Symmetry analysis of the numerical instabilities in the transfer matrix method

Luque-Raigon, Jose Miguel; Halme, Janne; Míguez, Hernán; Lozano, Gabriel

doi:10.1088/2040-8978/15/12/125719

Cited by 12 publications

(21 citation statements)

References 11 publications

(58 reference statements)

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“…These instabilities can be avoided using the modified TMM that uses reference system transformation to achieve a numerically stable electric field solution. 19,20 The new electric field is given by E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 6 ; 1 5 3Ẽ…”

Section: Stable Representation Of the Transfer Matrix Methodsmentioning

confidence: 99%

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Angular optical behavior of photonic-crystal-based dye-sensitized solar cells

2019

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Theoretical modeling of the incidence angle dependence is important for the performance evaluation of solar cells especially when they employ structural photonics that enhance their aesthetics for building-integrated photovoltaic applications. We present an optical model based on transfer matrix method, which is tailored for the analysis of the angular optical characteristics of dye-sensitized solar cells (DSSC) that incorporate a porous one-dimensional photonic-crystal (1DPC) back reflector. We provide complete mathematical description of the angular optics and electromagnetic energetics of DSSC, including solutions that avoid numerical instabilities in the case of thick, strongly light-absorbing layers. The model showed excellent quantitative agreement with angle-dependent spectral transmittance measurements recorded from complete DSSCs, allowing detailed analysis of the light harvesting enhancement by the dye provided by back-reflection of light from the 1DPC. Determining the ratio of the device transmittance measured with and without a 1DPC is proposed as a simple and practical way to determine the internal reflectance of the 1DPC embedded in the device structure. The reported model provides an accurate description of the coherent angular optics of DSSCs, applicable for situations where light scattering in the device structure can be neglected.

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Section: Stable Representation Of the Transfer Matrix Methodsmentioning

confidence: 99%

“…The TMM model provides an accurate optical description of the angular characteristics of DSSCs in the case when light scattering effects are negligible, completing our earlier theoretical works on the topic. [18][19][20] (a) (b) Table 1.…”

Section: Introductionmentioning

confidence: 99%

Angular optical behavior of photonic-crystal-based dye-sensitized solar cells

2019

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“…Figure 3 b displays the spatial distribution of the square of the electric fi eld, | E | 2 /| E 0 | 2 , for light of wavelength λ = 254 nm impinging normally to the fi lm deposited on silicon. Calculations were carried out using a code based on a vector wave transfer matrix method written in MatLab [ 27 ] using as inputs real and imaginary parts of the dielectric constant attained by fi tting the measured total refl ectance and total transmittance of the fi lm supported onto a quartz substrate, following a procedure described elsewhere. [ 28 ] The extinction coeffi cient of the BCP fi lm is 0.0056 at λ = 254 nm.…”

Section: Resultsmentioning

confidence: 99%

Adaptable Ultraviolet Reflecting Polymeric Multilayer Coatings of High Refractive Index Contrast

Smirnov

Ito

Calvo

et al. 2015

Advanced Optical Materials

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a series of undesirable photoreactions promoted by the absorption of UV photons, which lead to the deterioration of their mechanical and optical properties. Polymers are usually transparent to part of the UV spectrum, so a commonly employed synthetic strategy to attain UV blocking fi lms is based on embedding inorganic [3][4][5][6][7] or organic [8][9][10] UV absorbers within a polymeric matrix. The main drawback of this approximation is the short term durability of the shielding effect as a result of the photodegradation of either host, guest, or both, caused by the absorption of the same radiation from which protection is sought after. [11][12][13] Approaches based on fl exible inorganic nano structured multilayers that effi ciently refl ect radiation in an arbitrary spectral range as a result of interference effects, rather than by absorption, present a promising alternative route worth to be explored. [14][15][16][17] Unfortunately, a similar approach based on the alternation of polymeric fi lms exclusively is not feasible since the refractive index contrast typically achieved is so small that a large number of layers is required to reach a signifi cant refl ectance, and only in a narrow spectral range. [ 18,19 ] The use of all-polymeric materials of high refractive index contrast to build multilayer back refl ectors or UV shields will also be an advantage in the fi eld of fl exible and polymeric solar cells, in which some approaches based on inorganic materials have already been developed. [ 20,21 ] Very recently, some of us proved that a porous stratifi ed structure displaying strong refl ection peaks in the UV range can be attained from a block copolymer (BCP) fi lm. [ 22 ] In particular, it was demonstrated that a fi lm made of a diblock copolymer containing polystyrene (PS) and polymethyl methacrylate (PMMA), in brief [poly(styreneblock -methyl methacrylate) PS-b -PMMA)], can be used as starting material to attain ordered porous multilayers through a process that involves collective osmotic shock (COS). The fi nal structure shows alternate dense and porous layers, with signifi cant refractive index contrast, which endow it with photonic crystal properties in the UV range. At that moment, the appearance of the layered structure was hypothetically attributed to dynamic effects during the COS process occurring over ordered arrangements of isolated PMMA spheres embedded in a cross-linked PS matrix in the starting slab, which had previously been subjected to thermal and UV annealing processes. Further studies, herein reported, have demonstrated that the mechanism of formation of the porous layered structure is different to that originally A synthetic route is demonstrated to build purely polymeric nanostructured multilayer coatings, adaptable to arbitrary surfaces, and capable of effi ciently blocking by refl ection a targeted and tunable ultraviolet (UV) range. Refl ection properties are determined by optical interference between UV light beams refl ected at the interfaces between polystyrene layers of diff...

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“…This simply reverts to a product of matrices associated with the individual scattering units, allowing an efficient parallel numerical evaluation, while the scattering-matrix approach yields a recursion (see equation (5)) that has to be evaluated step by step. However, despite its advantages, the transfer-matrix method may suffer from numerical instabilities [35], which are not encountered in the scattering-matrix method [36].…”

Section: Theory For Layered Optomagnonic Structuresmentioning

confidence: 99%

High-efficiency triple-resonant inelastic light scattering in planar optomagnonic cavities

et al. 2019

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Optomagnonic cavities have recently been emerging as promising candidates for implementing coherent photon-magnon interactions, for applications in quantum memories and devices, and next generation quantum networks. A key challenge in the design of such cavities is the attainment of high magnon-mediated optical-to-optical conversion efficiencies, which could, e.g., be exploited for efficient optical interfacing of superconducting qubits, as well as the practicality of the final designs, which ideally should be planar and amenable to on-chip integration. Here, on the basis of a novel time-Floquet scattering-matrix approach, we report on the design and optimization of a planar, multilayer optomagnonic cavity, incorporating a cerium-substituted yttrium iron garnet thin film, magnetized in-plane, and operating in the triple-resonant inelastic light scattering regime. This architecture allows for magnon-mediated optical-to-optical conversion efficiencies of about 5% under realistic conditions, which is orders of magnitude higher than that attained in alternative optomagnonic designs. Our results suggest a viable way forward for realizing practical information inter-conversion, with high efficiencies, between microwaves, strongly coupled to magnons, and optical photons, as well as a platform for fundamental studies of classical and quantum dynamics in magnetic solids and for the implementation of futuristic quantum devices.

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Symmetry analysis of the numerical instabilities in the transfer matrix method

Cited by 12 publications

References 11 publications

Angular optical behavior of photonic-crystal-based dye-sensitized solar cells

Angular optical behavior of photonic-crystal-based dye-sensitized solar cells

Adaptable Ultraviolet Reflecting Polymeric Multilayer Coatings of High Refractive Index Contrast

High-efficiency triple-resonant inelastic light scattering in planar optomagnonic cavities

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