1. Introduction

Advances in nanowire lasers are occurring at a rapid pace, with optically pumped lasers demonstrated in a variety of semiconductor material systems, including Group III-nitrides [1–6], Group III-V [7, 8], and Group II-VI [9, 10]. To achieve single-mode lasing, Xiao et al. used a CdSe active medium and a complex resonator comprising of coupled loops of long, flexible nanowires [11]. Recently, Scofield et al. reported single-mode lasing from a defect mode in an InGaAs photonic crystal consisting of a 2-dimensional array of InGaAs nanowires [12]. To circumvent the need for fabrication and manipulation of complicated optical structures, we concentrated our effort towards a simple, linear, Fabry-Perot nanowire laser, where the factors enabling single-mode lasing are short cavity length, small cross section and very high material gain. By reducing the nanowire size, the number of cavity modes within the gain bandwidth is dramatically reduced. This in turn requires high material gain, necessary to compensate for the reduced gain length. Low defect density and high sample uniformity are also necessary to reduce carrier losses and inhomogeneous broadening, in order to achieve high carrier density and increase gain competition, respectively. By satisfying these requirements, we are able to demonstrate single-mode lasing with a linewidth of ~0.12 nm and >18dB side-mode suppression ratio, in a 135 nm wide, 4.7 μm long GaN nanowire, under optical pumping. Single-mode operation is maintained far above lasing threshold. With GaN (or InGaN), the payoff is single-mode laser operation at ultraviolet (or green) wavelengths, which is an important spectral region not covered well by present semiconductor lasers.

2. Experiment

To achieve single mode lasing, precise control over the nanowire geometry is required. This requirement is satisfied by a top-down fabrication technique which produces uniform and vertically aligned GaN nanowire arrays from c-plane GaN epilayers on sapphire with low defect density and smooth sidewalls. We previously demonstrated this technique to fabricate nanowire LED structures with an axial GaN/InGaN multi-quantum structure [13]. Figure 1 shows SEM images of top-down GaN nanowires during the fabrication process. Starting from Si-doped planar GaN epilayers grown on 2” c-plane sapphire wafers in a Veeco D-125 metal organic chemical vapor deposition reactor, a 2-step etching process is used: a lithographic dry etch followed by an anisotropic wet etch. Following a process reported by Reculusa and Ravaine [14], a monolayer of 3 μm diameter silica colloids was self-assembled on the GaN surface in a Langmuir-Blodgett trough prior to etching to serve as a semi-periodic lithographic etch mask. GaN posts are subsequently formed by a plasma (dry) etch. As shown in Fig. 1(a), the resulting posts are tapered with large cross-section areas, and therefore, are unsuitable for single-mode nanowire lasers. Moreover, ion bombardment during the plasma etch damages the nanowire surface, as evidenced by significant increase in yellow luminescence [13]. These issues are resolved during the second (wet) etch step [Figs. 1(b)–1(d)]. With the anisotropic wet-etch step, non-tapered GaN nanowires are created with damage-free surfaces, hexagonal cross sections with m-plane {10-10} sidewall facets, and a top c-plane (0001) resonator (end) facet. The GaN nanowire length is determined by the original GaN epilayers thickness and its width is determined by the duration of the wet-etch. Similar axial GaN/InGaN nanowire LED structures prepared by this top-down approach were largely dislocation free (~94% of the nanowires) [13].

 

Fig. 1 Cross sectional SEM images showing GaN posts morphology transiting into GaN nanowires (a) before wet etch, (b) after 2 hours, (c) after 6 hours and (d) after 9 hours from start of wet etch. All images have the same magnification. Scale bars are 2 μm.

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The nanowires were characterized by scanning electron microscopy (SEM), x-ray diffraction (XRD) and transmission electron microscopy (TEM). For the optical pumping measurements, the nanowires were removed from their sapphire growth substrate and transferred to clean Si₃N₄ surfaces on TEM grids. Each nanowire was optically pumped at room temperature with a 10 kHz, 100 ps pulsed quadrupled YAG laser emitting at 267 nm. The intensity incident on the nanowire was varied using neutral density filters. A 50 × ultraviolet objective lens is used to image the pump laser output to an approximately 5 µm diameter spot on the GaN nanowire. Optical emission from the nanowire was collected with the same objective lens. The collected light was analyzed by a cooled CCD detector and a 300 mm spectrometer with a 2400 groove/mm holographic grating. The schematic of the optical pumping measurement set up is given in Fig. 2 .

 

Fig. 2 Schematic of the GaN nanowire optical pumping and measurement setup.

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3. Theory

First, the nanowire passive-cavity eigenmodes are determined using a finite-difference time-domain (FDTD) solver. To determine which of the passive-cavity modes will be lasing, the FDTD information is fed into a laser model. We use a semiclassical multimode laser model, where the time evolution of the intensity I_n in a passive-cavity mode $n$ is given by [15]

The set of coupled mode intensity equations (numbering roughly 300) is solved numerically for the steady-state solution for a given excitation level, α₁/β₁. Plotting the steady-state I_n versus the passive cavity-mode frequency Ω_n gives the emission spectrum.

4. Results and discussion

The optical properties of the GaN nanowires were characterized by optical pumping using a micro-photoluminescence setup as sketched in Fig. 2(a). For comparison, two nanowires of similar diameters but different lengths were fabricated and characterized. A 135 nm diameter, 4.7 μm long nanowire and a 145 nm diameter, 7.2 μm long nanowire were positioned on SiN substrates. Figures 3(a) and 3(b) show CCD images of optical emission from the shorter GaN nanowire at two pump intensities. At low pump intensity, the CCD image shows roughly uniform optical emission from the entire nanowire length, indicating that unguided (out-of-plane) and guided (on-axis) emission intensities are basically equal [see Fig. 3(a)]. The inference is that the optical emission is entirely from spontaneous emission. At a higher pump intensity, a distinctly different emission pattern emerges. The on-axis emission grows significantly, appearing as two bright spots at the ends of the nanowire indicative of Fabry-Perot lasing, as shown in Fig. 3(b). The light collected by the objective lens is directly from the highly diverging output beam and indirectly from scattering of the output beam by the SiN surface. The large divergence angle of output beam is because of diffraction from a sub-wavelength nanowire aperture. At the same time, there is a clamping of the unguided spontaneous emission, which appears as a darkening (relative to the bright ends and with filters in place) of the entire length of the nanowire, also shown in Fig. 3(b). Also present in the CCD image are concentric rings of optical interference fringes, which is an indication of the spectral coherence of the emitted light.

 

Fig. 3 CCD images of a GaN nanowire pumped below (a) and above (b) lasing threshold, respectively. The nanowire laser emits a highly divergent beam from the facets, some of which is collected by the objective lens. The objective lens also collects radiation emitted from the facets that is scattered by the SiN substrate surface, as well as spontaneous emission exiting perpendicular to the nanowire axis. Scale bars are 2 µm.

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Figure 4 plots the light out versus pump power and output intensity spectra for the two nanowire lasers of different lengths. The experiment was performed at T = 300 K. For both nanowires, the light out versus pump power curves show abrupt slope changes indicative of lasing threshold. Also, the peak intensity grew linearly with no sign of saturation throughout the excitation range. Emission spectra were measured at various pump intensities. The right column shows spectra for the two nanowire lasers at four optical pumping intensities. For the 4.7 μm long nanowire laser, the emission spectrum (lowest curve, Fig. 4(c)) is featureless and broad, with a full-width at half-maximum (FWHM) of approximately 6 nm at a pump intensity of 150kW/cm². At the next higher pump intensity of 268kW/cm², the emission spectrum starts to exhibit many sharp peaks, suggesting the onset of amplified spontaneous emission. For a pump intensity of 323kW/cm², the spectrum shows a single sharp peak with FWHM < 0.12 nm over a broad background. The single-mode behavior remains (see highest intensity spectrum, Fig. 4(c)) as the pump intensity continues to increase. For this laser, the mode spacing was measured to be 1.9 nm. Side-mode suppression ratio is also maintained at greater than 18dB. An increase in the nanowire length results in a significant reduction in side-mode suppression, leading to emission characteristic of multimode lasing, as evidenced by the 7.2 μm long nanowire shown in Fig. 4(f). For this laser, the mode spacing was measured to be 1.3 nm. We note that multimode lasing was typical for the larger diameter nanowires (e.g. > ~180 nm), with <1.5 nm measured mode spacing. Thus, both the length and the diameter play an important role in the ability to fabricate a single-mode nanowire laser. The reduction of transverse modes is achieved by limiting the diameter and the reduction of longitudinal modes is similarly achieved by limiting the length.

 

Fig. 4 (a, d) Nanowire laser intensity versus pump laser intensity, for two different nanowires with lengths of 4.7 µm and 7.2 µm (top and bottom, respectively). (c,f) Photoluminescence spectra from the nanowire lasers under uniform excitation for pump intensities as indicated in the figures. (b,e) Scanning electron micrographs of the GaN nanowire lasers. (b) shows the smaller dimensioned nanowire with a width of 135 nm and length of 4.7 µm (e) shows the larger dimensioned nanowire with a width of 145 nm and length of 7.2 µm.

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Summarizing the experimental results at this point, Figs. 3 and 4 together provide strong evidence of single-mode lasing. Figure 3(b) shows the clamping of spontaneous emission and interference fringes indicating coherence in optical emission [19]. There is the presence of a lasing threshold [Fig. 4 (left column, top)] and spectral narrowing to single frequency [Fig. 4 (right column, top)].

The experiments were modeled to better understand the mechanisms leading to single-mode lasing and to develop an analytical tool for designing future nanowire lasers. A combination of mode simulations, multimode-laser modeling and many-body laser-gain calculation were employed. First, the nanowire passive-cavity eigenmodes were determined using a full vectorial commercial mode solver from Lumerical Inc. Then, multimode semiclassical laser theory [15] and many-body gain [18] calculations were used to determine which of the passive-cavity eigenmodes will be above lasing threshold for given experimental conditions. Emission spectra at different excitations were computed for nanowire lasers with dimensions approximating those experimentally measured. Figure 5(a) shows the intensity spectra for increasing excitation for a 140 nm diameter, 4.5 µm long nanowire. The spectra show multiple resonances initially, which condense to only one mode operating above lasing threshold. A criterion for lasing is spectral line narrowing, as clearly exhibited by the mode at 363 nm. On the other hand, each side mode remains broader than the central mode, with width determined by the passive Fabry-Perot resonance. Amplified spontaneous emission gives rise to the side-mode intensity. Figure 5(b) shows the case of a longer 7.3 μm long (140 nm diameter) nanowire laser. Side-mode suppression is decreased by roughly a factor of 3 when compared to the shorter nanowire laser for α₁/β₁ > 1, where α₁ is the net modal gain and β₁ is the self-saturation coefficient. Convincing evidence for multimode operation is from side-mode spectral narrowing to width comparable to the central mode, indicating that they are above lasing threshold. Figure 5 is qualitatively consistent with the experimental results described in Fig. 4. Simulations were also performed for longer nanowire devices. We found multimode operation for lasers longer than ~7 μm, consistent with earlier reports and experiments performed at Sandia.

 

Fig. 5 Emission spectra for 4.5 μm (a) and 7.3 μm (b) long nanowire lasers and different excitation, α₁/β₁ as indicated. The results are obtained using F = 0.05 and θ_nm/β₁ = 1 for all n and m. Laser intensity is in dimensionless units, I = (µE/ħ)²T₁T₂ where µ,E,T₁, and T₂ are the dipole matrix element, electric field amplitude, population lifetime and dephasing decay time, respectively

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The value of the above modeling exercise is three-fold. First is a better understanding of the mechanisms giving rise to single-mode lasing. According to the multimode laser model, single-mode lasing depends on two factors: (1) suppression of modes (e.g. transverse modes) close to the single lasing mode via mode competition, and (2) absence of net gain in the further lying modes because of large longitudinal mode spacing and finite gain bandwidth. The second purpose of the model is to determine the laser parameters necessary for using the multimode laser model to design future lasers. Most important is the determination of the mode-coupling parameter [11], C≡θ_nmθ_mn/(β_nβ_m), which is extremely difficult to obtain from first-principles because of complicated many-body correlation effects. Theory/experiment comparisons with different length nanowire lasers gives 0.7 < C < 1.0, putting the GaN active medium in the upper end of the weak-coupling regime. Consequently, suppression of side modes comes entirely from the effective net gain α_n-θ_nmα_m/β_m<0 [8] which gives rise to the condition of longitudinal mode space > 10 meV and Γ_T/ Γ_L < 0.9 for single-mode lasing, where Γ_T and Γ_L are transverse and longitudinal mode confinement factors, respectively. Further study is necessary to confirm these conditions. The third value of the modeling is to provide information on the laser gain and carrier density achieved in our experiments. We estimated material gain and carrier density created under optical pumping to be ≈5.8 × 10³ cm⁻¹ and 1.4 × 10¹⁹ cm⁻³, respectively, which are appreciably higher than found in conventional lasers and is evidence for high material quality.

5. Conclusion

We have demonstrated stable, single-frequency output from single, as fabricated nanowire lasers operating far above lasing threshold. Each laser consists of a linear, double-facet GaN nanowire functioning as gain medium and optical resonator. A single-mode linewidth of ~0.12 nm and >18dB side-mode suppression ratio are measured. Crucial to achieving single-mode lasing is reducing the number of cavity modes within the gain bandwidth. This requires significant reduction and precise control of nanowire dimensions, as well as high material gain necessary to compensate for the reduced gain length. These challenges are met using a top-down technique that exploits a tunable dry etch plus anisotropic wet etch. Numerical simulations based on a multimode laser theory indicate that single-mode lasing arises from strong mode competition and narrow gain bandwidth.