# Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Statement and Methods

#### 2.1. Boundary Value Problem Statement

**p**. A scheme of the considered scattering problem can be found in Figure 1.

#### 2.2. Generalization of the Optical Theorem

**I**—idem factor. Subsequently, the corresponding electric field of the multipole in ${D}_{0}$ appears as:

#### 3. Results

**Theorem**

**1.**

_{x},p

_{y},p

_{z}), localized at the point M

_{0}= (0,0,z

_{0}) of the Cartesian coordinate system. Then, the extinction cross-section${C}_{ext}:={C}_{scs}+{C}_{abs}$[27] accepts the following form:

#### 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

## References

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**MDPI and ACS Style**

Eremin, Y.A.; Wriedt, T. Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate. *Mathematics* **2021**, *9*, 3244.
https://doi.org/10.3390/math9243244

**AMA Style**

Eremin YA, Wriedt T. Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate. *Mathematics*. 2021; 9(24):3244.
https://doi.org/10.3390/math9243244

**Chicago/Turabian Style**

Eremin, Yuri A., and Thomas Wriedt. 2021. "Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate" *Mathematics* 9, no. 24: 3244.
https://doi.org/10.3390/math9243244