Design and Dynamics of Discrete Mode Diode Lasers

In these pages we describe our work on the design and dynamical properties of discrete mode or index-patterned diode lasers. These edge-emitting devices incorporate a spatially varying effective index profile, which is designed according to the spectral output desired of the laser. Our design approach is naturally understood in terms of an inverse problem solution, and this approach has enabled us to design both single-mode and multiwavelength devices, where the starting point in each case is the Fabry-Perot laser geometry. We first describe how the inverse problem solution is formulated. We then review our work on the nonlinear dynamical response of dual-mode devices with optical injection and feedback, and finally we describe our recent results on passive mode-locking of devices designed to support discrete combs of modes.

The Scattering Inverse Problem in a Fabry-Perot Laser

The Fabry-Perot laser comprises an active gain medium and two external mirrors providing feedback for oscillation. In this geometry the lasing mode wavelengths are determined by the half-wave resonance condition, and the cavity length determines the mode spacing. Discrete mode lasers employ a spatially varying refractive index profile to filter the spectral output of the Fabry-Perot cavity. We have developed an approach to this design problem that directly relates the index pattern in real space to the threshold gain modulation in wavenumber space. This inverse problem solution enables us to design devices with precisely tailored optical spectra. The optical spectrum of a single-mode device designed using our approach is shown in Fig. 1. (a), where one can see that we have obtained excellent spectral purity in excess of 50 dB. For comparison, the spectrum of a plain Fabry-Perot laser fabricated on the same bar is shown in Fig. 1 (b). Here we provide a brief overview of how the inverse problem is solved following a perturbative transfer matrix treatment of the lasing modes.


Fig.1: (a) Optical spectrum of a single mode index patterned device at twice threshold. (b) Spectrum at twice threshold of an equivalent Fabry-Perot laser

Nonlinear Dynamics of Dual-Mode Devices

Semiconductor lasers are known to have a very rich nonlinear dynamical response to optical injection and feedback. While single-mode dynamics have been extensively studied, our device design approach enables us to address the problem of multimode dynamics in a systematic way. For example, we have performed a detailed experimental study of the dynamics of a dual-mode semiconductor laser with optical injection. The device is  designed to  support two primary modes with a terahertz frequency spacing. Fig. 2 illustrates one example of the rich dynamical behaviour we have observed in our injection experiments. Phenomena that we have observed and understood using a rate equation modelling approach include all-optical memory based on the injection locking bistability, antiphase dynamics mediated by torus bifurcations and on-off intermittency. Here we describe how modern numerical continuation tools such as AUTO enable us to understand the global bifurcation structure in this system. We also demonstrate numerically how optical feedback can induce wavelength bistability in dual-mode devices, with possible applications as fast switching memory elements.


Fig. 2: Optical spectra of a dual-mode device as the frequency detuning of the injected signal from the long-wavelength primary mode is varied.

Passive Mode-locking of Discrete Mode Lasers

Some of our most recent results involve passive mode-locking of discrete combs of Fabry-Perot modes. In Fig. 3 an example device where four primary modes are selected is shown. Mode-locking is induced by applying a reverse bias voltage to the saturable absorber section. In this case we have found that the intensity output in the mode-locked state is essentially sinusoidal. Such devices could have interesting applications as optical carriers for mmWave and THz signals. Where larger numbers of modes are selected we have obtained near transform-limited picosecond pulsed output. Because we can address the losses of each mode in the comb on an individual basis, we believe that our approach may be suited to designing frequency comb sources where the number and intensity of the modes in the comb is prescisely specified. Sources such as these could have interesting applications in high-bandwidth data networks and spectrally efficient communication systems.

Using numerical simulations, we have also recently shown that we can address the frequency dispersion of the primary lasing modes directly through the grating profile. The grating structures that we consider in this case will require a high resolution technique such as electron beam lithography to implement. Higher spatial resolution will enable us to tailor dispersion and to integrate these devices directly within passive waveguides. 


Fig. 3: Four-mode device with a saturable absorber section for mode locking. (a) Feature density function and laser cavity schematic. Inset: Modal threshold gain. (b) Optical spectrum of the device in the mode-locked state. The inset shows the intensity autocorrelation demonstrating sinusoidal ouput at the mode-locking frequency [160 GHz].

Dr. Stephen O'Brien

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