Probing microcavity switching events on the picosecond time scale using quantum dots as a broadband internal fluorescent source

It is well known that the frequency of the resonant modes of semiconductor microcavities, and thus their optical response, can be changed in a transient and reversible way through a modification of the refractive index of the constituent material.^1,2 This effect, known as “cavity switching,” was initially implemented in the mid-1980s on pillar microcavities, in view of ultrafast all-optical data processing and computing. Nowadays, “cavity switching” induced by the electrical injection of free carriers is widely used on the microsecond time scale for the reconfiguration of integrated photonic circuits.³ Cavity switching can be achieved in a much faster way through optical modifications of the refractive index. All-optical switching on a sub-ps time scale has been achieved using the electronic Kerr effect,⁴ and the optical injection of free charge carriers is routinely used to induce cavity switching on the few-ps time scale.^1,2,5–9 Ultrafast all-optical cavity switching encounters renewed interest motivated by its important potential applications in the field of quantum photonics. Cavity switching enables modifying at will the detuning between a mode and an artificial atom such as a quantum dot. It could be used to switch on and off Rabi oscillations in the strong coupling regime or to control in a dynamic way the magnitude of the Purcell effect,^10,11 for example to tailor the temporal envelope of a single photon pulse.¹² Finally, the switching of high-Q microcavities changes the frequency of trapped light as demonstrated in “color change” experiments;^6,13 this effect could be in the future at work in single photon frequency translators.

In view of such applications, a precise knowledge of the dynamics of cavity switching events is mandatory. Reports of advanced characterization of switching events are rather scarce for the well-known micropillar geometry, which is an essential workhorse of quantum photonics, both for basic cavity quantum electrodynamics (CQED) experiments^14,15 and for the development of novel devices such as microlasers,¹⁵ single photon sources,^16–18 or bistable devices.¹⁹ The mainstream approach is ultrafast pump–probe spectroscopy in reflection geometry, which has been used to investigate switching events in planar cavities^2,4,5 and later in micropillars.²⁰ Despite providing excellent time resolution, such experiments are relatively slow, which hinders extensive parametric studies. Furthermore, transmission or reflection spectroscopy only permits probing the modes that present a non-zero overlap with the probe beam. As an example, for a Gaussian beam whose waist is matched to the top facet of a pillar microcavity, only the fundamental mode of the pillar contributes to the reflection or transmission signal.^1,21 Considering now other microcavities such as ring resonators of photonic crystal cavities, information on the switching event has also been obtained as a by-product of color-change experiments. In the (standard) adiabatic regime, the color change indeed exactly reflects the frequency shift of the resonant cavity mode that has been used to store and convert light.⁶ In such experiments, information is obtained for one mode at a time. Finally, information about the dynamic evolution of mode frequencies can also be extracted from photoluminescence experiments on active microcavities containing one or several quantum dots (QDs) as shown for single-mode photonic crystal cavities.^9,11

We introduce our experimental approach in Sec. II: A broadband internal light source lights up all the resonant modes of a cavity prior to the switching event, and a detection setup combining a grating spectrometer and a streak camera enables tracking the time-dependent frequencies of the resonant modes during the entire switching event with picosecond time resolution. Although our method can potentially be used to study any cavity, and noticeably photonic crystal nanocavities, we chose in this work GaAs/AlAs micropillars as a first example. In our experiments, information is simultaneously obtained for a large (>10) set of resonant modes and for all relevant time delays. We highlight in Sec. III the interest of this experimental approach via the study of the on/off switching times for a GaAs/AlAs micropillar as a function of the switching pulse energy. A switch-on time constant as short as 1.5 ps is observed for optimized pumping conditions. We also report in Sec. IV the observation of major transient differential switching effects including the degeneracy lifting of a pillar mode, induced by breaking the rotational pillar symmetry through an asymmetric injection of free carriers.

We study GaAs/AlAs pillar microcavities that contain a large ensemble of InAs QDs, as described in Ref. 14. Since the mid-1990s, embedded QDs have been widely used to probe the frequencies, quality factors, and radiation patterns of resonant cavity modes.^21–23 In the spontaneous emission regime, QDs work as independent punctual emitters and light up systematically all cavity modes present within the broad frequency range covered by their inhomogeneously broadened emission line.²² For the micropillars under study, the diameter is between 2 μm and 7 μm and the quality factor Q of the fundamental mode varies between 4000 and 5000.

Our experimental setup is sketched in Fig. 1. The QD-micropillar sample is placed at 4 K inside a He-flow cryostat. The pump beam is delivered by a mode-locked Ti:sapphire laser (200 fs pulse duration, 76 MHz repetition rate), which is used both to excite the QDs and to switch the cavity through the injection of free carriers in all GaAs sublayers. The pump beam is focused on the top facet of an isolated micropillar by a NA = 0.25 microscope objective. The photoluminescence of the QD-micropillar is collected by the same objective and analyzed spectrally and temporally using a system composed of a Jobin-Yvon Triax320 monochromator and a Hamamatsu C10910 streak camera. This system provides a temporal resolution around 2 ps, combined with a 0.3 meV resolution in the photon energy/frequency domain, close to the limit imposed by the time-energy uncertainty principle. A sub-ps time resolution can also be obtained by using the spectrometer grating in its 0th order diffraction mode.

When QDs are excited through optical injection of electron–hole pairs within the wetting layer or GaAs barrier, their photoluminescence rise time is about 25 ps due to the delays induced by carrier capture and relaxation.¹⁴ Therefore, when both QD pumping and micropillar switching are both induced by the same pump pulse, one cannot study the switch-on behavior during the first picoseconds after the pulse, as shown in previous reports,^9,24 because the QD-photoluminescence is too weak. We use for this reason a two-pulse pumping sequence to ensure that the internal light source is bright enough to probe the entire switching event. We use a fibered system to split the pulsed delivered by the Ti:sapphire laser into a weak pulse, which lights up the QDs but does not induce significant switching, and a stronger one, which is delayed by $Δ$ ps with respect to the first one and switches the cavity. We define γ (respectively, 1 − γ) the fraction of the pump power that goes into the strong (respectively, weak) pulse.

In order to give a better idea of how raw data generated by the streak camera look like, we show in Fig. 2, as a first example, an image obtained by switching a 5.3 μm-diameter micropillar. Here, the pump photon energy is 1.57 eV, and the diameter of the pump beam is much larger at its waist (10 μm) than the pillar diameter so as to ensure a uniform injection of electron–hole pairs in the GaAs cavity layer. Thanks to the QDs uplighting prior to the switching pulse, the spectral position of the six lowest frequency emission lines of the micropillar is clearly seen before the switching event that is induced around t = 0. We identify the emission lines from a standard modeling.²² We start with a calculation of the effective indices of the guided modes of a 5.3 μm diameter cylinder in air.²⁵ Each guided mode m of the cylinder gives rise to a single resonant mode in the micropillar, whose resonance frequency ν_m is given by²² $ν2D/νm=nmeff/n$⁠, where n is the refractive index of undoped GaAs, ν_2D is the resonance frequency of the planar cavity from which the micropillar has been defined, and $nmeff$ is the effective index of the guided mode m. In Fig. 2, we use as labels for the pillar modes the usual names²⁵ HE_ij or EH_ij of their “parent” guided modes in the GaAs cylinder. Several modes, which are close in frequency, contribute to a common emission line in the micropillar spectrum. The three lower frequency lines appear brighter than the higher frequency ones, since their frequencies are closer to the center of the inhomogeneous distribution of QDs (located at around 1.36 eV).

In this experiment, QDs are most of the time decoupled from any cavity mode. Apart from short transient coupling events with modes, their excitonic population decays on a time scale of the order of 1 ns. Thanks to this relatively slow decay, the QDs can be employed to monitor the entire switching event. This is exemplified in Fig. 2, which shows a measurement using the long time-range mode of the streak camera. Due to the uniform modification of the refractive index of GaAs, all modes display the same switching behavior. The second pump pulse induces a sudden blue-shift of the mode frequencies. Here, the switching amplitude is around 1.8 meV, which corresponds to seven mode linewidths, and the switch-on time (not resolved in this long time-range mode) is below 20 ps. Next, all modes relax toward their original frequency due to the recombination of the electron–hole pairs. Here, the relaxation dynamics is close to exponential with a 200 ps time constant after t = 100 ps. In this time range, the dynamics is dominated by the non-radiative recombination (NRR) at sidewalls, as shown for similar micropillars in Ref. 20. At short delays after the switch pulse (0 < t < 100 ps), the density of the electron–hole plasma is higher and the radiative recombination of electron–hole pairs enters into play, which leads to a faster relaxation of the modes. In Fig. 2, the time-dependence of the frequency of the fundamental mode HE₁₁ is well reproduced by a biexponential curve with time constants 50 ps and 200 ps. The same curve, shifted along the frequency axis by an amount corresponding to the frequency spacing between unswitched pillar modes, describes the behavior of higher order modes. We see that a very similar behavior is observed for all modes, thanks to the uniform injection of free carriers. The amplitude of this global blue shift of the modes (≈1.8 meV) corresponds to a δn = −4.5 × 10⁻³ change of the refractive index of GaAs at around 1.39 eV.

A streak camera image such as the one shown in Fig. 2 is the result of a 20-min-long experimental run, including background level acquisition and subtraction. By contrast, several days would be necessary to obtain similar information using pump–probe spectroscopy. The method that is introduced here looks particularly well suited for performing extensive parametric investigations. In Secs. III and IV, we will focus our attention on the ultrafast switch-on behavior of micropillars.

Figure 3 shows two streak camera images obtained in a high temporal resolution mode (70 ps time range, 1 ps resolution) from a 3 μm diameter micropillar. Here, the pump photon energy is 1.55 eV. The pump beam diameter at the waist is matched to the micropillar top facet and two different switching pulse energies, 0.5 pJ and 7 pJ, are used. We study the switch-on behavior of the first two unresolved sets of modes of the micropillar, labeled Line 1 for the two-fold degenerate fundamental mode HE₁₁ and Line 2 for the second set, which comprises non-degenerate modes HE₀₁ and EH₀₁ and the polarization-degenerate mode HE₂₁. Thanks to the excitation of the QDs by the first pump pulse 200 ps prior to the switching pulse, one can observe Line 1 and Line 2 before and during the switching event, induced at around t = 20 ps. These emission lines are observed at frequencies that remain constant between 0 ps and 20 ps, and are identical to those of the unswitched micropillar. This confirms that the residual density of electron–hole pairs due to the excitation by the first pulse is small enough to avoid any significant frequency shift of the pillar modes. We can use these frequencies as references to track switching effects.

The important properties of free-carrier switching are deduced from the analysis of Fig. 3. As we can track mode frequencies during the switching event, we can probe precisely the dynamics of the physical processes responsible for the blue shift (“switch-on”) and for the relaxation (“switch-off”) of the modes. Considering Line 1, we see that raising the pump power increases (as expected) the magnitude of the frequency shift and accelerates very significantly the switch-on. Slightly longer switch-on times, albeit still in the few-ps range, are observed for Line 2.

As discussed in detail in Ref. 26, three effects contribute to changes in the absorption coefficient of the semiconductor (and thus to its refractive index owing to the Kramers–Kronig relations): bandgap shrinkage related to many-body effects, interband absorption bleaching (IAB) due to state filling in the conduction and valence bands, and intraband free carrier absorption (FCA). At plasma densities well above 10¹⁷ cm⁻³, which are typically used in free carrier switching experiments such as ours, the dominant effect is IAB with an additional contribution from FCA. According to Kramers–Kronig relationships, modifications of the absorption coefficient close to the semiconductor bandgap induce larger changes in the refractive index. Although the hot carriers induced by the pump should, in principle, induce FCA, and some instantaneous change of the refractive index, we do not detect such an effect for P = 0.5 pJ in Fig. 3. Our results are fully compatible with a dominant role of IAB. The thermalization and cooling of the electron–hole plasma results in a filling of states at the bottom of the conduction and valence bands and in an increased modification of the refractive index.

To precisely estimate relevant time constants, we have fitted the time-dependence of the line frequencies using a simple rate equation model. We consider that the pump pulse injects free carriers within 0.9 ps into high-energy states, which behave as a reservoir. They relax from this reservoir toward the extrema of the conduction and valence bands with a characteristic time τ_on, thereby inducing a change in the absorption and refractive index of GaAs. Free carriers also recombine with a time constant τ_off. We assume that the modification of the refractive index, and consequently the shift of the modes, is proportional to the density of relaxed carriers, which is a reasonable approximation for carrier densities above 10¹⁷ cm⁻³.²⁶ We use τ_on, τ_off, and the switching amplitude as fitting parameters. As shown in Fig. 3, this elementary model captures adequately the shape of the entire switching event for both small and large switching energies.

We plot in Fig. 4 the evolution of τ_on as a function of the switching pulse energy P. For Line 1, we observe a strong decrease in τ_on, from 6 ps for small Ps down to 1.5 ps–2 ps for the largest Ps. We attribute this effect to enhanced electron scattering at high carrier densities. As cooling of the electron–hole plasma occurs most efficiently through LO-phonon emission, carrier–carrier scattering plays an essential role as it ensures filling high-energy states located more than one LO-phonon energy above the bottom of the band, favoring thermalization mediated by LO-phonons. The slight apparent increase in τ_on that is observed above 6 pJ is an experimental artifact. In this power range, nonlinear effects in the optical fibers induce a stretching of the pump pulses from 200 fs to about 2 ps and a smoothing of the switch-on behavior. Quite remarkably, we observe values of τ_on as short as 1.5 ps under optimum pumping conditions (here, P ≈ 4 pJ). This value is significantly shorter than the previously published data extracted from pump–probe experiments using a two-photon excitation scheme (e.g., 6 ps in Ref. 5). By contrast, our results agree well with prior studies of carrier relaxation after excitation by a femtosecond pulse at 1.55 eV, which reveal a drastic evolution of GaAs absorption around its bandgap during the first picosecond.²⁷ It is likely that a two-photon excitation well above the gap, as used in Ref. 5, creates a hotter electron–hole plasma than the one-photon pumping scheme that is used in our study, which delays the cooling of the electron–hole plasma.

Considering now Line 2, we observe a slightly longer switch-on time. As we have matched the pump beam size to that of the top facet of the micropillar, the electron–hole plasma density is larger around the micropillar axis, and a transverse diffusion of the charge carriers occurs during and after the cooling. As can be seen in Fig. 5, all four modes contributing to Line 2 possess a node at the pillar axis. Therefore, their best overlap with the free carrier distribution is obtained once some lateral diffusion has occurred, which induces a further delay for Line 2 on top of the switch-on time constant of Line 1. As shown in Ref. 20, such behavioral differences between Line 1 and Line 2 can be modeled in a quantitative way when the ambipolar lateral diffusion of electron–hole pairs is taken into account.

Finally, this experiment also provides information on the switch-off dynamics, i.e., on the electron–hole recombination time. We observe the same behavior for both lines and obtain through the fitting procedure very similar τ_off time constants. For our smallest pump powers (P ≈ 1 pJ), τ_off is close to 110 ps, i.e., smaller than for the 5.3 μm diameter micropillar used as an example in Fig. 2. It is well known that the NRR time related to surface recombination scales as S/L for a thin semiconductor slab, where S is the surface recombination velocity and L is the slab thickness.²⁸ One can easily show that for a cylinder of diameter D, this time scales as S/D. Taking as a reference the 200 ps value obtained for D = 5 μm in Fig. 2, one obtains a 130 ps estimate for D = 3 μm. Thanks to the excellent agreement with our experimental result, we can conclude that NRR at pillar sidewalls is the dominant carrier recombination process for small pump powers. For higher pump powers, radiative recombination enters into play. Over this limited time range (30 ps–70 ps), i.e., up to 50 ps after the pump pulse, the decay is characterized by a smaller time constant of the order of 50 ps for the highest Ps (P ≈ 10 pJ).

Differential switching, i.e., the ability to switch in different ways the modes of a cavity, has been recently observed for micropillars using a non-uniform injection of free carriers. For instance, when free carriers are injected in a focused way close to the pillar axis, a larger switching amplitude and faster switch-on behavior is observed for Line 1, when compared to Line 2.²⁰ These differences can simply be explained by considering the drastically different field distributions of cavity modes: while modes related to Line 2 have a donut shape and zero intensity on the pillar axis, mode HE₁₁ has an antinode there.

Besides its size, the radial position of the focused pump spot is another useful degree of freedom. Interestingly, an off-axis injection of free carriers breaks the axial symmetry of the micropillar and is expected to lift the degeneracy of polarization-degenerate modes HE_∓mn and EH_∓mn. We show in Fig. 6 the result of such an experiment. We study the same 5.3 μm diameter micropillar as the one studied in Fig. 2 and use a 1.1 μm diameter pump beam that is displaced about 0.9 μm to the left of the pillar axis along the transverse x-direction.

Just after the switching pulse, we observe a splitting of Line 2 into two branches. The splitting develops and, 5 ps after the pulse, reaches an amplitude as large as 1 meV, then decreases, and 20 ps later is no longer observable. By contrast, there is no such splitting for Line 1.

These experimental data are well reproduced by numerical simulations, whose results are shown by the dashed lines in Fig. 6. We have already shown for an on-axis carrier injection that differential switching can be modeled accurately, provided that the lateral distribution of free carriers in the cavity layer of the micropillar is suitably described, taking into account the localized injection of the carriers, their lateral ambipolar diffusion, and their recombination processes.²⁰ We follow a similar approach in the present work. We first solve Fick’s law in two dimensions, taking into account the diffusion and recombination processes. We assume that the refractive index change scales linearly with the density of the electron–hole plasma. Knowing the (non-circular symmetric) refractive index map at all times, we compute the guided modes m and their effective indices $nmeff(t)$ for the 5.3 μm diameter cylinder of GaAs that forms the cavity layer of the micropillar using a commercial software (RSOFT release 2019.09 from Synopsis). The resonance frequencies ν_m(t) of micropillar modes are then deduced at all times as²² $ν2D/νm(t)=nmeff(t)/n$⁠. We use a single fitting parameter δn_max, which is the maximum refractive index change of GaAs (in absolute value), obtained at the center of the Gaussian pump spot. We obtain a very good overall agreement with our experimental data using δn_max = −0.06.

In order to better understand this ultrafast transient line splitting, it is helpful to consider the field maps of the modes of the unperturbed micropillar and of the switched micropillar, as shown in Fig. 5. We keep in these simulations the same shape and position for the pump spot as in the experiment (1.1 μm diameter, 0.9 μm lateral displacement along x, with respect to the pillar axis z) but reduce intentionally the maximum refractive index change δn_max down to −0.01. According to Fig. 6, this situation is representative of our experiment at the onset of the switch-on, typically 1 ps after the pulse. The index change breaks the circular symmetry but preserves the mirror symmetry with respect to the xz-plane. Therefore, according to the perturbation theory for guided modes,²⁹ couplings shall be induced only between modes that share the same symmetry properties. The inspection of unswitched field maps (or of the analytic expressions of modes fields for the unperturbed pillar²⁵) shows that, among the four modes that contribute to Line 2, EH₀₁ couples only with HE₂₁, while HE₂₁′ only couples with HE₀₁. These couplings lead to the formation of modes 3–6, whose maps are shown in the right part of Fig. 5. We see that the lowest frequency mode 3 corresponds approximately to the sum of EH₀₁ and HE₂₁. Its field intensity is close to zero on the x axis, especially in the perturbation spot. Therefore, its frequency shifts only moderately with respect to the ones of modes EH₀₁ and HE₂₁. By contrast, mode 5 originates mainly from the difference EH₀₁–HE₂₁, whose field map has an antinode at the location of the perturbation spot. As a result, mode 5 appears at a much higher frequency, and its field map is severely modified with respect to the one of EH₀₁–HE₂₁. Similar considerations hold for modes 4 and 6, and explain the splitting of Line 2 into two branches comprising two modes each, and the observation, just after carrier injection, of a much larger switching amplitude for modes 5 and 6 than for modes 3 and 4.

In marked contrast to this behavior, we do not observe any splitting of Line 1. Looking at the field maps of HE₁₁ and HE′₁₁ in Fig. 5, we see that these modes do not have the same symmetry with respect to the xz-plane and are therefore not coupled by the perturbation. Both modes experience the same blue shift, since they have very similar field intensities within the perturbed area.

Turning our attention to longer time delays (5 ps–30 ps after the pulse), carrier diffusion out of the pump spot plays a dominant role. Free carriers reach regions where modes 3 and 4 have a large field intensity in Fig. 5; hence, diffusion induces an additional blue shift for modes 3 and 4. In the opposite way, lateral diffusion reduces the shift for modes 5 and 6. Hence, the splitting between the two branches decreases and vanishes once carriers are fully redistributed over the entire section of the cavity layer. After 30 ps, all modes shift back together toward their reference frequencies due to the recombination of the free carriers.

Let us finally notice that focused off-axis switching induces a spectacular change of the field maps of the two first modes of the micropillar, as seen by comparing, e.g., HE₁₁ and mode 1. This effect, which is obtained for a small refractive index change, could find interesting applications. A monochromatic emitter that is initially coupled to HE₁₁, and placed on the left side of the pump spot in Fig. 5, would become decoupled from modes 1 and 2 because of their blue shift and additionally because of the change of their field maps. Thanks to this combination of effects, one could likely achieve a stronger quenching of the Purcell effect, until carrier diffusion in the entire pillar restores the initial field maps of modes 1 and 2, i.e., during around 20 ps.

In this work, we have investigated ultrafast switching events induced by all-optical injection of free charge carriers in a micropillar cavity. Unlike previous work based on pump–probe spectroscopy, we are able to track with picosecond time resolution all cavity modes at a time, during the entire switching event. We use a broadband internal light source, which is already active prior to the switch pulse, to funnel photons into all cavity modes present within a broad spectral band and during the entire switching event. As first results obtained with this experimental approach, we observe very short switch-on times, down to 1.5 ps for optimum pumping conditions. We also report the observation of a transient splitting of one of the micropillar emission lines, which lasts for roughly 20 ps only, just after a focused and asymmetric injection of free carriers, and which results from a breaking of the circular symmetry of the micropillar. Besides highlighting some key assets of this characterization method, our results pave the way to a more systematic exploration of switching events, and noticeably of transient reconfigurations of the set of resonant cavity modes, in micropillars as well as in more sophisticated photonic systems such as photonic molecules¹⁵ or coupled cavities, which are particularly attractive for the dynamic control of the emission of a single quantum emitter.^11,30 Beyond their fundamental interest, such transient changes of the modal structure could also be useful to switch the emission of embedded emitters from one mode to another and achieve, e.g., ultrafast beam steering or (when applied to cavities containing a single QD) superposition states of a single photon shared by two modes.

T.S. and G.M.T. contributed equally to this work.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The authors would like to thank W. L. Vos for numerous discussions and insightful advice. This work was supported by the French National Agency of Research (ANR) under the contract NOMOS (Grant No. ANR-18-CE24-0026). G.M.T. and P.L.S. acknowledge funding from CAPES (Grant No. PDSE 88881.187056/2018.1) and CNPq.