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Semiconductor laser linewidth theory revisited

2021, Wenzel, Hans, Kantner, Markus, Radziunas, Mindaugas, Bandelow, Uwe

More and more applications require semiconductor lasers distinguished not only by large modulation bandwidths or high output powers, but also by small spectral linewidths. The theoretical understanding of the root causes limiting the linewidth is therefore of great practical relevance. In this paper, we derive a general expression for the calculation of the spectral linewidth step by step in a self-contained manner. We build on the linewidth theory developed in the 1980s and 1990s but look from a modern perspective, in the sense that we choose as our starting points the time-dependent coupled-wave equations for the forward and backward propagating fields and an expansion of the fields in terms of the stationary longitudinal modes of the open cavity. As a result, we obtain rather general expressions for the longitudinal excess factor of spontaneous emission (K-factor) and the effective α-factor including the effects of nonlinear gain (gain compression) and refractive index (Kerr effect), gain dispersion, and longitudinal spatial hole burning in multi-section cavity structures. The effect of linewidth narrowing due to feedback from an external cavity often described by the so-called chirp reduction factor is also automatically included. We propose a new analytical formula for the dependence of the spontaneous emission on the carrier density avoiding the use of the population inversion factor. The presented theoretical framework is applied to a numerical study of a two-section distributed Bragg reflector laser.

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Ultrashort optical solitons in transparent nonlinear media with arbitrary dispersion

2013, Amiranashvili, Shalva, Bandelow, Uwe, Akhmediev, Nail

We consider the propagation of ultrashort optical pulses in nonlinear fibers and suggest a new theoretical framework for the description of pulse dynamics and exact characterization of solitary solutions. Our approach deals with a proper complex generalization of the nonlinear Maxwell equations and completely avoids the use of the slowly varying envelope approximation. The only essential restriction is that fiber dispersion does not favor both the so-called Cherenkov radiation, as well as the resonant generation of the third harmonics, as these effects destroy ultrashort solitons. Assuming that it is not the case, we derive a continuous family of solitary solutions connecting fundamental solitons to nearly single-cycle ultrashort ones for arbitrary anomalous dispersion and cubic nonlinearity.

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Cancellation of Raman self-frequency shift for compression of optical pulses

2017, Pickartz, Sabrina, Brée, Carsten, Bandelow, Uwe, Amiranashvili, Shalva

We study to which extent a fiber soliton can be manipulated by a specially chosen continuous pump wave. A group velocity matched pump scatters at the soliton, which is compressed due to the energy/momentum transfer. As the pump scattering is very sensitive to the velocity matching condition, soliton compression is quickly destroyed by the soliton self-frequency shift (SSFS). This is especially true for ultrashort pulses: SSFS inevitably impairs the degree of compression. We demonstrate numerically that soliton enhancement can be restored to some extent and the compressed soliton can be stabilized, provided that SSFS is canceled by a second pump wave. Still the available compression degree is considerably smaller than that in the Raman-free nonlinear fibers.

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Rotational symmetry breaking in small-area circular vertical cavity surface emitting lasers

2010, Babushkin, Ihar, Bandelow, Uwe, Vladimirov, Andrei

We investigate theoretically the dynamics of three low-order transverse modes in a small-area vertical cavity surface emitting laser. We demonstrate the breaking of axial symmetry of the transverse field distribution in such a device. In particular, we show that if the linewidth enhancement factor is sufficiently large dynamical regimes with broken axial symmetry can exist up to very high diffusion coefficients 10 um^2/ns.

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Efficient Current Injection Into Single Quantum Dots Through Oxide-Confined p-n-Diodes

2016, Kantner, Markus, Bandelow, Uwe, Koprucki, Thomas, Schulze, Jan-Hindrik, Strittmatter, Andre, Wunsche, Hans-Jurgen

Current injection into single quantum dots embedded in vertical p-n-diodes featuring oxide apertures is analyzed in the low-injection regime suitable for single-photon emitters. The experimental and theoretical evidence is found for a rapid lateral spreading of the carriers after passing the oxide aperture in the conventional p-i-n-design. By an alternative design employing p-doping up to the oxide aperture, the current spreading can be suppressed resulting in an enhanced current confinement and increased injection efficiencies, both, in the continuous wave and under pulsed excitation.

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Calculation of ultrashort pulse propagation based on rational approximations for medium dispersion

2011, Amiranashvili, Shalva, Bandelow, Uwe, Mielke, Alexander

Ultrashort optical pulses contain only a few optical cycles and exhibit broad spectra. Their carrier frequency is therefore not well defined and their description in terms of the standard slowly varying envelope approximation becomes questionable. Existing modeling approaches can be divided in two classes, namely generalized envelope equations, that stem from the nonlinear Schrödinger equation, and non-envelope equations which treat the field directly. Based on fundamental physical rules we will present an approach that effectively interpolates between these classes and provides a suitable setting for accurate and highly efficient numerical treatment of pulse propagation along nonlinear and dispersive optical media.

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Sasa-Satsuma equation: Soliton on a background and its limiting cases

2012, Bandelow, Uwe, Akhmediev, Nail

We present a multi-parameter family of a soliton on a background solutions to the Sasa-Satsuma equation. The solution is controlled by a set of several free parameters that control the background amplitude as well as the soliton itself. This family of solutions admits a few nontrivial limiting cases that are considered in detail. Among these special cases is the NLSE limit and the limit of rogue wave solutions

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Influence of the carrier reservoir dimensionality on electron-electron scattering in quantum dot materials

2013, Wilms, Alexander, Mathé, Peter, Schulze, Franz, Koprucki, Thomas, Knorr, Andreas, Bandelow, Uwe

We calculated Coulomb scattering rates from quantum dots (QDs) coupled to a 2D carrier reservoir and QDs coupled to a 3D reservoir. For this purpose, we used a microscopic theory in the limit of Born-Markov approximation, in which the numerical evaluation of high dimensional integrals is done via a quasi-Monte Carlo method. Via a comparison of the so determined scattering rates, we investigated the question whether scattering from 2D is generally more efficient than scattering from 3D. In agreement with experimental findings, we did not observe a significant reduction of the scattering efficiency of a QD directly coupled to a 3D reservoir. In turn, we found that 3D scattering benefits from it’s additional degree of freedom in the momentum space

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Spatio-temporal pulse propagation in nonlinear dispersive optical media

2012, Brée, Carsten, Amiranashvili, Shalva, Bandelow, Uwe

We discuss state-of-art approaches to modeling of propagation of ultrashort optical pulses in one and three spatial dimensions.We operate with the analytic signal formulation for the electric field rather than using the slowly varying envelope approximation, because the latter becomes questionable for few-cycle pulses. Suitable propagation models are naturally derived in terms of unidirectional approximation.

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Sasa-Satsuma hierarchy of integrable evolution equations

2018, Bandelow, Uwe, Ankiewicz, Adrian, Amiranashvili, Shalva, Pickartz, Sabrina, Akhmediev, Nail

We present the infinite hierarchy of Sasa-Satsuma evolution equations. The corresponding Lax pairs are given, thus proving its integrability. The lowest order member of this hierarchy is the nonlinear Schrödinger equation, while the next one is the Sasa-Satsuma equation that includes third-order terms. Up to sixthorder terms of the hierarchy are given in explicit form, while the provided recurrence relation allows one to explicitly write all higher-order terms. The whole hierarchy can be combined into a single general equation. Each term in this equation contains a real independent coefficient that provides the possibility of adapting the equation to practical needs. A few examples of exact solutions of this general equation with an infinite number of terms are also given explicitly.