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arXiv:2012.00352 · Journal of Modern Physics

Stochastic Simulation of Emission Spectra and Classical Photon Statistics of Quantum Dot Superluminescent Diodes

Kai Niklas Hansmann, R. Walser

Published Jan 1, 2021• 3 citations
arXivHTMLPDF

Abstract

We present a stochastic procedure to investigate the correlation spectra of quantum dot superluminescent diodes. The classical electric field of a diode is formed by a polychromatic superposition of many independent stochastic oscillators. Assuming fields with individual carrier frequencies, Lorentzian linewidths and amplitudes we can form any relevant experimental spectrum using a least square fit. This is illustrated for Gaussian and Lorentzian spectra, Voigt profiles and box shapes. Eventually, the procedure is applied to an experimental spectrum of a quantum dot superluminescent diode which determines the first- and second-order temporal correlation functions of the emission. We find good agreement with the experimental data and a quantized treatment. Thus, a superposition of independent stochastic oscillators represents the first- and second-order correlation properties of broadband light emitted by quantum dot superluminescent diodes.

DOI
10.4236/jmp.2021.121003

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We present a stochastic procedure to investigate the correlation spectra of quantum dot superluminescent diodes. The classical electric field of a diode is formed by a polychromatic superposition of many independent stochastic oscillators. Assuming fields with individual carrier frequencies, Lorentzian linewidths and amplitudes we can form any relevant experimental spectrum using a least square fit. This is illustrated for Gaussian and Lorentzian spectra, Voigt profiles and box shapes. Eventually, the procedure is applied to an experimental spectrum of a quantum dot superluminescent diode which determines the first- and second-order temporal correlation functions of the emission. We find good agreement with the experimental data and a quantized treatment. Thus, a superposition of independent stochastic oscillators represents the first- and second-order correlation properties of broadband light emitted by quantum dot superluminescent diodes.
Commercial devices for optical coherence tomography greatly benefit from the exceptional features of broadband light-emitting quantum dot superluminescent diodes (QDSLDs). Here, light generation occurs at the transition from spontaneous to stimulated emission, the regime of the amplified spontaneous emission. In this context, initially spontaneously emitted photons are amplified by stimulated emission processes when traversing through the QDSLD, which leads to strong light amplification. The suitable choice of the waveguide geometry and the gain medium formed by quantum dots, enables large spectral widths of some terahertz combined with a rather higher degree of spatial coherence. Modern measurement methods based on two-photon absorption processes provide a temporal resolution of some femtoseconds and thus allow correlation studies of the emitted QDSLD light. Also from a theoretical point of view, the characterization of the amplified spontaneous emission generated by QDSLDs and their associated photon statistics represents an interesting and challenging research topic. Especially in a particular temperature regime these devices exhibit uncommon properties with regard to the temporal field and intensity correlations: While the field correlation reflects the rather highly incoherent nature of light emitted by QDSLDs due to its spectral width of several THz, a reduction of the second order correlation from 2 to 1.33 at a temperature of T=190K was observed in the Semiconductor Optics group of Prof. W. Elsäßer at the Technical University of Darmstadt in 2011. The understanding of the occurrence of these hybrid coherent light states, which are simultaneously incoherent in first and coherent in second order correlation function is the subject of this thesis. In a first step we find the quantum mechanical light state associated with the QDSLD to be well described by a multimode phase-randomized Gaussian state by comparison with experimental results. In the second step we present a microscopic theory of the amplified spontaneous emission, which allows an explanation of the temperature-dependent noise suppression of broadband QDSLDs. For this purpose we consider distinguishable quantum dots, which are embedded in a strongly absorptive bulk material that defines a waveguide. Tilted and anti-reflection coated output facets, leading to a suppression of longitudinal modes, are modeled by beam splitters that couple the internal field to the surroundings. Regarding the spectral properties of QDSLDs, the broadband light generated inside the diode is described by a multimode electric field. This multimode quantum field theory yields rate equations for the optical power densities and the level occupation of the inhomogeneous ensemble of quantum dots within the diode. With the help of the input-output formalism, we determine the optical power spectrum. As a main result, we find the broadband external power spectrum to be a convolution of the intra-diode photon spectrum with a Lorentzian response. This finding corresponds with experimentally available spectra. Furthermore, based on the quantum theory of QDSLDs we determine the central second-order degree of coherence. It reveals a reduction within a special detuning regime and therefore allows the interpretation of the hybrid coherent light phenomenon from a quantum optical point of view.
We analyze the statistics of photons originating from amplified spontaneous emission generated by a quantum dot superluminescent diode.Experimentally detectable emission properties are taken into account by parametrizing the corresponding quantum state as a multimode phase-randomized Gaussian density operator.The validity of this model is proven in two subsequent experiments using fast two-photon-absorption detection observing second-order equal-time and second-order fully time-resolved intensity correlations on femtosecond timescales.In the first experiment, we study the photon statistics when the number of contributing longitudinal modes is systematically reduced by applying well-controlled optical feedback.In a second experiment, we add coherent light from a single-mode laser diode to quantum dot superluminescent diode broadband radiation.Tuning the power ratio, we realize tailored second-order correlations ranging from Gaussian to Poissonian statistics.Both experiments are very well matched by theory, thus giving first insights into the quantum properties of radiation from quantum dot superluminescent diodes.
Temperature dependent suppression of intensity noise below thermal fluctuations g (2) (0) < 2 in incoherent quantum dot superluminescent diodes (QDSLDs) has been observed by Blazek et al. in 2011 [1] . First-order temporal correlation properties of QDSLDs have been investigated using quantized treatments [2] and stochastic simulations [3] . We show that the noise suppression can be interpreted as a nonlinear damping effect by considering the interaction between a statistically distributed classical electric field and a pumped atomic three-level-system.
We demonstrate experimentally that the first- and second-order coherence properties of light emitted by a quantum dot superluminescent diode can be simultaneously tailored by well-controlled optical feedback. Depending on feedback intensity and feedback spectral range we achieve a spectral width Δλ between 120 and 0.26 nm, corresponding to a coherence length in first order in the range between 13 and 5820 μm, while the central second-order coherence degree g((2))(τ=0) is tuned gradually from a thermal value of g((2))(0)~1.8 down to the coherent laser limit of g((2))(0)=1.0. These results are complemented by comprehensive investigations of relative intensity noise, which are in excellent agreement with the observed intensity correlation behavior.
We investigate the intensity correlation properties of single photons emitted from an optically excited single semiconductor quantum dot. The second order temporal coherence function of the photons emitted at various wavelengths is measured as a function of the excitation power. We show experimentally and theoretically that a quantum dot is not only a source of nonclassically correlated monochromatic photons but is also a source of multicolor photons with tunable correlation properties. We found that the emitted photon statistics can be varied by the excitation rate from a sub-Poissonian one, where the photons are temporally antibunched, to super-Poissonian, where they are temporally bunched.