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We measure fast carrier decay rates (6 ps) in GaAs photonic crystal cavities with resonances near the GaAs bandgap energy at room temperature using a pump-probe measurement. Carriers generated via photoexcitation using an above-band femtosecond pulse cause a substantial blue-shift of three time the cavity linewidth for the cavity peak. The experimental results are compared to theoretical models based on free carrier effects near the GaAs band edge. The probe transmission is modified by nearly 30% for an estimated above-band pump energy of 4.2 fJ absorbed in the GaAs slab.
© 2015 Optical Society of America
1. Introduction
Nonlinear optical elements are considered to be key components in future optical communication networks [1]. Such networks will require fast, low-power nonlinear optical devices on a robust, scalable platform, and may eventually enable data processing entirely in the optical domain. Optical switching has been demonstrated at attojoule levels using single atomic systems as the nonlinear medium for applications in both classical and quantum information processing, but these systems are usually not viable for large-scale processing [2, 3]. A more scalable approach is to use bulk nonlinearities involving free carriers, but enhanced substantially by using photonic cavities that support strong field intensities in small volumes [4–8]. These devices offer the benefit of small footprints and may allow large scale integration for applications in optical communication, memory and logic. III–V materials are particularly interesting for many of these applications because sources, detectors and modulators can be engineered on the same material platform, and carrier dynamics have been studied in both GaAs [4, 8–10] and InP [11–13] platforms. The demonstration of a III–V material all-optical switch that nominally operates below femtojoule energy levels near the material band-edge, and achieves a high operational speed of 40 Gbps due to fast free carrier diffusion has been particularly promising in this respect [5].
Studying the dynamics of nonlinear processes in single photonic cavities is the first step in the development of advanced photonic circuits or optical delay lines, where the single cavities can be used as building blocks that perform switching or logic operations. In this study, we investigate free-carrier dynamics in a gallium arsenide (GaAs) photonic crystal cavity that confines light in a small volume (V ≈ (λ/n)3, where λ is the wavelength and n is the refractive index of the medium), and supports a high quality factor optical mode (Q = 3600). GaAs cavities are chosen to operate near the direct bandgap energy at 1.42 eV (cavity resonance λ0 > 870 nm). At photon energies near the band gap, one expects enhanced optical response per injected carrier (dn/dN) than at energies well below the band gap [5, 14]. Previous studies have investigated carrier dynamics in (Al)GaAs photonic crystals without a defect [9], or GaAs photonic cavities far away from the material band-edge where resonant nonlinearities are not expected to play a significant role [4, 10]. All experiments here are performed without the use of any active materials so that free carrier effects may be unambiguously observed. All experiments are performed at room temperature.
2. Device design and fabrication
The devices used in this work are fabricated on a GaAs wafer that is epitaxially grown by IQE. Two-dimensional photonic crystals are designed for room-temperature operation in the 890–910 nm wavelength range. Photonic crystals are defined using electron beam lithography followed by dry etching. The final devices are formed by undercutting a sacrificial layer (thickness 800 nm) of aluminum gallium arsenide (Al0.8Ga0.2As) underneath the 110-nm GaAs layer, forming a free-standing membrane. A linear defect (three missing air holes) is located at the center of the photonic crystal as shown in Fig. 1(a) [15], allowing for a confined, high-quality resonator mode. The device parameters are as follows: lattice period a = 240 nm, radius r = 70 nm and thickness t = 110 nm. The nearest holes on either side of the cavity are shifted away from the cavity by 0.15 a. The calculated quality factor and mode volume are 105 and 0.8 (λ/n)3. However when band-edge absorption is taken into account, the maximum theoretical Q is limited to less than 104.
Fig. 1 (a) Scanning electron micrograph of fabricated photonic crystal device. A linear defect cavity is formed by removing 3 holes along a row of the photonic crystal lattice. Scale bar 1 μm. (b) Low power reflectivity spectrum of cavity optical mode.
3. Experiments
Measurements are performed at room temperature and atmospheric pressure. The devices are first characterized by their low-power spectra using cross-polarized detection. A low-power 6 μW tunable laser (New Focus Velocity) is focused vertically on the sample using a 63× objective lens (1.4 μm2 laser spot size), and the reflected laser signal is recorded using a spectrometer. In this scheme, the cavity spectrum appears as a peak in the reflected laser spectrum. The cavity spectrum is shown in Fig. 1(b) with a resonance wavelength of 903.2 nm (1.37 eV) and a fitted Q of 3600 (cavity decay rate γ/(2π)=92.5 GHz). The cavity lifetime is given by τ = 1/γ = 1.7 ps.
In order to study nonlinear dynamics in the photonic cavity, carriers are generated in the cavity region using a Ti:saph laser at a pump wavelength of 796 nm, with a pulse duration of approximately 200 fs and a repetition rate of 75 MHz. The average above-band pump power is 16 μW after the objective lens (peak power = 1W). The pump laser is synchronized to a spectrally resolved Hamamatsu streak camera system, with a measured time resolution of 3.4 ps. The photo-generated carriers cause a change in the refractive index in the cavity region, resulting in a blue-shift of the cavity. This shift can be monitored by scanning the continuous wave tunable laser at low powers (probe laser) through the spectral region of the cavity. Individual time-resolved spectra corresponding to different wavelengths of the tunable laser are shown in Fig. 2(a). The data show that when the probe laser is blue-shifted from the cavity resonance, the arrival of the pump laser results in a peak due to the shift of the cavity that brings it on resonance with the probe laser. On the other hand, when the probe laser is slightly red-shifted from the original cavity resonance, the reflected signal shows a pronounced dip due to the cavity blue-shift. In Fig. 2(b), we show a heat plot where the reflected tunable laser intensity (incident power 6 μW) is shown as a function of tunable laser wavelength and delay between pump and probe. The probe laser is scanned between wavelengths of 902 nm and 904 nm in increments of 0.02 nm, and at each laser wavelength, the laser signal is integrated for two seconds on the streak camera. The pump-probe measurement simultaneously offers high spectral and temporal resolution. The pump laser arrival time at 22 ps can be directly observed on the streak camera at the pump laser wavelength. The figure shows that after the pump arrival (Delay Δt > 22 ps), the cavity is considerably blue-shifted, and recovers over a timespan of several tens of ps.
Fig. 2 (a) Reflected probe intensity as a function of pump-probe delay for probe laser wavelengths between 902.4 nm and 903.2 nm. (b) Heat plot showing the reflected laser intensity as a function of probe laser wavelength and pump probe delay. The pump laser arrives at 22 ps (c) Cavity maximum as a function of pump-probe delay. Blue circles: Experiment. Red Curve: Exponential fit (d) Simulated cavity dynamics based on experimentally measured parameters.
In Fig. 2(c), we plot the cavity maximum as a function of the delay between pump and probe, by fitting the instantaneous cavity spectra using Lorentzians. The plot shows a total shift of 0.75 nm for the cavity resonance, corresponding to Δλ = 3Δλ0, and a 13 dB on/off ratio. Fitting the cavity decay rate to a single exponential gives a recovery time of 6 ps.
We can estimate the photogenerated carrier concentration Nexp in our device by using the simple formula
where P is the pump laser average power measured after the objective lens, η = 0.14 is the fraction of incident light that is absorbed in the GaAs photonic crystal slab computed using finite difference time domain (FDTD) simulations, RL is the repetition rate of the laser, ħ is the reduced Plancks constant, ωpump is the pump frequency, Aeff = 1.15 μm2 is the effective mode area, computed using a Gaussian laser spot profile and accounting for the fact that carriers are not generated in the hole regions of the photonic crystal, and L = 110 nm is the thickness of the GaAs slab. Using the above equation we estimate Nexp = 1.1 × 1018 cm−3. From the carrier concentration, we can derive an experimental value of dn/dN = (Δλ) × ng/(λNexp) = −2.26 × 10−21 cm3, where ng = 3.0 is the group index of light in the GaAs photonic crystal computed using FDTD simulations.The observed dynamics can be simulated by using dynamic coupled mode equations for the cavity field amplitude a(t) and carrier density N(t), given by
where κ is the coupling rate between the external optical input s(t) and the cavity mode a, τc is the free-carrier lifetime, and J(t) describes the optical carrier injection (200 fs Gaussian pulse), ω0 is the cavity resonant frequency and ω is the probe laser frequency. The total cavity loss rate γ incorporates scattering, absorption, and can incorporate free-carrier absorption via a carrier dependence. We assume a linear change in refractive index with carrier density (dn/dN) which is shown to be valid for carrier densities below 1020 cm−3 [14]. These simplified equations neglect carrier generation via probe absorption, which is not expected to be a significant.Figure 2(d) plots simulated cavity spectra as a function of pump-probe delay and probe wavelength, based on the experimentally derived nonlinear parameters and carrier relaxation time. A comparison between the simulations and experimental data show that the system is described well by the coupled mode equations presented above.
We further present experimental results for different powers of the pump laser. Figure 3(a) shows temporal scans of the tunable probe laser when fixed at the cavity resonance wavelength with increasing powers of the above-band pump laser. At a low excitation power, the probe laser is mostly reflected, however with increasing pump pulse energy between 15 and 230 fJ measured after the objective lens, the probe laser shows a pronounced dip when the pump laser arrives due to a blue-shift of the cavity resonance. These experiments are performed on a separate but similar device (Q = 1000, λ0 = 902.9 nm, Δλ = 1.6 nm). A heat plot of the probe laser reflectivity with pump-probe delay at 400 fJ incident pump pulse energy is shown in the inset to Fig. 3(b). We define a normalized transmission parameter β based on the maximum and minimum values of the reflected probe laser signal as
where Rmax and Rmin are the reflected laser signal at the original cavity resonance for incident pump pulse energies of 300 fJ and 1.6 fJ, respectively, and R is the reflected laser signal at pulse energy Ep. In Fig. 3(b), we plot β as a function of the pump pulse energy. Based on these values, we estimate that a value of β = 0.3 is achieved for incident pulse energy of 30 fJ (2 × 104 absorbed photons, corresponding to 4.2 fJ absorbed pump energy), and β = 0.1 is achieved for incident pulse energy of 100 fJ.Fig. 3 (a) Reflected probe intensity as a function of pump pulse energy when the probe is resonant with the original (low power) cavity mode resonance wavelength. (b) Normalized transmission β as a function of pump pulse energy.
4. Comparison with theoretical models
The experimentally observed index shifts are compared to theoretical models of bulk free carrier effects near the GaAs bandgap energy. Theoretically predicted values for the index shift are computed directly using equations in ref. [14] and material parameters for GaAs at the wavelength of interest. The model incorporates effects of bandfilling dispersion, bandgap renormalization, and free carrier absorption (plasma effect). Following that work, in the case of bandfilling dispersion and bandgap renormalization, the change in refractive index is computed from the theoretical change in the absorption coefficient using Kramers Kronig formalism. In the case of plasma dispersion, the Drude model is used. A comparison between the results computed using equations in ref. [14] and experiments is shown in Fig. 4 for different devices used in experiments, showing the change in refractive index as a function of carrier concentration (calculated experimentally from the incident pump power). In the figure, “Total” refers to a theoretical combination of all three effects, where the effect of bandgap renormalization is first computed, followed by the other two effects based on the modified bandgap. The theoretical changes in index due to each individual effect are also included in this figure. Because bandgap renormalization is a red-shifting nonlinearity that appears above 1.4 times the Mott critical density, the theoretical net effect shows a window of spectral “red-shift” at concentrations beyond this density.
Fig. 4 Comparison between theory in ref. [14] and experimental data. BFD: Bandfilling dispersion; BGR: Bandgap renormalization; FCA: Free carrier absorption (plasma dispersion)
The experimental data is shown on the figure using grey diamonds. In experiments, we are not able to isolate a redshifting nonlinearity at any pump power, and observe only blue-shifts in the cavity resonance as we change the pump power (and thereby the carrier concentration). We extract an experimental value of dn/dN = −2.4 × 10−21 cm3, which is lower than the value expected from theory (dn/dNtheory = −1 × 10−20 cm3, given from the slope of the solid red curve in the linear regime).
The origin of the discrepancy between the theory presented in [14] and our work cannot be known for certain based on these experiments, because we cannot isolate the three theoretical effects individually. One possible source of the discrepancy may be that when carriers are pumped above the GaAs bandgap, some carriers relax to the lowest available conduction and valence band states via rapid thermalization, causing band-edge nonlinearities, while other carriers recombine at surfaces or via other trap states and are lost. The most significant error that can occur in the experimental calculations is in the estimate for the pump laser spot size due to slight deviations from optimal focus, and this is estimated to be less than 20%. Alternatively, our data may suggest that perhaps a more intricate model for band-edge nonlinearities is required for the photonic crystal cavity system.
We also did experiments where we measured the carrier lifetime as we changed the pump laser spot size between 1 and 20 μm2, but did not observe any change in the measured lifetime. We believe that the change in wavelength over time cannot be attributed solely to the diffusion of carriers out of the cavity region. The observed decay is likely due to the rapid recombination of carriers at the photonic crystal surfaces [9]. However, carrier diffusion rates may still play an important role in how fast the carriers reach the surfaces [16].
5. Conclusion
In conclusion, we have demonstrated low-power nonlinear carrier dynamics in a nanoscale GaAs photonic crystal cavity. We measure a blue-shifting nonlinear effect with a measured lifetime of 6 ps. We observe a shift in the cavity resonance of 3 times the cavity linewidth by using 213 fJ of incident pump energy. This corresponds to a photo-injected carrier concentration of 1.1 × 1018 cm−3. The probe transmission is modified for ultra-low pump energy of 4.2 fJ, when low absorption in the GaAs slab is taken into account. The experiments are compared with coupled mode equations based on a linear change in refractive index with carrier density, and are found to be consistent with this model. We have further compared our results with free-carrier models near the material band-edge, but find that our experiment shows a smaller blueshift than expected from theory, and does not show any evidence of bandgap renormalization. In separate measurements, we have achieved absorption-limited Qs exceeding 104 at the wavelength of interest. The observed nonlinear dynamics can be used to demonstrate a low power optical switch by using a below-band pump laser at or near the cavity resonance. Eventually, many of these single nonlinear devices may be connected via integrated optics in advanced optical circuits [17].
Acknowledgments
This work is supported by the Defense Advanced Research Projects Agency under Agreement No. N66001-12-2-4007. The authors would like to acknowledge Kelley Rivoire and Victor Acosta for helpful discussions. Electron beam lithography was performed at the Stanford Nanofabrication Facilities for some devices.
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