Mode Switching and Filtering in Nanowire Lasers - Nano Letters (ACS

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Mode switching and filtering in nanowire lasers Robert Röder, Themistoklis P.H. Sidiropoulos, Robert Buschlinger, Max Riediger, Ulf Peschel, Rupert F Oulton, and Carsten Ronning Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b00811 • Publication Date (Web): 23 Mar 2016 Downloaded from http://pubs.acs.org on March 24, 2016

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Mode switching and filtering in nanowire lasers Robert Röder,1,*,# Themistoklis P.H. Sidiropoulos,2,* Robert Buschlinger,3,* Max Riediger,1 Ulf Peschel,3 Rupert F. Oulton,2 Carsten Ronning1,# 1

Friedrich-Schiller-University Jena, Institute of Solid State Physics, Max-Wien-Platz 1, 07743 Jena, Germany 2 Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2BZ London, United Kingdom 3 Friedrich Schiller University Jena, Institute of Condensed Matter Theory and Solid State Optics, Max-Wien-Platz 1, 07743 Jena, Germany * These authors contributed equally to this work # Corresponding authors

Coherent light sources confining the light below the vacuum wavelength barrier will drive future concepts of nano-sensing, nano-spectroscopy and photonic circuits. Here, we directly image the angular emission of such a light source based on single semiconductor nanowire lasers. It is confirmed that the lasing switches from the fundamental mode in a thin ZnO nanowire to an admixture of several transverse modes in thicker nanowires approximately at the multimode cutoff. The mode competition with higher order modes substantially slows down the laser dynamics. We show that efficient photonic mode filtering in tapered nanowires selects the desired fundamental mode for lasing with improved performance including power, efficiency and directionality important for an optimal coupling between adjacent nanophotonic waveguides. Keywords: Nanowire laser, semiconductor nanowire, far-field characterization, transverse mode, laser emission, numerical simulation TOC:

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The growing demand for faster communications and the inherent limitations of electronic integrated circuits [1] have stimulated research into nanophotonics. In particular semiconductor nanowires (NWs) have received considerable attention due to their nearperfect material quality making them exceptional photodetectors [2, 3], waveguides [4], and connectors between electronic and nanophotonic elements [5]. The demonstration of laser emission from single nanowires [6, 7, 8] with wavelength tunability [9, 10], ultrafast modulation [11, 12] and integration on silicon [13] suggest their viability as on-chip nanoscale coherent light sources [14]. Despite this progress, we urgently require a better understanding and control over the optical modes of these lasers to exploit them as nanophotonic light sources; e.g. isolating the fundamental transverse mode of a nanowire laser would be crucial to efficient coupling between nanophotonic components. In this article we demonstrate transverse mode selection in nanowire lasers verified by directly imaging ‘head-on’ their far field emission. We find that the fundamental transverse mode dominates laser emission in thin nanowires, despite being thought impossible at room temperature [15]. In contrast thick nanowires lase in multiple transverse modes dominated by an azimuthally polarized mode profile. The discovery of ultrafast switching between laser modes near a critical nanowire thickness supports our mode competition interpretation. With this insight, we demonstrate mode filtering in a tapered nanowire to guarantee lasing of the fundamental transverse mode. In this combinatory study, we use three recently developed experimental and theoretical techniques to assess both the transverse modes and the dynamics of individual ZnO NW lasers as a function of diameter. While it is relatively straightforward to control the number of longitudinal Fabry-Pérot (FP) laser modes by the nanowire length or distributed feedback, for example, the selection of specific transverse modes is more challenging as these are determined by the nanowire cross-section [16], which is difficult to modify post-growth. Moreover, we apply suitable experimental methods to directly image which transverse modes operate in single nanolasers and determine their influence over laser dynamics within the semiconductor material. Zinc oxide (ZnO) NWs generate robust ultra violet laser emission at room temperature due to their high optical gain supplied by the formation of an electron-hole plasma [17, 18, 15, 19]. Here, the intensity of laser emission from individual ZnO NWs with diameters below and above single mode cut-off of ~ 180 nm is sampled using a back-focal plane polarization imaging technique, as schematically shown in Figure 1a (and Supplementary Information figure S1a; this technique is usually applied to NW arrays in spontaneous emission regime [20, 21]). Although fundamental mode lasing was believed to be hardly possible in ZnO NWs thinner than ~ 180 nm due insufficient modal-gain and feedback at room temperature [15], we observe a transverse mode switching from the dominant TE01 mode to the fundamental HE11 mode near this cut-off condition (for field plots of the basic modes see the Supplementary Information). This observation is combined with an ultrafast time domain study that reveals mode competition at the onset of lasing in multi-transverse mode NWs > 180 nm. These findings broadly agree with an integrated finite-difference-time-domain (FDTD) and semiconductor Bloch equation model [22]. These studies allow us not only to expose the gain dynamics of these devices at the picosecond scale, but also to identify how the higher order modes successfully compete and win gain


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from the fundamental mode. Remarkably, the output pulse width and absorption recovery time of ZnO NW lasers increase abruptly between 180 and 200 nm corroborating the mode switching. Starting from this new insight, we predict single mode operation along with enhanced laser performance using a tapered NW, confirming the potential of NWs as transverse mode filters to select the desired laser mode in these devices (Fig. 1a).

Figure 1 | Calculated transverse nanowire modes and far field pattern of single nanowires. a, Calculated electric field distribution, polarization and far field patterns of the HE11b mode for a 140 nm diameter ZnO nanowire (left) and the TE01 mode for a 300 nm diameter ZnO nanowire (middle), respectively. The output pulse width changes from ~ 5 ps with an electric field polarization along the NW (green) in thin NWs to ~ 15 ps with a polarization perpendicular to the NW axis in thick NWs (orange). Tapered NW structure starting with a diameter well in the multimode regime and ending in the single-mode regime for efficient mode filtering shows single mode operation with superior emission properties compared to thin NWs. The refractive index n of ZnO was set to ~ 2.1 like in a highly excited ZnO according to [23]. b, Scanning electron microscopy (SEM) image of a ZnO nanowire ensemble with typical diameters between 130 – 300 nm and length of few µm.

Zinc oxide NWs (Fig. 1b) were grown by vapor transport [24] and transferred onto the edge of a dielectric substrate by a modified dry imprint technique (Supplementary Information figure S1b). In this way a single NW rests only partially on the substrate and one NW end is suspended in air. The conventional confocal measurement geometry used throughout the literature (Supplementary Information figure S2) prevents direct access to the emission from the end facet and thus obscures the polarization and angular distribution of the laser mode in the far field. Here, we overcome this problem using a ‘head-on’ measurement setup [25] (Supplementary Information figure S1a), where we can directly collect the laser emission from the end facet of a single optically excited ZnO NW. Thus, we directly identify the transverse laser mode in the angular range determined by the numerical aperture (NA) of the objective without the need for e.g. the interference of FP-modes between the two end facets and additional numerical simulations [26, 27]. Furthermore, the technique is


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capable to directly image the laser mode distribution and allows us to angularly resolve its Stokes parameters S0 – S3 [28].

Figure 2 | Angle resolved nanowire laser emission. a, Angular resolved polarized laser emission of a thin ~ 140-150 nm diameter ZnO NW emitting in the fundamental HE11 mode. The pump power was set to ~ 3x the laser threshold. b, Far field pattern of the HE11 mode calculated for a respective thin ZnO NW with circular cross section. Simulated and measured far field pattern qualitatively coincide as indicated also by the linescans (blue in a and red in b) shown in c. d, Angular resolved laser emission of a thick 300 nm diameter ZnO NW. e, Polarized part of the angular resolved laser emission shown in d using the Stokes parameters. f Vertically polarized part of the angular resolved laser emission using a linear polarizer. All plots are normalized to their maximum.

Firstly, we investigated a thin ZnO NW below the single mode cut-off with a diameter at its thinnest of ~ 140-150 nm (see Supplementary Information figure S3). Optical pumping was applied at 355 nm with 10 ns pulses at a 100 Hz repetition rate and a linear pump beam polarization perpendicular to the NW axis. The evolution of the emission spectra accompanied by the power dependence followed a multimode laser model fit (see Supplementary Information figure S4), unambiguously proving laser oscillations in this particular ZnO NW. Figure 2a shows the angularly resolved distribution of the intensity of the fully polarized part of the laser emission of the thin ZnO NW derived from the

superposition of the Stokes parameters S1 – S3 as . This emission pattern arises from the operating dominant transverse laser mode exhibiting the highest emission intensity at the center with an isotropic decrease towards higher emission angles. The obtained Fourier plane image coincides qualitatively well with the simulated far field


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emission of the fundamental HE11 mode propagating within either a circular or hexagonal (see Supplementary Information figure S5) ZnO NW of that thickness, see Fig. 2b. Thus, the occurrence of the fundamental HE11 mode lasing in this thin ZnO NW with a diameter below the single mode cut-off is clearly proven. Also the linescan along a polar angle of 0° in Fig. 2c almost perfectly matches the theoretical predictions. The Fourier image acquisition averages over ~ 1000 excitation pulses with each pulse being a single 10 ns experiment (without time resolution). The measured far field pattern is reproducible and furthermore independent of the polarization of the optical pump beam (see Supplementary Information figure S6). The emission of this particular NW laser reveals a rather low degree of polarization / with a value of ~ 50 – 70 % (see Supplementary Information figure S7). This is an indication of variations of the polarization state either during one pulsed excitation or between different shots possibly leading to an incoherent superposition of the respective Stokes parameters of differently polarized HE11 modes and therefore a reduced P value. Next, we investigated a thick ZnO NW laser with about twice the diameter of the preceding one (d ~ 280 – 360 nm; Supplementary Information figure S3). The mode calculation (Supplementary Information figure S8) suggests that this NW allows for efficient multimode waveguiding of up to at least 6 modes. Again, the power output dependence with pump intensity for this NW proves laser action (Supplementary Information figure S4). However, the angular distribution of the total NW laser emission in Fig. 2d is clearly distinct from that of the Fourier image of the thin NW. Weak emission at the center that decreases towards emission angles of ± 15 – 20° is surrounded by an intense emission annulus at angles of ~ 30°. An emission annulus is completely absent for the thin wire. Furthermore, out of the transverse modes available in a 300 nm diameter NW, only the fundamental HE11 emits along the NW axis with the most intense emission angle of 0° (see Supplementary Information figure S9). These observations suggest that the total emission for this thicker NW laser is an admixture of several transverse modes with contributions from the HE11 and a higher-order mode with an annular distribution at ~ 30°. Figure 2e shows the measured polarized part of the emission of the thick NW with a minimum in the center and the highest intensity emitted at around 30°. The vertically polarized emission pattern in Fig. 2f as well as the Fourier images of the Stokes parameter S1,2 (Supplementary Information figure S10) reveal that this emission annulus is azimuthally polarized, which is consistent with the polarization of the TE01 mode (see Fig. 1). Thus, the laser emission from the thick nanowire appears to be an admixture of the TE01 mode with a small contribution of the HE11 mode, similar to theoretical results obtained for CdS nanowires [22]. Note, that the emission pattern of both NWs is nearly homogeneous below the laser threshold, because the spontaneous luminescence is emitted isotropically. The experimentally observed diameter dependent single/multimode operation is corroborated using a recently developed numerical simulation method combining both finite-difference-time-domain (FDTD) and Semiconductor Bloch Equations [22]. The algorithm takes into account spontaneous and stimulated emission into account and has already been adapted to II-VI semiconductor nanowires, so that it is easily applied to the ZnO material system by using appropriate material parameters. We have simulated wires


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with a circular cross-section and a length of l = 9 μm (see figure 3), which fits well to the experimentally investigated nanowire lasers. Firstly, we consider a thin nanowire with a diameter of d = 140 nm (Fig. 3a,b), which should only support the fundamental transverse HE11 mode. Indeed, we clearly observe lasing of the fundamental mode (Fig. 3b), but find that the polarization orientation of the HE11 mode varies, when the numerical experiment is repeated several times. This coincides nicely with our experimental observation of a rather low degree of polarization for the thin NW, which is caused by the sensitivity to the initial conditions at the onset of lasing. To support our expectations of multimode lasing at higher diameters, we subsequently simulate a NW with d = 220 nm (Fig. 3c,d), which is closer to the critical diameter for the transition from single to multimode lasing as seen in our experiments. We now observe a temporally and spatially varying transverse field profile, which is dominated by the TE01 mode. Thus, the simulation results are in good agreement with both experimental results and the predictions from quasi-static calculations. Additionally, we obtain an admixture of the HE11 mode similar to the measured far field of the thick NW device (compare Fig. 2d), which leads to a crescent-shaped intensity profile as shown in Fig. 3d; a consequence of the interference of the two transverse modes.

Figure 3 | Intensity distributions within nanowire lasers. Temporal snapshots of the normalized electromagnetic field strength |E|2 inside different ZnO nanowire lasers as calculated by FDTD simulations with a material model supplied by the Semiconductor Bloch Equations. The panels in the top row show a single-mode NW with thickness d = 140nm (green), the middle row shows a multimode wire with d = 220nm (orange). Panels a and c show longitudinal cross sections, while b and d show transverse field profiles. Panels e and f show the longitudinal cross section and the transverse field profile, respectively, of the optimized nanowire laser with a tailored geometry with a diameter starting in the multimode regime (dmax = 220 nm) and ending in the single-mode regime (dmin = 120 nm).


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In macroscopic laser systems multimode operation usually leads to significantly changed laser dynamics [29, 30], which recently has also been predicted to hold in nanoscale laser systems [31, 32]. Here, we characterize the dynamics of several NW lasers in the confocal geometry (Supplementary Information figure S2) using a recently introduced ultrafast double-pump technique, which is capable of resolving the ultrafast picosecond scale laser dynamics (Supplementary information and Methods) [12].

Figure 4 | Diameter dependent temporal lasing characteristics. a, Normalised change in the laser emission ΔP/P0 when excited with two pulses separated by a time τ with respect to the excitation with a single strong pulse. The three panels show the double-pump response for nanowires with diameters of ~ 151 nm (green), 210 nm, and 281 nm (orange), respectively. For each nanowire the vertical black line indicates the time delay of the maximum double-pump response . b, Absorption recovery time versus the nanowire diameter. The orientation of the arrow symbols indicates the dominant laser output polarisation with respect to the nanowire axis. The two horizontal lines show the average for nanowires with diameters below (green; ~ 5 ps) and above 200 nm (orange; ~ 17 ps).

We compare the double-pump response of three selected nanowires with diameters of ~ 151 nm, 210 nm, and 281 nm, displayed in Fig. 4a. In these experiments, an ultrafast pump pulse (twice the laser threshold) induces laser action and a weaker second pump pulse (0.2 times the threshold) of the same energy probes the state of the laser. At negative time delays, τ, the weaker pump pulse arrives first. In this case the double-pump response is indicative of the spontaneous emission lifetime, hence the nearly diameter independent decay response for all three devices. Conversely, for positive the double-pump response becomes sensitive to the laser dynamics as the weak pulse follows the strong pulse, which induces laser action. Clear differences between the devices become apparent, as shown in Fig. 4a. In particular, the time when the double-pump signal approaches its maximum, !" , is related to the absorption recovery of the nanowire [12]. This can be understood by the fact that excited carriers must be depleted from energy levels excited by the pump before the second pump pulse can be maximally absorbed. The significant variations of !" between thin and thick NWs suggest not only differences in the response times of the various transverse modes, but also their competition. The thinnest ~ 151 nm diameter nanowire reaches !" at a delay of ~ 6 ps and shows the fastest overall response. Since this can be interpreted as the time taken for the carrier inversion to deplete sufficiently to allow absorption of the second pump pulse, tmax also indicates the laser output pulse duration. In contrast, the thicker nanowires show more complicated time-integrated responses exhibiting two maxima indicating a clear change in


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the lasers’ operation. For the ~ 210 nm diameter NW, an initial maximum at ~ 1.5 ps decays rapidly only to revive into a secondary maximum at ~ 14 ps. The thickest ~ 281 nm diameter nanowire also shows two !" with a first maximum at ~ 3 ps and a second at ~ 20 ps. In the larger two NWs, as the second pulse cannot be absorbed maximally until much larger time delays, τ, a mode with a longer cavity lifetime is successfully competing for the available gain within the nanowire. We conclude that the strong second peak of the thickest ~ 281 nm wide NW laser implies the laser emission is dominated by the higher quality cavity mode. The dependence of !" on the nanowire diameter is highlighted in Fig. 4b. Note that for devices with two maxima only the slower and more dominant one is plotted. On average, devices with diameters thinner than ≤ 200nm show ̅ !" ~ 6 ps, which is faster than thicker devices exhibiting a ̅ !" ~ 16 ps, on average. In general, the change in the laser dynamics from single to double maxima response is accompanied by a change in the laser output polarization. This is indicated in Fig. 4b by the orientation of the data symbols. Note that only polarization components parallel and perpendicular to the nanowire axis can be distinguished in the confocal geometry, in contrast to the head-on measurements above. The evaluated Stokes parameters from the head-on measurements showed that the TE01 mode has a large azimuthal electric field component, corresponding to a strong transverse polarization component perpendicular to the nanowire axis in the confocal measurement geometry (oscillating electric field in y-direction (orange) in Fig. 1). Conversely, the HE11 modes have the largest field component in longitudinal direction parallel to the nanowire axis and parallel to the substrate surface (oscillating electric field in z-direction (green) in Fig. 1). Here, the change from a parallel laser output polarization to a perpendicular polarization at diameters around 200 nm is indicative of the switching from the HE11 mode to a dominating TE01 mode for larger diameters. The change in the laser dynamics and the output polarization further confirm the change of the operating laser mode, as observed in the head-on measurements. Yet, in the case of the double-pump response, it is not immediately apparent which of the two operating modes shows the faster dynamics, but one would intuitively assign the fast component to the HE11 and the slow one to TE01 due to the given results above. This is also consistent with the expected higher feedback of the dominant TE01 mode [15], which would thus have a slower dynamical response time. Nevertheless, the critical nanowire diameter of about 200 nm is in good agreement with the mode calculations (see Supplementary Information figure S8). The experimental and theoretical results presented here reveal the trade-offs in choosing the NW laser device diameter. While thin NWs operating in the fundamental mode benefit from a defined emission profile and the fastest response times due to single transverse mode operation, they suffer from low emission intensity due to the smaller device volume. In contrast, thicker NW lasers unfortunately exhibit multimode operation leading e.g. to a less directional emission and a slower dynamic response. However, the NW morphology is adjustable to optimize optical properties, e.g. emission [33] and absorption [34]. Therefore, we explored here the possibility of the hybrid situation of a waveguide taper. We carefully selected the geometric properties of a NW starting with a diameter well in the multimode regime (dmax = 220 nm) and ending in the single-mode regime (dmin = 120 nm), as shown in Fig. 3e. Theoretically, the NW should effectively filter out undesirable high order modes.


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Indeed, experimentally grown ZnO nanowires are frequently tapered and can thus provide such morphologies [35]. Note that the thin ZnO NW already exhibits such a tapered morphology (see Supplementary information figure S3). As Figs. 3e,f show, in its thinner regions the NW exclusively supports a single mode enforcing a transverse mode profile that is strongly dominated by the fundamental mode (Fig. 3f). These results clearly indicate that by careful selection of the geometric properties it is possible to adjust NW lasers to have higher emission intensity caused by the larger volume of a thick wire with the more defined emission characteristics of a thin, single-mode wire. Indeed, on average our numerical experiments show that the tapered NW laser emits 90 % of the power radiated by the thick NW, while the percentage emitted by the homogeneously thin wire only amounts to about 70 %. In conclusion, Fourier imaging of the angular emission unambiguously proves single transverse mode lasing of the fundamental HE11 mode in a thin ZnO NW with a diameter below the cutoff of the TE01 mode, even though the feedback of the TE01 mode was previously expected to be crucial for NW laser oscillations at room temperature [15, 25]. The respective short laser pulses are in the range of 5 ps demonstrating extremely fast modulation capabilities of the lasers. At the transition diameter from single- to multi-mode waveguiding, we observed that the absorption recovery time increases abruptly, accompanied by a change in output polarization corresponding to a switching in transverse modes. Lasing in thick multimode ZnO NWs beyond ~ 200 nm diameters is then dominated by the TE01 mode with a strong admixture of the fundamental HE11 mode, as indicated by the angular emission pattern as well as by dynamical simulations. Tapered NWs are an effective method to create the bright and efficient laser operation of a thick nanowire while selecting only the fundamental transverse mode for laser action.

Methods. Dynamical simulations. Full time-domain calculations were done using the FDTD and Semiconductor Bloch Equations approach developed in [22]. In order to model ZnO, appropriate material parameters have to be chosen. We mostly used parameters from [23], where the permittivity of ZnO at different excitation densities was calculated with a BetheSalpeter approach and compared to experiments. We obtain a static permittivity εdc = 6.56, electron and hole masses meff,e = 0.28 me and meff,a/b = 0.59 me and bandgap energies Egap,a = 3372 meV and Egap,b = 3382 meV. We also use the formulation of the Coulomb-Hole-SelfShift used in [23]. Since the Semiconductor Bloch Equations approach includes different approximations than the one used in [23], some of the parameters had to be adjusted in order to obtain consistency. We use a dipole matrix element d0 = 0.42nm × e and an excitation dependent dephasing γ(N) = - γ0 + γaN0.3

(1)

with the parameters γ0 = 30 ps-1 and γa = 2e - 5cm/ps. Typical values for relaxation and recombination times are γf,e = 1012s-1, γf,h = 1013s-1 and γrec = 109s-1.


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In order to correctly describe the coupling of different field components to the semiconductor material, we use the 3-band model appropriate for 2-6 semiconductors as described in [22]. The model includes a single electron occupation probability ne and separate hole occupation probabilities na/b for the two relevant valence bands. In the beginning of the simulations, the quasi-particle occupation probabilities ne and na/b were initialized with quasi-fermi distributions for T = 300K at quasi-particle densities Ne = 3 × 1019cm-3 for electrons and Nh,a/b = 1.5 × 1019cm-3 for holes in both valence bands.

Sample preparation. The ZnO NWs were synthesized using a thermal transport technique within a horizontal tube furnace. The source material consisting of a mixture of ZnO and carbon (molar ratio 1:1) powder within an alumina boat was evaporated at 1050°C and transported downstream by argon carrier gas towards the Si growth substrate with a 500 nm layer of sputtered Al doped ZnO on top. The pressure within the tube during growth is usually kept between 10 – 100 mbar resulting in ZnO NW batches with NW diameters between 100 – 400 nm and NW length of several µm. Single ZnO NWs were subsequently transferred either onto low refractive index substrates consisting of SiO2 (n ~ 1.4) for the double-pump measurement or onto the edge of CaF2 single crystals (n ~ 1.4) for the ‘headon’ measurements.

Optical setup. The optical wavelength for the lasing experiments was always set to 355 nm. The optical setup for the double-pump measurement to assess the temporal lasing dynamics is explained in detail in [12] and in the supporting information. The ‘head-on’ setup is explained in more detail in [25]. Here, it was additionally equipped with a lens to image the back focal plane of the objective (100×, NA = 0.9, Zeiss epiplanneofluar pol). The excitation spot was adjusted to exhibit a diameter of ~ 40 µm.

Supporting Information. Supporting information including schematics of the ‘head-on’ setup, double-pump setup, sample preparation, SEM images and laser characteristic of ZnO NWs, calculated mode distributions and the respective far-field patterns, measured far-field patterns for excitations of different polarization, measured degree of polarization and Stokes parameters with angular resolution and simulated double-pump responses.

Acknowledgments. We gratefully acknowledge funding by the German Research Society (DFG) within the project FOR1616.

Corresponding authors. E-mail: [email protected] and [email protected]

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Author contributions. M.R. and R.R. carried out the nanowire growth and the ‘head-on’ measurements; the double-pump experiments were conducted by T.P.H.S., the dynamical simulations were performed by R.B.; results were discussed and interpreted by all authors; the manuscript was written by R.R. and T.P.H.S. with feedback from all co-authors.

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