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We investigate the influence of pumping (i.e. population inversion) of the nonlinear material on the optical bistability of semiconductor microresonators, the reduction of sustaining power for bright and dark solitons by pumping, and the influence of pumping on dynamics of solitons and the background on which they exist. Reduction of soliton sustaining power by a factor of 300 is observed for dark solitons and the role played by material transparency and laser threshold is clarified.
©2005 Optical Society of America
1. Introduction
Optical dissipative solitons or localized structures have been observed in a diverse class of nonlinear materials [1–3]. Particularly, the existence and properties of spatial solitons in nonlinear optical resonators, such as degenerate 4-wave mixing [4] and laser with nonlinear absorber [5–7] was investigated. To be closer to applications of these solitons as optical switching-, and memory elements, the existence of spatial solitons in semiconductor microresonators [8–12] was recently investigated. For such solitons the sustaining power is in the ~1 mW range, impractically high for parallel use of large numbers of such solitons. It appeared, however, that coupling with an additional (incoherent) energy reservoir, i.e. population inversion in the semiconductor material, would permit to reduce these sustaining powers. Indeed we have found a substantial reduction of sustaining power for bright solitons, by more than an order of magnitude, using optical pumping to create initial populations, different from thermal equilibrium [13]. This result corresponded to the experiments on spatial solitons in electrically pumped VCSEL resonators, where solitons exist at smaller sustaining power [11]. Due to limitation of the pump laser power we were unable in [13] to reach the limits of reduction, which should supposedly be at material transparency. At transparency all material nonlinearities should change sign i.e. go through zero.
We investigate here the reduction of sustaining power for bright and also for dark solitons by optical pumping and elucidate the role of transparency and (solitary) laser threshold.
2. Experimental set-up
The experimental arrangement is shown in Fig. 1. Light from a tuneable Ti:Al2O3-laser is illuminating the sample (semiconductor resonator) in a spot of ~60 μm diameter with intensities up to 10 kW/cm2. A quarter-wave plate in front of the sample together with the polarizing beam splitter serve to direct the light reflected from the sample to the observation equipment. This consists of a CCD camera with a fast shutter (electro optical modulator) for taking snapshots on a nanosecond scale, and a fast photodiode which can be imaged into different points of the illuminated area.
Fig. 1. Experimental set-up. PBS: polarizer beam splitter, λ/2: halfwave plate, λ/4: quarterwave plate, L: lens, BS: beam splitter, EOM: electro-optical modulator, PD: photodiode to record intensity in time in certain points of the patterns. Beam waist placed on the sample surface is 60 μm diameter.
Pump laser radiation (4.5 W semiconductor laser at 808 nm) is focused onto the sample to a spot size of ~110 μm diameter with intensities up to 25 kW/cm2. The pump laser wavelength corresponds roughly to a reflection minimum, with a residual reflection of 20 %, on the short wavelength side of the front Bragg mirror of the resonator. Changing the sample resonator resonance wavelength (by changing the location on the sample) this minimum shifts somewhat in wavelength.
The pump laser spectrum is about 2 nm wide, roughly corresponding to the width of the reflection minimum. By temperature control the central laser wavelength can be adjusted ±3nm. Since it is not for all locations on the sample possible to tune the pump laser to the reflection minimum, the reflection of the pump radiation was always measured and the incident pump intensity corrected accordingly.
The spot of pump laser and Ti:Al203-laser are centered on the sample. The pump spot has larger diameter than the Ti:Al203-spot to create reasonably homogeneous pump conditions across the Ti:Al203-laser spot. The pump- as well as the Ti:Al203-laser are passed through a common chopper. The pump illumination lasts about twice as long as the Ti:Al203-laser illumination. The pump illumination starts well before the Ti:Al203-illumination and terminates well after it, thereby giving reasonably constant pump conditions in time for the duration of the Ti:Al203-laser illumination. For the Ti:Al203-laser the typical illumination time is 5 μs and the time between two illuminations is 1 ms, thus reducing substantially heating of the sample. The observations are triggered by the opening of the chopper. The opening of the camera-shutter can be delayed by a variable time so that snapshots can be taken for any time after the opening of the chopper.
The semiconductor resonator sample is made up of two Bragg mirrors of ~99,8 % reflection, forming a 3/2 λ cavity, filled with 18 quantum wells of 10 nm/10 nm thickness of GaAs/GaAlAs. This microresonator reaches laser threshold at a pump intensity of 12 kW/cm2 (corrected for reflection of the resonator front mirror). Figure 2(a) shows the pump illumination together with the laser intensity for a resonator wavelength (= laser emission wavelength) of 860 nm. The slow decrease of the laser emission intensity is due to an increase of material temperature while the pump light is admitted. Figure 2(b) shows the pump radiation together with the Al2O3-laser radiation on top of the laser emission.
Fig. 2. a) Pump intensity at 808 nm (upper trace), laser emission at 860 nm (lower trace); b) pump intensity (upper trace), laser emission with sustaining field superimposed (lower trace).
3. Sustaining power for solitons
The sustaining power of solitons was measured with the set-up of Fig. 1.
Figure 3(a) shows the switch-on intensity for bright solitons (dark in reflection, see Fig. 4(a)) as a function of pump intensity measured at 860 nm. A limit for the observation of these bright solitons is reached at 7 kW/cm2 pump intensity, above which only bright spots (dark solitons?) are observable. It appears that above a certain pump intensity bright solitons (dark spots) might not exist. The massive pumping has to be radiated away, so that only bright spots – for which the distinction into bright and dark solitons is not clear from observations in reflection – are observable [14].
Fig. 3. (a) Measured switch-on intensity for a bright soliton near the band edge (860 nm) as a function of pump; (b) measured switch-on intensity for a dark soliton below semiconductor band gap (880 nm) as a function of pump.
Fig. 4. Bright (a) and dark (b) solitons as observed experimentally. Reflectivity is plotted as Z coordinate and as grey scale. X,Y are transverse coordinates (with different scales for (a) and (b)).
For dark solitons (bright spots in reflection, Fig. 4(b)) which appear preferentially in the long wavelength range with dispersive nonlinearity (880nm), Fig. 3(b) shows the dependence of switch-on intensity on pump intensity. The limit reached at 11.5 kW/cm2 pump intensity is a purely technical observability limit. With decreasing soliton switch-on intensity, the brightness of the (reflected) spot, or the peak soliton intensity, decreases. At 11.5 kW/cm2 pump the soliton disappears in background light. Presumably the soliton sustaining intensity drops further beyond 11.5 kW/cm2 pump.
For bright as well as dark solitons we measure thus a reduction of sustaining intensity with pump increase, from zero pump, of 2.5 orders of magnitude. This corresponds to a power, sustaining a soliton, of a few microwatt, a value certainly satisfactory for applications.
We noted that dark solitons are usually of smaller diameter than bright solitons (Fig. 4(a),(b) show different scales in transverse coordinates). We think that the smaller size of the dark solitons relates to the higher intensities of which they appear compared to bright solitons. In [15] it is correspondently found that two different unstable wave numbers for dissipative structures exist in such systems.
4. Material transparency
When using pumping one expects the nonlinearities (dissipative as well as reactive) to cross zero at material transparency. At this point bistability and solitons could not exist. When crossing the transparency point, bright and dark solitons should exchange their roles, in certain respects. In the soliton experiments we could, however, not see clear evidence of such a transition. We measured therefore the slope of the bistability region in the intensity-detuning plane. For a purely absorptive nonlinearity the bistability range is symmetric with respect to zero detuning of the exciting field with respect to the resonator resonance. For a predominantly dispersive nonlinearity the bistability region is asymmetric with respect to zero detuning. Thus, the slope of the switch-on intensity as function of detuning mirrors the sign of the dispersive nonlinearity.
Figure 5 shows the measurement of the switch-on curves with the pump intensity as a parameter. One does see that the slope changes sign around above 3 kW/cm2 pump. (The exciting light also influences the material inversion so that the slope changes with the exciting intensity for medium pump intensities (e.g., for 3.3 and 6.5 kW)). The 10.4 kW/cm2 curve has the change of slope very close to zero sustaining field intensity. One can thus estimate that material transparency occurs around 10 kW/cm2 pump: a plausible value in view of the 12 kW/cm2 laser threshold.
Fig. 5. Measured sustaining intensity of plane wave bistability as a function of detuning of sustaining field from resonator resonance, with the pump intensity as a parameter.
5. Influence of (solitary) laser threshold
If the pump intensity is large enough to reach laser emission of the resonator (solitary laser threshold) and if simultaneously a field is applied near the resonator resonance frequency we encounter the familiar situation of “laser with injected field” (or laser “injection locking”). Depending on the ratio of the “injected field” and the laser field magnitude, on their frequency difference, and resonator finesse, the injected and the laser field can coexist, or if the injected field is sufficiently strong, it can phase-lock the laser field. When the two fields are not phase-locked, the dynamics is dominated by the temporal interference (beating) between them. Between independence of fields and phase-locking all types of dynamics characteristic of phase-lock circuits can occur, like period doubling, chaos… etc. This situation has been analyzed for the case of laser with large Fresnel number, as appropriate here, in [16].
The main result is in line with the picture of injection locking: below laser threshold there is only the “injected” field; thus no dynamics. Above laser threshold for not too high ratio of injected to laser field the two fields are independent. The dynamics, for the large Fresnel number case here, dominated by the (spatio-temporal) interference (beating), is a background with dynamic structure on which a reasonably stable soliton sits [16]. For larger ratio of injected- to laser field, the injected field phase-locks the laser field so that the beating stops and the background and solitons are stable again.
We confirm these predictions qualitatively in the experimental recordings of Fig. 6. The upper row shows the formation of a soliton with pump below (solitary) laser threshold. A soliton grows with little dynamics of the background. The middle row is recorded with pump above laser threshold and relatively small sustaining intensity. Here the soliton is accompanied by a background showing emerging and disappearing (in any case dynamical) structures. This dynamical background disappears (lowest row) when the sustaining field is raised, consistent with a phase-locking of the two fields.
Fig. 6. Experimental snapshots showing the formation of solitons during an illumination time of 5 μs for different powers of pump and sustaining field. Upper row: 1.9 kW/cm2 of sustaining field intensity, 9 kW/cm2 of pump intensity. Middle row: 0.14 kW/cm2 of sustaining field intensity, 15.4 kW/cm2 of pump intensity. Lowest row: 8.5 kW/cm2 of sustaining field intensity, 15.4 kW/cm2 of pump intensity. 3-Dimensional representation of reflectivity as in Fig. 4. Discussion, see text.
Although due to the limited time resolution of the camera (~10 ns) we cannot observe dynamics in 2D on a faster time scale, the appearance of a dynamic background above laser threshold and its disappearance with higher sustaining intensity is in agreement with the predictions of [16] and with what one expects qualitatively from the ”laser injection-locking” analogy.
6. Summary
We have investigated the effects of (optical) pumping of a semiconductor microresonator on the properties of spatial resonator solitons. The soliton sustaining field intensity can be reduced to a few microwatt by pumping the nonlinear material. We determine the material transparency point, and find the behaviour of solitons when the pump is around laser threshold in line with the qualitative picture of “laser injection locking”, as theoretically treated in [16].
References and links
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