Slow-Light in Nonuniform Quantum Dot Waveguide

We analyzed a new variable all-optical buffer using semiconductor quantum dots (QD). We show that an Ids-InGaAs-GaAs QD waveguide with 20meV inhomogeneous linewidth can achieve substantial buffering with a novel unbalanced multi-wavelength pumping scheme. Introduction: The advancement of 111-V semiconductor quantum dots (QD) has made many interesting applications, such as ultra-low threshold diode laser, high-speed direct modulation, hole burning memory, and efficient nonlinear optical devices possible [ 11, [2]. These applications play important roles in achieving large bandwidth, low power consumption, and all-optical interconnect networks on an integrated platform. Recently, we proposed a possible new direction of QD devicesa variable all-optical buffer [3], [4] one of the most critically sought after components in optical communications and signal processing while to this date has never been realized. Our basic idea centers on making the QD that can controllably slow down the optical transmission such that it is effectively an optical memory. We proposed a structure that consists of multiple stacks of QDs in the core of a typical ridge waveguide [3]. The coupling of an external pump laser into this waveguide induces a large slope in the dielectric function spectrum &,(a) experienced by the signal via a phenomenon known as the electromagnetically induced transparency (EIT) [5]. This large slope (an/aw where n t Re(&,)”*) slows down the signal group velocity (vg =c / {n + 4~3n/aw]}). A group velocity slow-down factor (S c/vg) can be as large as 70 at 300K for a uniform InAs/GaAs QD array. In general, S reaches a maximum for a particular pump power density and can be as high as lo7 at a very low temperature (T = 7K). S is variable via the control of the extemal pump power density or the application of an external voltage across the QD [4]. Novel Pump Scheme in Nonuniform QD: One of the major obstacles of observing EIT in semiconductor structures, in particular quantum wells, is the large absorption linewidth (AyH) [6]. In QDs, the linewidth can be considerably reduced to peV range if the dots can be made uniform. State-of-the-art QDs fabricated by Stranski-Krastinow nucleation, however, exhibit a large nonunifonnity which results in a much larger inhomogeneous linewidth ( h y ~ , typically 20-60 meV [5]) than A ~ H (5 meV [7], [SI) at room temperature. Due to the nonunifodty, both the signal and the pump will experience different detuning from the electronic transition energy when interact with different dots and therefore result in a significant reduction of S if a single-component pump source (SP) is used as shown in Fig. 1. To overcome this deficiency, we proposed and analyzed an unbalanced multi-color pump (UMP) scheme in this Letter. In this new UMP scheme, the pump source is comprised of several spectrally resolvable components. We assume the power density for each spectral component and the spacing between two adjacent components can be controlled independently. An schematic of UMP is shown in the inset of Fig. 2 together with the energy levels of a nonuniform QD array which is divided into N groups of slightly different energy levels. Each group has different detuning 6el and hP(’) fiom the signal and the n-th pump component, respectively. From the density matrix formalism, the steady state value of E, can be derived as follows. In (l), the integration is over the entire inhomogeneous broadening spectrum j d 6 e l . U,, and are proportional to the average signal oscillation strength and pump power density of the n-th component, respectively. Their explicit expressions are given in [3]. A$) is the pump detuning. The index of the pump component n is a function of the detuning 6al and is chosen to be the most resonant component for a given Sal. The dephasing linewidths A E ~ ’ s are temperature dependent and their values are approximately given by hyH/ 2 where the factor 1 I 2 is purely due to convention (we define hyH by its full-width at half maximum). Given that the signal wavelength has to be fured, 6al varies for the N groups. If the SP is used, the slow down factor for the detuned QDs may be very small or even negative which results in a large reduction in the slow down effect. On the other hand, in the UMP scheme, the nonunifomity effect can be largely eliminated. The reasons are the following. First, with a tailored pump power density Ql.;,“ for each QD group with detuning Sal, the pump detuning A$) evaluated from the 0-7803-7888-1/03/$17.0002003 IEEE 441 nearest pump component is much smaller. Second, each pump component can have different power density (which is proportional to 0:;) to optimize S. Hence, the part of ss conhhuted from QDs with larger S a , can he equalized by the application of a larger Numerical Results: To get more insights of how UMP can enhance the performance, Fig. 2 shows the degradation of S for a variety of pump component spacing, normalized to h y ~ . The degradation of S is defmed as the ratio between S s in QD arrays with and without nonuniformity. In our calculations, hya,,~ is set as 20 meV [7] and h y ~ as 4.54 meV (T = 300K). We look for a scheme to achieve the highest S. The volume factor Vir is set as 1 . 4 ~ IO-!’cmJ . A denser pump arrays has less degradation. The dash line represents the case the pump spacing and hyH are equal. In that case, the factor S could still be 40. Fig. 3 shows the corresponding pump power density (-0::) of each pump component optimized for S. In the results above, the pump components are equally spaced in frequency. “he more general case that the pump components not equally spaced is under investigation. From Fig. 2 and Fig. 3, we can see that the UMP effectively reduces the slowdown factor degradation in a nonuniform QD array. Discussion: In the derivation of (I), we have kept only the most resonant terms. In other words, at steady state, theheating terms between different pump components arc not taken into account. It is justifiable if these terms haverates of variation slowerthan the dephasing rates hyi,‘s (linear regime in Fig. 2). If this is not the case, these beatingterms will have higher-order corrections to the leading term results shown as the nonlinear regime of Fig. 2.In summary, the signal transmission through a nonuniform InAs QD waveguide can be slowed down by a factorof40 at room temperature with a novel unbalanced multicolor pumping scheme. 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