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VCSELs pp 19–75Cite as

VCSEL Fundamentals

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Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 166))

Abstract

In this chapter we outline major principles of vertical-cavity surface-emitting laser (VCSEL) design and operation. Basic device properties and generally applicable cavity design rules are introduced. Characteristic parameters like threshold gain and current, differential quantum efficiency and power conversion efficiency, as well as thermal resistance are discussed. We describe the design of Bragg reflectors and explain the transfer matrix method as a convenient tool to compute VCSEL resonator properties in a one-dimensional approximation. Experimental results illustrate the emission characteristics of high-efficiency VCSELs that apply selective oxidation for current and photon confinement. Both the 850 and 980 nm wavelength regions are considered. The basic treatment of laser dynamics and noise behavior is presented in terms of the small-signal modulation response as well as the relative intensity noise. Finally we give some examples of VCSEL applications in fiber-based optical interconnects, i.e., optical data transmission over short distances.

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Notes

  1. 1.

    The high wallplug efficiency result in [24] was first presented in [25].

  2. 2.

    This will become clearer from Fig. 2.7 presented later.

  3. 3.

    In the rate equations, the amount of stimulated emission is determined by the product of optical gain coefficient and photon density, the latter being proportional to the intensity of the electromagnetic field; see (2.59), (2.60).

  4. 4.

    In a simple approach, spectral deviations \(\delta\lambda_{\rm g}\) of gain peak and laser resonance can be treated by approximating \(g(n,\lambda)\,{=}\,g(n)(1+a_{g\pm}(\delta\lambda_{\rm g})^2),\) where \(a_{g+}\) and \(a_{g-}\) are the (negative) curvatures of \(g(\lambda)\) at both sides of the gain peak. Higher degrees of accuracy are obtained by considering the carrier density dependence of \(a_{g\pm}.\)

  5. 5.

    From the complex E(z), the real, time-dependent electric field is obtained as \(\tilde E(z,t)\propto {\rm Re}\{ E(z)\cdot\hbox{exp}\{ \hbox{i}\omega t\}\}\) with the time \(t\) and the angular frequency \(\omega.\)

  6. 6.

    Locally, in transition regions between predominant oscillation on different transverse modes, \(\eta_{\rm d}\,{=}\,\eta_{\rm dt}+\eta_{\rm db}>1\) arising from redistributions of the carrier density profile can be observed (see, e.g., [52]). Moreover, differential quantum efficiencies \(\eta_{\rm d}>1\) can regularly be obtained in laser diodes with cascaded pn-junctions (by means of tunnel junctions), at the expense of higher operating voltages [53, 54].

  7. 7.

    Free carriers cause optical absorption losses which have been found to scale as \(\alpha_{\rm fc}\,{=}\,(3\cdot 10^{-18}\\n+7\cdot 10^{-18}p)\,\hbox{cm}^2\) for GaAs (see [55], p. 175), where \(n\) and \(p\) are the electron and hole densities, respectively.

  8. 8.

    In other texts one often finds \(\alpha_{\rm m}\,{=}\,\alpha_{\rm mt}+\alpha_{\rm mb}\) with \(\alpha_{\rm mt,b}\,{=}\,-\!L_{\rm eff}^{-1}\ln\sqrt{R_{\rm t,b}}\) (compare with (2.17)) and thus \(\eta_{\rm ut,b}\,{=}\,\alpha_{\rm mt,b}/\alpha_{\rm m}\,{=}\,\ln R_{\rm t,b}/\ln (R_{\rm t}R_{\rm b}).\) For VCSELs we have \(R_{\rm t,b}\,{\approx}\, 1,\) and with the approximation \(\ln x\,{\approx}\, x-1\) we get \(\eta_{\rm ut,b}\,{\approx}\, T_{\rm t,b}/(T_{\rm t}+T_{\rm b}),\) which is also obtained from (2.42) when setting \(\sqrt{R_{\rm t}}\,{\approx}\, \,\sqrt{R_{\rm b}}\,{\approx}\, 1.\) In both cases, the ratio (2.43) is then \(P_{\rm t}/P_{\rm b}\,{\approx}\, T_{\rm t}/T_{\rm b}.\)

  9. 9.

    Although small-area VCSELs appear to have fairly competitive sheet resistances, threshold current densities tend to be in the kA/cm\(^2\) range.

  10. 10.

    The effect of the oxide aperture on laser mode formation can also be understood as that of a focusing lens. Since the refractive index is higher in the active area compared to the oxidized region, a phase shift is induced in the traveling wave which reduces its diffraction losses [48].

  11. 11.

    Namely there is no sum anymore in (2.59), \(g_{m}(n)\to g(n),\) \(N_{m}\to N,\) \(v_{{\rm gr,}m}\to v_{\rm gr},\) and there is only one equation (2.60), in which \(\varGamma_m\to\varGamma,\) \(\beta_{{\rm sp},m}\to\beta_{\rm sp},\) and \(\tau_{{\rm p},m}\to\tau_{\rm p}.\)

  12. 12.

    IEEE Standard 802.3ae-2002, IEEE, Piscataway, NJ, USA, June 2002. See URL http://www.ieee802.org/3/ae/.

  13. 13.

    In this case one speaks of OM3-grade fibers which guarantee 10 Gbit/s data transport over distances of at least 300 m [124]. Even more modern OM4-grade fibers have \({B\cdot L\ge 4{,}700\,{\rm MHz}\cdot {\rm km}}\) with \(L\ge 550\) m at 10 Gbit/s.

  14. 14.

    IEEE Standard 802.3aq-2006, Clause 68, “10GBASE-LRM” (long reach multimode), IEEE, Piscataway, NJ, USA, Sept. 2006. See URL http://www.ieee802.org/3/aq/.

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Acknowledgments

The author would like to thank all former and present members of the VCSEL team of Ulm University for many years of successful device and systems research.

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    Rainer Michalzik

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    Rainer Michalzik

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Michalzik, R. (2013). VCSEL Fundamentals. In: Michalzik, R. (eds) VCSELs. Springer Series in Optical Sciences, vol 166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24986-0_2

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