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arXiv:1010.5732 · Physical Review Letters

Observation of Slow Light in the Noise Spectrum of a Vertical External Cavity Surface-Emitting Laser

Abdelkrim El Amili, B.-X. Miranda, Fabienne Goldfarb, Ghaya Baili, G. Beaudoin, Isabelle Sagnes, Fabien Bretenaker, Mehdi Alouini

Published Nov 24, 2010• 21 citations
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Abstract

The role of coherent population oscillations is evidenced in the noise spectrum of an ultralow noise laser. This effect is isolated in the intensity noise spectrum of an optimized single-frequency vertical external cavity surface-emitting laser. The coherent population oscillations induced by the lasing mode manifest themselves through their associated dispersion that leads to slow light effects probed by the spontaneous emission present in the nonlasing side modes.

DOI
10.1103/physrevlett.105.223902

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The role of coherent population oscillations is evidenced in the noise spectrum of an ultralow noise laser. This effect is isolated in the intensity noise spectrum of an optimized single-frequency vertical external cavity surface-emitting laser. The coherent population oscillations induced by the lasing mode manifest themselves through their associated dispersion that leads to slow light effects probed by the spontaneous emission present in the nonlasing side modes.
Coherent population oscillations (CPO), an ubiquitous mechanism inducing slow and fast light (SFL), is present in any active medium provided that a strong optical beam saturates this medium. Thus, CPO must be present in any single frequency laser since the oscillating beam acts as a strong pump which saturates the active medium. This effect could be observed using an external probe whose angular frequency is detuned with respect to the oscillating mode, by less than the inverse of the population inversion lifetime. This effect should be visible in the laser excess noise, using the spontaneous emission present in the non-lasing side longitudinal modes of a single-frequency laser as probe of the CPO effect. Class-A vertical external cavity surface emitting semiconductor lasers (VECSELs) [1] recently developed for their low noise characteristics make them perfectly suited for the observation of CPO induced SFL in their noise spectrum. The single-frequency laser used in our experiment is a VECSEL which operates at ∼ 1 µm. We focus on the excess noise due to the beat notes between the laser line and the spontaneous emission noise at neighboring longitudinal mode frequencies [2,3]. At the pthFSR frequency pΔ, the noise spectrum is thus the sum of two Lorentzian peaks due to the beat notes of the lasing mode with the corresponding sidebands (pthand −pthmodes). When the pumping rate is increased, we found experimentally that the excess noise consists of two peaks separated by δf = fp− f−p∼ 100 kHz (inset of Fig.1(a)). This frequency shift is given by: δf ≈ ν0Lmover L+n0Lm(δnp+δn−p), where n0 is the bulk refractive index of the semiconductor structure, L and Lmare the length of the cavity and the gain medium respectively. δn±pare the modifications of the refractive index of the structure experienced by the ±p side modes and induced by the dispersion associated with the CPO effect. In a semiconductor active medium, thanks to the Bogatov effect [4], the dispersion is not an odd function of the frequency detuning with respect to ½0. Thus, δnp≠ −δn−pand the two beat note frequencies fpand f−pcorresponding to the p and −p modes occur at slightly different frequencies, as evidenced by the double peak of Fig.1(a). This CPO induced index modification can be derived from the gain medium rate equation including the phase-intensity coupling coefficient α (Henry's factor) that is responsible for the Bogatov effect. This CPO effect is also responsible for the modification of the refractive index seen by the side modes which modifies the round-trip phase accumulated by each side mode Fig.1(b). Notice also that since the cavity FSR Δ is sufficiently large that we are probe the wings of the dispersion profile of Fig.1(b), i. e., in the slow light regime. In conclusion, we experimentally evidenced the existence of intracavity slow light effects in a laser induced by the CPO mechanism. These effects are probed by the laser spontaneous emission noise present in the non lasing modes.
Characterization of a vertical cavity surface emitting laser source for a frequency reference that uses coherent population trapping with atomic rubidium is reported. The frequency reference requires a low-noise laser that operates in a single transverse mode at 794.7nm. We show that biasing the laser at low output power and modulating it at higher frequency than its low relaxation oscillation frequency are necessary to obtain symmetric modulation sidebands and improve the long-term performance of the frequency reference.
We develop a simple model for the slow lights in Vertical Cavity Surface Emission Lasers (VCSELs), with the combination of cavity and population pulsation effects. The dependences of probe signal power, injection bias current and wavelength detuning for the group delays are demonstrated numerically and experimentally. Up to 65 ps group delays and up to 10 GHz modulation frequency can be achieved in the room temperature at the wavelength of 1.3 μμμm. The most significant feature of our VCSEL device is that the length of active region is only several μμμm long. Based on the experimental parameters of quantum dot VCSEL structures, we show that the resonance effect of laser cavity plays a significant role to enhance the group delays.
We develop a model for the slow light in the vertical cavity surface emission lasers (VCSELs), with the combinations of cavity and the population pulsation effects. The dependences of pumping power, injection current and wavelength detuning for the group delays are demonstrated theoretically and experimentally. Up to 65 ps group delays and up to 10 GHz modulation frequency can be achieved in the room temperature at the wavelength of 1.3 mum. Based on the experimental parameters of quantum dot VCSEL structures, we show that the resonance effect of laser cavity plays a significant role to enhance the group delays.
We study the field correlation functions and the natural laser spectrum for a slow-inversion laser with the thresholdless intensity fluctuations. In such a laser, the spontaneous-emission-driven relaxation oscillations are responsible for some unique features: The field correlation function oscillates with the frequency of relaxation oscillations ${\ensuremath{\omega}}_{r}$ and the laser line changes its profile. We show that appreciably above threshold the laser spectrum consists of three lines. In addition to the main line at the frequency of the lasing mode ${\ensuremath{\omega}}_{c}$ appear two lines at frequencies ${\ensuremath{\omega}}_{c}+{\ensuremath{\omega}}_{r}$ and ${\ensuremath{\omega}}_{c}\ensuremath{-}{\ensuremath{\omega}}_{r}$. The spontaneous emission noise in such lasers gives rise to nonlinear stochastic effects: Quantum noise affects the oscillation frequency ${\ensuremath{\omega}}_{r}$ and the decay rates of the field correlation function.