# Harmonic modulation of radiation of an external-feedback semiconductor laser

## Abstract

The appearance of the harmonic modulation regime at the Hopf bifurcation point is described analytically for a delayed-feedback semiconductor laser. The second-order delay differential equation with complex coefficients is derived. The frequency of oscillations appearing at the Hopf bifurcation point is determined by the solution of two relatively simple transcendental equations, from which the bifurcation point itself is found. These equations contain dependences on all the control parameters of the problem. The exact upper and lower limits of the oscillation frequency are found. A comparison with numerical results shows that the modulation frequency is preserved almost constant in a broad range of feedback phases. A procedure is proposed for determining the parameters of the laser providing the presence of bifurcations with a passage to oscillations with the specified frequency. The results obtained in the paper are of interest for WDM communication systems. (control of laser radiation parameters)

- Authors:

- State Research Center of Russian Federation 'Troitsk Institute for Innovation and Fusion Research', Troitsk, Moscow Region (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21466617

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Quantum Electronics (Woodbury, N.Y.); Journal Volume: 37; Journal Issue: 2; Other Information: DOI: 10.1070/QE2007v037n02ABEH013213

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; COMPARATIVE EVALUATIONS; DIFFERENTIAL EQUATIONS; FEEDBACK; LASER RADIATION; MATHEMATICAL SOLUTIONS; MODULATION; OSCILLATIONS; SEMICONDUCTOR LASERS; ELECTROMAGNETIC RADIATION; EQUATIONS; EVALUATION; LASERS; RADIATIONS; SEMICONDUCTOR DEVICES; SOLID STATE LASERS

### Citation Formats

```
Sukharev, Aleksandr G, and Napartovich, A P.
```*Harmonic modulation of radiation of an external-feedback semiconductor laser*. United States: N. p., 2007.
Web. doi:10.1070/QE2007V037N02ABEH013213.

```
Sukharev, Aleksandr G, & Napartovich, A P.
```*Harmonic modulation of radiation of an external-feedback semiconductor laser*. United States. doi:10.1070/QE2007V037N02ABEH013213.

```
Sukharev, Aleksandr G, and Napartovich, A P. Wed .
"Harmonic modulation of radiation of an external-feedback semiconductor laser". United States.
doi:10.1070/QE2007V037N02ABEH013213.
```

```
@article{osti_21466617,
```

title = {Harmonic modulation of radiation of an external-feedback semiconductor laser},

author = {Sukharev, Aleksandr G and Napartovich, A P},

abstractNote = {The appearance of the harmonic modulation regime at the Hopf bifurcation point is described analytically for a delayed-feedback semiconductor laser. The second-order delay differential equation with complex coefficients is derived. The frequency of oscillations appearing at the Hopf bifurcation point is determined by the solution of two relatively simple transcendental equations, from which the bifurcation point itself is found. These equations contain dependences on all the control parameters of the problem. The exact upper and lower limits of the oscillation frequency are found. A comparison with numerical results shows that the modulation frequency is preserved almost constant in a broad range of feedback phases. A procedure is proposed for determining the parameters of the laser providing the presence of bifurcations with a passage to oscillations with the specified frequency. The results obtained in the paper are of interest for WDM communication systems. (control of laser radiation parameters)},

doi = {10.1070/QE2007V037N02ABEH013213},

journal = {Quantum Electronics (Woodbury, N.Y.)},

number = 2,

volume = 37,

place = {United States},

year = {Wed Feb 28 00:00:00 EST 2007},

month = {Wed Feb 28 00:00:00 EST 2007}

}