Abstract

Disorder is generally considered an undesired element in lasing action. However, in random lasers whose feedback mechanism is based on random scattering events, disorder plays a very important and critical role. Even though some unique properties in random lasers such as large-angle emission, lasing from different surfaces, large-area manufacturability, and wavelength tunability can be advantageous in certain applications, the applicability of random lasers has been limited due to the chaotic fluctuations and instability of the lasing modes because of weak confinement. To solve this, mode localization could reduce the spatial overlap between lasing modes, thus preventing mode competition and improving stability, leading to laser sources with high quality factors and very low thresholds. Here, by using a random array of III-V nanowires, high-quality-factor localized modes are demonstrated. We present the experimental evidence of strong light localization in multi-mode random nanowire lasers which are temporally stable at low temperatures.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Strong light scattering by random scatterers could increase the dwell time of light and the formation of closed optical loops. Lasing can occur in such systems if the modal gain exceeds the optical losses. In these types of lasers, which are called random lasers, the feedback mechanism is based on multiple scattering events induced by the random scatterers rather than defined optical cavities. Unlike regular lasers, in random lasers mirrorless cavities may lead to low-cost designs and the feasibility to form these lasers on a variety of surfaces, including paper [1], polyethylene terephthalate [2], etc. Random lasers have been used for a variety of applications that include dye-circulated structured microfluidic channels [3], optofluidic bio-lasers [4], optical batteries [5], cancer diagnostic [6], speckle-free full-field imaging [7], lab-on-a-chip random spectrometers [8], time-resolved microscopies [9], sensors [10], random distributed feedback fiber lasers [11], laser paints [12], and military purposes [13].

Random lasers can operate in either the strong localization or diffusive regime [Fig. 1(a)]. In the former, different resonant modes supported in the system could be spatially non-interactive leading to stable and multi-mode lasing. Several sharp peaks in the lasing spectrum corresponding to the different resonant modes are expected in random lasers operating in this regime. On the other hand, most random lasers operate in the delocalized regime [14] (also known as the diffusive regime), where mostly narrowing of the gain spectrum and hence single-mode operation is observed due to temporal and spatial averaging effect [15]. In other cases, where sharp peaks have been observed from diffusive samples [16], the resonance wavelength was generally bigger than the transport mean free path [1719]. These narrow peaks are due to reasons such as the interaction of the lasing modes through the spatial hole-burning [20] or the strong amplification of certain optical paths [17], and the observed narrowing of the peaks in these systems has nothing to do with the strong localization regime [15]. In the Anderson localization regime, light can be well confined inside the open disordered media, leading to behavior similar to conventional multi-mode lasers. In this regime, the modes are strongly confined and are spatially decoupled from other modes in multi-mode lasers, leading to stable mode operation. This localization can result in resonant cavities with high quality ($Q$) factors and lasers with low thresholds. These properties make the Anderson localization regime an interesting research topic. However, except in quasi-1D geometries [21], the vast majority of experiments on random lasers do not appear to be in the localized regime even though they exhibit discrete laser peaks above the threshold [22]. To achieve strong localization in a random scattering medium the transport mean free path, ${{l}_t}$, should be smaller than the wavelength of light, $\lambda$ (Ioffe–Regel criterion, ${{kl}_t} \approx {1}$, ${k} = {2}\pi {\rm /}\lambda$ is the wavenumber) [23]. Increasing the refractive index contrast of the scatterers relative to the refractive index of the background material could increase the scattering efficiency of the scatterers, leading to a lower ${{l}_t}$. It has been shown that high refractive index contrast is essential for strong light scattering, strong light localization, and high $Q$ factor cavities in disordered media [22].

 figure: Fig. 1.

Fig. 1. Design of the random nanowire lasers. (a) Illustration of the vertical random nanowire array used in this study. The nanowires are illuminated from the top by a pulsed laser with an intensity of ${{I}_0}(\lambda)$. The insets show pictorially the diffusive and localization regimes in random media. In the diffusive regime, normally a broad emission is observed at lasing, while in the localization regime, narrow spectral peaks over a broad background are observed at lasing. (b) The effects of filling factor and average nanowire diameter on ${{kl}_t}$. The red line indicates where the Ioffe–Regel criterion is satisfied. (c) The resonance spectrum calculated for a system with FF = 0.3, ${{d}_{\textit{av}}} = {125}\;{\rm nm}$, and L = 3 µm. The 2D spatial profiles for the three high $Q$ factor modes (Mode I: ${\lambda _r} = {829}\;{\rm nm}$, Mode II: ${\lambda _r} = {791}\;{\rm nm}$, and Mode III: ${\lambda _r} = {848}\;{\rm nm}$) are shown at a depth of 0.5 µm (i.e., at ${ z} = {2.5}\;\unicode{x00B5}{\rm m}$) from the tip of the nanowires, clearly showing strong localization in the $x - y$ plane. The inset in (c) also shows the 3D view of the simulated mode profile, where confinement can also be observed in the vertical direction and confined predominantly in the nanowires. The NW length is 3 µm, and the top of the NW corresponds to ${z} = {3}\;\unicode{x00B5}{\rm m}$. Only the top 2 µm of the NW array is shown in this inset.

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To obtain lasing in a disordered media, gain must be present and can be incorporated by using scatterers with gain [24] or adding a separate medium as gain [25]. Many compound semiconductors, due to their direct bandgaps, are excellent candidates as a lasing gain medium. Furthermore, they have a high refractive index in comparison to air, and in the nanostructure form they can be used as both highly efficient scatterers and gain materials in random lasers. Different semiconductor nanostructures with bandgaps in the UV and visible regions such as ZnO [26], AlGaN [27], and ${\rm SnO}_{2}$ [28] nanowires (NWs), GaN nanocolumns [29], and ZnS nanospheres [30] have been used in random lasers.

Here, we use wurtzite phase InP NWs with a bandgap in the near-infrared region (${{E}_g} = {1.42}\;{\rm eV}$ at room temperature) as both the scatterers and the gain medium. The very high refractive index contrast between InP and free space ($\Delta {n}\simeq{2.46}$) results in a high scattering efficiency for the NWs. Using numerical methods, the random array made up of vertically aligned InP NWs are designed to provide localized cavities that support high $Q$ factors (${\sim}{1200}$). The modes are localized in three dimensions, where the lateral localization (perpendicular to the NW’s axial direction) is due to the random scattering, and the vertical localization (along the NW’s axial direction) is provided by the refractive index contrast created by carrier generation at the tip of the NW due to external optical pumping. It is shown that this localization can increase the overlap between the modes of the cavity and the gain region leading to high modal gain and confinement factors, $\Gamma$ (higher than 0.6). Experimentally, we show that the system operates in a multi-mode and the near-field images show that the modes are spatially localized and have localization lengths, $\xi$, of 200–500 nm. Results from different excitation intensities and after illumination by a large number of pulses show that these lasing modes are stable.

2. METHODS

A. Numerical Calculations

For calculating ${{kl}_t}$ and mode profiles in Fig. 1, the commercial finite-difference time-domain (FDTD) software package (Lumerical FDTD solutions, https://www.lumerical.com) was used. We identified resonant modes in the nanowire arrays by introducing electrical dipole sources, positioned in the array, and perfectly matched layer absorbing boundary conditions were used to examine the decay of the electromagnetic fields.

B. Substrate Preparation

Before growth, a standard preparation process [31,32] for patterned substrates was used. Using plasma-enhanced chemical vapor deposition, $\sim {30}\;{\rm nm}$ thick ${{\rm SiO}_x}$ was deposited on semi-insulating (111)A InP substrates as a mask, followed by electron beam lithography to create the randomly positioned holes on the resist. The pattern was then transferred to the ${\rm SiO}_{x}$ mask through dry etching using ${{\rm CHF}_3}$. The patterned substrate was trim-etched in 10% ${{\rm H}_3}{{\rm PO}_4}$ to remove any native oxide layer [32] and then immediately loaded into the metal-organic chemical vapor deposition (MOCVD) system for nanowire growth.

C. MOCVD Growth

In this work, a close-coupled showerhead reactor (Aixtron CCS ${3} \times {2}$) was used for the epitaxial growth. The reactor was operated at a low pressure of 100 mbar and ultra-high purity ${{\rm H}_2}$ was used as the carrier gas with a total flow of ${10}\;{\rm L}\;{{\rm min}^{- 1}}$. Trimethylindium (TMIn) and phosphine (${{\rm PH}_3}$) were used as precursors for In and ${ P}$, respectively. All substrates were first annealed in a ${{\rm PH}_3}$ ambient at a surface temperature of 660°C in the reactor. After a 10 min annealing step, the reactor was ramped up to a (wafer) surface temperature of 680°C. Epitaxial growth was carried out by introducing TMIn into the chamber for 8 min. To reduce the possibility of NWs merging (i.e., to minimize radial growth), the molar flow of ${{\rm PH}_3}$ and TMIn was ${1.25} \times {{10}^{- 3}}$ and ${2.1} \times {{10}^{- 6}}\;{\rm mol}\;{{\rm min}^{- 1}}$, respectively, leading to a high V/III ratio of $\sim {595}$.

D. Optical Characterization

A frequency-doubled solid-state laser (femtoTRAIN IC-Yb-2,000, ${\lambda _{{\rm source}}} = {522}\;{\rm nm}$, repetition rate 20.8 MHz, pulse length 300 fs) with a Gaussian profile beam shape [full width at half-maximum $({\rm FWHM})\sim{5}\;\unicode{x00B5}{\rm m}$] was used to pump the random NWs. The NWs were excited through an aberration-corrected ${60} \times {/0.70}$ numerical aperture, long working distance objective lens (Nikon CFI Plan Fluor), and the resulting emission was collected through the same lens. The collected light was passed through a bandpass filter to remove the pump laser wavelength. Spectral measurements were made using a grating spectrometer (Acton, SpectraPro 2,750) and a CCD (Princeton Instruments, PIXIS). Low-temperature (${T} = {6}\;{\rm K}$) experiments were conducted in a He-cooled cryostat (Janis research). The schematic diagram of the optical setup used for the characterization is illustrated in Supplement 1 Fig. 10.

3. RESULTS AND DISCUSSION

Figure 1(a) illustrates our vertically aligned InP NW array and the insets show the schematic of the two different regimes. To simulate the random NW arrays, distributions of diameters, pitch, and fill factor are defined. Under certain conditions, the scattering efficiency and mean path can achieve the Ioffe–Regel criterion for strong localization. For example, as shown by the red line in Fig. 1(b), for NWs with a diameter, ${d} = {140}\;{\rm nm}$, and filling factor, ${\rm FF} \approx {0.25}$, at 850 nm strong light localization can be achieved (for further details see Supplement 1 Section 1.1).

In the Ioffe–Regel regime, cavities with a high $Q$ factor and small mode volumes are expected [27,33], which are essential for low threshold [34] or thresholdless lasing [35]. In our system, as shown in Supplement 1 Fig. 6, the amount of disorder or randomness can have noticeable effects on the $Q$ factor of the system. In addition, it has also been shown that the size of scatterers and the filling factor of the system [27,29,36] can also influence the $Q$ factor in random lasers. Simulation results show to support high $Q$ factor cavities with resonance wavelength, ${\lambda _r}$, in the range of 800–850 nm, our InP NW array needs to have FF = 0.3, ${{d}_{\textit{av}}} = {120 {-} 130}\;{\rm nm}$, and a maximum deviation center of 50 nm (${\sigma _{c,\max}} = {50}\;{\rm nm}$) (for further details, see Supplement 1 Section 1.2).

To understand better how the designed system localizes uncoupled high $Q$ factor modes in three dimensions, we use Lumerical FDTD Solutions to solve Maxwell’s curl equations. The resonance spectrum of the random structure with geometrical parameters of FF = 0.3, ${{d}_{\textit{av}}} = {125}\;{\rm nm}$, ${L} = {3}\;\unicode{x00B5}{\rm m}$, and ${{L}_x} = {{L}_y} = {5}\;\unicode{x00B5}{\rm m}$ is shown in Fig. 1(c) (${L}$ is the length of the NWs, ${{L}_x}$ and ${{L}_y}$ are the lateral sizes of the random system in the $x$ and $y$ directions). The lateral profiles of three modes (Mode I: $Q = {1182}$, ${\lambda _r} = {829}\;{\rm nm}$; Mode II: $Q = {949}$, ${\lambda _r} = {791}$; and Mode III: $Q = {1001}$, ${\lambda _r} = {848}\;{\rm nm}$) with the highest $Q$ factors are presented in the inset of Fig. 1(c). Additionally, the vertical profile of Mode I is also shown in the inset. This inset shows that most of the mode is localized at the top 1.5 µm of the NW array leading to negligible leakage of the mode to the InP substrate (note that the tip of the NW corresponds to ${z} = {3}\;\unicode{x00B5}{\rm m}$). These mode profiles confirm the 3D localization of light within the random NW array. The lateral confinement (in the $x - y$ plane) of the mode is due to 2D Anderson localization, while the 1D vertical confinement is a result of the change in refractive index along the length of the NWs as the carriers are generated at the top of the NWs. The NWs are excited by a pulsed laser from the top, with photo-generated carriers mostly within the top 300 nm of the NWs, and considering the effect of carrier diffusion, they will be mostly confined in the top 1.1 µm of the NWs [37] (see Supplement 1 Fig. 8). Furthermore, as a result of the increase in temperature [38] because of thermal relaxation of carriers and high density of photo-excited carriers [39], a change in the refractive index in this segment of the NWs is expected. As a result of this refractive index contrast along the NW array, as shown in the inset of Fig. 1, the mode profile is localized in the vertical direction within this 1.1 µm segment. As discussed in Supplement 1 Section 2.2, considering the average carrier density of ${\sim}{2.1} \times {{10}^{18}}\;{{\rm cm}^{- 1}}$ at a pump intensity of ${{P}_{{\rm in}}} = \sim{1200}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ and a temperature difference of ${\sim}{200}\;{\rm K}$, this region would experience a refractive index difference of ${\sim}{0.087}$ compared to the rest of the NWs, resulting in mode confinement in the $z$ direction. Thus, by using a random InP NW array, optical confinement in three dimensions can be achieved through a combination of lateral confinement due to randomness (2D Anderson localization) and vertical confinement due to refractive index contrast along the length of the NWs.

The lateral size of Mode I is ${0.634}\;\unicode{x00B5}{\rm m}^2$ (${\sim}{11}{(\lambda {/n})^2}$), which is much smaller than the area of the active scattering region (${5} \times {5}\;\unicode{x00B5}{\rm m}^2$ in the simulation), which is a necessary condition for operation in the strong localization regime [23]. The confinement in the $z$ direction as a result of increased refractive index results in a decrease of mode leakage into the substrate, leading to an increase of the $Q$ factor by more than a factor of 3 times for the resonant modes. Furthermore, it can also be observed from the mode profile of Mode I in Fig. 1(c) that the mode encompasses several nanowires and most of the field is confined inside those nanowires, leading to a mode confinement factor, $\Gamma$, of ${\sim}{0.58}$ (for further details, see Supplement 1 Section 2). Due to the strong mode confinement factor and the high gain provided by InP, it is expected that lasing will occur in this NW system.

 figure: Fig. 2.

Fig. 2. Single-mode lasing behavior from the random nanowire array. (a) SEM image showing a tilted view of our nanowire array (scale bar 1 µm). The inset shows a top view confirming the random nature of the nanowires in the $x - y$ plane (scale bar 500 nm). (b) Emission spectra at 6 K from the nanowire array at various pump fluences. The normalized spectral map (inset) shows a broadening of the spectrum with increasing fluence up to the transition to the amplified spontaneous emission (${550}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse) but then a sudden reduction in the linewidth above ${{P}_{{\rm in}}} = {550}\;\unicode{x00B5}{\rm J}\;{{\rm cm}^{- 2}}$ per pulse. (c) Light output versus excitation fluence plotted on a log–log scale, showing an “S-like” while the same data plotted on a linear scale (inset) shows a “kink-like” threshold behavior—indications of lasing from the nanowire array. The shaded gray area is the region of amplified spontaneous emission. The data points are the experimental results, and the red lines are just a guide to the eye.

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Comparing the profiles of Modes I and II, although these modes are spectrally decoupled, there is a spatial overlap between these modes. On the other hand, Modes I and III are both spectrally and spatially decoupled, which is one of the advantages of random lasers operating in the localized regime to support stable and multi-mode operations.

We grew the random distribution of InP NW arrays using selective area [31] metal-organic vapor phase epitaxy (see Section 2). To create the designed pattern, i.e., FF = 0.3 and ${{ d}_{\textit{av}}}\simeq{125}\;{\rm nm}$, taking into account additional lateral growth, a random array of hole openings with a diameter of $\sim{90}\;{\rm nm}$ was patterned onto a 30 nm ${{\rm SiO}_x}$ layer deposited on the InP substrate as a growth mask. Figure 2(a) shows a scanning electron micrograph of the InP NW array. As shown in Supplement 1 Fig. 9, the average diameter of the NWs is around 116 nm with a standard deviation of ${\sim}{13}\;{\rm nm}$ (${\sim}{12}\%$ diameter variation according to the average diameter). The FF of the fabricated system is ${\sim}{0.25}$, which is quite close to the designed value.

Figure 2(b) shows the spectra from a random NW laser array at low temperature (6 K) at several pump fluences. The array was pumped from the top of the NWs using a 522 nm pulsed laser (see Section 2), which had a Gaussian beam shape profile with a FWHM of ${\sim}{5}\;\unicode{x00B5}{\rm m}$. The spectra are offset vertically for clarity. At low pump fluence, a broad emission is observed but as the fluence is increased, the emission intensity increases and is accompanied by broadening of the spectrum due to the band filling effect. At a pump fluence of ${\sim}{550}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse, we observe a shoulder appearing at 843 nm, which is further amplified with increasing fluence. The inset indicates first a broadening of the spectrum with increasing fluence, and a sudden narrowing after a threshold fluence is reached, an indication that the array is lasing. By fitting the spectrum at ${P} = {693}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse with three Lorentzian functions, the lasing peak and its FWHM are determined to be 841 nm and ${\sim}{2}\;{\rm nm}$, respectively, resulting in a $Q$ factor of 420 (for further details, see Supplement 1 Section 3.3). The power-dependent output intensity [Fig. 2(c)] follows the typical “S”-curve shape where three emission regimes could clearly be observed. Spontaneous emission dominates at low excitation intensities until the transition to the amplified spontaneous emission at ${\sim}{550}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse, followed by a super-linear increase indicative of amplified spontaneous emission (shaded gray region), and finally, the emergence of lasing above ${733}\;\unicode{x00B5}{\rm J}\;{{\rm cm}^{- 2}}$ per pulse [4042]. A small emission with a peak centered at ${\sim}{875}\;{\rm nm}$ can also be observed in the spectra, which correspond to emission from the underlying InP substrate (zincblende phase) [43].

Figure 3 shows the spectra of another random NW array at different excitation fluences, where multi-mode lasing is observed. At excitation fluence (${386}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse) below the threshold, two broad peaks are observed, corresponding to the substrate (zincblende phase at ${\sim}{875}\;{\rm nm}$) and NWs (wurtzite phase at ${\sim}{830}\;{\rm nm}$) peaks, as discussed above. With increasing fluence, the long wavelength peak increases in intensity but remains broad, confirming lasing is not from the underlying InP substrate. On the other hand, for the NW emission, sharp peaks can clearly be observed in addition to a broad background above a fluence of ${1720}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse. The number and intensity of these sharp peaks increase with excitation fluence. Figure 3(b) shows a log–log plot of three L−L curves corresponding to the wavelength region I (${769} \lt \lambda \lt {787}\;{\rm nm}$), region II (${787} \lt \lambda \lt {807}\;{\rm nm}$), and the total spectrum of the NW region (${725} \lt \lambda \lt {850}\;{\rm nm}$) for comparison. The onset of amplified spontaneous emission for the modes in regions I and II occurs at ${\sim}{1720}$ and ${\sim}{1937}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse, respectively. The power intensity at which this transition has happened for the spectral region of the NWs is almost similar to the value of the mode in region II. This is because emission from region II is much higher than that from region I and therefore higher excitation fluence is required for the latter region to achieve lasing. The near-field emission profiles as viewed from the top of the NWs at different pumping intensities are shown in Figs. 3(c), 3(e), and 3(g). At low pump fluence, a broad profile is observed but as the fluence is gradually increased, spatially localized peaks begin to appear above the broad Gaussian-like emission profile. Line scans across the profile in various directions confirm this observation [Figs. 3(d), 3(f), 3(h)]. At ${{P}_{{\rm in}}} = {2435}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse, three high-intensity spots appear, which can be correlated to the three predominant modes at $\lambda = {788}$, 799, and 826 nm in Fig. 3(a). Increasing the pump fluence further to ${{P}_{{\rm in}}} = {3072}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse leads to the lasing mode at 799 nm becoming more dominant [Figs. 3(g) and 3(h)]. Fitting the profiles of the three localized regions with exponential decay functions [44] gives average localization lengths, $\xi$, of 210, 492, and 508 nm for each of the three modes. The number of nanowires in which the mode is localized, ${{N}_{{\rm NW}}}$, can be calculated through ${{N}_{{\rm NW}}} = \pi {\xi ^2}$. ${\rm FF}/{{A}_{\textit{av}}}$, where ${{A}_{\textit{av}}}$ is the average cross-sectional area of the NW. This results in around 4, 20, and 22 NWs interacting with each of the three localized modes, respectively. Since $\xi$ is much smaller in size than the area of the active scattering region (which is approximately the pumped area whose FWHM is around 5 µm), this is confirmation that 2D Anderson localization effect in the $x - y$ plane is achieved in these random scatterers. In addition, as shown in Figs. 3(c)–3(h), the modes are spatially isolated, i.e., the distance between the modes is higher than the sum of the localization length of the modes along the lines connecting them (for further details, see Supplement 1 Section 4). These features are consistent with the theoretical prediction for multi-mode random lasing in the Anderson localization regime [45]. On the other hand, in diffusive random lasers, the lasing wavelength is primarily determined by the spectral peak of the gain medium [24] and only weak dispersion is incorporated into the scattering medium, resulting in a significantly broader lasing peak. Here in our case where localization occurs, lasing modes even at wavelengths in the lower part of the gain spectrum (758 and 778 nm) can also be observed, which is in agreement with the random lasing in the localization regime [15].

 figure: Fig. 3.

Fig. 3. Multi-mode lasing and near-field emission profiles from the random nanowire array. (a) Emission spectra from the nanowire array at various pump fluences. Emission from the substrate is indicated, while emission from the nanowires occurs below 850 nm. (b) Log–log plot of integrated light output versus fluence from two spectral regions indicated in (a): shaded red region I (${769} \lt \lambda \lt {787}\;{\rm nm}$) and green region II (${787} \lt \lambda \lt {807}\;{\rm nm}$). The results for total light output from the nanowire array (${725} \lt \lambda \lt {850}\;{\rm nm}$) are also shown for reference. (c), (e), (g)Near-field emission profiles from the nanowire array at three different excitation fluences: ${{P}_{{\rm in}}} = {386}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse, ${{ P}_{{\rm in}}} = {2}{,}{435}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse, and ${{P}_{{\rm in}}} = {3}{,}{072}\;\unicode{x00B5}{\rm J}\;{{\rm cm}^{- 2}}$ per pulse (scale bars 2 µm). (d), (f), (h) Corresponding line scan across the near-field intensity profiles in (c), (e), and (g) along three directions, AB, CD, and EF. The cross-section mode profiles clearly indicate strong localization above the lasing threshold as indicated in (f) and (h). The localization lengths for the mode profiles are indicated in the image (g). All measurements were done at 6 K.

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Unlike random lasers operating in the diffusive regime, where the single-shot emission spectrum is unstable and changes from shot to shot [46], in our random NW system the spectrum is stable under successive pulsed excitation. Figure 4 shows how the different modes evolved with increasing excitation fluence over a numerous number of pulses, for two different locations on the sample. $\Delta {{N}_{{\rm pulse}}}$ at a particular excitation fluence is defined as the difference between the number of pulses at that excitation fluence and the lowest excitation fluence. For example, $\Delta {{N}_{{\rm pulse}}} = {375} \times {{10}^6}$ at ${{ P}_{{\rm in}}} = {2258}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse in Fig. 4(a) means the NW array has been subjected to an additional ${375} \times {{10}^6}$ pulses recording the spectrum at ${{P}_{{\rm in}}} = {386}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse. It can be seen at both locations whose spectra are shown in Figs. 4(a) and 4(b), even though lots of pulses have excited the sample, the modes are stable and well defined even with increasing the excitation fluence with only a small blueshift due to changes in refractive index with carrier density and temperature [47,48].

 figure: Fig. 4.

Fig. 4. Lasing stability. Emission spectra at different excitation fluences from two different regions of the random nanowire array which support (a) three and (b) five lasing modes (${T} = {6}\;{\rm K}$). With increasing fluences, the nanowire array has been subjected to more excitation pulses. The difference in the total number of pulses used to collect each spectrum from those used for the lowest fluence is indicated by $\Delta {{N}_{{\rm pulse}}}$.

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 figure: Fig. 5.

Fig. 5. Statistical distribution of several key parameters of the random nanowire laser. (a) Measured pumping intensity distribution taken at the commencement of amplified spontaneous emission. (b) Experimentally measured $Q$ factor of the modes. (c) Calculated distribution of the mode confinement factor. (d) Calculated distribution of the spatial lateral mode size.

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In the field of random lasers, unlike lasers with conventional feedback mechanisms, there is a lack in the quantification of various lasing parameters. The statistical quantification of several key parameters shown in Fig. 5 provides an insight into the variability of the performance of our random nanowire system. In Fig. 5(a) the pump intensities at the onset of amplified spontaneous emission show an almost normal distribution with most of the modes having a pump intensity between ${1500 {-} 2000}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse. It is shown [Supplement 1 Figs. 7 and 8(c)] that this range of pump intensities is sufficient to achieve positive material gain for modes in the wavelength range of 790–850 nm. Figure 5(b) shows the distribution of the experimental quality factor of the resonant cavities. The distribution of simulated $Q$ factors for different modes and their correlation with the mode confinement factor and lateral size are presented in Supplement 1 Fig. 13. The highest values for the calculated and measured $Q$ factor are 1181 and 420, respectively. The median for the $Q$ factor and wavelength resonance are ${{Q}_{m,\exp}} = {165}$, ${\lambda _{m,\exp}} = {790}\;{\rm nm}$ and ${{Q}_{m,{\rm sim}}} = {380}$, ${\lambda _{m,{\rm sim}}} = {819}\;{\rm nm}$ for the experimental and simulated results, respectively. The measured $Q$ factors are generally less than the conventional cavities such as Fabry–Perot (FP) cavities ($Q$ factor is usually ${{10}^3} {-} {{10}^4}$) [49,50] and cavities supporting whispering gallery modes ($Q$ factor is usually ${{10}^4} {-} {{10}^5}$) [51,52]. Figure 5(c) shows the calculated mode confinement factor for our system is mostly more than 0.5 and some modes even have confinement factor values as high as 0.62. Although these values are lower than in conventional nanowire lasers operating in the FP mode [53,54], they are higher than those expected for those operating in the diffusive regime. In the diffusive regime, the lower $Q$ factor leads to more leakage of the field from the NWs and consequently lower confinement factors. The correlation between $Q$ factor and $\Gamma$ is quantified by Spearman’s rank correlation coefficients, ${{r}_s}$, and is around 0.61, which shows a good correlation between these two parameters, where modes with lower $Q$ factors usually show less localization [Supplement 1 Fig. 13(c)]. For example, in our simulation results, a mode with $Q = {568}$ has a $\Gamma = {0.62}$; however, another mode with $Q = {188}$ shows only a confinement factor of 0.48. Figure 5(d) shows the calculated size distribution of the lateral mode. The average, minimum, and maximum values for the lateral mode area are 1.67 (${\sim}{29}{({ n/}{\lambda _{\textit{av}}})^2}$), 0.24 (${\sim}{4.7}{({n/}\lambda)^2}$), and ${3.74}\;\unicode{x00B5}{\rm m}^2$ (${\sim}{62}{({n/}\lambda)^2}$), respectively. These calculated values are much smaller than the pumping area, confirming the possibility of supporting localized modes shown in Fig. 3. Considering the values of the minimum and maximum lateral mode areas, the smallest and the largest modes encompass 4 and 91 NWs, respectively. Furthermore, as shown in Supplement 1 Fig. 13(b), the poor correlation of ${r_s} = - {0.45}$ between the $Q$ factor and lateral mode size indicates that a high $Q$ factor does not necessarily lead to smaller modes. Indeed, high $Q$ factor modes could involve scattering between more NWs than a mode with a lower $Q$ factor.

4. CONCLUSION

We have designed and experimentally demonstrated that by using InP random NW arrays, Anderson localization in random lasers could be achieved due to their high gain and strong scattering properties. Light is confined in three dimensions, where the lateral confinement is provided by random scattering (2D Anderson localization) while the vertical confinement is provided by refractive index contrast. The near-field images of the mode profiles show exponential decay of the localized modes. The strong spatial confinement of the modes results in the stable multi-mode operation of random lasers. Mode control in random lasers opens up new opportunities for the facile fabrication of lasers over large areas (${10s {-} 100s}\;\unicode{x00B5}{\rm m}^2$) for application in the next-generation meta-optical systems.

Funding

Australian Research Council (Discovery Project-DP170102530).

Acknowledgment

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.

Supplemental document

See Supplement 1 for supporting content.

REFERENCES

1. I. Viola, N. Ghofraniha, A. Zacheo, V. Arima, C. Conti, and G. Gigli, “Random laser emission from a paper-based device,” J. Mater. Chem. C 1, 8128–8133 (2013). [CrossRef]  

2. Y.-J. Lee, C.-Y. Chou, Z.-P. Yang, T. B. H. Nguyen, Y.-C. Yao, T.-W. Yeh, M.-T. Tsai, and H.-C. Kuo, “Flexible random lasers with tunable lasing emissions,” Nanoscale 10, 10403–10411 (2018). [CrossRef]  

3. B. S. Bhaktha, N. Bachelard, X. Noblin, and P. Sebbah, “Optofluidic random laser,” Appl. Phys. Lett. 101, 151101 (2012). [CrossRef]  

4. X. Fan and S.-H. Yun, “The potential of optofluidic biolasers,” Nat. Methods 11, 141 (2014). [CrossRef]  

5. L. Xu, H. Zhao, C. Xu, S. Zhang, and J. Zhang, “Optical energy storage and reemission based weak localization of light and accompanying random lasing action in disordered Nd3+ doped (Pb, La)(Zr, Ti)O3 ceramics,” J. Appl. Phys. 116, 063104 (2014). [CrossRef]  

6. R. Polson and Z. Vardeny, “Cancerous tissue mapping from random lasing emission spectra,” J. Opt. 12, 024010 (2010). [CrossRef]  

7. B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012). [CrossRef]  

8. B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 746–751 (2013). [CrossRef]  

9. A. Mermillod-Blondin, H. Mentzel, and A. Rosenfeld, “Time-resolved microscopy with random lasers,” Opt. Lett. 38, 4112–4115 (2013). [CrossRef]  

10. Q. Song, S. Xiao, Z. Xu, J. Liu, X. Sun, V. Drachev, V. M. Shalaev, O. Akkus, and Y. L. Kim, “Random lasing in bone tissue,” Opt. Lett. 35, 1425–1427 (2010). [CrossRef]  

11. S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4, 231–235 (2010). [CrossRef]  

12. F. Luan, B. Gu, A. S. Gomes, K.-T. Yong, S. Wen, and P. N. Prasad, “Lasing in nanocomposite random media,” Nano Today 10(2), 168–192 (2015). [CrossRef]  

13. J. Dubois and S. La Rochelle, “Active cooperative tuned identification friend or foe (ACTIFF),” U.S. patent US5966227A (12 October 1999).

14. D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996). [CrossRef]  

15. R. Sapienza, “Determining random lasing action,” Nat. Rev. Phys. 1, 690–695 (2019). [CrossRef]  

16. K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Quantitative analysis of several random lasers,” Opt. Commun. 278, 110–113 (2007). [CrossRef]  

17. S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93, 053903 (2004). [CrossRef]  

18. H. Cao, J. Y. Xu, S. H. Chang, and S. T. Ho, “Transition from amplified spontaneous emission to laser action in strongly scattering media,” Phys. Rev. E 61, 1985–1989 (2000). [CrossRef]  

19. S. V. Frolov, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, “Laser-like emission in opal photonic crystals,” Opt. Commun. 162, 241–246 (1999). [CrossRef]  

20. H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008). [CrossRef]  

21. V. Milner and A. Z. Genack, “Photon localization laser: low-threshold lasing in a random amplifying layered medium via wave localization,” Phys. Rev. Lett. 94, 073901 (2005). [CrossRef]  

22. J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photonics 3, 88–127 (2011). [CrossRef]  

23. H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497 (2005). [CrossRef]  

24. H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278 (1999). [CrossRef]  

25. N. M. Lawandy, R. Balachandran, A. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994). [CrossRef]  

26. C. Liu, J. A. Zapien, Y. Yao, X. Meng, C. S. Lee, S. Fan, Y. Lifshitz, and S. T. Lee, “High-density, ordered ultraviolet light-emitting ZnO nanowire arrays,” Adv. Mater. 15, 838–841 (2003). [CrossRef]  

27. K. H. Li, X. Liu, Q. Wang, S. Zhao, and Z. Mi, “Ultralow-threshold electrically injected AlGaN nanowire ultraviolet lasers on Si operating at low temperature,” Nat. Nanotechnol. 10, 140–144 (2015). [CrossRef]  

28. H. Y. Yang, S. F. Yu, S. P. Lau, S. H. Tsang, G. Z. Xing, and T. Wu, “Ultraviolet coherent random lasing in randomly assembled SnO2 nanowires,” Appl. Phys. Lett. 94, 241121 (2009). [CrossRef]  

29. M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97, 151109 (2010). [CrossRef]  

30. J. Bingi, A. R. Warrier, and C. Vijayan, “Raman mode random lasing in ZnS-β-carotene random gain media,” Appl. Phys. Lett. 102, 221105 (2013). [CrossRef]  

31. N. Wang, X. Yuan, X. Zhang, Q. Gao, B. Zhao, L. Li, M. Lockrey, H. H. Tan, C. Jagadish, and P. Caroff, “Shape engineering of InP nanostructures by selective area epitaxy,” ACS Nano 13, 7261–7269 (2019). [CrossRef]  

32. Q. Gao, D. Saxena, F. Wang, L. Fu, S. Mokkapati, Y. Guo, L. Li, J. Wong-Leung, P. Caroff, H. H. Tan, and C. Jagadish, “Selective-area epitaxy of pure wurtzite InP nanowires: high quantum efficiency and room-temperature lasing,” Nano Lett. 14, 5206–5211 (2014). [CrossRef]  

33. J. Liu, P. D. Garcia, S. Ek, N. Gregersen, T. Suhr, M. Schubert, J. Mørk, S. Stobbe, and P. Lodahl, “Random nanolasing in the Anderson localized regime,” Nat. Nanotechnol. 9, 285–289 (2014). [CrossRef]  

34. L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits (Wiley, 2012).

35. I. Prieto, J. M. Llorens, L. E. Muñoz-Camúñez, A. G. Taboada, J. Canet-Ferrer, J. M. Ripalda, C. Robles, G. Muñoz-Matutano, J. P. Martínez-Pastor, and P. A. Postigo, “Near thresholdless laser operation at room temperature,” Optica 2, 66–69 (2015). [CrossRef]  

36. B. Fazio, P. Artoni, M. A. Iatì, C. D’andrea, M. J. L. Faro, S. Del Sorbo, S. Pirotta, P. G. Gucciardi, P. Musumeci, and C. S. Vasi, “Strongly enhanced light trapping in a two-dimensional silicon nanowire random fractal array,” Light Sci. Appl. 5, e16062 (2016). [CrossRef]  

37. H. J. Joyce, C. J. Docherty, Q. Gao, H. H. Tan, C. Jagadish, J. Lloyd-Hughes, L. M. Herz, and M. B. Johnston, “Electronic properties of GaAs, InAs and InP nanowires studied by terahertz spectroscopy,” Nanotechnology 24, 214006 (2013). [CrossRef]  

38. K. A. Meradi, F. Tayeboun, S. Ghezali, R. Naoum, and H. T. Hattori, “Design of a thermal tunable photonic-crystal coupler,” J. Russ. Laser Res. 32, 572–578 (2011). [CrossRef]  

39. B. R. Bennett, R. A. Soref, and J. A. D. Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quantum Electron. 26, 113–122 (1990). [CrossRef]  

40. M. A. Zimmler, J. Bao, F. Capasso, S. Müller, and C. Ronning, “Laser action in nanowires: observation of the transition from amplified spontaneous emission to laser oscillation,” Appl. Phys. Lett. 93, 051101 (2008). [CrossRef]  

41. S. W. Eaton, M. Lai, N. A. Gibson, A. B. Wong, L. Dou, J. Ma, L.-W. Wang, S. R. Leone, and P. Yang, “Lasing in robust cesium lead halide perovskite nanowires,” Proc. Natl. Acad. Sci. USA 113, 1993–1998 (2016). [CrossRef]  

42. D. Saxena, S. Mokkapati, P. Parkinson, N. Jiang, Q. Gao, H. H. Tan, and C. Jagadish, “Optically pumped room-temperature GaAs nanowire lasers,” Nat. Photonics 7, 963–968 (2013). [CrossRef]  

43. A. Mishra, L. V. Titova, T. B. Hoang, H. E. Jackson, L. M. Smith, J. M. Yarrison-Rice, Y. Kim, H. J. Joyce, Q. Gao, H. H. Tan, and C. Jagadish, “Polarization and temperature dependence of photoluminescence from zincblende and wurtzite InP nanowires,” Appl. Phys. Lett. 91, 263104 (2007). [CrossRef]  

44. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007). [CrossRef]  

45. P. Stano and P. Jacquod, “Suppression of interactions in multimode random lasers in the Anderson localized regime,” Nat. Photonics 7, 66–71 (2013). [CrossRef]  

46. S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76, 033807 (2007). [CrossRef]  

47. C. Tessarek, R. Goldhahn, G. Sarau, M. Heilmann, and S. Christiansen, “Carrier-induced refractive index change observed by a whispering gallery mode shift in GaN microrods,” New J. Phys. 17, 083047 (2015). [CrossRef]  

48. P. Zhao, Z. Feng, F. Qi, A. Qi, Y. Wang, and W. Zheng, Blue Shift of Laser Mode in Photonic Crystal Microcavity (SPIE, 2014).

49. P. Liu, X. He, J. Ren, Q. Liao, J. Yao, and H. Fu, “Organic–inorganic hybrid Perovskite nanowire laser arrays,” ACS Nano 11, 5766–5773 (2017). [CrossRef]  

50. R. Agarwal, C. J. Barrelet, and C. M. Lieber, “Lasing in single cadmium sulfide nanowire optical cavities,” Nano Lett. 5, 917–920 (2005). [CrossRef]  

51. R. Chen, B. Ling, X. W. Sun, and H. D. Sun, “Room temperature excitonic whispering gallery mode lasing from high-quality hexagonal ZnO microdisks,” Adv. Mater. 23, 2199–2204 (2011). [CrossRef]  

52. K. Wang, S. Sun, C. Zhang, W. Sun, Z. Gu, S. Xiao, and Q. Song, “Whispering-gallery-mode based CH3NH3PbBr3 perovskite microrod lasers with high quality factors,” Mater. Chem. Front. 1, 477–481 (2017). [CrossRef]  

53. D. Saxena, F. Wang, Q. Gao, S. Mokkapati, H. H. Tan, and C. Jagadish, “Mode profiling of semiconductor nanowire lasers,” Nano Lett. 15, 5342–5348 (2015). [CrossRef]  

54. A. Z. Mariano, C. Federico, M. Sven, and R. Carsten, “Optically pumped nanowire lasers: invited review,” Semicond. Sci. Technol. 25, 024001 (2010). [CrossRef]  

References

  • View by:

  1. I. Viola, N. Ghofraniha, A. Zacheo, V. Arima, C. Conti, and G. Gigli, “Random laser emission from a paper-based device,” J. Mater. Chem. C 1, 8128–8133 (2013).
    [Crossref]
  2. Y.-J. Lee, C.-Y. Chou, Z.-P. Yang, T. B. H. Nguyen, Y.-C. Yao, T.-W. Yeh, M.-T. Tsai, and H.-C. Kuo, “Flexible random lasers with tunable lasing emissions,” Nanoscale 10, 10403–10411 (2018).
    [Crossref]
  3. B. S. Bhaktha, N. Bachelard, X. Noblin, and P. Sebbah, “Optofluidic random laser,” Appl. Phys. Lett. 101, 151101 (2012).
    [Crossref]
  4. X. Fan and S.-H. Yun, “The potential of optofluidic biolasers,” Nat. Methods 11, 141 (2014).
    [Crossref]
  5. L. Xu, H. Zhao, C. Xu, S. Zhang, and J. Zhang, “Optical energy storage and reemission based weak localization of light and accompanying random lasing action in disordered Nd3+ doped (Pb, La)(Zr, Ti)O3 ceramics,” J. Appl. Phys. 116, 063104 (2014).
    [Crossref]
  6. R. Polson and Z. Vardeny, “Cancerous tissue mapping from random lasing emission spectra,” J. Opt. 12, 024010 (2010).
    [Crossref]
  7. B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
    [Crossref]
  8. B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 746–751 (2013).
    [Crossref]
  9. A. Mermillod-Blondin, H. Mentzel, and A. Rosenfeld, “Time-resolved microscopy with random lasers,” Opt. Lett. 38, 4112–4115 (2013).
    [Crossref]
  10. Q. Song, S. Xiao, Z. Xu, J. Liu, X. Sun, V. Drachev, V. M. Shalaev, O. Akkus, and Y. L. Kim, “Random lasing in bone tissue,” Opt. Lett. 35, 1425–1427 (2010).
    [Crossref]
  11. S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4, 231–235 (2010).
    [Crossref]
  12. F. Luan, B. Gu, A. S. Gomes, K.-T. Yong, S. Wen, and P. N. Prasad, “Lasing in nanocomposite random media,” Nano Today 10(2), 168–192 (2015).
    [Crossref]
  13. J. Dubois and S. La Rochelle, “Active cooperative tuned identification friend or foe (ACTIFF),” U.S. patentUS5966227A (12October1999).
  14. D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
    [Crossref]
  15. R. Sapienza, “Determining random lasing action,” Nat. Rev. Phys. 1, 690–695 (2019).
    [Crossref]
  16. K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Quantitative analysis of several random lasers,” Opt. Commun. 278, 110–113 (2007).
    [Crossref]
  17. S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93, 053903 (2004).
    [Crossref]
  18. H. Cao, J. Y. Xu, S. H. Chang, and S. T. Ho, “Transition from amplified spontaneous emission to laser action in strongly scattering media,” Phys. Rev. E 61, 1985–1989 (2000).
    [Crossref]
  19. S. V. Frolov, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, “Laser-like emission in opal photonic crystals,” Opt. Commun. 162, 241–246 (1999).
    [Crossref]
  20. H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
    [Crossref]
  21. V. Milner and A. Z. Genack, “Photon localization laser: low-threshold lasing in a random amplifying layered medium via wave localization,” Phys. Rev. Lett. 94, 073901 (2005).
    [Crossref]
  22. J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photonics 3, 88–127 (2011).
    [Crossref]
  23. H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497 (2005).
    [Crossref]
  24. H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278 (1999).
    [Crossref]
  25. N. M. Lawandy, R. Balachandran, A. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
    [Crossref]
  26. C. Liu, J. A. Zapien, Y. Yao, X. Meng, C. S. Lee, S. Fan, Y. Lifshitz, and S. T. Lee, “High-density, ordered ultraviolet light-emitting ZnO nanowire arrays,” Adv. Mater. 15, 838–841 (2003).
    [Crossref]
  27. K. H. Li, X. Liu, Q. Wang, S. Zhao, and Z. Mi, “Ultralow-threshold electrically injected AlGaN nanowire ultraviolet lasers on Si operating at low temperature,” Nat. Nanotechnol. 10, 140–144 (2015).
    [Crossref]
  28. H. Y. Yang, S. F. Yu, S. P. Lau, S. H. Tsang, G. Z. Xing, and T. Wu, “Ultraviolet coherent random lasing in randomly assembled SnO2 nanowires,” Appl. Phys. Lett. 94, 241121 (2009).
    [Crossref]
  29. M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97, 151109 (2010).
    [Crossref]
  30. J. Bingi, A. R. Warrier, and C. Vijayan, “Raman mode random lasing in ZnS-β-carotene random gain media,” Appl. Phys. Lett. 102, 221105 (2013).
    [Crossref]
  31. N. Wang, X. Yuan, X. Zhang, Q. Gao, B. Zhao, L. Li, M. Lockrey, H. H. Tan, C. Jagadish, and P. Caroff, “Shape engineering of InP nanostructures by selective area epitaxy,” ACS Nano 13, 7261–7269 (2019).
    [Crossref]
  32. Q. Gao, D. Saxena, F. Wang, L. Fu, S. Mokkapati, Y. Guo, L. Li, J. Wong-Leung, P. Caroff, H. H. Tan, and C. Jagadish, “Selective-area epitaxy of pure wurtzite InP nanowires: high quantum efficiency and room-temperature lasing,” Nano Lett. 14, 5206–5211 (2014).
    [Crossref]
  33. J. Liu, P. D. Garcia, S. Ek, N. Gregersen, T. Suhr, M. Schubert, J. Mørk, S. Stobbe, and P. Lodahl, “Random nanolasing in the Anderson localized regime,” Nat. Nanotechnol. 9, 285–289 (2014).
    [Crossref]
  34. L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits (Wiley, 2012).
  35. I. Prieto, J. M. Llorens, L. E. Muñoz-Camúñez, A. G. Taboada, J. Canet-Ferrer, J. M. Ripalda, C. Robles, G. Muñoz-Matutano, J. P. Martínez-Pastor, and P. A. Postigo, “Near thresholdless laser operation at room temperature,” Optica 2, 66–69 (2015).
    [Crossref]
  36. B. Fazio, P. Artoni, M. A. Iatì, C. D’andrea, M. J. L. Faro, S. Del Sorbo, S. Pirotta, P. G. Gucciardi, P. Musumeci, and C. S. Vasi, “Strongly enhanced light trapping in a two-dimensional silicon nanowire random fractal array,” Light Sci. Appl. 5, e16062 (2016).
    [Crossref]
  37. H. J. Joyce, C. J. Docherty, Q. Gao, H. H. Tan, C. Jagadish, J. Lloyd-Hughes, L. M. Herz, and M. B. Johnston, “Electronic properties of GaAs, InAs and InP nanowires studied by terahertz spectroscopy,” Nanotechnology 24, 214006 (2013).
    [Crossref]
  38. K. A. Meradi, F. Tayeboun, S. Ghezali, R. Naoum, and H. T. Hattori, “Design of a thermal tunable photonic-crystal coupler,” J. Russ. Laser Res. 32, 572–578 (2011).
    [Crossref]
  39. B. R. Bennett, R. A. Soref, and J. A. D. Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quantum Electron. 26, 113–122 (1990).
    [Crossref]
  40. M. A. Zimmler, J. Bao, F. Capasso, S. Müller, and C. Ronning, “Laser action in nanowires: observation of the transition from amplified spontaneous emission to laser oscillation,” Appl. Phys. Lett. 93, 051101 (2008).
    [Crossref]
  41. S. W. Eaton, M. Lai, N. A. Gibson, A. B. Wong, L. Dou, J. Ma, L.-W. Wang, S. R. Leone, and P. Yang, “Lasing in robust cesium lead halide perovskite nanowires,” Proc. Natl. Acad. Sci. USA 113, 1993–1998 (2016).
    [Crossref]
  42. D. Saxena, S. Mokkapati, P. Parkinson, N. Jiang, Q. Gao, H. H. Tan, and C. Jagadish, “Optically pumped room-temperature GaAs nanowire lasers,” Nat. Photonics 7, 963–968 (2013).
    [Crossref]
  43. A. Mishra, L. V. Titova, T. B. Hoang, H. E. Jackson, L. M. Smith, J. M. Yarrison-Rice, Y. Kim, H. J. Joyce, Q. Gao, H. H. Tan, and C. Jagadish, “Polarization and temperature dependence of photoluminescence from zincblende and wurtzite InP nanowires,” Appl. Phys. Lett. 91, 263104 (2007).
    [Crossref]
  44. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
    [Crossref]
  45. P. Stano and P. Jacquod, “Suppression of interactions in multimode random lasers in the Anderson localized regime,” Nat. Photonics 7, 66–71 (2013).
    [Crossref]
  46. S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76, 033807 (2007).
    [Crossref]
  47. C. Tessarek, R. Goldhahn, G. Sarau, M. Heilmann, and S. Christiansen, “Carrier-induced refractive index change observed by a whispering gallery mode shift in GaN microrods,” New J. Phys. 17, 083047 (2015).
    [Crossref]
  48. P. Zhao, Z. Feng, F. Qi, A. Qi, Y. Wang, and W. Zheng, Blue Shift of Laser Mode in Photonic Crystal Microcavity (SPIE, 2014).
  49. P. Liu, X. He, J. Ren, Q. Liao, J. Yao, and H. Fu, “Organic–inorganic hybrid Perovskite nanowire laser arrays,” ACS Nano 11, 5766–5773 (2017).
    [Crossref]
  50. R. Agarwal, C. J. Barrelet, and C. M. Lieber, “Lasing in single cadmium sulfide nanowire optical cavities,” Nano Lett. 5, 917–920 (2005).
    [Crossref]
  51. R. Chen, B. Ling, X. W. Sun, and H. D. Sun, “Room temperature excitonic whispering gallery mode lasing from high-quality hexagonal ZnO microdisks,” Adv. Mater. 23, 2199–2204 (2011).
    [Crossref]
  52. K. Wang, S. Sun, C. Zhang, W. Sun, Z. Gu, S. Xiao, and Q. Song, “Whispering-gallery-mode based CH3NH3PbBr3 perovskite microrod lasers with high quality factors,” Mater. Chem. Front. 1, 477–481 (2017).
    [Crossref]
  53. D. Saxena, F. Wang, Q. Gao, S. Mokkapati, H. H. Tan, and C. Jagadish, “Mode profiling of semiconductor nanowire lasers,” Nano Lett. 15, 5342–5348 (2015).
    [Crossref]
  54. A. Z. Mariano, C. Federico, M. Sven, and R. Carsten, “Optically pumped nanowire lasers: invited review,” Semicond. Sci. Technol. 25, 024001 (2010).
    [Crossref]

2019 (2)

R. Sapienza, “Determining random lasing action,” Nat. Rev. Phys. 1, 690–695 (2019).
[Crossref]

N. Wang, X. Yuan, X. Zhang, Q. Gao, B. Zhao, L. Li, M. Lockrey, H. H. Tan, C. Jagadish, and P. Caroff, “Shape engineering of InP nanostructures by selective area epitaxy,” ACS Nano 13, 7261–7269 (2019).
[Crossref]

2018 (1)

Y.-J. Lee, C.-Y. Chou, Z.-P. Yang, T. B. H. Nguyen, Y.-C. Yao, T.-W. Yeh, M.-T. Tsai, and H.-C. Kuo, “Flexible random lasers with tunable lasing emissions,” Nanoscale 10, 10403–10411 (2018).
[Crossref]

2017 (2)

P. Liu, X. He, J. Ren, Q. Liao, J. Yao, and H. Fu, “Organic–inorganic hybrid Perovskite nanowire laser arrays,” ACS Nano 11, 5766–5773 (2017).
[Crossref]

K. Wang, S. Sun, C. Zhang, W. Sun, Z. Gu, S. Xiao, and Q. Song, “Whispering-gallery-mode based CH3NH3PbBr3 perovskite microrod lasers with high quality factors,” Mater. Chem. Front. 1, 477–481 (2017).
[Crossref]

2016 (2)

S. W. Eaton, M. Lai, N. A. Gibson, A. B. Wong, L. Dou, J. Ma, L.-W. Wang, S. R. Leone, and P. Yang, “Lasing in robust cesium lead halide perovskite nanowires,” Proc. Natl. Acad. Sci. USA 113, 1993–1998 (2016).
[Crossref]

B. Fazio, P. Artoni, M. A. Iatì, C. D’andrea, M. J. L. Faro, S. Del Sorbo, S. Pirotta, P. G. Gucciardi, P. Musumeci, and C. S. Vasi, “Strongly enhanced light trapping in a two-dimensional silicon nanowire random fractal array,” Light Sci. Appl. 5, e16062 (2016).
[Crossref]

2015 (5)

K. H. Li, X. Liu, Q. Wang, S. Zhao, and Z. Mi, “Ultralow-threshold electrically injected AlGaN nanowire ultraviolet lasers on Si operating at low temperature,” Nat. Nanotechnol. 10, 140–144 (2015).
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F. Luan, B. Gu, A. S. Gomes, K.-T. Yong, S. Wen, and P. N. Prasad, “Lasing in nanocomposite random media,” Nano Today 10(2), 168–192 (2015).
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I. Prieto, J. M. Llorens, L. E. Muñoz-Camúñez, A. G. Taboada, J. Canet-Ferrer, J. M. Ripalda, C. Robles, G. Muñoz-Matutano, J. P. Martínez-Pastor, and P. A. Postigo, “Near thresholdless laser operation at room temperature,” Optica 2, 66–69 (2015).
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D. Saxena, F. Wang, Q. Gao, S. Mokkapati, H. H. Tan, and C. Jagadish, “Mode profiling of semiconductor nanowire lasers,” Nano Lett. 15, 5342–5348 (2015).
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C. Tessarek, R. Goldhahn, G. Sarau, M. Heilmann, and S. Christiansen, “Carrier-induced refractive index change observed by a whispering gallery mode shift in GaN microrods,” New J. Phys. 17, 083047 (2015).
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2014 (4)

X. Fan and S.-H. Yun, “The potential of optofluidic biolasers,” Nat. Methods 11, 141 (2014).
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L. Xu, H. Zhao, C. Xu, S. Zhang, and J. Zhang, “Optical energy storage and reemission based weak localization of light and accompanying random lasing action in disordered Nd3+ doped (Pb, La)(Zr, Ti)O3 ceramics,” J. Appl. Phys. 116, 063104 (2014).
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Q. Gao, D. Saxena, F. Wang, L. Fu, S. Mokkapati, Y. Guo, L. Li, J. Wong-Leung, P. Caroff, H. H. Tan, and C. Jagadish, “Selective-area epitaxy of pure wurtzite InP nanowires: high quantum efficiency and room-temperature lasing,” Nano Lett. 14, 5206–5211 (2014).
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J. Liu, P. D. Garcia, S. Ek, N. Gregersen, T. Suhr, M. Schubert, J. Mørk, S. Stobbe, and P. Lodahl, “Random nanolasing in the Anderson localized regime,” Nat. Nanotechnol. 9, 285–289 (2014).
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2013 (7)

H. J. Joyce, C. J. Docherty, Q. Gao, H. H. Tan, C. Jagadish, J. Lloyd-Hughes, L. M. Herz, and M. B. Johnston, “Electronic properties of GaAs, InAs and InP nanowires studied by terahertz spectroscopy,” Nanotechnology 24, 214006 (2013).
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B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 746–751 (2013).
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A. Mermillod-Blondin, H. Mentzel, and A. Rosenfeld, “Time-resolved microscopy with random lasers,” Opt. Lett. 38, 4112–4115 (2013).
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I. Viola, N. Ghofraniha, A. Zacheo, V. Arima, C. Conti, and G. Gigli, “Random laser emission from a paper-based device,” J. Mater. Chem. C 1, 8128–8133 (2013).
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J. Bingi, A. R. Warrier, and C. Vijayan, “Raman mode random lasing in ZnS-β-carotene random gain media,” Appl. Phys. Lett. 102, 221105 (2013).
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P. Stano and P. Jacquod, “Suppression of interactions in multimode random lasers in the Anderson localized regime,” Nat. Photonics 7, 66–71 (2013).
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D. Saxena, S. Mokkapati, P. Parkinson, N. Jiang, Q. Gao, H. H. Tan, and C. Jagadish, “Optically pumped room-temperature GaAs nanowire lasers,” Nat. Photonics 7, 963–968 (2013).
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2012 (2)

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
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B. S. Bhaktha, N. Bachelard, X. Noblin, and P. Sebbah, “Optofluidic random laser,” Appl. Phys. Lett. 101, 151101 (2012).
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2011 (3)

K. A. Meradi, F. Tayeboun, S. Ghezali, R. Naoum, and H. T. Hattori, “Design of a thermal tunable photonic-crystal coupler,” J. Russ. Laser Res. 32, 572–578 (2011).
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J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photonics 3, 88–127 (2011).
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R. Chen, B. Ling, X. W. Sun, and H. D. Sun, “Room temperature excitonic whispering gallery mode lasing from high-quality hexagonal ZnO microdisks,” Adv. Mater. 23, 2199–2204 (2011).
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2010 (5)

A. Z. Mariano, C. Federico, M. Sven, and R. Carsten, “Optically pumped nanowire lasers: invited review,” Semicond. Sci. Technol. 25, 024001 (2010).
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M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97, 151109 (2010).
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R. Polson and Z. Vardeny, “Cancerous tissue mapping from random lasing emission spectra,” J. Opt. 12, 024010 (2010).
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Q. Song, S. Xiao, Z. Xu, J. Liu, X. Sun, V. Drachev, V. M. Shalaev, O. Akkus, and Y. L. Kim, “Random lasing in bone tissue,” Opt. Lett. 35, 1425–1427 (2010).
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S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4, 231–235 (2010).
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2009 (1)

H. Y. Yang, S. F. Yu, S. P. Lau, S. H. Tsang, G. Z. Xing, and T. Wu, “Ultraviolet coherent random lasing in randomly assembled SnO2 nanowires,” Appl. Phys. Lett. 94, 241121 (2009).
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2008 (2)

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
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M. A. Zimmler, J. Bao, F. Capasso, S. Müller, and C. Ronning, “Laser action in nanowires: observation of the transition from amplified spontaneous emission to laser oscillation,” Appl. Phys. Lett. 93, 051101 (2008).
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2007 (4)

A. Mishra, L. V. Titova, T. B. Hoang, H. E. Jackson, L. M. Smith, J. M. Yarrison-Rice, Y. Kim, H. J. Joyce, Q. Gao, H. H. Tan, and C. Jagadish, “Polarization and temperature dependence of photoluminescence from zincblende and wurtzite InP nanowires,” Appl. Phys. Lett. 91, 263104 (2007).
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T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
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S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76, 033807 (2007).
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K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Quantitative analysis of several random lasers,” Opt. Commun. 278, 110–113 (2007).
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2005 (3)

V. Milner and A. Z. Genack, “Photon localization laser: low-threshold lasing in a random amplifying layered medium via wave localization,” Phys. Rev. Lett. 94, 073901 (2005).
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H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497 (2005).
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R. Agarwal, C. J. Barrelet, and C. M. Lieber, “Lasing in single cadmium sulfide nanowire optical cavities,” Nano Lett. 5, 917–920 (2005).
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2004 (1)

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93, 053903 (2004).
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2003 (1)

C. Liu, J. A. Zapien, Y. Yao, X. Meng, C. S. Lee, S. Fan, Y. Lifshitz, and S. T. Lee, “High-density, ordered ultraviolet light-emitting ZnO nanowire arrays,” Adv. Mater. 15, 838–841 (2003).
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2000 (1)

H. Cao, J. Y. Xu, S. H. Chang, and S. T. Ho, “Transition from amplified spontaneous emission to laser action in strongly scattering media,” Phys. Rev. E 61, 1985–1989 (2000).
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1999 (2)

S. V. Frolov, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, “Laser-like emission in opal photonic crystals,” Opt. Commun. 162, 241–246 (1999).
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H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278 (1999).
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1996 (1)

D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
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1994 (1)

N. M. Lawandy, R. Balachandran, A. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
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1990 (1)

B. R. Bennett, R. A. Soref, and J. A. D. Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quantum Electron. 26, 113–122 (1990).
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Agarwal, R.

R. Agarwal, C. J. Barrelet, and C. M. Lieber, “Lasing in single cadmium sulfide nanowire optical cavities,” Nano Lett. 5, 917–920 (2005).
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Akkus, O.

Alamo, J. A. D.

B. R. Bennett, R. A. Soref, and J. A. D. Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quantum Electron. 26, 113–122 (1990).
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Andreasen, J.

J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photonics 3, 88–127 (2011).
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Ania-Castañón, J. D.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4, 231–235 (2010).
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Arima, V.

I. Viola, N. Ghofraniha, A. Zacheo, V. Arima, C. Conti, and G. Gigli, “Random laser emission from a paper-based device,” J. Mater. Chem. C 1, 8128–8133 (2013).
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Artoni, P.

B. Fazio, P. Artoni, M. A. Iatì, C. D’andrea, M. J. L. Faro, S. Del Sorbo, S. Pirotta, P. G. Gucciardi, P. Musumeci, and C. S. Vasi, “Strongly enhanced light trapping in a two-dimensional silicon nanowire random fractal array,” Light Sci. Appl. 5, e16062 (2016).
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Asatryan, A. A.

J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photonics 3, 88–127 (2011).
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Babin, S. A.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4, 231–235 (2010).
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Bachelard, N.

B. S. Bhaktha, N. Bachelard, X. Noblin, and P. Sebbah, “Optofluidic random laser,” Appl. Phys. Lett. 101, 151101 (2012).
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Balachandran, R.

N. M. Lawandy, R. Balachandran, A. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
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M. A. Zimmler, J. Bao, F. Capasso, S. Müller, and C. Ronning, “Laser action in nanowires: observation of the transition from amplified spontaneous emission to laser oscillation,” Appl. Phys. Lett. 93, 051101 (2008).
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R. Agarwal, C. J. Barrelet, and C. M. Lieber, “Lasing in single cadmium sulfide nanowire optical cavities,” Nano Lett. 5, 917–920 (2005).
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Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
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S. V. Frolov, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, “Laser-like emission in opal photonic crystals,” Opt. Commun. 162, 241–246 (1999).
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B. R. Bennett, R. A. Soref, and J. A. D. Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quantum Electron. 26, 113–122 (1990).
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B. S. Bhaktha, N. Bachelard, X. Noblin, and P. Sebbah, “Optofluidic random laser,” Appl. Phys. Lett. 101, 151101 (2012).
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Bingi, J.

J. Bingi, A. R. Warrier, and C. Vijayan, “Raman mode random lasing in ZnS-β-carotene random gain media,” Appl. Phys. Lett. 102, 221105 (2013).
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J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photonics 3, 88–127 (2011).
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J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photonics 3, 88–127 (2011).
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Cao, H.

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 746–751 (2013).
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B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
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J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photonics 3, 88–127 (2011).
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H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278 (1999).
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M. A. Zimmler, J. Bao, F. Capasso, S. Müller, and C. Ronning, “Laser action in nanowires: observation of the transition from amplified spontaneous emission to laser oscillation,” Appl. Phys. Lett. 93, 051101 (2008).
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Q. Gao, D. Saxena, F. Wang, L. Fu, S. Mokkapati, Y. Guo, L. Li, J. Wong-Leung, P. Caroff, H. H. Tan, and C. Jagadish, “Selective-area epitaxy of pure wurtzite InP nanowires: high quantum efficiency and room-temperature lasing,” Nano Lett. 14, 5206–5211 (2014).
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A. Z. Mariano, C. Federico, M. Sven, and R. Carsten, “Optically pumped nanowire lasers: invited review,” Semicond. Sci. Technol. 25, 024001 (2010).
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H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278 (1999).
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H. Cao, J. Y. Xu, S. H. Chang, and S. T. Ho, “Transition from amplified spontaneous emission to laser action in strongly scattering media,” Phys. Rev. E 61, 1985–1989 (2000).
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Chen, R.

R. Chen, B. Ling, X. W. Sun, and H. D. Sun, “Room temperature excitonic whispering gallery mode lasing from high-quality hexagonal ZnO microdisks,” Adv. Mater. 23, 2199–2204 (2011).
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B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
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S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4, 231–235 (2010).
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B. Fazio, P. Artoni, M. A. Iatì, C. D’andrea, M. J. L. Faro, S. Del Sorbo, S. Pirotta, P. G. Gucciardi, P. Musumeci, and C. S. Vasi, “Strongly enhanced light trapping in a two-dimensional silicon nanowire random fractal array,” Light Sci. Appl. 5, e16062 (2016).
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H. J. Joyce, C. J. Docherty, Q. Gao, H. H. Tan, C. Jagadish, J. Lloyd-Hughes, L. M. Herz, and M. B. Johnston, “Electronic properties of GaAs, InAs and InP nanowires studied by terahertz spectroscopy,” Nanotechnology 24, 214006 (2013).
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S. W. Eaton, M. Lai, N. A. Gibson, A. B. Wong, L. Dou, J. Ma, L.-W. Wang, S. R. Leone, and P. Yang, “Lasing in robust cesium lead halide perovskite nanowires,” Proc. Natl. Acad. Sci. USA 113, 1993–1998 (2016).
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J. Liu, P. D. Garcia, S. Ek, N. Gregersen, T. Suhr, M. Schubert, J. Mørk, S. Stobbe, and P. Lodahl, “Random nanolasing in the Anderson localized regime,” Nat. Nanotechnol. 9, 285–289 (2014).
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S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4, 231–235 (2010).
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M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97, 151109 (2010).
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Fan, S.

C. Liu, J. A. Zapien, Y. Yao, X. Meng, C. S. Lee, S. Fan, Y. Lifshitz, and S. T. Lee, “High-density, ordered ultraviolet light-emitting ZnO nanowire arrays,” Adv. Mater. 15, 838–841 (2003).
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X. Fan and S.-H. Yun, “The potential of optofluidic biolasers,” Nat. Methods 11, 141 (2014).
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B. Fazio, P. Artoni, M. A. Iatì, C. D’andrea, M. J. L. Faro, S. Del Sorbo, S. Pirotta, P. G. Gucciardi, P. Musumeci, and C. S. Vasi, “Strongly enhanced light trapping in a two-dimensional silicon nanowire random fractal array,” Light Sci. Appl. 5, e16062 (2016).
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S. V. Frolov, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, “Laser-like emission in opal photonic crystals,” Opt. Commun. 162, 241–246 (1999).
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Q. Gao, D. Saxena, F. Wang, L. Fu, S. Mokkapati, Y. Guo, L. Li, J. Wong-Leung, P. Caroff, H. H. Tan, and C. Jagadish, “Selective-area epitaxy of pure wurtzite InP nanowires: high quantum efficiency and room-temperature lasing,” Nano Lett. 14, 5206–5211 (2014).
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Gao, Q.

N. Wang, X. Yuan, X. Zhang, Q. Gao, B. Zhao, L. Li, M. Lockrey, H. H. Tan, C. Jagadish, and P. Caroff, “Shape engineering of InP nanostructures by selective area epitaxy,” ACS Nano 13, 7261–7269 (2019).
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Q. Gao, D. Saxena, F. Wang, L. Fu, S. Mokkapati, Y. Guo, L. Li, J. Wong-Leung, P. Caroff, H. H. Tan, and C. Jagadish, “Selective-area epitaxy of pure wurtzite InP nanowires: high quantum efficiency and room-temperature lasing,” Nano Lett. 14, 5206–5211 (2014).
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Supplementary Material (1)

NameDescription
Supplement 1       Supplemental document

Data availability

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

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Figures (5)

Fig. 1.
Fig. 1. Design of the random nanowire lasers. (a) Illustration of the vertical random nanowire array used in this study. The nanowires are illuminated from the top by a pulsed laser with an intensity of ${{I}_0}(\lambda)$. The insets show pictorially the diffusive and localization regimes in random media. In the diffusive regime, normally a broad emission is observed at lasing, while in the localization regime, narrow spectral peaks over a broad background are observed at lasing. (b) The effects of filling factor and average nanowire diameter on ${{kl}_t}$. The red line indicates where the Ioffe–Regel criterion is satisfied. (c) The resonance spectrum calculated for a system with FF = 0.3, ${{d}_{\textit{av}}} = {125}\;{\rm nm}$, and L = 3 µm. The 2D spatial profiles for the three high $Q$ factor modes (Mode I: ${\lambda _r} = {829}\;{\rm nm}$, Mode II: ${\lambda _r} = {791}\;{\rm nm}$, and Mode III: ${\lambda _r} = {848}\;{\rm nm}$) are shown at a depth of 0.5 µm (i.e., at ${ z} = {2.5}\;\unicode{x00B5}{\rm m}$) from the tip of the nanowires, clearly showing strong localization in the $x - y$ plane. The inset in (c) also shows the 3D view of the simulated mode profile, where confinement can also be observed in the vertical direction and confined predominantly in the nanowires. The NW length is 3 µm, and the top of the NW corresponds to ${z} = {3}\;\unicode{x00B5}{\rm m}$. Only the top 2 µm of the NW array is shown in this inset.
Fig. 2.
Fig. 2. Single-mode lasing behavior from the random nanowire array. (a) SEM image showing a tilted view of our nanowire array (scale bar 1 µm). The inset shows a top view confirming the random nature of the nanowires in the $x - y$ plane (scale bar 500 nm). (b) Emission spectra at 6 K from the nanowire array at various pump fluences. The normalized spectral map (inset) shows a broadening of the spectrum with increasing fluence up to the transition to the amplified spontaneous emission (${550}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse) but then a sudden reduction in the linewidth above ${{P}_{{\rm in}}} = {550}\;\unicode{x00B5}{\rm J}\;{{\rm cm}^{- 2}}$ per pulse. (c) Light output versus excitation fluence plotted on a log–log scale, showing an “S-like” while the same data plotted on a linear scale (inset) shows a “kink-like” threshold behavior—indications of lasing from the nanowire array. The shaded gray area is the region of amplified spontaneous emission. The data points are the experimental results, and the red lines are just a guide to the eye.
Fig. 3.
Fig. 3. Multi-mode lasing and near-field emission profiles from the random nanowire array. (a) Emission spectra from the nanowire array at various pump fluences. Emission from the substrate is indicated, while emission from the nanowires occurs below 850 nm. (b) Log–log plot of integrated light output versus fluence from two spectral regions indicated in (a): shaded red region I (${769} \lt \lambda \lt {787}\;{\rm nm}$) and green region II (${787} \lt \lambda \lt {807}\;{\rm nm}$). The results for total light output from the nanowire array (${725} \lt \lambda \lt {850}\;{\rm nm}$) are also shown for reference. (c), (e), (g)Near-field emission profiles from the nanowire array at three different excitation fluences: ${{P}_{{\rm in}}} = {386}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse, ${{ P}_{{\rm in}}} = {2}{,}{435}\;\unicode{x00B5} {\rm J}\;{{\rm cm}^{- 2}}$ per pulse, and ${{P}_{{\rm in}}} = {3}{,}{072}\;\unicode{x00B5}{\rm J}\;{{\rm cm}^{- 2}}$ per pulse (scale bars 2 µm). (d), (f), (h) Corresponding line scan across the near-field intensity profiles in (c), (e), and (g) along three directions, AB, CD, and EF. The cross-section mode profiles clearly indicate strong localization above the lasing threshold as indicated in (f) and (h). The localization lengths for the mode profiles are indicated in the image (g). All measurements were done at 6 K.
Fig. 4.
Fig. 4. Lasing stability. Emission spectra at different excitation fluences from two different regions of the random nanowire array which support (a) three and (b) five lasing modes (${T} = {6}\;{\rm K}$). With increasing fluences, the nanowire array has been subjected to more excitation pulses. The difference in the total number of pulses used to collect each spectrum from those used for the lowest fluence is indicated by $\Delta {{N}_{{\rm pulse}}}$.
Fig. 5.
Fig. 5. Statistical distribution of several key parameters of the random nanowire laser. (a) Measured pumping intensity distribution taken at the commencement of amplified spontaneous emission. (b) Experimentally measured $Q$ factor of the modes. (c) Calculated distribution of the mode confinement factor. (d) Calculated distribution of the spatial lateral mode size.

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