On the Optimum Performance of Variable and Nonreciprocal Networks

Schaug-Pettersen, T.; Tonning, A.

doi:10.1109/tct.1959.1086535

Cited by 18 publications

(10 citation statements)

References 5 publications

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“…Such a loss may be due to back‐reflection, to scattering into other channels, or to absorption inside the switching region. Following the theory outlined in , and proved in the Supplementary Material for a device of arbitrary geometry, it turns out that the insertion losses are ultimately determined solely by the complex permittivity of the switching material employed in the device. In formulas:

\begin{matrix} true \\ right \frac{4 \min [T_{I}, T_{II}]}{{(1 - \min [T_{I}, T_{II}])}^{2}} \leq 0true max_{boldr \in V} \frac{| ɛ_{I} (r) - ɛ_{II} {(r) |}^{2}}{4 ɛ_{I}^{''} (r) ɛ_{italicII}^{''} (r)} \equiv γ_{mat}, \end{matrix}

where

T_{I}

and

T_{II}

are the intensity transmittances of the device in states I and

I I

ɛ_{I} (boldr)

and

ɛ_{italicII} (boldr)

are the (complex) permittivities inside the volume V where the switching action takes place, and

ɛ^{''}

denotes the imaginary part of the permittivity.…”

Section: Fundamental Limit On the Losses Of Phase Actuatorsmentioning

confidence: 99%

“…Such a loss may be due to back-reflection, to scattering into other channels, or to absorption inside the switching region. Following the theory outlined in [25,26], and proved in the Supplementary Material for a device of arbitrary geometry, it turns out that the insertion losses are ultimately determined solely by the complex permittivity of the switching material employed in the device. In formulas:…”

Section: Fundamental Limit On the Losses Of Phase Actuatorsmentioning

confidence: 99%

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Fundamental limits on the losses of phase and amplitude optical actuators

Zanotto

Morichetti

Melloni

2015

Laser & Photonics Reviews

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Amplitude and phase are the basic properties of all wave phenomena; as far as optical waves are concerned, the ability to act on these variables is at the root of a wealth of switching devices. To quantify the performance of an optical switching device, an essential aspect is to determine the tradeoff between the insertion loss and the amplitude or phase modulation depth. Here it is shown that every optical switching device is subject to such a tradeoff, intrinsically connected to the dielectric response of the materials employed inside the switching element itself. This limit finds its roots in fundamental physics, as it directly derives from Maxwell's equations for linear dielectrics, and is hence applicable to a wide class of optical components. Furthermore, a result is that concepts such as filtering, resonance, and critical coupling could be of advantage in approaching the limit.

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\begin{matrix} true \\ right \frac{4 \min [T_{I}, T_{II}]}{{(1 - \min [T_{I}, T_{II}])}^{2}} \leq 0true max_{boldr \in V} \frac{| ɛ_{I} (r) - ɛ_{II} {(r) |}^{2}}{4 ɛ_{I}^{''} (r) ɛ_{italicII}^{''} (r)} \equiv γ_{mat}, \end{matrix}

where

T_{I}

and

T_{II}

are the intensity transmittances of the device in states I and

I I

ɛ_{I} (boldr)

and

ɛ_{italicII} (boldr)

are the (complex) permittivities inside the volume V where the switching action takes place, and

ɛ^{''}

denotes the imaginary part of the permittivity.…”

Section: Fundamental Limit On the Losses Of Phase Actuatorsmentioning

confidence: 99%

Section: Fundamental Limit On the Losses Of Phase Actuatorsmentioning

confidence: 99%

Fundamental limits on the losses of phase and amplitude optical actuators

Zanotto

Morichetti

Melloni

2015

Laser & Photonics Reviews

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show abstract

“…rameters, as in (1) or (4); can be removed by a-perturbation 07 ihe 1 Singularities occurring in matrices containing the embedding Daembedding elements since this does not affect the invariants. Sineularities occurring in matrices involving only values of the set N, as 7n (2). can be removed in a way analogous to that indicated in [3, p. 411, or when possible, simply by changing the sequence of the indices.…”

Section: Invariants For Four-value N-port Networkmentioning

confidence: 99%

“…INvARIANTSF~RTW~-AND THREE-VALUENETWORKS By using any of the symmetry operations, it is possible to reduce from four to two the number of independent values appearing in the cross-ratio matrix (2). For instance, by using Tz and a choice of Z3= -Zl*, or Zq = -Zz*, we obtain from (2) v = $(.z, -Zz)R1-'.…”

Section: Transformation Symmetries Appropriate Operator Equatiomentioning

confidence: 99%

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The Invariance Properties of a Multivalue n-Port in a Linear Embedding

Heuven¹,

Rozzi²

1972

IEEE Trans. Circuit Theory

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Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices

Tamagnone¹,

Fallahi²,

Mosig³

et al. 2014

Nature Photon

113

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The potential of graphene for use in photonic applications was evidenced by recent demonstrations of modulators, polarisation rotators, and isolators. These promising yet preliminary results raise crucial questions: what is the optimal performance achievable by more complex designs using multilayer structures, graphene patterning, metal additions, or a combination of these approaches, and how can this optimum design be achieved in practice? Today, the complexity of the problem, which is magnified by the variability in graphene parameters, leaves the design of these new devices to time-consuming and suboptimal trial-and-error procedures. We address this issue by first demonstrating that the relevant figures of merit for the devices above are subject to absolute theoretical upper bounds. Strikingly these limits are related only to the conductivity tensor of graphene; thus, we can provide essential roadmap information such as the best possible device performance versus wavelength and graphene quality. Second, based on the theory developed, physical insight, and detailed simulations, we demonstrate how structures closely approaching these fundamental limits can be designed, demonstrating the possibility of significant improvement. These results are believed to be of paramount importance for the design of graphene-based modulators, rotators, and isolators and are also directly applicable to other 2-dimensional materials.In recent years, there has been a surge of interest in graphene-based devices for various photonic and optoelectronic applications 1-15 . Among other very promising passive devices, including amplitude modulators 5, 16-23 , Faraday and Kerr polarisation rotators 24-26 , and non-reciprocal isolators 27,28 have been demonstrated. These essential photonic blocks might constitute some of the most important applications of graphene; thus, there is a significant and growing effort to transform the above-mentioned initial demonstrations into real capabilities. However, this prospect still requires drastic performance improvements. For this purpose, researchers have now started to develop graphene-based devices with multiple degrees of freedom by considering several technological solutions (see Figure 1e), including multilayer structures 22, 29, 30 , graphene patterning 7, 22, 25, 31 , substrate engineering, and combining metal and graphene 13,14,18,21,29,32 .

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On the Optimum Performance of Variable and Nonreciprocal Networks

Cited by 18 publications

References 5 publications

Fundamental limits on the losses of phase and amplitude optical actuators

Fundamental limits on the losses of phase and amplitude optical actuators

The Invariance Properties of a Multivalue n-Port in a Linear Embedding

Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices

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