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Controlling Disorder by Electric Field Directed Reconfiguration of Nanowires to Tune Random Lasing Philip P Donahue, Chenji Zhang, Nicholas Nye, Jennifer Miller, Cheng-Yu Wang, Rong Tang, Demetrios Christodoulides, Christine D. Keating, and Zhiwen Liu ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b03829 • Publication Date (Web): 27 Jun 2018 Downloaded from http://pubs.acs.org on June 27, 2018

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ACS Nano

Controlling Disorder by Electric Field Directed Reconfiguration of Nanowires to Tune Random Lasing

Philip P. Donahue1,3, Chenji Zhang1, 2, Nicholas Nye5, Jennifer Miller3, Cheng-Yu Wang2, Rong Tang2, Demetrios Christodoulides5*, Christine D. Keating3* and Zhiwen Liu2,4* 1

These authors contributed equally

Departments of 2Electrical Engineering and 3Chemistry, and the 4Materials Research Institute, Pennsylvania State University, University Park, PA 16802 5

CREOL, The College of Optics & Photonics, University of Central Florida, Orlando, Florida

32816, USA * corresponding authors: [email protected]; [email protected]; [email protected]

Abstract

Top-down fabrication is commonly used to provide positioning control of optical structures; yet, it places stringent limitations on component materials and oftentimes, dynamic reconfigurability is challenging to realize. Here we present a reconfigurable nanoparticle platform that can

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integrate heterogeneous particle assembly of different shapes, sizes, and chemical compositions. We demonstrate dynamic control of disorder in this platform and use it to tune random laser emission characteristics for a suspension of titanium dioxide nanowires in a dye solution. Using an alternating current electric field, we control the nanowire orientation to dynamically engineer the collective scattering of the sample. Our theoretical model indicates that a change of up to 22% in scattering coefficient can be achieved for the experimentally determined nanowire length distribution upon alignment. Dependence of light confinement on anisotropic particle alignment provides a means to reversibly tune random laser characteristics; a nearly 20-fold increase in lasing intensity was observed with aligned particle orientation. We illustrate the generality of the approach by demonstrating enhanced lasing for aligned nanowires of other materials including gold, mixed gold/dielectric and vanadium oxide (VxOy).

Keywords: self assembly, nanoparticle, reconfigurable, disorder, random lasers

Control of the organization of micro- or nano-structures plays an essential role in manipulating light propagation, which is the basis of a wide variety of photonic metamaterials.1-3 For instance, a periodic arrangement can result in a photonic bandgap within which no propagating mode exists,4 while in structures of increasing disorder light propagation can transition from the diffusion regime to the Anderson localization regime.5 Fabrication of nanostructure components and accurate control of their relative positions are commonly achieved by top-down approaches. Unfortunately, optical materials created by such top-down methods typically suffer by being expensive to fabricate, and exhibiting non-tunable properties due to their constituent nanostructures having fixed positions on a substrate. These limitations present a significant


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barrier for realizing dynamically reconfigurable optical materials. Further, top-down approaches have inherent difficulties to incorporate a diverse variety of heterogeneous component materials, in particular, anisotropic nanomaterials with different sizes, shapes, chemical compositions, and optical functionalities. Nanoparticle anisotropy offers a number of appealing optical properties due to their anisotropic linear and nonlinear susceptibilities, which, for example, can result in differences in absorbance and scattering for light impinging on the particles in longitudinal vs. transverse orientations.6-9 Individual nanowires have also been used to serve as waveguides for subwavelength photonics or as tiny light sources,10-12 while nanowire collections can function as metamaterials, polarizers or scattering media for random lasing.6,7,9,13,14 By integrating reconfigurable particle assemblies15 into photonic platforms, control over the optical response of the system can be achieved.16-22 For example, applied electric fields have been used to control orientation of anisotropic nanoparticles or liquid crystals, generating reconfigurable polarizers.17,23 Less explored, the incorporation of particle anisotropy in a medium with gain should also enable control over the interplay of light amplification, absorption, and scattering, thus providing a means for creating dynamic, active optical materials and devices. We present a reconfigurable nanoparticle platform that can incorporate anisotropic nanomaterials of diverse sizes and shapes to overcome the fundamental limitations of the topdown approaches. This is accomplished by manipulating collective anisotropy within particle systems through electric field driven assembly. Random lasing arrangements present exemplary models in order to demonstrate how complex optical phenomena can be dynamically controlled via the general approach of high aspect ratio particle assembly; herein we present a reconfigurable active material system based on scatterer orientation, and propose the underlying mechanism for the observed response. Specifically, we demonstrate control over disorder by


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electric field directed reconfiguration of TiO2 nanowires suspended in gain medium. Alternating current (AC) electric field driven alignment of these anisotropic scatterers was used to tune random laser emission in real time (Figure 1). We also show that this approach is general by demonstrating it using other anisotropic materials including solid metallic and metal oxide nanowires as well as composite metal/dielectric particles. Results/Discussion Nanowire-based random lasing Random lasing arises from the confinement of light within disordered gain media leading to mirrorless laser emission.24 Potential applications of random lasing include speckle free imaging, data encryption, and biosensing.25-28 A common variety of random laser is comprised of nanoparticles suspended in fluorescent dye solution, acting as random scatterers and gain medium respectively.29 Light is confined via multiple scatterings within the particle matrix and is amplified by the gain medium (Figure 1b). At sufficiently high scattering strengths and above a certain pump pulse threshold energy, random lasing emission occurs atop the fluorescence background. A representative random lasing spectrum for a sample of TiO2 nanowires (Figure 1c) suspended in a rhodamine B solution is shown in Figure 1d. Sharp emission peaks can be seen, corresponding to multiple lasing modes. The uneven spacing between these peaks is a characteristic of random lasers, and can be further represented by the field autocorrelation curve, which is the Fourier transform of the emission spectrum, as a function of the effective cavity lengths (Figure 1e).


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Figure 1: Nanowire based random lasing. Illustrations of conventional and nanowire based random laser, TEM of particles used in experiments, and representative experimental random lasing spectrum and analysis. (a) Depiction of lasing buildup in a conventional Fabry Perot laser cavity. (b) Depiction of random lasing in nanowire suspension assembly in dye solution. (c) Representative TEM images of individual TiO2 nanowires. (d) Experimental random lasing spectra produced by a TiO2 nanowire suspension (4.37 × 107 wires/mL) in rB EG dye solution (2 mM). (e) Field autocorrelation curve (Fourier transform of the emission spectrum depicted in (d)) and (inset) effective mode cavity lengths indicating random lasing. Orientation-dependent scattering Random laser emission characteristics have been shown to vary according to not only the number density30,31 but also the shape of scattering features.32-34 For anisotropic scatterers, the orientation with respect to impinging light can be expected to impact scattering strength. For example, light that is incident parallel to a nanowire’s long axis may experience a different


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scattering cross section compared to light incident perpendicularly to the long axis. Hence, the rotation angle of an anisotropic particle will influence its scattering interactions. We performed numerical calculations of the scattering cross section of an individual nanowire to validate this hypothesis (Supplementary Text). The simulation results in Figure 2a,c reveal that for light parallel to the long axis of the nanowires, little angular scattering is observed in both the nearand far-field diagrams. The resonances observed are attributed to the excitation of the fundamental mode along the wire. This arrangement can be considered as a cylindrical guiding structure

(core:

TiO2,

cladding:

ethylene

glycol),

with

V-number

equal

to

! = 𝜋𝐷 𝑛!!"!! − 𝑛!" 𝜆! ≈ 2.1. The latter implies single mode operation, while finite element

calculations indicate a respective effective index of 𝑛!"" = 1.8. The nanowire acts like a cavity with resonances being 𝛥𝑧 = 𝜆! 2𝑛!"" = 160 nm apart, which is verified in Figure 2a. On the other hand, light incident perpendicular to the wire’s long axis shows a larger deviation from its original propagation direction both in the near and far field, including a strong backscattering component (Figure 2b,d). In this case, resonances can no longer be sustained, while the far-field diagram (Figure 2d) appears to be azimuthally asymmetric, owing to the large anisotropy between the longitudinal and transverse dimensions of the wire (𝐿/𝐷 = 7.2). Smaller contrast ratios will result in more symmetric radiation diagrams with reduced scattering and thus inferior lasing performance (Supplementary Text). The orientation-dependent scattering is supported experimentally in Figure 2e by the observed increase of the backscattered light intensity from a TiO2 wire suspension (illuminated with a xenon arc light source) under random and perpendicular aligned orientations. Due to the enhanced scattering of individual nanowires as shown in simulation, the overall backscattered intensity increased as a result of wire alignment.


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Each individual scatterer exhibits a strong angular scattering field component (Figure 2a-d). Such angular scattering can be significantly enhanced in a nanoparticle ensemble, if the nanowires have identical orientation, and can impact the laser emission directionality.35 A nanowire suspension aligned perpendicularly to the propagation direction will more strongly confine and amplify light, resulting in improved laser quality at reduced pump pulse threshold energy. Furthermore, if average nanowire orientation uniformity can be tailored within the assembly, the net scattering strength of the suspension can be tuned in order to optimize the lasing performance. In Supplementary Text, by treating the nanowire ensemble as a probalistic setting, we analytically show how the relative orientation (𝜃! , 𝜑! ) of the scatterers affects the peak scattering strength in the far-field. The optimum case appears when all the nanowires are parallely oriented (𝜃! = 0! ), resulting in improved lasing performance in active environments. Moreover, the randomness in the location of the individual nanoantennas is shown to mitigate the interference effects among the scatterers. As a result, the overall far-field diagrams can be readily deduced by studying the radiation characteristics from each individual nanowire. In the case of nonuniform distribution of wire lengths, the total scattering cross section can be retrieved by averaging over the wire ensemble.36,37


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Figure 2: Orientation-dependent scattering. Near- and far-field plots representing scattering direction and intensity from a single TiO2 nanowire of length 1.3 μm for incident circularly polarized 585 nm light: (a) near-field pattern with light incidence parallel to wire long axis, (b) near-field pattern with light incidence perpendicular to wire long axis, (c) far-field intensity pattern with light incidence parallel to wire long axis, (d) far-field intensity pattern with light incidence perpendicular to wire long axis. The first row (top) corresponds to near-field cross sections of field E. The second row (bottom) depicts a 3D perspective of the far-field intensity (|E|2). (e) Experimental backscattered light intensity from a TiO2 nanowire suspension under random and perpendicular aligned orientations. Due to the enhanced scattering of individual nanowires, the overall backscattered intensity increased as a result of wire alignment.

While anisotropic particles have been previously shown to impact lasing properties in random but fixed configurations, reconfigurable particle orientation has hitherto not been used as a tool to control the lasing emission characteristics. Tuning of random lasers has primarily been


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approached by techniques such as liquid crystal alignment, which generates local differences in refractive index to introduce scattering38-41 and spatial light modulation of pump beams, which used to manipulate the spatial distribution of gain in the lasing medium.42,43 In contrast, our approach is based on controlling the orientation of nanowires as anisotropic scatterers using an electric field, and thus provides opportunities to dynamically control a variety of parameters including both the scattering and gain landscapes. Alignment of nanowires in suspension is accomplished through a technique called electroorientation, in which an AC electric field is applied across the sample. The field induces the formation of a dipole along the long axis of the wires, which readily rotate in order to align their poles parallel to the field lines.44-47 A custom assembly cell was designed in order to facilitate this reversible assembly (Figure 3a, Supplementary Figure 1). Conductive indium tin oxide (ITO) cell walls connected to a function generator, generate the AC field across the random laser system (TiO2 wires suspended in 2 mM rB EG). The wires transition from random orientations (Figure 3b,d) to a uniform aligned state (Figure 3c,e) in response to the field (Supplementary Video). Decreasing the applied voltage returns the nanowires to a Brownian motion governed randomized orientation.


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Figure 3: Reconfigurable nanowire random laser system. Schematic, optical images, and alignment characteristics of tunable random laser nanowire suspensions. (a) 3D schematic representation of wire assembly cell depicting reversible wire alignment. ITO is separated by a 500 µm thick silicone spacer (not shown). Samples are pumped and emission is epi-collected by a 100× oil immersion objective. When no field is applied across the assembly gap, wires randomly orient via a Brownian motion mechanism (left). Application of an electric field (80 V/mm, 400 kHz) across the sample orients the wires parallel to the horizontal field lines (right). The transition between random and aligned orientation states is reversible. (b, c) Transmission bright field optical microscope images of TiO2 wires suspended in rB EG solution confined in an assembly cell under (b) unassembled and (c) assembled conditions. (d, e) Autocorrelation results indicating the random and aligned wire orientation character depicted in (b) and (c) respectively.

Reconfigurable random lasing To experimentally verify the impact of reconfigurable wire alignment on random lasing, we constructed a hybrid experimental setup, which enables simultaneous particle assembly, gain medium excitation, lasing emission analysis, and nanoparticle imaging (Supplementary Figure 1). A pulsed Nd:YAG laser (wavelength: 532 nm, repetition rate: 10 Hz, pulse width: 5 ns) is coupled into an inverted Nikon microscope. Samples are excited in a 60 µm diameter spot by a 100× oil immersion objective. Sample emission is then epi-collected and analyzed by an optical spectrometer. For low nanowire concentration (4.3×107 particles/mL) lasing is not observed at any applied pulse excitation energy due to insufficient scattering (particles in a random orientation state (Figure 4a). However, by applying the electric field the nanowires become


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aligned and lasing is observed at up to a 20-fold intensity increase, even at low pumping energies (Figure 4b). Figure 4c displays this response directly, presenting emission spectra collected from a single location of the device both before and after assembly. The fluorescence spectrum (black curve) corresponds to the initial unassembled state, while the spectrum in red shows the formation of lasing peaks owing to the wire alignment. This behavior is shown to be reversible, and is used to modulate light emission between fluorescence and lasing configurations (Figure 4d). Moreover, by aligning the scatterers such that their long axes are parallel to each other and perpendicular to the sample’s excitation/collection angle, we can significantly improve the random lasing performance. In agreement with simulation, maximizing the particle assembly’s anisotropic character can enhance the scattering strength, hence light confinement and lasing performance. This can be seen by the asymmetry in the radiation patterns of Figure 2, and is attributed to the light scattering characteristics of TiO2 wires. In order to quantify the collective effect of the nanowires from the scattering simulation results of single particles, the anisotropy factor 𝑔 is used, which provides a measure of the relative portion of scattering towards the forward/backward direction. To interpret the lasing emission characteristics of the TiO2 nanowire ensemble, the reduced ! scattered coefficient 𝜇!" ,

48-50

! defined as 𝜇!" = 1 − 𝑔 𝜇!" , where 𝜇!" represents the scattering

strength (𝜇!" = 𝑁!" 𝜎!" , 𝑁!" : concentration of scatterers, σsc : scattering cross section), is used to describe the diffusion of photons undergoing several scattering events. In order to better determine how nanoparticle anisotropy is impacting the switchable lasing ! response observed, we numerically calculate the coefficient 𝜇!" for different wire length

distributions of experimental samples (Supplementary Figure 2). In Figure 4e, the graphs of the effective scattering coefficients under random and aligned configurations are depicted. The


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scattering cross section for a nanowire without alignment, is estimated after averaging over different orientations (θc,φc) of the nanowire. Owing to the cylindrical symmetry of each nanowire, the elevation angle θc is varied in the interval [0 900], while φc is kept the same (assuming incidence radiation along z axis). Immediately prominent is that as wire length increases beyond 0.6 µm, 𝜇!! values show dependency on the assembly condition, while little change is observed for wires with smaller aspect ratios. The difference between unassembled and assembled reduced scattering coefficients (visualized by the shaded area between the plots), further confirms that wire alignment is the key factor influencing lasing configurability, showing a net improvement of nearly 20% when wires are aligned vs. random for this experimental sample. In our analysis the equivalent scattering cross section of the nanowire ensemble is evaluated as the weighted average of the scattering cross section (see derivations in Supporting Section S.2) based on the experimentally determined nanowire length distribution of our sample. Even as wire percent composition reduces to below 5 % of the total sample composition, for long wires the contrast in scattering coefficient remains impressively large.


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Figure 4: Reconfigurable lasing response. Emission spectra and calculated reduced scattering coefficients of randomly oriented nanowire/dye suspensions vs. horizontally assembled nanowire/dye suspensions. (a) Plot of emission spectra of randomly oriented nanowires as excitation energy is increased. (b) Spectra collected from the same sample at the same pumping energies while wires are aligned. (c) Spectra depicting assembly facilitated transition from florescence (black) to lasing (red). Both spectra were collected from the same location of a sample, before and after particle alignment respectively. The absorption cross section dominates the scattering cross section at the pump wavelength. As a result, the fluorescence background levels for aligned and unaligned wires are nearly identical. (d) All spectra shown are collected from a single sample of TiO2 wires (2.16 × 108 wires/mL) suspended in rB EG solution (2 mM). Each plot displays six spectra (initial conditions correspond to top spectra set) obtained from several sample locations. Wire alignment conditions were cycled between unassembled (black) to assembled (red). Ability to turn lasing on/off repeatedly shows robustness of the response. (e) Calculated reduced scattering coefficient plots (black line: randomly oriented wires, red line: wires aligned via applied field) dependent on the heterogeneous wire lengths of sample (blue bars). The shaded region between lines represents the increase in reduced scattering coefficient due to assembly.

The region of Figure 4e corresponding to wires of length shorter than 0.6 µm indicates that alignment of nanowires with short aspect ratios should have minimal impact on scattering coefficient or lasing quality. In order to verify the prominent role of the particle aspect ratio on the random lasing performance, an ensemble of nanowires with shorter lengths was investigated experimentally and numerically. Near- and far- field scattering simulations show that wires of that dimension lead to scattering largely insensitive to the angle of incident radiation


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(Supplementary Figure 3). Furthermore, experimentally observed emission spectra for the short wire suspension show no discernible change as a function of wire alignment (Supplementary Figure 3). The latter is also verified by the observation that respective reduced scattering coefficient plots are nearly identical for these shorter particles (Supplementary Figure 3). Overall, we can deduce that nanoscale material-light interactions can be manipulated through appropriate nanoparticle assembly schemes. By controlling the orientation of the nanowires through an externally applied AC electric field, the scattering cross section can be changed to optimize an optical response. In principle, this effect should be generally applicable to any anisotropic particle that can be oriented in the applied field. Generality of tunable lasing response with other anisotropic scatterers We studied several additional anisotropic particles to validate this generality. Figure 5 shows the reconfigurable lasing response for solid silver nanowires (3.35 ± 0.89 µm), metal/dielectric segmented particles that consist of 1 μm Au and 1 μm hollow (solvent-filled) segments, encased in a thin silica shell,51,52 and multiphase vanadium oxide nanowires that are heterogeneous in length (4.11 ± 3.71 µm). All of these particles could be oriented in the electric field, and all of them exhibited enhanced lasing when oriented with their long axes perpendicular to the light incidence. The metallic nanowires performed especially well, exhibiting the lowest pump energy threshold (2 μJ as compared with 6 μJ for similarly sized titania and multiphase vanadia wires). The strong improvement of lasing performance supplied by metallic wires is likely due to plasmonic effects, which has potential to be useful for many optical applications.53


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Figure 5: Ubiquity across material composition. (top) TEM images of different anisotropic nanomaterials and (bottom) respective assembly enabled random lasing response for particles suspended in 2 mM rB EG dye solution. (a) Bare silver nanowires synthesized by electrodeposition, (b) glass coated hybrid wire made of gold (dark region) and a solvent filled glass silica shell, (c) multiphase vanadium oxide nanowires, where different phases can be observed in different density regions. (d) Ag nanowire lasing response when (black plot) wires are randomly oriented and (red plot) aligned. (e) Lasing response for hybrid gold/silica wires shown in (b) before (black plot) and after (red plot) horizontal alignment of the wires via assembly. (f) Random lasing tuning behavior of VxOy wire assembly in unaligned (black plot) and aligned (red plot) states.

Conclusions These examples demonstrate the generality of the proposed nanoparticle platform to incorporate a diverse variety of anisotropic nano-materials, including segmented metal/dielectric


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particles and metal oxide phase-transition nanowires that are difficult to fabricate and assemble using conventional top-down approaches. Segmented metal/dielectric particles are highly customizable in design,51 making them candidates for complex reconfigurable ordered or disordered optical systems. Insulator-to-metal phase transitions in certain vanadium oxides (VO2) have been shown to be a powerful means to tune optical properties.54 Although this work focuses on the case study of controlling random lasers, we expect that the proposed nanoparticle optical architecture can incorporate heterogeneous materials of a wide range of optical functionalities, including gain, scattering, plasmonic resonance, and nonlinearity, and will thus enable similar reconfigurable optical responses in applications beyond random lasing, such as the realization of dynamic metamaterials in which the organization of nanostructures plays a key role in determining their optical properties. By introducing an “active” nanoparticle platform enabled with electric field directed assembly, which can exert control over the position and orientation of the constituent heterogeneous nano-materials at the single particle level, we provide a strategy for tuning light-matter interactions and hence the collective function of the nanoparticle ensemble.

Methods/Experimental Random laser suspension preparation and device fabrication: Random laser samples were prepared in 1.5 µL micro centrifuge tubes. Rhodamine B powder was weighed by microbalance and dissolved in EG to produce desired concentration dye solutions. TiO2 nanowire powder was weighed in the same fashion and suspended in dye solution by vortexing. Suspensions were then bath sonicated in brief pulses to disperse particle aggregates, or probe sonicated for 60 minutes as a means to reduce average nanowire length.55 A 600 W Misonix Sonicator S-4000 system


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with a titanium microtip was used to probe sonicate TiO2 wires in set time intervals to control wire length and reduce aggregation. The microtip pulsed at a 5 s on/3 s off interval; the amplitude was set to 25% power. Samples were placed in an ice bath to avoid heating of the sample. Random laser suspension concentrations were determined post sonication by hemocytometer and adjusted to desired concentration by dilution with additional dye solution. The heterogeneity of particle dimensions was characterized by transmission electron microscopy and recorded as histograms (Supplementary Figure 2). Supplementary Figure 1 shows images of sample cells constructed to perform nanowire assembly. ITO coated coverslips were separated by 500 µm thick silicone spacer material. Spacers were cut to size and shape to form wells for sample confinement during experiments such that 20 µL of solution fills the cell. Device walls were secured to the coverslip substrate by using a 90-degree support template and hot glue adhesive. Hybrid optical/assembly setup: In order to conduct reconfigurable random lasing experiments, a custom optical system was designed and built by integrating a 532 nm 5 ns 10 Hz Nd:YAG laser with a Nikon TE2000-U inverted microscope and a high-resolution optical spectrometer with a liquid nitrogen cooled CCD camera (Princeton Instruments, SpectraPro 2500i). Detailed setup is shown by Supplementary Figure 1. In general, the pump laser beam was coupled into the microscope’s side port enabling excitation of the sample assembly region through a 100× oil immersion objective. Resultant emission signal was epi-collected via the same objective and coupled out of the microscope. A power attenuator (formed by a half waveplate and a polarizing beam splitter (PBS)) was used to finely adjust the excitation pulse energy. In detail, the half waveplate rotates the input polarization of the laser beam, which changes the power ratio between the s polarized and the p polarized components. As the polarizing beam splitter only


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allows the p polarization light to pass through and reflects the s polarization light, we can control the power entering the system. For excitation spot size control, we utilized a convex and concave lens pair with 150 mm and 100 mm focal lengths respectively. In conjunction with a 100× objective, this allowed for an excitation spot size of 60 µm in diameter. Separation of the excitation beam and the emission signal was achieved by using a non-polarizing beam splitter followed by a 550 nm long pass filter. Random laser signal was finally coupled into a large core multimode fiber by a focusing lens and analyzed by the spectrometer. Data acquisition for random lasing experiments: Random laser samples were placed onto the microscope stage. Gold thread (Ametek Electronic Components) and silver adhesive (Electron Microscopy Sciences) were used to electrically connect ITO coverslips (8−12 Ω, SPI) to leads of a function generator. To perform experiments random laser suspensions were first loaded into custom assembly cells. Optimal AC field parameters for TiO2 wire alignment in rB EG solution were determined to be 80 V/mm and 0.4 MHz by optical microscopy based calibration experiments. Modulation between field “on” and “off” states was then applied in order to assemble and disassemble wire suspensions respectively. Single shot excitation and emission spectrum collection was performed via a custom shutter controlled serially by a computer as needed for each alignment condition throughout experiments. To prevent bleaching of dye in a local area and to ensure spectra collected were representative, the observed location was changed frequently within a sample. Three distinct locations were studied per set of experimental parameters. The respective spectra were collected and subsequently analyzed using WaveMetrics IGOR Pro and OriginPro for normalization of fluorescent backgrounds between comparable experiments. Experiments were generally performed within 30 min. of sample preparation to avoid changes in lasing response due to particle sedimentation.


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Fourier transform analysis of lasing emission spectra: The inherent randomness of the emission spectra from a random laser arrangement can be further demonstrated by applying the Fourier Transform (FT) analysis. Specifically, emission spectra are expressed as a function of the wavenumber (1/λ, λ is wavelength of the light); the field autocorrelation can then be obtained after performing the Fourier transform as follows. ∞

2π

∞

λ

G( x) = ∫ |E(

2

)| e

−j

2π

λ

x

d

2π

(3)

λ

Where G(x) is the field autocorrelation function. This means that every peak in G(x) corresponds to a length at which signals exhibit a high degree of coherence (in conventional Fabry Perot lasers G(x) is peaked at integer multiples of the cavity round trip length). Results of randomly spaced coherence lengths as opposed to evenly spaced ones are shown in Figure 1e confirm that lasing observed is supported by random particle assembly. Assembly image autocorrelation calculations: To quantify and visualize the degree of particle alignment, an image autocorrelation technique was applied. Images were run through a threshold and binarization process to remove background and clearly distinguish nanowires. The autocorrelation results shown in Figure 3d and e allow one to estimate the correlation distance of features in the original image. For the unassembled case, since the particles are oriented randomly, the correlation is isotropic in shape. On the other hand, the assembled particles exhibit uniform orientation along the horizontal direction in the image. Therefore, the autocorrelation function extends on the horizontal axis, indicating net wire alignment in this direction. The datasets generated during and/or analyzed during the current study are available from the corresponding authors on reasonable request.


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ASSOCIATED CONTENT Supporting Information containing additional figures illustrating the experimental setup, nanowire length distribution histograms, results for shorter nanowires (scattering simulations, orientation-dependent lasing, and reduced scattering coefficient/nanowire length histogram plot), and lasing emission for nanowire reorientation using a top/bottom electrode geometry. Supporting information also includes a video file displaying real time particle assembly and light response, as well as additional text and equations detailing the scattering simulations. This material is available free of charge via the Internet at http://pubs.acs.org. Acknowledgements: This work was funded by the Penn State MRSEC, Center for Nanoscale Science, under the award NSF DMR-1420620, with additional support to D. C. from the Qatar National Research Fund (QNRF, grant 9-020-1-006). J. R. M was supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1255832. N. S. N. acknowledges the support of the Alexander S. Onassis Public Benefit Foundation and the Foundation for Education and European Culture. References 1.

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