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Solitary Quantum Dot Laser

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Dynamics of Quantum Dot Lasers

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Abstract

In this chapter, the model for the solitary semiconductor QD laser is introduced and its turn-on dynamics is studied.

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Notes

  1. 1.

    For this model, \(\rho _{\mathrm{inv }}\) is not a very useful coordinate to simplify the calculation of the steady states, because there is no simple expression for the spontaneous emission terms \(-\rho _e\rho _h\) in the QD Eqs. (3.12c) and (3.12d) in terms of \(\rho _{\mathrm{inv }}\). However, introducing \(\rho _{\mathrm{inv }}\) permits to directly compare the modeling results with most of the literature on three variable models (\(R\), \(\Psi \), \(\rho _{\mathrm{inv }}\)) of QW lasers under optical injection, where the rescaled inversion is usually denoted by \(N\) or \(Z\). For recent reviews of the literature see for example [48] and [49].

  2. 2.

    In the following, the Landau symbol \(\mathcal {O}\) is frequently used to describe the scaling of a quantity, e.g., ‘\(\gamma F_b\) is of order one’ may be written as \(\gamma F_b=\mathcal {O}(1)\) [52].

  3. 3.

    Note that often in the literature (cf. [48, 49, 56, 57]) a rescaled field amplitude \(R\equiv \sqrt{r^{\mathrm{QW }}}{\mathcal {E}}\) is introduced, such that the rescaled intensity \(I\equiv R^2\) is of \(\mathcal {O}(1)\). However, to compare the findings of this section with those derived for the QD model in the next sections, \({\mathcal {E}}^2=N_{\mathrm{ph }}\) is used.

  4. 4.

    Typically, \(N_{\mathrm{ph }}=\mathcal {O}(10^{4})\), which implies that the product of \(r_wN_{\mathrm{ph }}^{0}\) is a \(\mathcal {O}(1)\).

  5. 5.

    Note that \(\Gamma _{\mathrm{RO }}^{\mathrm{vf }}\) and \(\omega ^{\mathrm{vf }}_{\mathrm{RO }}\) are given by \(\Gamma _{\mathrm{RO }}^{\mathrm{vf }}=2\kappa \gamma \Gamma ^{\mathrm{vf }}_1\) and \(\omega ^{\mathrm{vf }}_{\mathrm{RO }}=2\kappa \sqrt{\gamma }\omega ^{\mathrm{vf }}_{1/2}\), respectively.

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Authors and Affiliations

  1. Research Domain II - Climate Impacts and Vulnerabilities, Potsdam Institute for Climate Impact Research, Potsdam, Germany

    Christian Otto

  2. Institute of Theoritical Physics, Berlin Institute of Technology, Berlin, Germany

    Christian Otto

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Otto, C. (2014). Solitary Quantum Dot Laser. In: Dynamics of Quantum Dot Lasers. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-03786-8_2

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