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Linewidth of a quantum-cascade laser assessed from its frequency noise spectrum and impact of the current driver

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Abstract

We report on the measurement of the frequency noise properties of a 4.6-μm distributed-feedback quantum-cascade laser (QCL) operating in continuous wave near room temperature using a spectroscopic set-up. The flank of the R(14) ro-vibrational absorption line of carbon monoxide at 2196.6 cm−1 is used to convert the frequency fluctuations of the laser into intensity fluctuations that are spectrally analyzed. We evaluate the influence of the laser driver on the observed QCL frequency noise and show how only a low-noise driver with a current noise density below \({\approx} 1~\mbox{nA/}\sqrt{}\mbox{Hz}\) allows observing the frequency noise of the laser itself, without any degradation induced by the current source. We also show how the laser FWHM linewidth, extracted from the frequency noise spectrum using a simple formula, can be drastically broadened at a rate of \({\approx} 1.6~\mbox{MHz/}(\mbox{nA/}\sqrt{}\mbox{Hz})\) for higher current noise densities of the driver. The current noise of commercial QCL drivers can reach several \(\mbox{nA/}\sqrt{}\mbox{Hz}\), leading to a broadening of the linewidth of our QCL of up to several megahertz. To remedy this limitation, we present a low-noise QCL driver with only \(350~\mbox{pA/}\sqrt{}\mbox{Hz}\) current noise, which is suitable to observe the ≈550 kHz linewidth of our QCL.

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Notes

  1. In this paper, we introduce the notion of frequency noise inherent to the laser, not to be confused with the commonly used concept of intrinsic frequency noise of the laser. The intrinsic frequency noise represents the white frequency noise induced by spontaneous emission in the laser and is related to the intrinsic linewidth described by the Schawlow–Townes relation [18]. Here, the frequency noise inherent to the laser corresponds to the frequency noise originating from the laser itself, without any contribution from the current source. It includes the contributions of both the flicker noise and the intrinsic noise of the laser.

  2. A further interesting point when discussing the frequency noise of a laser is the white noise component S w, which is directly related to the laser intrinsic linewidth by Δν int=π⋅S w [24, 26, 29]. The intrinsic linewidth corresponds to the Schawlow–Tones linewidth given by [15, 18]:

    $$\varDelta \nu_{\mathrm{ST}} = \frac{v_{g}^{2}hvn_{\mathrm{sp}}\alpha _{\mathrm{tot}}\alpha _{m}(1+ \alpha _{e}^{2})}{4\pi P_{0}}.$$

    As mentioned in Sect. 1, the linewidth enhancement factor α e is close to 0 in QCLs and notably lower than in other semiconductor lasers (typical value in the range 2–10 [36]). Theoretical considerations about the intrinsic linewidth in QCLs have also led to the modified Schawlow–Townes formula introduced by Yamanishi and co-workers [16]. The Schawlow–Townes linewidth can be computed from the above expression where both the total losses α tot (mirror and waveguide) and the mirror losses α m must be known. While the total losses can be straightforwardly determined in a Fabry–Pérot laser, this is not the case in a DFB laser as the losses of the grating (α DFB) have to be accounted for. To estimate the total losses in our DFB, we compared its threshold current with those of a similar Fabry–Pérot device. Assuming similar waveguide losses α wg=4.5 cm−1 in both cases (measured by the manufacturer on Fabry–Pérot devices) and using typical values of the laser parameters provided by the manufacturer, the losses of the grating are estimated to α DFB=1.47 cm−1. The estimated losses are in good agreement with literature data [37] for a 9-μm QCL (α wg=6.7 cm−1, α DFB=0.7 cm−1). With the spontaneous emission coefficient n sp=1, optical power P 0=6 mW and α e=0, we calculate an intrinsic linewidth Δν ST≈380 Hz, which is close to the upper limit of the white frequency noise experimentally assessed from Fig. 5.

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Acknowledgements

The authors would like to thank Prof. Markus. W. Sigrist (ETH Zurich) for the loan of the absorption gas cell. This work was financed by the Swiss National Science Foundation (SNSF), by the Swiss Confederation Program Nano-Tera.ch which was scientifically evaluated by the SNSF, and by the Gebert-Ruef Foundation in Basel, Switzerland.

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  1. Laboratoire Temps-Fréquence, Institut de Physique, Université de Neuchâtel, Avenue de Bellevaux 51, 2000, Neuchâtel, Switzerland

    L. Tombez, S. Schilt, J. Di Francesco, G. Di Domenico, D. Hofstetter & P. Thomann

  2. Institut für Angewandte Physik, AG Laser und Quantenoptik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289, Darmstadt, Germany

    T. Führer, B. Rein & T. Walther

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  1. L. Tombez
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Tombez, L., Schilt, S., Di Francesco, J. et al. Linewidth of a quantum-cascade laser assessed from its frequency noise spectrum and impact of the current driver. Appl. Phys. B 109, 407–414 (2012). https://doi.org/10.1007/s00340-012-5005-x

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