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Abstract
Random lasers, which rely on random scattering events unlike traditional Fabry-Pérot cavities, are much simpler and cost-effective to fabricate. However, because of the chaotic fluctuations and instability of the lasing modes, controlling the lasing properties is challenging. In this study, we use random InP nanowire (NW) arrays that operate in the Anderson localization regime with stable modes as the random lasers. We show that by changing the design parameters of the NW arrays, such as filling factor, dimensions of the NWs, degree of randomness, and the size of the array, the properties of the lasing modes including the number of modes, lasing wavelengths, and lasing threshold can be controlled.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Unlike traditional lasers with cavities supporting Fabry-Perot or whispering gallery modes that need precise fabrication to support the lasing modes, random lasers do not require well-defined cavities and can be obtained by multiple scattering of light within a gain medium. This property has given some unique properties to random lasers including low-cost and unrestricted angular emission. On the other hand, the randomness of the scattering events results in lasing modes that cannot be easily controlled. Therefore, controlling the lasing modes in random lasers is important for the further development of sensors [1–3], speckle-free imaging [4], integrated devices [5], and spectral super-resolution spectroscopy [6].
Changing the gain material is one of the methods developed for controlling the lasing modes. For example, by mixing various laser dyes with gold nanostructures, Ziegler et al. were able to achieve random lasing throughout the visible up to the infrared range [7] or using a two-dye system with broadband plasmonic resonance scatterers, Wang et al. achieved coherent dual-color random lasing [8]. Changing the pump beam profile is another way to tune the lasing modes. It was shown by using a spatial light modulator to shape the pump beam profile, single-mode lasing at a particular wavelength can be achieved [9,10]. Using the same method, emission directionality [11], lasing threshold [12], and modal interactions [13,14] have also been controlled. Leonetti et al. have also shown by changing the pump beam shape from disc-shaped to stripe-shaped it is possible to move from a system with non-resonant feedback to a resonant one [15]. We have previously shown that by defocusing the pump beam in random lasers based on GaAs-AlGaAs core-shell NWs it is possible to suppress the resonant modes [16]. Using liquid crystal [1] and magnetic materials whose properties can be tuned by temperature [17], externally applied voltage [18], and magnetic field [19] are other ways to control the lasing threshold and emission of random lasers. Nevertheless, most studies reported that the rise in temperature or increase in applied voltage would decrease the emission intensity, which is not ideal for practical applications [20]. Changing the geometry and structure of the scatterers are other ways to modify lasing properties. It was shown using monodisperse scatterers can create resonant feedback and by changing the scatterers diameter and refractive index it was possible to control single-mode lasing wavelength [21]. Consoli et al. have demonstrated that by controlling the randomness degree by shaping the roughness of the scattering surfaces it is possible to tune the average number of lasing modes in random lasers with spatially localized feedback [22]. Using a photonic crystal structure with a transport mean free path, lt of 2–3 µm, which is almost five times bigger than the lasing wavelength, the random laser was reported to operate in the diffusive regime [23]. In diffusive random lasers (also known as delocalized random lasers), sharp emission peaks are usually not present, and only an overall linewidth narrowing around the peak of the gain spectrum is observed [24]. However, some theoretical works have predicted the possibility of lasing in resonant feedback mode even in diffusive systems with low-Q resonances [25,26]. Unlike the diffusive regime, in the localization regime, where klt ≤ 1 (k is the wavenumber), these lasing modes are more stable and can exhibit a higher degree of controllability due to spatial confinement of the modes [27].
We have previously reported a random laser system made of random InP nanowire arrays which operated in the Anderson localization regime where stable multi-mode lasing was observed [27]. Here, we report our systematic investigation into how the various parameters of the nanowire arrays, such as average diameter, nanowire length, filling factor, degree of randomness, and system lateral size can be used to design the lasing modes of these random InP nanowire arrays.
2. Results and discussion
For a disordered media to support cavities in the localized regime, according to Ioffe-Regel criterion, lt should be smaller than the wavelength of light, λ (klt ≈ 1, k = 2π/λ is the wavenumber) and the sample dimension should be larger than the diffusive critical volume, or in other words, the sample size should be bigger than lt [28]. In these systems, like all other types of lasers, lasing can occur if the gain is large enough to balance the loss mechanisms. There are two main loss mechanisms in random lasers: (i) out-coupling loss to the surrounding media and (ii) internal absorption loss. To quantify the first mechanism, the quality factor, QF of the system can be used. However, the second mechanism is mainly due to material loss. In the following section, it is shown that the geometrical parameters, such as filling factor (FF, filling factor is defined as the ratio between the volume of NW region and the volume of the disordered medium) and diameter of the random laser could affect the cavity’s QF and the carrier generation.
Using the commercial finite-difference time-domain (FDTD) Lumerical software package, the effects of FF and NW average diameter, dav on the random NW system have been shown in Fig. 1. The inset of Fig. 1(a) shows the optical carrier generation, Gop of a randomly distributed InP NWs (n=3.73+i0.446, where n is the refractive index on InP at the excitation wavelength) with FF = 0.3, dav = 125 nm, and length, LNW = 3 µm. To calculate Gop, FDTD Solutions was used to solve Maxwell's equations and determine the spatial distribution of the electric field, E(r,λsource), for the disordered medium. Then using
Fig. 1. The effects of dav and FF on carrier generation and resonant modes. (a) Carrier generation profile along the nanowire length for arrays with different average diameters and FFs. The insets show the optical carrier generation on the z-y (top) and x-y (bottom) planes. (b,c) Probability of finding high QF (QF > 3000) arrays systems with different FFs and average diameters, in the wavelength range of 725 nm < λr < 775 nm (b) and 800 nm < λr < 850 nm (c) using 2D simulation setups.
Fig. 2. The effect of dav, FF, and σc on the statistical distribution of QF and λr using 2D simulation setups. (a,b) The effect of dav at FF = 0.3 and σc = 50 nm on Q and λr of the cavity mode. (c,d) The effect of FF at dav = 130 nm and σc = 50 nm on QF and λr of the cavity mode. (e,f) The effect of FF and dav at a fixed σc value for two arrays, A and B (array A: FF = 0.25, dav = 125 nm; array B: FF = 0.15, dav = 90 nm). (g,h) The effect of σc at dav = 130 nm and FF = 0.3 on QF and λr of the cavity mode.
To design the random InP NW arrays, we took into account the limitations of the fabrication and epitaxial growth processes. The randomness of the NW position distribution was chosen in such a way that they do not significantly overlap. In our simulation, we first assumed the NWs are arranged in a square photonic lattice, and randomly deviated the NW locations from their periodic positions. The value of this deviation from the NW center, σc was varied between 0 and 50 nm. The smaller the σc value, the possibility of NWs overlapping (merging) decreases. To completely prevent any overlapping σc should be smaller than half of the pitch size of the non-disordered square photonic lattice. The NWs were assumed to have a 15% variation in diameter. As for the excitation source, an electrical dipole source whose electric field is along the NW axis (z-direction) was used. The system was assumed to be passive, i.e. a system without gain, and the NWs were InP with a refractive index of n = 3.456. It can be seen from Fig. 1(b) at the higher wavelength range, arrays with FF = 0.2–0.3 and dav = 118–130 nm have the highest probability of finding high QF cavities. However, for the lower wavelength range, as shown in Fig. 1(c), arrays with FF = 0.2–0.3 and dav = 105–120 nm have the highest probability of finding high QF cavities. The results show that to tune the emission of the random nanowire lasers to a lower wavelength, generally a smaller dav is required.
Using the same 2D simulation setup used for Fig. 1(b) and Fig. 1(c), the effects of increasing dav on QF and λr of the cavities are shown in Fig. 2(a) and Fig. 2(b), respectively. By increasing dav of the NW, a redshift to the resonance wavelength is observed. Besides, in systems with a smaller NW diameter, the number of modes with QF > 3000 is higher, and as the diameter increases the number of modes decreases. As dav of the NW decreases, at a constant FF, the number of scatterers increases leading to higher scattering events. Therefore the number of cavities with high QF also increases. The effects of increasing FF on QF and λr of the cavities are depicted in Fig. 2(c) and Fig. 2(d). It can be seen that increasing FF of the arrays would result in a blue-shift of the resonance wavelength. Besides, in arrays with lower FF, the number of modes is low, and as FF increases the number of the modes and especially the possibility of getting low QF modes decreases. Similar to the effect of decreasing dav, increasing FF, increases the number of scatterers, leading to higher scattering events, and therefore higher number of cavities with high QF.
Comparing Fig. 2(a) and Fig. 2(b) with Fig. 2(c) and Fig. 2(d), it can be seen that the effect of changing dav is more pronounced than changing FF in shifting λr. For example, increasing dav by 25% (from 120 to 150 nm) results in a redshift of 229 nm to the average λr. However, to obtain a redshift of 185 nm, FF needs to change by 100% (from 0.4 to 0.2). This effect is further exemplified in two different arrays (array A: dav = 120 nm, FF = 0.25 and array B: dav = 90 nm, FF = 0.15). As shown in Fig. 2(e) and Fig. 2(f), even though the FF of array B is slightly lower than that of array A, the effect of decreasing nanowire diameter on λr is significantly higher, with a blue-shift of the cavity resonance by about 60 nm.
Using the same 2D simulation setup, the effect of deviation from the NW center, σc which also quantifies the degree of randomness is analyzed for an array with dav = 130 and FF = 0.3. Ten different cases for 4 different random arrays (σc = 10, 50, 70 nm, and completely random system) were analyzed. Note that in the completely random case, the centers of the nanowire positions were generated by a random number generator without constraining it to a certain σc value. The results in Fig. 2(g) and Fig. 2(h) show that in the 3 ‘restricted’ random cases the QFs of the cavities are more than four times higher than that of the array where the NWs are completely random, indicating that even for random laser, some degree of engineering of the randomness could noticeably improve the device performance. For example, it has been shown that increasing the QF of lasing modes could make non-resonant lasing systems into resonant ones [16]. That is to say, engineering the randomness could increase the QFs of the modes and reduce the coupling and overlapping between modes which then lead to random lasers with highly localized modes [27] with resonant feedback [16]. Indeed, in the completely random array, there is a very small probability of finding cavities with high QFs. Furthermore, the results show that the amount of disorder can also significantly affect the resonance wavelengths of the modes in addition to QF of the arrays. As the amount of disorder is increased the possibility of obtaining modes with lower λr increases together with the bandwidth of the resonance. This is because as σc is increased the possibility of making NWs locally dense is increased so the possibility of getting resonances with lower wavelength resonances is increased. In other words, increasing the randomness degree would make the regional filling factor more non-uniform so according to Fig. 2(c) and Fig. 2(d) the bandwidth increases. Considering InP NWs having gain in the wavelength region of 800 to 850 nm at low temperature, the array with σc = 50 nm has the best overlap with the gain profile of the NWs.
In our system, the disorder is only in the xy-plane and just for comparative purposes (and to reduce simulation time), 2D simulation setup was used in Fig. 1(a), Fig. 1(b), and Fig. 2. The values of the QF obtained in these calculations are much higher than the QFs supported in the real device (i.e. in the 3D case). That is to say, in the 2D setup the modes are completely confined in the z-direction; however, in the real devices, which is a 3D structure, the mode can leak into the underlying substrate leading to modes with much lower Q factors. To better quantify the effects of array size on mode leakage, the number of the modes and their QFs, using Lumerical FDTD solution, 3D structures with dav = 125, FF = 0.3, σc,max = 50, LNW=3 µm, but different lateral sizes were analyzed (Fig. 3). For each array size, 10 different cases were analyzed. The selected resonance modes have two criteria: (I) QF > 100 and (II) 750 nm < λr < 900 nm. A single dipole source was placed at the center of the random array, so only the modes located in the middle of the systems were excited. Similar to our reported work, the top 1.1 µm of the NWs was assumed to have a higher refractive index in comparison to the rest of the NWs because of carrier generation and increased temperature [27]. It can be seen from Fig. 3 when the size of the array (Lx, Ly) is less than 1 µm, the system cannot support a mode due to the size of the mode being larger than the array size that results in mode leakage. In other words, the lateral size of the array should be much bigger than lt to be in the localization regime and not the diffusive regime [32]. It can also be seen that at lateral sizes of around Lx, Ly = 2 µm the system has the highest confinement property. The lateral area of the mode in this system for modes with QF > 100 is between ∼0.05–3.75 µm2, therefore the lateral size of Lx, Ly = 2 µm (area size of 4 µm2) is big enough to support a maximum number of the modes. At a larger array size, the number of supported modes begins to decrease. This trend can be understood from the fact that the surrounding region (air) of the array acts as an optical ‘cladding’ layer for the modes. At 2 µm array size, the size of the modes is of the order of the array size and hence the surrounding region provides a good optical contrast to confine the modes. However, with increasing array size, the modes are now further away from the surrounding region, and because of the presence of other NWs the effect of optical contrast is now diminished, leading to reduced lateral confinement strength. Figure 3(a) and Fig. 3(b) show the statistical distribution of λr and QF of the modes in an array of size Lx, Ly = 1 µm, where there are only a few modes that are supported. Due to the small size, out of the 10 cases studied, only five of them can support any modes with QF >100. Furthermore, each system only supports a single-mode, implying that single-mode lasing is possible from small systems.
Fig. 3. Effect of array lateral size on the cavity mode using 3D simulation setups. (a-f) Statistical distributions showing the effect of Lx, Ly with FF = 0.3, dav = 130 nm, LNW=3 µm and σc.max = 50 nm on QF (top row) and λr (bottom row). (g) Effect of Lx, Ly on the number of modes with QF > 100 and Qmax.
For optimizing the length of the NWs, LNW a similar 3D simulation as the previous setup for the analysis of the effect of array size was conducted. Figures 4(a) and (b) present the statistical distribution of λr and QF of the modes in two arrays with LNW = 1.5 and 3 µm, respectively, for a fixed Lx, Ly = 4 µm and FF = 0.3. For both systems, the same random distribution of NWs was used. It can be seen for the system with the shorter NWs the number of supported modes is very low and the QF of the modes is about one-fourth of the array with longer NWs. In Fig. 4(c-f) the electrical field intensity profiles of a mode at λr ∼799 nm in the two systems are shown. The mode profiles along the length of the NWs (Fig. 4(d) and Fig. 4(f)) and in the x-y plane are very similar for both arrays; however, the shorter NW sample shows a slightly higher leakage into the substrate, resulting in lower QFs and number of resonant modes as shown in Fig. 4(a).
Fig. 4. Effect of NW length on the cavity modes and optical profile. Top row is for an array with NWs of length LNW = 1.5 µm whilst the bottom row is for LNW=3 µm. (a,b) Statistical distributions for QF and λr (inset) of the two arrays with shorter and longer NWs. (c-f) Electrical field intensity profile of a mode at λr ∼799 nm on y-z (c,d) and x-y (e,f) planes of the two arrays with shorter and longer NWs. (g,h) Emission spectra of the two arrays with shorter and longer NWs. The inset SEM images show the tilted view of the two NW arrays grown by MOCVD (scale bars: 1 µm). The upper left inset in Fig. 4(h) shows the log-log plot of light output from the random NW laser vs excitation power. The grey area is the region of amplified spontaneous emission.
Figure 4(g) and Fig. 4(h) show the experimental emission spectra at different excitation powers from the random arrays with the shorter (LNW ∼1.5 µm) and longer (LNW ∼3 µm) NWs, respectively. The insets show the SEM images of the InP nanowires of the two arrays which were grown using selective area epitaxy growth by metal-organic chemical vapor deposition [33] similar to our previous work [27]. Using electron-beam lithography and etching processes randomly positioned holes were transferred to the SiOx mask which was pre-deposited on the (111)A InP substrate. Then the prepared sample was transferred to the MOCVD reactor for the epitaxial growth of the NWs. Optical characterization was carried out at low temperature (T = 6 K) using a frequency-doubled solid-state laser (femtoTRAIN IC-Yb2,000, λsource = 522 nm, repetition rate 20.8 MHz, pulse length 300 fs, Gaussian profile (FWHM = 5 µm)) similar to the setup used for our previous work [27]. The sample was excited through an aberration-corrected 60 × /0.70 numerical aperture, a long working distance objective lens (Nikon CFI Plan Fluor), and the emission light was collected through the same lens. Spectral measurements were carried out using a grating spectrometer (Acton, SpectraPro 2750). As shown in Fig. 4(g) and Fig. 4(h), the emission spectra of the two systems have two peaks at the same wavelengths. The first peak at ∼830 (FWHM ∼22 nm) is due to emission from the NWs (wurtzite crystal phase) and the second peak at ∼875 nm (FWHM ∼13 nm) is from the substrate (zincblende phase). It can be seen in the shorter NWs the intensity of the light emitted from the substrate is much stronger than the one emitted from the nanowire. In the system with longer NWs, at the pump fluence of ∼550 µJ cm−2 per pulse, we observe a small peak appearing at 843 nm, which is further amplified with increasing excitation power. Beyond lasing threshold of around 733 µJ cm−2, a sharp lasing peak (FWHM = 2 nm) is observed at 843 nm. The light input-light output (L-L) characteristic of the laser on the log-log scale (upper left inset of Fig. 4(h)) has been obtained by integration of the emission intensities in the wavelength range of the lasing wavelength (λlasing = 843 nm) at different pumping intensities. It can be seen that the L-L characteristic of the system shows the typical “S”-curve shape depicting all three PL regimes: spontaneous emission dominating at low excitation intensities until the onset of amplified spontaneous emission (ASE) at ∼550 µJ cm−2 (grey color region) and finally, the emergence of lasing at ∼733 µJ cm−2 [34–36]. In the short system, since the mode leakage to the substrate is high, the Q factor of the mode is low leading to higher out-coupling loss.
Figure 5 shows the experimental studies on the effect of the average NW diameter on the modes for two different arrays corresponding to array A and array B mentioned above. As shown by our simulation results in Fig. 1 and Fig. 2, decreasing dav results in a blue-shift of the resonance wavelength. This is consistent with reports that have shown decreasing the NW diameter would reduce the scattering cross-section [37] leading to the blue-shift of the resonance wavelength. In Fig. 5(a) the SEM images of these two arrays and their diameter distribution (inset) are shown. The fabricated lateral size of the array is around 30 µm (Lx=Ly≈30 µm). The emission spectra from an arbitrary area of these two arrays are plotted in Fig. 5(b). In both cases, lasing occurs in the range of around 725–850 nm, corresponding to the gain profile of InP NWs. The statistical distributions of the lasing wavelengths and threshold at which the ASE region starts in these two arrays are plotted in Fig. 5(c) and Fig. 5(d), respectively. For statistical analysis, for each case, several arrays with the same FF, dav, Lx (=Ly≈30 µm), LNW, σc,max, but different NW positions (distributions) were fabricated. Then several random positions in each array were pumped (FWHM of the pumping laser is around 5 µm) to get a set of spectra. Then the lasing wavelengths and thresholds of the lasing modes in these spectra were analyzed to find sets of values for those lasing parameters for each case whose distributions are presented in Fig. 5(c) and Fig. 5(d). It can be seen, unlike Fabry-Perot mode lasing [38,39] and non-resonant random lasers [16] where the lasing wavelength is around the maximum of the gain with a narrow bandwidth of around Δλ < 50 nm, in each of these two resonant random lasers the lasing bandwidth is broader (Δλ = 100 nm) and most of the lasing wavelengths are at wavelengths lower than the wavelength where the gain is maximum. In array A, the minimum, maximum, and average lasing wavelengths are 742, 735, and 787 nm, respectively, and for array B where the average diameter is smaller, the corresponding lasing wavelengths are 725, 811, and 775 nm, respectively. So, decreasing the average diameter of the NW results in an overall blue-shift of the resonance wavelength, confirming the results shown in Fig. 2(e) and Fig. 2(f).
Fig. 5. Experimental results showing the effect of average NW diameter on the emission and threshold of two different arrays, corresponding to array A (top row) and array B (bottom row). (a) Top-view SEM images (scale bars are 500 nm). The insets show the diameter distributions of the two arrays. (b) Emission spectra with increasing pump fluence around the threshold. (c,d) Statistical distributions of the emission wavelength (c) and lasing threshold (d).
As shown in Fig. 5(d), the lasing threshold in array B has generally increased, which could be due to two reasons. First, there is a lower probability of finding high QF modes in array B in comparison to array A (see Fig. 2(e)) (higher loss due to out-coupling loss to the surrounding media). Secondly, the emission intensity of the wurtzite NWs in array A is higher than from the zincblende substrate (Fig. 5(b)); however, in array B the emission of the substrate is higher than the emission of the NW array. As discussed in relation to Fig. 1(a), this is because in array B the FF is lower so the carrier generation inside the gain medium is lower leading to lower gain. Additionally, the smaller diameter can lead to a higher surface recombination rate which results in lower carrier lifetime and higher optical loss. Higher emission in array A means a higher number of photons could be created with lower excitation power, so the lasing threshold would decrease.
3. Conclusion
In this study, we have shown the controllability of the lasing properties in random NW lasers in the localization regime. By changing the design parameters of this random laser, it is possible to change the lasing threshold, the number of lasing modes, the Q factor, and the wavelength resonances of the modes. For example, changing the lateral size of the array would lead to a change from multi-mode to single-mode lasing. It was also shown by changing the density and diameter of the NWs, and the degree of randomness could change the resonance wavelength of the modes. This could expand the application of random lasers in photonic devices where controlling and managing the lasing properties are required.
Funding
Australian Research Council (Discovery Project (DP170102530)).
Acknowledgments
We acknowledge the Australian Research Council for the financial support. Access to the epitaxial growth and fabrication facilities is made possible through the Australian National Fabrication Facility, ACT Node.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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