1. Introduction

The miniaturization of electronic devices, in pursue of faster and more efficient data processing, has led to issues such as the increased tunneling current and Joule heating [1,2]. As an alternative to electronic counterparts, the optical logic devices have emerged as a promising solution [3–5]. Among these devices, the optical switch, which uses on/off states to express logic, is a crucial component for ultrafast data processing [4,5]. Optical switching can be achieved through nano–laser devices that emit strong light with specific energy, phase, and direction when the pump energy is above a threshold [6,7]. Due to the reduced mode volume, these nano–laser devices have merits in achieving high-speed operation and low energy consumption, but require strong light-matter interaction to overcome the cavity loss [8–11].

Surface plasmons (SPs) are collective and quantized electron oscillations that occur at the interface between a metal and dielectric [12,13]. They have broad applications in fields such as the SP resonance (SPR) biosensors and the surface-enhanced Raman spectroscopy [14–20]. The possibility of subwavelength coherent light sources has made SP lasing, in which the SP polariton is amplified from the adjacent optical gain, an area of great interest. One promising SP laser configuration is the use of semiconductor nanowires on a metallic substrate with a thin dielectric spacer layer, which reduces the dissipative energy loss into to the metals [21–23]. Another good candidate for SP lasers is the periodic structure of metals on a semiconductor gain, where the momentum mismatch can be managed by the geometrical periodicity. Furthermore, the periodic metal grating placed on a semiconductor can serve as a distributed feedback cavity to enable the efficient SP lasing [24].

Recently, we reported on the SP lasing in the telecommunication band of 1100–1600 nm from the metal grating structure on InGaAsP/InP semiconductor [25]. And, Wang et al. investigated the photon dynamics of SP lasing in two-dimensional metal nanoparticle arrays integrated with dye solution by performing the time-resolved photoluminescence (TRPL) [26]. However, to the best of our knowledge, the carrier dynamics of the gain medium in correlation with SP lasing has not yet been experimentally studied.

In this paper, we report on the lasing dynamics of one-dimensional Au gratings fabricated on InGaAs semiconductor, which are pumped by ultrashort optical pulses at a wavelength of 800 nm. We investigate the build-up of lasing processes that occur through stimulated light amplification, corresponding to the coherent energy transfer from the carrier reservoir of the semiconductor gain into the photon reservoir of the SP cavity. This investigation is performed using the time-resolved pump-probe (TRPP) for the carrier dynamics in the semiconductor and the TRPL for the photon dynamics in the SP cavity. The correlated behavior that the photon signal is increased with consuming the carrier energy is manifested by comparing the carrier and photon dynamics and is interpreted by numerically solving the nonlinear rate equation on the carrier and photon density. The lasing build-up process, which is accelerated as the pump-induced gain is stronger, is observed in both the carrier and photon dynamics, and is supported by numerical simulation.

2. Optically pumped surface plasmon lasing characteristics

The one-dimensional metal gratings to study SP lasing was fabricated on a semiconductor using e-beam lithography techniques. Figure 1(a) shows a schematic of the fabricated sample structure, consisting of an In_0.35Ga_0.47As epi-layer grown on an InP substrate using metal-organic chemical vapor deposition. The grating patterns are formed from a 50 nm thick Au layer deposited on the InGaAs by e-beam evaporation, with a variation in period from 380 to 470 nm. Different grating designs is prepared in a single piece, where the size of each pattern is 50 µm × 50 µm, and the metal stripe is filling approximately 60% of the total area. The inset in Fig. 1(a) shows the SEM image of a 390 nm period metal grating. In order to test SP lasing, the metal grating devices are cooled down to 80 K in a cryostat and pumped by 100 fs optical pulses with a wavelength of 800 nm from a Ti:sapphire oscillator. An objective lens is used to focus the pump beam to a spot diameter of approximately 28 µm in the sample. The spectral features of the emission are characterized by collecting the light generated from the pump excitation through the same objective lens and directing it to a monochromator equipped with an InGaAs CCD detector.

 

Fig. 1. (a) Schematic of one-dimensional metal grating on InGaAs/InP semiconductor for optically pumped SP lasing. The inset is the SEM image of the fabricated Au grating with $\Lambda$=390 nm. (b) Lasing spectra obtained from different grating periods at an optical pump energy of 0.53 nJ. The inset is the lasing wavelength as a function of grating period. (c) Output emission energy as a function of the pump energy for the grating structure with $\Lambda$=440 nm. The inset shows the emission spectrum below the threshold pump energy of 0.15 nJ and that above the threshold pump energy of 1.74 nJ. (d) FDTD simulation of the electric field amplitude profile of the grating period of 440 nm under the lasing condition.

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Figure 1(b) depicts the lasing spectra obtained from different grating periods at a pump pulse energy of 0.53 nJ. It can be observed that the surface plasmon lasing wavelength increases as the grating period increases. The inset of Fig. 1(b) displays a plot of the lasing wavelength versus grating period. According to the surface plasmon dispersion relation, the SP wavelength is determined by the product of the grating period and the effective refractive index of the Au grating on In_0.53Ga_0.47As/InP [27]. In Fig. 1(c), we show the power characteristics of the lasing for the grating with $\Lambda$=440 nm. The threshold pump energy of the SP lasing is approximately 0.30 nJ at 80 K. The inset of Fig. 1(c) displays the emission spectra obtained below the threshold pump condition (E_pump= 0.15 nJ) and above the threshold condition (E_pump= 1.74 nJ). The spectral width of the emission significantly narrows as the SP lasing is established. On contrast, below the lasing threshold, the signature of the amplified spontaneous emission is observed near 1450 nm, along with the band tail emissions near 1550 nm [28]. The observed emission spectrum changes as well as the typical output power behaviors above the threshold pump energy confirm the optically pumped lasing of the metal grating on the InGaAs semiconductor [29]. The emission is found to be polarized parallel to the grating axis (x-direction), consistent with the SP mode lasing. In Fig. 1(d), we display the electric field amplitude profile in the grating period of 440 nm under the lasing condition, obtained through finite-difference time-domain (FDTD) simulations with negative extinction coefficients of InGaAs material to account for optically pumped gain. The field profile shows strong concentration near the Au metal interfaces, with providing evidence for the SP mode lasing.

We note note that our device is quasi-two dimensional, enabling systematic tunning of SP mode coupling to the gain medium by varying the grating period of the distributed feedback cavity. In contrast, nanowire-based SP lasing devices are quasi-one dimensional, with small mode volumes operating at the lowest threshold condition determined by the gain spectrum and SP propagation loss. Another point to be considered is that dissipative energy transfer of excited carriers to the Au metal can occur in close proximity to the Au/InGaAs interface [30], and that reduced gain due to this energy loss mechanism can be overcome by inserting a spacer layer between Au and InGaAs, a strategy employed in nanowire-based SP lasers [21–23].

3. Carrier dynamics measurement

We investigate the carrier dynamics during the lasing process of the device with $\Lambda$=440 nm by performing TRPP spectroscopy. The schematic of the experimental setup is presented in Fig. 2(a). The 100 fs pump pulse with a wavelength of 800 nm from a Ti:sapphire laser is incident on the sample to enable SP lasing, and the transmission change of the probe pulse at a wavelength of 1300 nm is measured as a function of the time delay between the pump and probe pulse. An objective lens is used to focus the pump and probe beam into a spot on the sample. In the TRPP measurements, the change in the carrier density during the lasing process can be measured via the transmission change of the probe beam [31]. The probe wavelength of 1300 nm is chosen because it is relatively sensitive to the transient carrier dynamics in the InGaAs semiconductor.

 

Fig. 2. (a) Schematic of time-resolved pump–probe setup. (b) Probe transmission change induced by the pump pulse at a SP lasing condition of E_pump= 0.79 nJ for the grating with Λ = 440 nm. The lasing build-up time (t_B) as denoted by the arrow was determined by the crossing of the two linear interpolations in the semi-log plot (c) Time-resolved transmission changes measured at different pump pulse energies. (d) Lasing build-up time as a function of pump pulse energy.

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Figure 2(b) shows the TRPP signal obtained at a pump energy of 0.79 nJ. When the pump energy is above the lasing threshold, the lasing build-up process, in which the carrier energy is converted to photons, is expected to lead to additional carrier decay in addition to the general process due to the radiative and nonradiative carrier recombinations. The TRPP signal reveals the signature of the lasing-induced carrier decay, as indicated by the red arrows in Fig. 2(b). We note that the position of lasing build-up is determined by the crossing of the two linear interpolations in the semi-log plot of Fig. 2(b). One corresponds to the signal decay due to carrier relaxation, while the other corresponds to the additional decay due to the lasing action. As shown in Fig. 2(c), the time of lasing build-up becomes faster as the pump energy increases. The measured build-up time as a function of the pump energy in Fig. 2(d) also indicates that the lasing build-up time becomes faster as the pump energy increases. This transient behavior can be explained that the SP lasing is accelerated when the pump-induced gain becomes higher.

4. Photon dynamics with time-resolved photoluminescence

While the lasing-induced transient carrier dynamics can be studied from the TRPP signal, the photon dynamics occurring through the mutual interactions with the carrier population can be revealed by TRPL [32–34]. Figure 3(a) shows a schematic of the TRPL experiment. The temporal evolution of the lasing emission after the optical pump pulse excitation at 800 nm is measured using a streak camera with a temporal resolution of about 4 ps. Figure 3(b) displays the TRPL signals obtained at various pump pulse energies for the grating with $\Lambda$=440 nm at 80 K. Here, we note that the pump energy in the TRPL experiment is calibrated to match the threshold energy of TRPP case, taking into account the different pump conditions for the two cases. It is revealed that the lasing emission is delayed relative to the pump excitation, and the delay time becomes shorter as the pump energy increases. In Fig. 3(c), we plot the PL maximum time as a function of the pump energy. This behavior in the photon dynamics is consistent with the carrier density dynamics in the TRPP, in that both exhibit faster lasing process at high pump energies. Additionally, Fig. 3(d) compares the TRPL signal with the TRPP obtained at a similar pump energy. It is found that the lasing-induced carrier depletion observed in the TRPP coincides in time with the lasing emission in the TRPL.

 

Fig. 3. (a) Schematic of TRPL measurement system using a streak camera. (b) TRPL signals from the Λ=440 nm grating at 80 K obtained at different pump pulse energies. The gray dashed line represents the instrument response function of the streak camera system. (c) The time of maximum TRPL intensity as a function of the pump pulse energy. (d) The TRPL signal compared with the TRPP signal obtained at similar pump energies.

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5. Rate equation model simulation

To gain a deeper understanding of the lasing dynamics that occurs through the light-matter interaction in the metal grating on the semiconductor, we conducted a rate equation simulation of the time-dependent changes in the photon density (N_p) and the carrier density (N) following optical pump pulse excitation. The rate equations are written as follows [35].

Here, N_pump is the excited carrier density in response to the Gaussian time-domain profile pump pulse, with a pulse duration of 100 fs. The rates of spontaneous emission and non-radiative recombination are represented by R_sp and R_nr, respectively, and can be expressed as Rsp = BN2 and Rsp = CN3.The photon lifetime in a cavity is τp. The gain parameter g can be approximated by the following logarithmic function as a function of photon and carrier density.

Here, Ns is an offset used to prevent the divergence at N = 0, Ntr is the transparency carrier density, and ɛ is the gain compression factor. Γ is the confinement factor, which is equal to the active region volume divided by the cavity volume. For the simulation, we adopted the material parameters listed in Table 1, which were used for a In0.2Ga0.8As/GaAs quantum well system [24].

Table 1. Parameters for the rate equation model simulation

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According to the simulation, the lasing is achieved when the total amount of Npump exceeds a threshold value of 3.77 × 1018 cm-3. We numerically solved the equations, and Fig. 4(a) shows the temporal evolution of the N and N_p after creating a carrier density of 1.89 × 10¹⁹cm^-3. Initially, the gain is generated by the pump pulse’s carrier excitation, and the photon signal grows exponentially with the rate determined by the gain value. The stimulated emission rate increases as the light intensity rises, resulting in accelerated carrier decay and decreased gain. The lasing ends as the gain or the carrier density falls below the threshold value. Consequently, the initial decay region of the carrier density, where the photon density is very low, is determined by the radiative and nonradiative recombination rates. On the contrary, stimulated emission is prominent in the carrier decay after lasing build-up time, where the photon density is considerable. The simulation clearly reveals that the carrier density depletion is accompanied by the laser build-up, and this depletion stops as the lasing terminates. As the pump intensity increases in the rate equation simulation, the lasing is established in a shorter time after the photoexcitation. In Fig. 4(b), we plot the carrier density dependence of the turn-on delay, defined as the time interval required for the lasing emission to reach 10% of the maximum after the carrier generation. We need to mention that although these simulations are performed under simplified device parameters that neglect the SP-induced light-matter interactions, they satisfactorily reproduce important dynamical properties of the SP lasing, such as the correlated behaviors of the photon and carrier density and the pump energy dependence of the lasing turn-on time.

 

Fig. 4. (a) Temporal profile of the carrier (N) and photon density (N_p) obtained by numerically solving the rate equations for the lasing model of a semiconductor laser with the parameters in Table 1 and the pumped carrier density of 1.89 × 10¹⁹cm^-3. (b) Carrier density dependence of the simulated turn-on delay, defined as the time interval required for the lasing emission to reach 10% of the maximum after the carrier generation.

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6. Conclusion

The SP lasing dynamics in the device structure consisting of a metal grating fabricated on InGaAs semiconductor is investigated using TRPP and TRPL spectroscopy, which provide information on the temporal evolution of the carrier density and the photon density, respectively. While the build-up of the lasing action is observed through the accelerated carrier depletion in the TRPP signal, the TRPL signal directly provides the temporal profile of the photon density in the SP cavity. Both signals reveal that the lasing action occurs earlier when the initial carrier density is higher. This correlated behavior of the carrier and photon density in the lasing dynamics originates from the energy transfer from the carriers to photons during the stimulated emission process. We interpret the main experimental features of the lasing dynamics by performing the simplified rate equation simulation for carrier and photon densities. The results of this study on the SP lasing dynamics can shed light on the light-matter interactions in active nano-photonic devices including ultrafast SP-based optical switches and photon sources.