Recent dramatic experimental demonstration of slow and fast light has stimulated considerable interest in dynamic control of the group velocity of light and in the development of tunable all-optical delays for applications such as optical buffers [1–4]. Earlier slow light studies have used electromagnetically induced transparency (EIT) and coherent population oscillation (CPO). To realize tunable optical delays, more recent experimental studies have also pursued a variety of other physical mechanisms, including stimulated Brillouin and stimulated Raman scatterings [5–8], and optical wavelength conversion [9]. The materials used in these studies range from atomic vapors [1–3], doped ions in crystals [4], optical fibers [5–9], and semiconductors [10–14]. For compact all-optical buffers, chip-scale semiconductor-based tunable optical delays are highly desirable.

In EIT and CPO, optical interactions between a signal and a pump induce a narrow transparency window within an absorption resonance. Tunable optical delay can be achieved via the pump intensity dependence of the spectral width as well as the depth of the transparency window. In stimulated light scattering, the parametric gain depends on the intensity of the pump beam, which can be used to generate tunable optical delay for the signal beam. In optical wavelength conversion, the spectral dependence of the group velocity in a fiber provides a convenient mechanism for tunable optical delay. All these schemes are based on the use of coherent nonlinear optical processes.

In this paper, we propose and demonstrate experimentally a scheme that uses incoherent nonlinear optical processes to realize tunable optical delays in semiconductors. The proposed scheme exploits the strong Coulomb interactions between excitons and free carriers and uses optical injection of free carriers to broaden and bleach an exciton absorption resonance. A fractional delay exceeding 200% has been obtained for an 8 ps optical pulse propagating near the heavy-hole (HH) excitonic transition in a GaAs quantum well (QW) structure. Tunable optical delay employing free carrier injection avoids strong absorption for the pump beam and is also robust against variations or fluctuations in the frequency of the pump beam.

When an optical pulse with frequency, v, propagates in a dielectric medium, the phase velocity is c/n, where n is the refractive index, and the group velocity is given by

Near an absorption resonance, the group velocity depends strongly on both the spectral lineshape as well as the transition strength associated with the resonance. Varying the spectral lineshape as well as the transition strength modifies the group velocity, resulting effectively in a tunable optical delay.

In a direct gap semiconductor, optical transitions near the band edge are characterized by excitonic resonances. Nonlinear optical properties of an excitonic system are strongly modified by manybody Coulomb interactions [15]. In particular, exciton-exciton scattering or exciton-carrier scattering can induce significant dephasing or spectral broadening of the exciton resonance. These excitation-induced dephasing processes play an important role in both coherent and incoherent nonlinear optical responses in semiconductors [16, 17].

To realize tunable optical delay via spectral broadening and bleaching of an excitonic resonance, we propose to optically inject free carriers with a pump beam slightly above the band gap. At relatively low excitation levels, exciton-carrier scattering is considerably more efficient than exciton-exciton scattering in broadening the excitonic resonance. Perhaps more importantly, the use of an off-resonant pump avoids the strong pump absorption occurring when the pump is resonant or nearly resonant with the relevant optical transition.

 

Fig. 1, (a) Schematic of the experimental setup for the time-of-flight measurement of a signal pulse. (b) Schematic of the energy level structure for the HH and LH transitions in GaAs QWs.

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The experimental studies are carried out in a high quality undoped (001) GaAs/Al_0.3Ga_0.7As QW sample grown by molecular beam epitaxy. The sample contains 50 periods of 17.5 nm GaAs wells and 15 nm Al_0.3Ga_0.7As barriers. For transmission measurements, the substrate of the QW sample is removed with selective chemical etching. The QW sample glued onto a sapphire disc is mounted on a cold finger of a helium flow cryostat. The signal pulse used in our study features a duration of 8 ps and a spectral linewidth of 0.2 nm. A spectral pulse shaper is used to derive the nearly transform-limited signal pulse from a femtosecond mode-locked Ti:Sapphire laser. The output coming directly from the femtosecond mode-locked Ti:Sapphire laser has a pulse duration of 150 fs and is used to measure the delay and temporal lineshape of the signal pulse via sum frequency generation in a BBO crystal, as shown schematically in Fig. 1(a). For optical injection of free carriers, a separate picosecond mode-locked Ti:Sapphire laser with a pulse duration of 60 ps is used. The two mode-locked lasers are synchronized with a repetition rate of 80 MHz.

 

Fig. 2. Absorption spectra near the band edge obtained in the presence of free carrier injection by a pump beam at λ=795 nm and with the pump power indicated in the figure. (a) T= 80 K. (b) T=20 K. The dashed lines show, as a reference, the absorption spectra obtained in the absence of free carrier injection.

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Figure 2 shows absorption spectra of the QW sample near the band edge with and without optical injection of free carriers. In the absence of free carrier injection, the absorption spectra are characterized by well resolved HH and light-hole (LH) exciton absorption resonances [see Fig. 1(b) for a schematic of the energy level structure and the optical selection rule of the HH and LH transitions]. The HH exciton resonance features a linewidth of 0.78 nm at T=80 K and 0.55 nm at T=20 K. For optical injection of free carriers, we set the wavelength of the pump beam to λ=795 nm, slightly above the band gap of the GaAs QW. From the absorption of the sample at the pump wavelength, we estimate that a pump beam with an average power of 1 mW (using a pump spot size of order 200 μm) generates approximately a carrier density of 3×10⁹/cm². The free carrier injection leads to highly efficient broadening of the exciton resonance. At T=80 K, the exciton resonance nearly vanishes at a pump power near 10 mW, as shown in Fig. 2(a).

The spectral broadening of the exciton resonance depends on details of the exciton and carrier dynamics as well as details of the underlying manybody Coulomb interactions. A thorough discussion of these processes is beyond the scope of this paper. Within the context of tunable optical delays, we wish to point out that as shown in Fig. 2, free carrier injection induces a much greater broadening of the exciton resonance at T=80 K than that at T=20 K. Earlier studies of transient four-wave mixing have indicated that at relatively low excitation levels, the collision coefficient for exciton-free carrier scattering is nearly eight times greater than that for exciton-exciton scattering [18]. At low temperature, a significant fraction of free carriers injected can subsequently form excitons. As a result, the effective carrier density at lower temperature can be considerably smaller than that at higher temperature, leading to a strong temperature difference in the spectral broadening of the exciton resonance. It should be pointed out that at relatively high carrier densities, screening of Coulomb interactions becomes important. The exciton spectral broadening is thus not expected to scale linearly with the carrier density at these high carrier densities. We also note that in addition to optical injection of free carriers, other approaches, such as Franz-Keldysh effects, for which an external electric field is applied in the plane of the QW, can also be used to broaden and bleach the exciton resonance [19].

 

Fig. 3. Time-of-flight measurements of the signal pulse after its transmission through the QW sample. The central wavelength of the signal pulse is indicated in each figure. The results were obtained at 20 K and with the sum frequency generation shown schematically in Fig. 1. Note that t=0 was set to the peak of the signal pulse when the pulse was tuned far below the HH exciton resonance. The average intensity of the signal pulse is 0.2 W/cm².

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To illustrate how the exciton absorption affects the group velocity of a nearly resonant optical pulse, we plot in Fig. 3 the result of a time-of-flight measurement of a weak signal pulse after its transmission through the QW sample (no free carrier injection was used in these measurements). As shown in Fig. 3, the signal pulse becomes more delayed, i.e. arrives at a later time, as the central wavelength of the pulse approaches the heavy-hole (HH) resonance. Away from the absorption line center, the optical delays we have measured are in general agreement with a theoretical analysis based on Eq. (1), in which we model the exciton absorption as an inhomogeneously broadened absorption resonance. This simple model, however, cannot account satisfactorily the pulse delays observed at the exciton absorption line center and in the region of the anomalous dispersion. In this region, the group velocity can become negative, i.e. the peak of the pulse can emerge from the sample before the peak of the pulse enters the sample. As shown in earlier experimental and theoretical studies, this negative group velocity arises from pulse reshaping, namely, the leading edge of the pulse is less attenuated than the trailing edge of the pulse [20]. The discrepancy between the experiment and the simple theoretical analysis may arise from multiple reflections at the interface between the GaAs well and AlGaAs barrier. Since the primary emphasis here is to demonstrate tunable optical delay by modifying the group index, we will discuss in more detail pulse propagation in the anomalous dispersion region in semiconductors in a separate publication.

 

Fig. 4. Time-of flight measurements of a signal pulse after its transmission through the QW sample with (open circles) and without (squares) free carrier injection by a pump beam at λ=795 nm. (a) T=80 K and I_pump=2 mW. (b) T=20 K and I_pump=4 mW. The solid lines are numerical fit to a Gaussian. The central wavelength of the signal pulse is at λ=815.69 nm and λ=811.72 nm for (a) and (b), respectively. Note that here, t=0 was set to the peak of the signal pulse in the presence of optical injection of free carriers.

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The spectral broadening and optical bleaching of the exciton absorption resonance shown in Fig. 2 provides an effective mechanism for realizing tunable optical delay. Figure 4 compares directly time-of-flight measurements of the signal pulse after its transmission through the QW sample with and without the optical injection of free carriers by a pump beam. For clarity of display, normalized intensity is shown in Fig. 4. The free carrier injection leads to a 2-fold increase in the signal transmission for Fig. 4(a) and an 8-fold increase in the signal transmission for Fig. 4(b). Fractional pulse delay (the ratio of the pulse delay over the incident pulse duration) exceeding 200% has been observed at T=20 K [see Fig. 4(b)]. Smaller fractional delays have been observed at higher temperatures. The fractional delays observed in Fig. 4 agree well with what is expected for the group delay induced near the HH exciton absorption resonance shown in Fig. 3. The pulse delay, however, is also accompanied by a significant broadening or reshaping of the temporal line shape of the signal pulse. For both Fig. 4(a) and Fig. 4(b), the pulse broadening is nearly 30% of the incident pulse width. The primary limitation for achieving greater fractional delay is the strong absorption of the signal beam near the exciton resonance since the fractional group delay scales with αl where α is the absorption coefficient and l is the sample length. The bandwidth of the tunable optical delay is limited by the spectral linewidth of the exciton resonance. Much greater bandwidth can be achieved at higher temperature or with exciton resonances that are strongly inhomogeneously broadened. For example, a delay bandwidth exceeding 300 GHz can be achieved with an exciton absorption linewidth of 5 meV.

Finally, we note that dynamically shifting the exciton resonance can also be used as a mechanism for tunable optical delay since near an exciton resonance, the group index and thus the optical delay depend strongly on the relative spectral position between the exciton resonance and the signal pulse, as shown in Fig. 3. Resonant or near resonant excitation of excitons can shift and broaden the exciton resonance via exciton-exciton interactions and/or optical Stark effects. Quantum confined Stark effects also provide a highly effective mechanism for shifting the exciton resonance [19].

In summary, we have demonstrated tunable optical delay by broadening and bleaching exciton absorption resonance with optical injection of free carriers. Fractional delay exceeding 200% has been achieved with an 8 ps signal pulse propagating near the exciton absorption resonance. We hope that these studies will stimulate further activities of exploiting unique optical properties of semiconductors for applications in tunable optical delay.

This work has been supported by the slow light program of DARPA-DSO and by the DARPA-MTO university photonics research center.