity is introduced as an effective potential in the Schrödinger equation and translates the electronic Colombian repulsion. We have used the transfer matrix formalism and the plane wave functions approximation to solve numerically the equation and calculate the electronic transmission coefficient. We have shown the occurrence of two allowed states within the same well instead of a single, translating the presence of two resonant states at two different energies. The first allowed state intensity strongly decreases with increasing the nonlinear parameter, whereas the second one called the degeneracy state increases. Both the two states evolve towards higher resonances energies.

Delocalization of Acoustic Waves in a One-Dimensional Random Dimer Media

The propagation of classical waves in one-dimensional random media is examined in presence of short-range correlation in disorder. A classical analogous of the Kronig-Penney model is proposed by means a chain of repeated sub-systems, each of them constituted by a mass connected to a rigid foundation by a spring. The masses are related to each other by a string submitted to uniform tension. The nature of the modes is investigated by using different transfer matrix formalisms. It is shown that in presence of short-range correlation in the medium which corresponds to the RD model- the localization-delocalization transition occurs at a resonance frequency . The divergence of near is studied, and the critical exponent that characterizes the power-law behavior of near is estimated. Moreover an exact analytical study is carried out for the delocalization properties of the waves in the RD media. In particular, we predict the resonance frequency at which the waves can propagate in the entire chain. The transmission properties of the system are numerically studied using a statistical procedure yielding various physical magnitudes such the transmission coefficient, the localization length and critical exponents. In particular, it is shown that the presence of correlation in disorder restores a large number of extended Bloch-like modes in contradiction with the general conclusion of the localization phenomenon in one-dimensional systems with correlated disorder.

Tamm plasmon polaritons in multilayered cylindrical structures

It is shown that cylindrical Bragg reflector structures with either a metal core, a metal cladding, or both can support Tamm plasmon polaritons (TPPs) that can propagate axially along the interface between the metallic layer and the adjacent dielectric. A transfer matrix formalism for cylindrical multilayered structures is used in association with cavity phase matching considerations to design structures that support Tamm plasmon polaritons at specified frequencies, and to explore the field distributions and the dispersion relations of the excitations. The cylindrical TPPs can exist in both the TE and TM polarizations for the special cases of modes with either azimuthal isotropy or zero axial propagation constant and also as hybrid cylindrical modes when neither of those conditions applies. In the cases considered the TPPs have low effective masses and low group velocities. Also, when there is both metallic core and cladding, near degenerate modes localized at each metallic interface can couple to produce symmetric and antisymmetric combinations whose frequency difference is in the terahertz regime.

Van der Waals interaction in uniaxial anisotropic media

Van der Waals interactions between flat surfaces in uniaxial anisotropic media are investigated in the nonretarded limit. The main focus is the effect of nonzero tilt between the optical axis and the surface normal on the strength of the van der Waals attraction. General expressions for the van der Waals free energy are derived using the surface mode method and the transfer-matrix formalism. To facilitate numerical calculations a temperature-dependent three-band parameterization of the dielectric tensor of the liquid crystal 5CB is developed. A solid slab immersed in a liquid crystal experiences a van der Waals torque that aligns the surface normal relative to the optical axis of the medium. The preferred orientation is different for different materials. Two solid slabs in close proximity experience a van der Waals attraction that is strongest for homeotropic alignment of the intervening liquid crystal for all the materials studied. The results have implications for the stability of plate-like colloids in liquid crystal hosts.

Polarization dependence of III-nitride superlattice transmission coefficient

We study the tunnelling process and behaviour of the transmission coefficient of an AlN/GaN superlattice as the internal polarizations in the composing layers change. Our calculations are based on the transfer matrix formalism and the exact solution of the Schrödinger's equation provided by the Airy functions. We also examine the dependence between the minizones width and the magnitude of the internal polarizations both for unbiased and biased structure.

Bio-inspired approach of the fluorescence emission properties in the scarabaeid beetle Hoplia coerulea (Coleoptera): Modeling by transfer-matrix optical simulations

Scales of the scarabaeid beetle Hoplia coerulea (Coleoptera) contain fluorescent molecules embedded in a multilayer structure. The consequence of this source confinement is a modification of the fluorescence properties, i.e., an enhancement or inhibition of the emission of certain wavelengths. In this work, we propose a bio-inspired approach to this problem. In other words, we use numerical simulations based on the one-dimensional transfer-matrix formalism to investigate the influence of a Hoplia-like system on emission characteristics and, from the results, we deduce potential technical applications. We reveal that depending on the choice of some parameters (layer thickness, dielectric constant, and position of the emitting source in the structure), it is possible to enhance or inhibit the fluorescence emission for certain wavelengths. This observation could be of great interest to design new optical devices in the field of optoelectronic, solar cells, biosensors, etc.

Energy transport in a one-dimensional harmonic ternary chain with Ornstein–Uhlenbeck disorder

In this paper we study a one-dimensional ternary harmonic chain with the mass distribution constructed from an Ornstein–Uhlenbeck process. We generate a ternary mass disordered distribution by generating the correlated Ornstein–Uhlenbeck process and mapping it into a sequence of three different values. The probability of each value is controlled by a fixed parameter b. We analyze the localization aspect of the above model by numerical solution of the Hamilton equations and by the transfer matrix formalism. Our results indicate that the correlated ternary mass distribution does not promote the appearance of new extended modes. In good agreement with previous work, we obtain extended modes for b → ∞; however, we explain in detail the main issue behind this apparent localization– delocalization transition. In addition, we obtain the energy dynamics for this classical chain.

Large area ITO-free organic solar cells on steel substrate

Large area ITO-free organic solar cells on steel substrates are demonstrated. The stainless steel was used as a substrate with excellent barrier properties and as a bottom electrode with very low sheet resistance. The low sheet resistance of the steel electrode allows manufacturing of large area devices with good performance. The individual cells with the size of 5×10cm2 and efficiency of 1.3% were manufactured. The OPV cells with steel electrode demonstrate fill factor in the range of 58–69%, as measured under illumination through a mask with an aperture of 1.0×1.0cm2. A thermally evaporated semitransparent top cathode, contained ZnS and thin metal layers, was used to complete the device stack. In order to quantitate effect of the cathode transmittance, the optical simulations using the transfer-matrix formalism has been performed.

Anchoring effects on the electrically controlled optical band gap in twisted photonic liquid crystals

We study a one-dimensional twisted photonic liquid crystal (TPLC), consisting of various nematic liquid crystal cells adopting a twisted configuration intercalated by isotropic dielectric layers, submitted to a dc electric field (Edc ) aligned along the periodicity axis. We write the corresponding Euler–Lagrange equations describing the nematic layer configuration. By assuming arbitrary anchoring quasi-planar boundary conditions, we calculate the equilibrium textures for the nematic, parametrized by the two types of strength of its interaction (polar and azimuthal) with the plane walls. We write the electromagnetic equations in a 4 × 4 matrix representation and using the transfer matrix formalism, we obtain the transmittance and reflectance coefficients for normal incidence as functions of the external electric field and anchoring strengths. We have observed a remarkable dependence of the electric field on the transmission and reflection spectra in opening and closing band gaps.

Spectral aspects of cavity tuned absorption in organic photovoltaic films

Concentration of light and infrared capture are two favored approaches for increasing the power conversion efficiency (PCE) of photovoltaic devices. Using optical transfer matrix formalism, we model the absorption of organic photovoltaic films as a function of active layer thickness and incident wavelength. In our simulations we consider the absorption in the optical cavity formed by the polymer bulk heterojunction active layer (AL) between the aluminum cathode and indium tin oxide (ITO) anode. We find that optical absorption can be finely tuned by adjusting the ITO thickness within a relatively narrow range, thus eliminating the need for a separate optical spacer. We also observe distinct spectral effects due to frequency pulling which results in enhanced long-wavelength absorption. Spectral sculpting can be carried out by cavity design without affecting the open circuit voltage as the spectral shifts are purely optical effects. We have experimentally verified aspects of our modeling and suggest methods to improve device design.

Resonance splitting effect through magnetic superlattices in graphene

Using the transfer-matrix formalism, the resonance splitting effect of Dirac electrons through two types of magnetic superlattices in graphene is studied theoretically. The numerical results show that the transmission presents (n − 1)-fold resonance splitting for the both magnetic superlattices with n-barrier, similar to Schrödinger electrons in semiconductor superlattices. It is believed that the Dirac electrons possess a general (n − 1)-fold splitting rule for n-barrier magnetic superlattices, of which the corresponding vector potential is periodic field. The magnetic superlattices with strong magnetic field can be used as a very efficient wave-vector filter for Dirac electrons. The splitting feature of the transmission probability also reflects in the conductance and shot noise. These properties should be useful for the design of graphene-based electronic devices.

Surface and optical phonon characteristics of ZnO/diamond heterostructure

Abstract In this paper, we report on surface and optical phonon properties of ZnO/diamond heterostructure. ZnO thin film was deposited via radio-frequency magnetron sputtering on p -type diamond substrate. Polarized IR reflectance and attenuated total reflection (ATR) techniques were employed to investigate the optical phonon and surface phonon polariton (SPP) of the ZnO/diamond heterostructure, respectively. The obtained experimental spectra were fitted by the theoretical spectra simulated using a standard transfer matrix formulation. Overall, the experimental and theoretical spectra were in good agreement. To verify the origin of the observed ATR dip, surface polariton dispersion spectrum of the studied structure was generated based on standard multilayer reflection mapping technique. The result reveals that the detected ATR dip was attributed to the leaky SPP mode of ZnO.

Effect of Ga+ irradiation on the magneto-optic spectra of Pt/Co/Pt sandwiches

Interfacial changes in rf sputtered Pt/Co(2.6nm)/Pt sandwiches grown onto sapphire (Al2O3) substrates induced by irradiation of 30keV Ga+ ions at low dose (1014 ions/cm2) have been investigated by magneto-optic polar Kerr rotation (PKR) spectroscopy between 1 and 5eV. The irradiation resulted in an increase of PKR over the whole spectral range. The measured PKR spectra were compared with those computed from the transfer matrix formalism using known polar Kerr rotation and ellipticity spectra for Co and five CoxPt1−x alloys. The comparison between measured and computed PKR spectra provided an in-depth profile of Co and Pt ion distributions across the sandwich and confirmed that irradiation favors alloying in the vicinity of the two interfaces. These results are in a good agreement with the profile evaluated independently by TRIDYN simulations. Our results evidence an asymmetry in the irradiation effect due to an excess of Pt–Co alloying at the upper interface. Moreover, the observation of a negative PKR peak around 3.2eV states definitively the presence of a chemically ordered Co0.75Pt0.25 alloy phase inside the irradiated film structure.

Linear and nonlinear optical absorption coefficients in GaAs/Ga1−xAlxAs concentric double quantum rings: Effects of hydrostatic pressure and aluminum concentration

The linear and nonlinear intra-band optical absorption coefficients in GaAs/Ga1−xAlxAs two-dimensional concentric double quantum rings are investigated. Taking into account the combined effects of hydrostatic pressure and aluminum concentration the energies of the ground (n=1,l=0) and the first excited state (n=2,l=1) have been found using the effective mass approximation and the transfer matrix formalism. The energies of these states and the corresponding threshold energy of the intra-band optical transitions are examined as a function of hydrostatic pressure and aluminum concentration for different sizes of the structure. We also investigated the dependencies of the linear, nonlinear, and total optical absorption coefficients as functions of the incident photon energy for different values of hydrostatic pressure, aluminum concentration, sizes of the structure, and incident optical intensity. Its is found that the effects of the hydrostatic pressure and the aluminum concentration lead to a shifting of the resonant peaks of the intra-band optical spectrum.

ENERGY DYNAMICS IN A ONE-DIMENSIONAL APERIODIC ANHARMONIC LATTICE

We study the nature of collective excitations in classical anharmonic lattices with aperiodic and pseudo-random harmonic spring constants. The aperiodicity was introduced in the harmonic potential by using a sinusoidal function whose phase varies as a power-law, ϕ ∝ nν, where n labels the positions along the chain. In the absence of anharmonicity, we numerically demonstrate the existence of extended states and energy propagation for a sufficiently large degree of aperiodicity. Calculations were done by using the transfer matrix formalism (TMF), exact diagonalization and numerical solution of the Hamilton's equations. When nonlinearity is switched on, we numerically obtain a rich framework involving stable and unstable solitons.

Omnidirectional band gaps in quasiperiodic photonic crystals in the THz region

In this work we calculate the emittance spectra of the electromagnetic radiation normally and obliquely incident (s- and p-polarized modes) on a one-dimensional multilayer quasiperiodic photonic structure made up by layered system of positive (SiO2) and negative (LiTaO3) refractive index materials organized in a quasiperiodic (Fibonacci-like) fashion. We model the negative refractive index material by an effective medium, whose electric permittivity ϵ(ω) is characterized by a phonon-polariton frequency dependent dielectric function, while for the magnetic permeability μ(ω) we have a Drude-like frequency-dependent function. The emittance spectra are determined by means of a well known theoretical model based on Kirchoff’s second law, together with a transfer matrix formalism. Our results shows that the omnidirectional band gaps appear in the THz regime, in well defined frequency intervals independently of the electromagnetic radiation’s polarized modes.

Design of high efficiency organic solar cell with light trapping

We have designed a high efficiency organic solar cell with light trapping structure on transference cylindrical substrate. An electrical and optical simulation of the light trapping structure has been performed on the basis of finite element and transfer matrix formalism methods. Absorption spectrum, internal quantum efficiency, external quantum efficiency, maximum power output and efficiency of the organic solar cell are simulated and presented in terms of three variables: the height, diameter of the glass substrate and the thickness of the organic active layer. The efficiency of the proposed organic solar cell with light trapping structure is enhanced by a factor of 2 than the similar structure on the flat plain glass substrate. The optimum organic active layer thickness to achieve the highest efficiency is shifted from 65 to 20 nm. Finally, we have investigated the effect of light incident angle on the performance of the proposed cell structure.

1D PHONON SCATTERING BY STABLE SPATIALLY INHOMOGENEOUS EQUILIBRIUM SOLUTION IN NONLINEAR DISCRETE KLEIN–GORDON MODEL: EXACT ANALYSIS

Nonlinear Discrete Klein–Gordon (NDKG) model is a nonlinear lattice model used to investigate different nonlinear phenomena raised in many physical contexts. In the present study we use this model to observe linear phonon scattering by stable spatially inhomogeneous equilibrium solution in the piece-wise linear (PWL) version (asymmetric double well) of nonlinearity instead of the conventional cubic or other types of nonlinearities. Considering one-site symmetric solution in such a system we are able to construct the exact expressions for the transmittance (T) and reflectance using the transfer matrix formalism. From the condition of perfect transmission (T = 1, hence reflectance, R = 0) in the elastic scattering process, we observe in our model, such a situation happens to appear at the threshold of a localized mode at the band-edge of the extended eigen modes. The advantage of the PWL version of nonlinearity is that all the results derived are exact.