# Time-reversal Symmetry in Antenna Theory

## Abstract

**:**

## 1. Introduction

## 2. Time-Reversal Symmetry

#### 2.1. General Case

#### 2.2. Time-Harmonic Variation

## 3. Application to Antenna Theory

#### 3.1. Polarization and Impedance Matching

#### 3.2. Time-Reversed Field Generated with a Far-Field Illumination

## 4. Conclusions

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Illustration of the effect of the time-reversal operation in a time-domain scattering problem: (

**a**) The incoming waves ${E}_{1}^{+}$ and ${E}_{2}^{+}$ are scattered by the junction and originate two outgoing waves ${E}_{1}^{-}$ and ${E}_{2}^{-}$. (

**b**) Time-reversed scenario where the roles of the incoming and outgoing waves are exchanged.

**Figure 2.**(

**a**) An antenna fed by a time-harmonic generator radiates in free-space. (

**b**) Time-reversed problem wherein all the radiated energy returns to the antenna. The antenna terminals are connected to a matched load.

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**MDPI and ACS Style**

Silveirinha, M.G.
Time-reversal Symmetry in Antenna Theory. *Symmetry* **2019**, *11*, 486.
https://doi.org/10.3390/sym11040486

**AMA Style**

Silveirinha MG.
Time-reversal Symmetry in Antenna Theory. *Symmetry*. 2019; 11(4):486.
https://doi.org/10.3390/sym11040486

**Chicago/Turabian Style**

Silveirinha, Mário G.
2019. "Time-reversal Symmetry in Antenna Theory" *Symmetry* 11, no. 4: 486.
https://doi.org/10.3390/sym11040486