The transfer matrix: A geometrical perspective

Sánchez-Soto, Luis L.; Monzón, J. J.; Barriuso, A. G.; Cariñena, José F.

doi:10.1016/j.physrep.2011.10.002

Cited by 106 publications

(112 citation statements)

References 225 publications

(249 reference statements)

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“…Because every left-invisible potential can be written as the complex-conjugate of a right-invisible potential (see (6) * to obtain an explicit realization of the potentials v ± (x), v j (x), and w ± (x) that appear in (9), (12), and (13). This completes our solution of the local inverse scattering problem for general scattering potentials.…”

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confidence: 62%

“…Throughout this investigation, we use the transfer matrix of one-dimensional scattering theory [13] as our main tool. For a scattering potential v(x), the general solution of the Schrödiger equation, −ψ ′′ (x)+v(x)ψ(x) = k 2 ψ(x), or the Helmholtz equation, ψ ′′ (x)+k 2 n (x) 2 ψ(x) = 0, has the asymptotic form: ψ ± (x) = A ± e ikx + B ± e −ikx for x → ±∞,…”

mentioning

confidence: 99%

“…Then we can use (2) to relate M to the transfer matrices M i of v i (x) according to M = M 2 M 1 . This, so-called composition property, makes the transfer matrix an extremely useful tool in dealing with a variety of physics and engineering problems [13].…”

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confidence: 99%

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Addendum to “Unidirectionally invisible potentials as local building blocks of all scattering potentials”

Mostafazadeh

2014

Phys. Rev. A

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We give a complete solution of the problem of constructing a scattering potential v(x) that possesses scattering properties of one's choice at an arbitrary prescribed wavenumber. Our solution involves expressing v(x) as the sum of at most six unidirectionally invisible finite-range potentials for which we give explicit formulas. Our results can be employed for designing optical potentials. We discuss its application in modeling threshold lasers, coherent perfect absorbers, and bidirectionally and unidirectionally reflectionless absorbers, amplifiers, and phase shifters.Complex scattering potentials in one dimension provide a fertile ground for modeling various active optical systems. Among these are systems displaying spectral singularities [1][2][3][4] and unidirectional reflectionlessness and invisibility [5][6][7][8][9]. Spectral singularities correspond to scattering states that behave exactly like zerowidth resonances [1]. In optics they give rise to lasing at the threshold gain [10] while their time-reversal is responsible for coherent perfect absorption (CPA) or antilasing [11,12]. Unidirectional reflectionlessness and invisibility are also of great interest, because they offer means of realizing one-way linear optical devices [5,7]. The task of designing scattering potentials that support such desirable properties is clearly a problem of basic theoretical and practical importance. In this article we give a complete solution for this problem.Throughout this investigation, we use the transfer matrix of one-dimensional scattering theory [13] as our main tool. For a scattering potential v(x), the general solution of the Schrödiger equation, −ψ ′′ (x)+v(x)ψ(x) = k 2 ψ(x), or the Helmholtz equation, ψ ′′ (x)+k 2 n (x) 2 ψ(x) = 0, has the asymptotic form:where k is the wavenumber, n (x) is a refractive index that we can relate to v(x) via n (x) = 1 − v(x)/k 2 , and A ± and B ± are complex coefficients. The transfer matrix of v(x) (and n (x)) is the 2×2 matrix M satisfyingWe can express it in terms of the left and right reflection amplitudes, R l and R r , and the transmission amplitude T of v(x) according to [1]:Recall that the asymptotic scattering solutions of the above Schrödinger and Helmholtz equations have the formand the reflection and transmission coefficients are given by |R l/r | 2 and |T | 2 . We can use (1), (2) and (3) whereWe respectively refer to these conditions as "left-reflectionlessness" and "right-reflectionlessness." Clearly the condition for bidirectional reflectionlessness is R l = R r = 0. If a potential that is unidirectionally reflectionless at a wavenumber k 0 has a unit transmission amplitude, i.e., T = 1, at this wavenumber, we call it "unidirectionally invisible" [5]. Similarly, we use "left-invisible", "right-invisible", and "bidirectionally invisible" to mean that a potential is respectively leftreflectionless, right-reflectionless, and bidirectionally reflectionless and in addition satisfies T = 1 at k = k 0 .In this article we use the properties of the transfer matrix to addres...

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confidence: 62%

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Addendum to “Unidirectionally invisible potentials as local building blocks of all scattering potentials”

Mostafazadeh

2014

Phys. Rev. A

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“…To compute the optical response of these structures we will use the transfer-matrix technique [64]. The αth word of FS(h, ) has the associated transfer matrix…”

Section: Generalized Fibonacci Quasicrystalsmentioning

confidence: 99%

Lempel-Ziv Complexity of Photonic Quasicrystals

Monzón¹,

Felipe²,

Sánchez-Soto

2017

Preprint

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The properties of photonic quasicrystals ultimate rely on their inherent long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be studied. We use the Lempel-Ziv measure, a basic tool for information theoretic problems, to characterize the complexity of the specific structure under consideration. Using the generalized Fibonacci quasicrystals as our thread, we adress the relation between the optical response and the associated complexity.

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“…The classified lake transfer matrix reflects the dynamic process of the mutual transformation of the lake area in a certain period of time (Sánchez-Soto et al, 2012). It not only includes the information of all graded lakes at a certain time, but also contains more abundant information about the conversion from lakes since the beginning and the transferred quantity to lakes until the ending (Liu and Zhu, 2010 …”

Section: Classified Lake Transfer Matrixmentioning

confidence: 99%

Information Mining of Spatio-Temporal Evolution of Lakes Based on Multiple Dynamic Measurements

Wang¹,

Troin²

2017

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:Lakes are important water resources and integral parts of the natural ecosystem, and it is of great significance to study the evolution of lakes. The area of each lake increased and decreased at the same time in natural condition, only but the net change of lakes' area is the result of the bidirectional evolution of lakes. In this paper, considering the effects of net fragmentation, net attenuation, swap change and spatial invariant part in lake evolution, a comprehensive evaluation indexes of lake dynamic evolution were defined,. Such degree contains three levels of measurement: 1) the swap dynamic degree (SDD) reflects the space activity of lakes in the study period. 2) the attenuation dynamic degree (ADD) reflects the net attenuation of lakes into non-lake areas. 3) the fragmentation dynamic degree (FDD) reflects the trend of lakes to be divided and broken into smaller lakes. Three levels of dynamic measurement constitute the three-dimensional "Swap -attenuation -fragmentation" dynamic evolution measurement system of lakes. To show its effectiveness, the dynamic measurement was applied to lakes in Jianghan Plain, the middle Yangtze region of China for a more detailed analysis of lakes from 1984 to 2014. In combination with spatial-temporal location characteristics of lakes, the hidden information in lake evolution in the past 30 years can be revealed.

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The transfer matrix: A geometrical perspective

Cited by 106 publications

References 225 publications

Addendum to “Unidirectionally invisible potentials as local building blocks of all scattering potentials”

Addendum to “Unidirectionally invisible potentials as local building blocks of all scattering potentials”

Lempel-Ziv Complexity of Photonic Quasicrystals

Information Mining of Spatio-Temporal Evolution of Lakes Based on Multiple Dynamic Measurements

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