1. Introduction

All-optical devices are expected to play an important role in the coming decade in the domain of information and communication technology due to their ability to bring efficient solutions to data transmission and processing. In this context, two-dimensional photonic crystals (2DPCs) have kindled interest for their potential use as active photonic devices. PCs [1] are a periodic arrangement of materials with different refractive indices where the periodicity is of the order of the wavelength of light which confers them with exciting possibilities to manipulate light signals within small volumes of materials [2]. In this work, we have fabricated an InP-based 2DPCs laser bonded with Silicon and explored its temporal capabilities.

In wavelength sized structures -VCSEL’s, micro-cavities and more recently photonic crystal lasers- three parameters have been presented as the pathway to breakthroughs for speed and compactness, namely the cavity quality factor Q, the volume of the resonator and the spontaneous emission rate: the β factor. Considerable effort has been devoted to optimising one or a combination of these factors to obtain a variety of impressive performances in terms of laser threshold, compactness and speed [3–7]. Manipulation of the β factor gives a handle on the spontaneous emission rate to tailor at will, the temporal response of the system. Similarly Q factors have been under scrutiny with the view to reducing threshold power levels. Mode volumes of the order of cubic wavelength have been achieved permitting strong confinement of light in three dimensions [7]. In semiconductor 2DPC lasers both the β factor and the Q factor are expected to be fairly high with attractive switching speeds with low threshold levels. The highest β factors reported so far are obtained in nanocavity systems [8,9]. To date the fastest laser reported is in a GaAs nanocavity containing InGaAs multiple quantum wells. It operates at 937nm at 100K [6] with a modulation speed of more than 100GHz. In the present work, we study the dynamics of the other type of photonic crystal laser which is the band-edge laser. Here, laser emission is obtained in a perfectly periodic system by exploiting the low group velocity modes occurring at the high symmetry points of the band structure [10]. These types of lasers are of interest because they favour the emission of higher powers than nanocavities due to their size and they enable more efficient collection as they are highly directional [11]. Here we report on the temporal properties of 1.55μm InGaAs/InP 2D photonic crystal band edge lasers operating at room temperature. We performed the measurements with an up-conversion technique [12] which gives us the required temporal resolution (150fs) adapted to the short time responses of these types of lasers. Further this has the advantage of being a direct measurement which does not involve deconvolution of the instrumental time resolution- which in the temporal measurements reported so far in photonic crystal laser- is often lower than the temporal characteristics of the system under study. In addition at 1.55μm, streak cameras are of low efficiency and thus, inefficient to measure the dynamics of such lasers. Our photonic crystal laser is integrated onto a Silicon chip rendering the present work potentially relevant in the context of a rapidly developing domain of hybrid structure devices and on-chip high speed data processing systems.

2. Design and fabrication of the PC structure

The 2D-PC structure consists of a 265 nm thick InP slab incorporating four InGaAs/InGaAsP QWs, emitting near 1.53 μm. A schematic of the 2D PC hetero-structure is shown in Fig. 1(a). The 2D PC is a graphite lattice of air holes drilled in the InP slab grown by MOCVD. The slab is integrated onto a Silicon wafer by means of Au/In bonding technology, which provides efficient heat sinking [13]. The InP epi layer is separated from the metallic joint by 785nm of silica, preventing thereby evanescent leakage of light into the metal as well as inducing destructive interference of light in the vertical direction at the centre of the membrane to improve the quality factor of the Bloch mode resonator [14]. The lattice parameters (lattice constant =745nm and holes diameter = 290nm) are chosen so that a slow group velocity Bloch mode is at ~1.52 μm, near the maximum of QW absorption. This mode is near the Γ. point of the photonic band diagram which enables vertical operation of the device. The photonic band structure of the studied PC is represented in Fig. 6(a). Graphite lattices exhibit both high areal density of gain material (with respect to other Bravais lattices) and high symmetry leading to large optical feedback, two properties which favour laser emission. A Scanning Electron Microscope image is shown in Fig. 1(b). The details of the processing technology are given in a previous article [15].

 

Fig. 1. (a) Schematic hetero-structure. (b) SEM top image of the PC structure.

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3. Laser characterization

First we recorded the reflectivity spectrum of the PC resonance under near-transparency condition for the gain material in order to evaluate the Q factor of the resonator, which is about 10000 [13]. Then a study of the laser emission intensity as a function of the pumping intensity was conducted using micro-photoluminescence measurements with excitation pulses of 5ps with 80MHz repetition rate delivered by a Ti-Saph laser emitting at 840 nm. The excitation pulses were focused on the sample by a long working distance optical microscope (NA=0.4). The excitation spot is roughly 5 μm. The emission, from luminescence to laser emission, is collected by the same microscope objective and separated from the pumping laser by means of a dichroic mirror and an antireflection silicon-coated filter. It is then spectrally dispersed by a 0.5m spectrometer and detected by a cooled InGaAs photodiode array.

 

Fig. 2. Laser intensity is plotted as a function of the pump power (squares: experimental and line: numerical calculation).

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In Fig. 2, we plot on a log-log scale (the blue squares) the laser peak power at 1.52μm as a function of the pump intensity. We observe the characteristic S-shaped curve [16] of the laser emission. The threshold will be derived in section 5 from a fitting procedure. The value we get is 2.3mW. Then, as pump power is increased above 4.2mW (52.5pJ), a saturation of the emitted power is observed.

4. Temporal studies

We record simultaneously the spectral response of the system using a spectrometer with an InGaAs nitrogen cooled photodiode and the temporal response using a β-Barium Borate (BBO) up-conversion crystal followed by a spectrometer and a photo-multiplier. The source used for the temporal studies is a regenerative amplified Ti-Saph laser providing 10μJ, 150fs, 1 kHz repetition rate pulses at 800 nm. The source is divided in two; one branch is used to optically pump the sample at normal incidence on the sample surface with a 10cm focal lens to a spot size of about 50μm. The other branch of the source is used as a gating pulse for the up-conversion system. The surface normal PC laser emission at 1.52μm is collected using the same lens as for optical pumping. A schematic of the experimental set-up is given in Fig. 3.

 

Fig. 3. Schematics of the experimental set-up. M1, M2, M3 denotes gold mirrors, D1 and D2 dichroic mirrors, BS a 90%–10% beam splitter, L1 a lens of focal distance 10cm, L2 a lens of focal distance 20cm, L3 a lens of focal distance 30cm, F a BG18 low pass filter filtering the light at 0.8μm and 1.5μm and PM a GaP photomultiplier.

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The up-conversion system is a nonlinear optical frequency converter [12,17], where one can detect IR radiation by taking advantage of the properties of highly efficient photomultiplier detectors at visible wavelengths. This conversion is accomplished by sum-frequency generation between a weak signal (here the laser emission at 1.52μm) and a strong pump (Ti-Saph at 800nm) in the BBO crystal. The intensity of the sum frequency (at 527nm) produced is proportional to the temporal overlap between the pump and the laser signal [18] and thus proportional to the signal intensity within the ultrashort pump pulse gate, hereto referred to as “gate”. This is recorded as a function of the relative delay giving an accurate representation of the full temporal shape of the signal. The BBO used here is a type I crystal with a thickness of 1mm chosen so as to give a temporal resolution limited only by the pulse duration i.e 150fs. The gate at 800nm and the laser emission at 1.52μm are collinearly incident and focused in the BBO crystal using AR coated lenses of focal distances 30cm and 20cm, respectively for the gate and the signal, giving rise to a sum frequency generation at 527nm. The up-converted signal is sent into a spectrometer and detected by a GaP photomultiplier. The spectrometer is only used as a filter to eliminate the extremely intense second harmonic of the gate at 400nm which is not easily stopped by ordinary filters, as the pump for up-conversion is 10⁵ times the signal. The signal is then sent into a boxcar averager with a 1ms gate triggered at 1 kHz by the laser. The signal is averaged over 3000 pulses. The averaged output signal from the boxcar is passed to a computer and recorded as a function of the delay between the laser emission and the pump pulses.

 

Fig. 4. (a) Up-converted laser intensity versus temporal delay between gating pulse and laser emission for three different pumping energies (green 260pJ, blue 290 pJ and red 500pJ); squares: experimental values (the lines joining the squares are a guide to the eye). Black lines are the numerical calculations as a result of the fitted parameters in the rate equation model. (b) Laser spectra for three different pumping energies (green 260pJ, blue 290 pJ and red 500pJ).

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The up-converted signal is displayed in Fig. 4(a) for three different pump energies. The zero in the x-axis corresponds to the instant when the pump for optically pumping the sample arrives at the sample. This is determined by measuring the up-conversion signal produced by combining the gate and the optical pump of the PC at the BBO crystal. The PC laser intensity is then plotted as a function of the delay (with respect to the measured zero) introduced in the path of the gate. The corresponding spectra of the laser emission are shown in Fig. 4(b). The PC laser response for the lowest energy, 250pJ shows a turn-on time (the interval between the pump and the peak of laser emission) of 30ps and a fall time of 9ps; the emission is at 1520.5nm with Δλ=0.7nm. When the pumping energy is increased to 290pJ the turn on time is 25.4ps and the peak shifts to 1520nm with Δλ=0.9nm; for the highest energy of 500pJ the turn-on time is 17ps, the peak further blue shifts to 1519nm with Δλ=5nm, probably due to a large chirp coming from amplitude-phase coupling in semiconductor active media [19].

 

Fig. 5. Turn-on time as a function of the pump energy, squares: experimental values; line: numerical calculation resulting from the fitting of the experimental data. Fitted parameters: R_th=75.7 pJ; γ_sp=0.004; $\overline{\tau }$ _rad =6.9; ntr=0.46.

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For low pumping energies the temporal signal is almost symmetrical whereas for a pumping energy of 500pJ, the fall time stretches over 15ps giving a strongly asymmetric temporal response. In Fig. 5 we plot the complete set of turn on times as a function of the pump energy. There is a clear decrease in the turn on time with respect to the optical excitation level. It is also seen that this decrease hits a limit around 17ps.

5. Discussion

We will now analyse the physics in play behind the characteristics of the temporal response of the low group velocity band-edge lasers. We model the transient response with a set of standard QW laser rate equations [16]. The equations read:

where S is the photon density, N is the carrier density in the quantum wells (per unit volume), τ_p is the photon lifetime, Γ is the optical confinement factor which takes into account the overlap of the mode field with the active region, v_g is the group velocity, g(N) = σ (N − N_tr) is the gain in the linear gain model with N_tr the carrier density at transparency and σ=dg/dN the differential gain, β is the spontaneous emission factor, β is the radiative recombination coefficient in the resonator, τ_nr is the nonradiative carrier recombination lifetime and R is the pumping rate. Variables S and N are adimensionalized and yield the following equations:

where n = Γv_gστ_pN, n_tr = Γv_gσN_tr, s = v_gστ_nrS, $\overline{\tau }$ _rad = τ_rad/τ_nr, γ_sp = βτ_nr/τ_rad and τ_rad = Γσv_gτ_p/B . Note that the carrier normalization constant (Γv_gστ_p)^-1 gives the additional carrier density required to take the system from the transparency to the laser regime for β=0. The parameter n_tr essentially gives the QW absorption normalised to optical losses. The photon density is normalized to that corresponding to the laser saturation intensity. τ_rad gives a characteristic time scale for radiative recombination processes. Finally, R_th=(n_tr+1)/(Γ_MDv_gστ_pτ_nr) is a normalization factor for the pumping rate, which corresponds to the pumping rate at the laser threshold for β=0 and $\overline{\tau }$ _rad ≥ 1. We integrate Eqs. (3)–(4) in time with a 4^th order Runge-Kutta algorithm. We model the femtosecond pumping as a gaussian pulse centred at t₀ and duration 2τ_fs,

For a sufficiently long time t₁ after the pumping pulse (t₁-t₀>>t_fs) almost all the carriers are excited, giving n(t₁) ≈ n₀ ≡ r(1 + n_tr) where r≡R₀/R_th is the pumping parameter. A very short pumping pulse as in our case allows approximating the gaussian by a Dirac function, i.e. R(t) = R₀τ_nrδ(t-t₀), which yields n(t₀₊)=n₀. We have verified that this kick-like pump accurately approximates the gaussian model of Eq. (5). Depending on the whole set of parameters -namely R_th, τ_p, τ_sp, τ_nr, τ_rad and n_tr - a laser pulse can develop and attain a peak intensity of s_max at t=t_max which gives the turn on time Δt=t_max-t₀. We have implemented an algorithm which allows the parameters to fit the experimental data by minimizing the distance between the experimental points and Δt(r) for the data shown in Fig. 5. For the fitting procedure we fixed τ_p to be Q/ω with Q= 10000, which gives τ_p=8.2ps, and τ_nr=200ps (in accordance with the previously measured value [20]). In Fig. 5, we plot the turn on time Δt as a function of pump intensity.

Now we carry out a crosschecking procedure; thus in order to verify the quality of the fit we use the converged parameters γ_sp, $\overline{\tau }$ _rad and n_tr obtained from fitting the curve in Fig. 5 and re-inject them into the equations. The remaining parameter R_th is re-scaled to the pump power of the peak intensity data, giving the threshold value in Fig. 2, R_th=2.3mW. The emission intensity is plotted as a function of pump intensity; the result is shown in Fig. 2. It is seen that the experimental values fit in very neatly with those derived from the model. We see that, starting from spontaneous emission level (Fig. 2) to well above the threshold, the experimental points concur with the simulated curve. Above this level of excitation, both in the intensity versus pump intensity (Fig. 2) curve and in the turn-on time dependency on pump energy curve (Fig. 5), the model deviates slightly from the experimental values probably due to gain compression for pump powers > 4.2mW. As a final verification, we plot the calculated temporal response of the laser for the 3 pump energies used on Fig. 4 a). Once again, we observe a very good agreement with the experiments, especially for the change in the shape of the signal with increasing pump powers.

We can now derive the physical parameters from the normalized ones. The fitting procedure yields the values of γ_sp, $\overline{\tau }$ _rad and n_tr. Firstly, the spontaneous emission factor can be extracted directly from the relation γ_sp = βτ_nr/τ_rad giving β=0.03. Next, the group velocity can be obtained though the relation n_tr=Γv_gτ_p a, where a is the QW absorption; using a=6000cm^-1 from absorption measurements together with a geometrical estimation of the optical confinement factor, Γ=0.2, we obtain v_g=5×10⁵ m/s. Finally, an estimation of the carrier density at transparency N_tr~10¹⁸ cm^-3 allows to obtain a value for the radiative recombination factor: B~3 10^-10 cm³/s in accordance with the value reported in literature [21].

 

Fig. 6. (a) Calculated 2D photonic band diagram of the studied PC. The blue line indicates the slow band where laser emission is obtained. Green dotted lines indicate the air and silica light lines, the guided modes cut-off at the silica light line. (b) Group index calculated for the blue band on Fig 6(a). The red dashed line indicates the extent of the pumped area of 50μm in reciprocal space.

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In order to verify the group velocity value which is deduced from our experimental fitting, the guided resonances of the graphite lattice structure were calculated using a Guided Mode Expansion technique [22], over a range of lattice constants and filling factors. This technique allows us to calculate the complex resonant frequencies of this asymmetric 3D structure (air/InP/Silica) as a function of wavevector. These frequencies (normalised to the 745nm period of the graphite lattice) are displayed in Fig. 6(a) for wavevectors aligned along the Γ-M direction of the lattice. In Fig. 6(b) we plot the group index (c/v_g) around the Γ point of the reciprocal lattice. The red dashed vertical line indicates the extent of the pumped area of 50μm in reciprocal space. Note these results compare favourably with 3D fully-vectorial FDTD calculations [23], which included the lower metal mirror/bonding layer. The simulation shows that the group index is about 380 corresponding to a group velocity of 7.9×10⁵m.s^-1. This value is of the same order of magnitude as the one found by fitting the experimental measurements further validating the quality of the fit.

6. Conclusion

In summary, we have carried out, for the first time, to our knowledge an accurate measurement of the temporal characteristics of a band-edge PC laser with graphite lattice, integrated on a silicon chip and operating in the telecom range at room temperature. The temporal response has been obtained with a precision of about 150fs using an up-conversion technique. It has been observed that the combination of a fairly high value of β(0.03) and a fairly low group velocity (5×10⁵m.s^-1) gives the possibility of obtaining lasing in very small structures with a modulation capacity of 30GHz. The fast response and the low threshold powers obtained indicate that these types of lasers will perfectly fit in their role of source in an all optical photonic circuits with the possibility of integrating these devices on silicon platforms.