# Electromagnetic-field amplification in finite one-dimensional photonic crystals

## Abstract

The electromagnetic-field distribution in a finite one-dimensional photonic crystal is studied using the numerical solution of Maxwell’s equations by the transfer-matrix method. The dependence of the transmission coefficient T on the period d (or the wavelength λ) has the characteristic form with M–1 (M is the number of periods in the structure) maxima with T = 1 in the allowed band of an infinite crystal and zero values in the forbidden band. The field-modulus distribution E(x) in the structure for parameters that correspond to the transmission maxima closest to the boundaries of forbidden bands has maxima at the center of the structure; the value at the maximum considerably exceeds the incident-field strength. For the number of periods M ~ 50, more than an order of magnitude increase in the field amplification is observed. The numerical results are interpreted with an analytic theory constructed by representing the solution in the form of a linear combination of counterpropagating Floquet modes in a periodic structure.

- Authors:

- Russian Academy of Sciences, Lebedev Physics Institute (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22617193

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 123; Journal Issue: 3; Other Information: Copyright (c) 2016 Pleiades Publishing, Inc.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLIFICATION; CRYSTALS; DISTRIBUTION; ELECTROMAGNETIC FIELDS; EQUATIONS; NUMERICAL SOLUTION; ONE-DIMENSIONAL CALCULATIONS; PERIODICITY; TRANSFER MATRIX METHOD; WAVELENGTHS

### Citation Formats

```
Gorelik, V. S., and Kapaev, V. V., E-mail: kapaev@sci.lebedev.ru.
```*Electromagnetic-field amplification in finite one-dimensional photonic crystals*. United States: N. p., 2016.
Web. doi:10.1134/S1063776116070062.

```
Gorelik, V. S., & Kapaev, V. V., E-mail: kapaev@sci.lebedev.ru.
```*Electromagnetic-field amplification in finite one-dimensional photonic crystals*. United States. doi:10.1134/S1063776116070062.

```
Gorelik, V. S., and Kapaev, V. V., E-mail: kapaev@sci.lebedev.ru. Thu .
"Electromagnetic-field amplification in finite one-dimensional photonic crystals". United States.
doi:10.1134/S1063776116070062.
```

```
@article{osti_22617193,
```

title = {Electromagnetic-field amplification in finite one-dimensional photonic crystals},

author = {Gorelik, V. S. and Kapaev, V. V., E-mail: kapaev@sci.lebedev.ru},

abstractNote = {The electromagnetic-field distribution in a finite one-dimensional photonic crystal is studied using the numerical solution of Maxwell’s equations by the transfer-matrix method. The dependence of the transmission coefficient T on the period d (or the wavelength λ) has the characteristic form with M–1 (M is the number of periods in the structure) maxima with T = 1 in the allowed band of an infinite crystal and zero values in the forbidden band. The field-modulus distribution E(x) in the structure for parameters that correspond to the transmission maxima closest to the boundaries of forbidden bands has maxima at the center of the structure; the value at the maximum considerably exceeds the incident-field strength. For the number of periods M ~ 50, more than an order of magnitude increase in the field amplification is observed. The numerical results are interpreted with an analytic theory constructed by representing the solution in the form of a linear combination of counterpropagating Floquet modes in a periodic structure.},

doi = {10.1134/S1063776116070062},

journal = {Journal of Experimental and Theoretical Physics},

number = 3,

volume = 123,

place = {United States},

year = {Thu Sep 15 00:00:00 EDT 2016},

month = {Thu Sep 15 00:00:00 EDT 2016}

}