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Correlation properties and drift phenomena in the dynamics of vertical-cavity surface-emitting lasers with optical feedback

Markus Sondermann and Thorsten Ackemann

Open Access Open Access

Abstract

We investigate experimentally the polarization dynamics of vertical-cavity surface-emitting lasers with isotropic optical feedback operating in the long-cavity regime. By means of an analysis of the correlation properties in the time domain and in the frequency domain a connection between a drift phenomenon and frequency components that deviate from the harmonics of the external cavity round-trip frequency is revealed. The latter frequency components are shown to result from an interaction of external cavity dynamics and relaxation oscillations. An analogy to the carrier-envelope effect in mode-locked lasers is drawn. Similar drift phenomena are observed also for other laser systems with delay.

©2005 Optical Society of America

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Figures (4)
Fig. 1.
Fig. 1. Characterization of the dynamics of a VCSEL with isotropic optical feedback: (a) measured time traces, (b) auto correlation functions, (c) cross correlation function, (d) power spectra of the polarization modes, (e) cross spectral density (CSD). In panels displaying data for both polarization modes, the red and blue lines denote the data corresponding to the two orthogonal polarization modes. The injection current is set to the threshold of the solitary laser. The threshold reduction with feedback is 6%. The detection bandwidth is 1 GHz.

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Fig. 2.
Fig. 2. Cross correlation function for the same parameters as in Fig. 1(c) but after elimination of the correlated (green line) and anticorrelated (red line) frequency components from the cross spectral density (see text for further explanations). The red line is raised by 0.2 units for better visibility.

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Fig. 3.
Fig. 3. Power spectrum of the dominant polarization mode and cross spectral density (CSD) of the dynamics of the both polarization modes for another device with a threshold reduction of 18% for injection currents 4% below (a,b) and 32% above (c,d) the threshold of the solitary laser, respectively. Red (blue) colour denotes anticorrelated (correlated) components. The inset in panel (d) is a magnification of the spectral components for frequencies larger than 2 GHz. The detection bandwidth is 6 GHz. The corresponding time series are amplified by 20 dB and the DC-component is cut off. The features near 1.7 GHz and 3.4 GHz in panel (b) are artefacts that are captured by the setup.

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Fig. 4.
Fig. 4. Auto correlation function (a) and power spectrum (b) of the dominant polarization mode of another device with isotropic feedback. The inset in (b) displays the frequencies (in GHz) of the spectral components at the first harmonic of the external cavity frequency as a function of the injection current normalized to the threshold of the solitary laser. The threshold reduction is 8%. The current is set to 0.95 times the threshold of the laser without feedback. The detection bandwidth is 1 GHz.

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