Mode-field switching of nanolasers

The miniaturization of laser sources at the nanoscale represents a remarkable achievement that may unlock various applications in many fields,¹ including optical interconnects,² sensors,^3,4 artificial optical neural networks,^5,6 and data storage.⁷ Within this context, photonic crystals (PhC) and self-assembled quantum dots (QDs) represent an interesting platform combining low optical loss, high carrier confinement, and thereby low threshold current.⁸ 

For applications in optical interconnects and data storage, a crucial requirement for nanolasers is the possibility to modulate their output at high speed (tens of GHz). In the solid-state, several methods have been implemented to achieve this task, e.g., by employing buried heterostructures combined with p-n junctions,² by exploiting non-linearities in the cavity mirror to sustain self-pulsing,⁹ or by implementing ultrafast optical pumping schemes with QDs¹⁰ and plasmonic nanowires¹¹ as gain media. In particular, gain switching leads to pulse generation down to the 10 ps timescales under optical pumping—and even sub-ps by exploiting the accelerated dynamics of surface plasmons.¹¹ However, when implemented electrically, all of these schemes require the injection of short current pulses into the nanolaser gain medium, which typically has sub-micrometer dimensions. This small dimension is coupled to a large series resistance and a parallel capacitance, leading to an RC time constant limiting the achievable modulation bandwidth well below the intrinsic one. Additionally, pulsed schemes with higher energy output, e.g., Q-switching or mode-locking, are challenging to implement in nanolasers due to the small dimensions involved. Due to these limitations, the progress in fast modulated nanolaser sources has been limited, calling for the development of new modulation schemes.

Coupled nanocavities offer a potential route to the modulation of the modal gain that is fundamentally different from the standard gain switching by current injection. Indeed, they feature coupled modes (or supermodes) whose spatial electromagnetic field (EM) distribution is very sensitive to small frequency changes, providing a way to control the light–matter interactions at the nanoscale.¹² More specifically, the EM field amplitude in a given (“target”) cavity depends on the frequency detuning Δ among the resonators¹³ [Fig. 1(a)]. Therefore, variations of Δ cause a redistribution of the EM field throughout the system, which in turn influences the light–matter interaction in the target cavity, as well as the modal losses, when the cavities are designed to have unbalanced quality (Q) factors.¹³ This scheme, named mode-field switching, has initially been implemented to control the spontaneous emission (SpE) rate (up to a factor ∼2) in two-cavity systems,¹⁴ and to dynamically vary the resonator Q factor,¹⁵ while recent work predicted and realized the complete inhibition of SpE of QDs in three-cavity structures.^13,16 The main feature characterizing the three-cavity coupled system is the presence of a mode, which can be deterministically tuned from bright to dark in the target cavity by varying the detuning Δ, therefore enabling the inhibition of all radiative processes, including stimulated emission (StE). In this context, we label the mode as “dark” when it presents a zero electromagnetic field at the position of the excited emitters so that emission is inhibited.¹³ 

Here we demonstrate the control of the nanolaser output via mode-field switching. We show that lasing can be turned off in three-cavity coupled PhC nanocavities, while the QDs in a target one are subjected to constant, above-threshold pumping. The lasing operation, investigated by spectral- and time-resolved analysis of the QD emission, is described with a model that combines coupled-mode theory (CMT)¹⁷ and semiconductor rate equations (REs).^18,19 This model provides an additional tool to investigate lasing via time-resolved measurements, as it describes a specific feature attributed to the onset of StE, i.e., the appearance of a fast decay channel observable in time-resolved experiments. Using the model, we predict the generation of short pulses when fast and symmetric variations of Δ are implemented. Differently from gain switching, it can be implemented by refractive index modulation, i.e., through the electro-optic effect, without injection of carriers in the lasing cavity, thereby circumventing the related electrical parasitics. Additionally, its general nature potentially allows its implementation in every platform displaying tuneable resonances.

The system considered here is schematically shown in Fig. 1(a). The gain medium (yellow box) interacts with the mode of the target cavity, which in turn is side-coupled to the other two resonators (control left and right) at a photon tunneling rate η. The controllable parameter Δ represents the frequency detuning among the control and target cavity frequencies (the latter indicated by ν_t).

The theoretical description of the three-coupled cavity interaction with the CMT formalism has been already formulated in Ref. 13, where the detuning-dependent supermode frequencies and field amplitudes are calculated via an eigenvalue problem (see details in the supplementary material). In particular, this system displays three supermodes [Fig. 1(b), green curves], here denoted by the indices 1, 2, and 3, that anti-cross at zero detuning. The mode with index 2 is the one of interest, as its frequency is independent of detuning and can become dark in the target cavity.^13,16 To understand the characteristics of the dark mode, the coupled system is initially considered in the limit of large detuning [Fig. 1(a), top], where the EM field interacting with the gain medium is equal to the field of the isolated target cavity $E(t)r→$⁠. Under this condition, the target mode is bright and the modal gain G_MAX is assumed to be sufficiently large to ensure lasing. As the detuning decreases, the EM field redistributes throughout the system due to the photonic coupling, with the net effect of decreasing the EM field in the target cavity, and consequently the modal gain G. Within the CMT formalism (see details in supplementary material), the field in the target cavity at the frequency of the dark mode can be expressed as $E2r→,Δ=α2tΔE(t)r→$⁠, where $α2t$ describes the ∆-dependence of the field, can assume values between −1 and 1, and is equal to zero when ∆ = 0. In the latter condition [Fig. 1(a), bottom], the absence of EM field implies that the mode is dark. Since the modal gain depends on the field as $G(Δ)∝d→if⋅E→2r→,Δ2$ (where $d→if$ is the dipole moment, Ref. 19), we have that $G(Δ)=α2tΔ2ΔGMAX$⁠. Therefore, for sufficiently small Δ, the modal gain becomes too small to sustain lasing operation.

Figure 1(c) schematically shows how the modal gain varies with the detuning, from the lasing to non-lasing regime (green and blue areas, respectively). We note that at Δ = 0 (zero gain), energy injected via the pumping is stored into the gain medium, as the excited carriers cannot radiatively recombine into the dark mode. As will be shown later, a fast change in detuning can convert this stored energy into a laser pulse. More details concerning the Δ-dependence of the field at the other supermode frequencies can be found in the supplementary material (see Sec. 2.1).

To quantitatively describe the modal gain in the presence of a tuneable field and fit the experimental data below, the Δ-dependent quantities calculated with CMT are inserted in a set of semiconductor REs (details on the derivation are discussed in the supplementary material). In particular, the radiative rate characterizing these REs are calculated from Fermi’s golden rule as in Ref. 19, and by considering a gain medium composed by a high-density ensemble of QDs.

The three-cavity scheme described above can be implemented in several platforms, spanning from nano-opto-mechanical devices²⁰ and microtoroid cavities²¹ to superconducting circuits and macro-sized resonators. In our experiment, we employed three PhC nanocavities [Fig. 2(a), top] with an ensemble of high-density self-assembled InAs QDs (areal density ≈ 200 dots/μm², ground state emission λ_em = 1220 nm at 77 K),²² which are randomly distributed throughout the whole membrane. The PhC is fabricated on a GaAs slab with a thickness of 220 nm (lattice constant a = 340 nm, hole radius r = 0.28a), and three line-defects of 7 and 50 missing holes (named L7 and L50) define the target and control cavities respectively (see details in the supplementary material, Sec. 1). The holes indicated by the yellow arrow in Fig. 2(a), bottom, have reduced radii of 0.8r and are displaced outwards by 0.18a to minimize radiation into the light cone, therefore decreasing the cavity losses.²³ To reduce the non-radiative recombination caused by surface states, the devices underwent an additional passivation step as described in Ref. 24. This step consists of chemical passivation obtained by dipping the sample into a diluted ammonia sulfide solution, followed by a plasma-enhanced chemical vapor deposition (PECVD) step resulting in a conformal thin layer of SiO₂ covering all surfaces, including the walls of the air holes.

The detuning Δ is controlled via thermal tuning by using a continuous-wave (cw) laser pumping with wavelength λ = 680 nm [green spots in Fig. 2(a)] to induce a linear temperature-dependent shift of the resonances.²⁵ To maximize this effect, air trenches are included in the design to limit the heat diffusion away from the cavity area, as shown in Fig. 2(a), top. The power of these detuning lasers, indicated with P_L and P_R as in Fig. 2(a), therefore determines the detuning of the left and right control cavity modes.

The QD emission from the L7 target cavity is investigated under pulsed optical pumping provided by a Ti:sapphire laser (λ_inj = 780 nm, pulse width τ_pulse = 3 ps). These pulses are focused onto the L7 area [red spot in Fig. 4(a), top, spot diameter ≈ 2 μm], therefore exciting the QDs located in that region, and the emission is first collected via the same objective and then measured with a spectrometer (frequency-domain) or with a superconducting single-photon photodetector (time-domain, Ref. 26). In the latter case, the QD emission at the frequency of the mode of interest is filtered by the spectrometer (as described in Ref. 16, with full-width half-maximum Δλ = 0.02 nm) and coupled into a single-mode fiber connected to the superconducting single-photon detector. The experiments are conducted at a temperature of 77 K to limit the homogeneous broadening of QDs and to reduce the non-radiative recombination of the carriers affecting the laser operation.²⁷ 

The emission spectrum of the QDs collected from the L7 target cavity in the absence of the detuning spots is reported in Fig. 2(b). The spectrum shows a dominant emission from a mode localized in the L7 cavity, corresponding to the uncoupled L7 fundamental mode, whereas the other modes (black arrows, detuned by 0.53 THz and 0.56 THz) are barely visible since they are localized in the control cavities and therefore not pumped/collected. To verify that this detuning is sufficiently large to ensure the device operates in the uncoupled cavity limit (Δ > η), two-mode anti-crossing measurements have been conducted for the estimation of the tunneling rates (Fig. 3). These measurements have been obtained by using one detuning spot (P_L or P_R), so that only one L50 cavity mode interacts with the L7 one. Figure 3(a) shows a stack plot with several spectra obtained by varying the power P_L of the left detuning laser with constant steps, where the labels $ν1′$ and $ν2′$ indicate the supermode frequencies of this two-mode coupling. As the laser power increases, the photonic coupling results in an anticrossing around 1.625 mW, which is a consequence of the strong photonic coupling. The frequency splitting $ν1′−ν2′$⁠, obtained by estimating the peak position of each supermode, is plotted in Fig. 3(b) (blue points). These points are fitted with the function that describes the frequency splitting of strongly coupled resonances as $ν1′−ν2′=Δl2+4ηl2=[δl(PL−P′L0)]2+4ηl2$ (red curve), where Δ_l = ν_l − ν_t is the frequency splitting, δ_l = ∂ν_l/∂P_L denotes the variation of the thermally tuned frequency ν_l with respect to P_L, $PL0′$ is the laser power corresponding to the anticrossing point, and η_l is the tunneling rate of the L7–L50 interaction.²⁸ The latter quantity, extracted from the fit, is equal to η_l = 0.05 THz. Analogously, Figs. 3(c) and 3(d) show the case in which only the right detuning laser is used, where the supermode frequencies are indicated by $ν1″$ and $ν2″$ [Fig. 3(c)], and their difference is plotted in Fig. 3(d) (blue squares) together with the fitted curve (red line). By following the same procedure as in Figs. 3(a) and 3(b), the right tunneling rate η_r is estimated as η_r = 0.06 THz. The difference in the values of the tunneling rates, attributed to fabrication imperfections, does not impact the presence of the dark mode, as shown in Ref. 16.

The tunneling rates η_l and η_r, together with the uncoupled mode loss rates and frequencies extracted from the PL spectra, will be used for the model of the photonic interaction based on the CMT formalism (see Sec. IV B, as well as Secs. 1.2 and 2 in the supplementary material).

First, lasing operation from the L7 mode is investigated in the uncoupled cavity limit shown in Fig. 2(b), where the energy of the excitation pulses is varied, and the photoluminescence (PL) is studied in both spectral- and time-domains (Fig. 4).

Starting from the frequency-domain, the light-in/light-out (LL) curve [Fig. 4(a), blue circles] is obtained by integrating the PL peaks at different pump pulse energies. This curve shows a close-to-linear behavior due to the high spontaneous emission coupling factor into the lasing mode,⁸ where only a small deviation from the linear behavior (black dashed line) is appreciable in the LL curve. Further evidence is therefore required to prove the transition to the StE regime. The first proof is provided by a strong increase of the first-order coherence, as measured from the pump-dependent linewidth behavior [Fig. 4(b), magenta squares]. At low excitation pulse energies (around 0.01 pJ, yellow area), the mode linewidth slightly decreases due to the reduced absorption losses induced by QD saturation in the SpE regime. At higher excitation energies (green and brown areas), a pronounced decrease of the linewidth suggests the presence of a laser transition,²⁹ since the observed narrowing (more than a factor of 2) is not expected in SpE. Additionally, the linewidth narrowing is accompanied by a plateau between 0.12 pJ and 0.20 pJ [black dashed box in Fig. 4(b)], which is considered as a signature of the onset of stimulated emission, especially in PhC nanocavities.³⁰ Indeed, while below and above threshold the linewidth decreases inversely with the output power, the coupling between intensity and phase noise causes a flattening of the linewidth curve that results in a plateau at threshold.^31,32 We adopt here the definition of lasing threshold, originally proposed in Ref. 33, as the point where the number of cavity photons equals one, so that stimulated emission exceeds spontaneous emission in the lasing mode.

Additional evidence of lasing is provided by the carrier dynamics, probed by time-resolved measurements. Figures 4(d)–4(i) show the evolution of the exponential decay (blue points) as a function of the pulse energy. At low energies (0.01–0.03 pJ), the decay is characterized by a double-exponential, where the fast component is interpreted as the spontaneous decay of the QDs, while the longer component is associated with emission from QDs spatially decoupled from the mode, which decays through emission in leaky modes and higher energy transitions³⁴ (at these powers, we measured a slow decay time τ_slow ≈ 2 ns with a slight pulse energy dependence). As the pulse energy is increased, a fast decay feature arises around 0.1 pJ, i.e., at the same pumping level of the linewidth plateau. The appearance of this fast dynamics, already observed in nanowire-based nanolasers,^35,36 is here associated with the onset of lasing. Indeed, as shown in detail in the supplementary material (Sec. 3.2), it takes place when the photon number in the cavity approaches unity, which corresponds to the definition laser threshold of micro- and nanolasers here adopted.³³  Figure 4(c) shows the fast decay times extracted from the decay curves as in Figs. 4(d)–4(i) The decay time does not show a relevant reduction when the QDs are weakly pumped (around 0.01 pJ, yellow area), while it substantially decreases at pulse energies corresponding to the linewidth narrowing as in Figs. 4(a) and 4(b) (green and brown areas). This enhancement (up to a factor of 3) of the radiative emission rate, which indeed has been previously related to laser transition in PhC nanolasers,³⁵ combined with the data collected in the spectral domain, proves that the studied device enters the StE regime. The red curves in Figs. 4(a) and 4(d)–4(i) represent the theoretical curves, calculated from the RE solution for the photon number and by choosing the adjustable parameters of the model that allow simultaneously fitting the LL and the decay curves (details in the supplementary material, Sec. 3).

In the second part of the experiment, the StE is controlled by varying the detuning Δ via the cw laser spots as in Fig. 2(a), therefore exploiting the linear relation between the cw power and the induced red-shift of the control cavity resonances introduced in Sec. III. Figure 5(a) shows the three-mode anticrossing obtained by stacking PL spectra acquired at various powers of the detuning lasers (in the same manner as in Ref. 16), by exciting the QDs with a cw laser with fixed power (λ_CW = 780 nm, power = 174 µW). For this power level, lasing is obtained at large detunings, as confirmed by the fact that at the largest detunings (downmost and uppermost curves), the linewidth of the central supermode is equal to 0.22 THz, which corresponds to an above-threshold value [as shown in Fig. 4(b)]. Note that the central mode frequency shows a red-shift of about 0.55 THz with respect to the uncoupled case of Fig. 4, which is caused by heating due to the detuning spots. This thermal cross-talk is considered into the CMT-based model (see Sec. 2.2 of the supplementary material), which well describes the experimental peak positions of the supermode frequencies [Fig. 5(a), dashed curves]. As the detuning decreases, the central supermode intensity is increasingly quenched, reaching its smallest amplitude at the anticrossing, as shown in Fig. 5(b). Around zero detuning, the residual counts are caused by the finite size of the excitation/collection spot, which partially overlaps with the control cavities. Therefore, the spurious PL signal from these cavities is partially collected. However, the observed quenching of the emission into the central supermode is consistent with the gain suppression associated with the evolution of the field distribution (mode-field tuning), as shown in Fig. 1. The dispersive behavior of the dark mode visible at the anticrossing in Fig. 5(a) is attributed to a combination of asymmetric detuning and coupling rates, which causes a deviation from the ideal non-dispersive behavior.¹⁶ More details on the electromagnetic energy distributions in the system and on the theory-experiment comparison are reported in the supplementary material (Secs. 1.3 and 2.2, respectively).

We now want to prove that the cavity is brought from the lasing to the non-lasing state by the tuning. To this aim, the QDs are excited by pulses with a fixed energy (0.99 pJ), which corresponds to above-threshold pumping as in Fig. 4, and the detuning Δ is varied. Figure 5(c) shows the linewidth and decay time variations as Δ decreases (blue circles and magenta squares respectively). The linewidth decreases from 0.025 THz at large detuning (above threshold value) to 0.032 THz (below threshold) at small detuning, while the decay time increases from 220 ps to 480 ps. The blue (magenta) dashed line indicates the linewidth (decay time) value before the plateau in Fig. 4(b), which is considered as the threshold. The linewidth broadening, together with the strong increase in decay time, clearly show that the reduced gain close to Δ = 0 prevents laser oscillation, and the increased phase noise due to SpE impairs the coherence of the radiation and eventually dominates.³⁷ 

Additionally, Fig. 5(d) shows three examples of decay curves obtained at the same pumping conditions and at different Δ. At large detunings (black and red symbols) the QD decays are characterized by the fast dynamics associated with StE (below 250 ps), while the blue symbol (Δ ≈ 0.02 THz) displays a longer decay time (≈480 ps) similar to the below-threshold value in Fig. 4(c), which confirms that the device is operating in the SpE regime. The solid curves represent the theoretical predictions obtained via our model, by using the same parameters of Fig. 4, except for the decay time τ_l associated with emission into the other channels (radiative and non-radiative). Indeed, the model best reproduces the data when the decay time τ_l is reduced from 2 ns (i.e., the value used in Sec. IV A) to 0.9 ns. This reduction is expected, since heating by the detuning lasers increases the non-radiative emission rate, which in turn decreases the corresponding decay time. The curves show good agreement, where the small mismatch at Δ = 0.02 THz can be primarily attributed to a saturation effect of the QDs that delays the decay process.

After having demonstrated the switching of laser operation by mode-field coupling, we move on to consider the potential applications to ultrafast modulation. Indeed, an intriguing consequence of mode-field coupling regards the possibility to produce short pulses when fast detuning variations are applied in the control cavities, as shown in Fig. 6(a). The three cavities [Fig. 6(a), top] are initially assumed to have equal frequencies (Δ = 0), and the gain medium in the target resonator is therefore uncoupled with the field of the central (dark) supermode. A cw injection provides an above-threshold pumping of the carriers, and since they cannot de-excite into the dark mode, the pumped energy is stored as population inversion. A fast and antisymmetric time-dependent detuning Δ(t), achievable, e.g., by varying the intra-cavity refractive index via the electro-optic effect, is applied to the control cavities at a time t = t₀, and triggers the redistribution of the EM field [Fig. 6(a), bottom]. Assuming that the maximum shift Δ_MAX of the resonances is sufficiently large to decouple the cavities (Δ_MAX > η), the mode-field inside the target resonator is restored to its maximum value $E(t)r→$⁠, and the energy accumulated by the carriers is suddenly released under the form of an optical pulse.

In the simulations [Fig. 6(b)] we assume mode volumes typical of microring resonators (17.1 μm³), in order to obtain a larger contrast between the lasing and non-lasing situations, and a QD active region, where the same adjustable parameters previously extracted for the QD laser in Sec. IV are used. The three uncoupled modes are assumed to have the same loss rates γ (here γ = 0.03 THz), and the right/left tunneling rate are considered equal (η = 0.06 THz). These two latter conditions ensure that the device operates in the strong coupling regime (η > γ), whereas the equal losses imply that the modulation affects solely the electromagnetic field, therefore avoiding the Q-switching mechanism due to the redistribution of the modal losses.¹³ Moreover, the time-dependent detuning Δ(t) is assumed to have a maximum amplitude Δ_MAX = 4η, so that the inter-cavity coupling becomes sufficiently small to regard the target resonator as uncoupled.

Figure 6(b) shows the simulated optical pulse (red curve) obtained after the time-dependent detuning (gray curve) is applied to the control cavities while a cw power of 4.1 mW pumps the QDs of the target cavity (see supplementary material, Sec. 4). The pulse is characterized by a full-width half-maximum (FWHM) duration τ_pulse = 36 ps. This value is determined by the parameters that determine the laser dynamics, e.g., by the gain and density of states, and is ultimately limited by the photon lifetime. Indeed, the sudden carrier recombination taking place when the field is restored at t = 0 generates a considerable amount of photons that couple with the outside world via the cavity losses. This aspect indicates that higher cavity losses are required to obtain shorter laser pulses, provided that the corresponding gain suffices to maintain the laser oscillation in the target cavity in the uncoupled limit. Additionally, a higher loss rate also implies broader lineshapes of the optical modes. As a consequence, larger tunneling rates are also needed, as the condition η > γ must hold to ensure the strong photonic coupling, which in turn implies higher detuning Δ_MAX > η to ensure the uncoupling of the target cavity. In practice, the condition Δ_MAX > η > γ ≈ 1/τ_pulse constrains the achievable pulse width τ_pulse, which is therefore determined by both the maximum detuning Δ_MAX and the tunneling rate η of the device design. We note that the presented approach based on CMT is valid as far as the intercavity photon tunneling is the fastest dynamics in the system.

The scheme here proposed, to the best of our knowledge, represents a novel effect in laser physics, which can be exploited in various platforms, including macro-sized cavities and superconducting circuits, and gives room to exploiting various design and detuning possibilities. Additionally, a gain medium characterized by higher density of states and faster dynamics, e.g., quantum wells, would unlock pulse widths close to the ultimate limit set by the loss rate, potentially enabling sub-ps widths in engineered devices. Furthermore, the proposed design in principle enables modulation without chirp, as it involves a dispersion-free optical mode, and the switching mechanism does not require the injection of current in the lasing cavity, which is normally the limiting factor in nanolaser modulation due to its small size and large parasitics.

In conclusion, we demonstrated the switching of laser operation via mode-field tuning in a three-cavity system. By means of spectral- and time-resolved experiments, we showed suppression of StE from the target cavity, obtained by thermally tuning the control cavity resonances. Additionally, a model combining CMT and semiconductor REs provides a theoretical framework that well describes lasing in these structures, also highlighting the role of the fast decay component arising around the laser threshold. Furthermore, we showed that the model predicts the production of short optical pulses when mode-field switching is combined with ultrafast tuning of cavity resonances. This method, therefore, provides a novel technique to modulate the laser output in every platform displaying tuneable resonances, with the advantage of the implementation in solid-state nanodevices, potentially impacting fields such as photonic integration, light-based sensing, neuromorphic optical computing, and optical interconnects.

See the supplementary material for more details on the design of the device, finite element method simulations, theoretical model derivation, experiment-theory comparison, and numerical results of the pulse.

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

This work was supported by the Netherlands Organisation for Scientific Research (NWO), under Projects No. 12PR3078 and 15PR3198, and by the NWO Zwaartekracht Research Center for Integrated Nanophotonics.