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Coherence characteristics of random lasing in a dye doped hybrid powder
Journal of Luminescence 169 (2016) 472–477
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Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Coherence characteristics of random lasing in a dye doped hybrid powder S. García-Revilla a,b, J. Fernández a,b,n, M. Barredo-Zuriarrain a, E. Pecoraro c,d, M.A. Arriandiaga e, I. Iparraguirre a, J. Azkargorta a, R. Balda a,b a
Departamento de Física Aplicada I, Escuela Superior de Ingeniería, Universidad del País Vasco UPV/EHU, Alda. Urquijo s/n, 48013, Bilbao, Spain Material Physics Center CSIC-UPV/EHU and Donostia International Physics Center, 20018, San Sebastián, Spain c Instituto de Telecomunicações, University of Aveiro, 3810-193, Aveiro, Portugal d Institute of Chemisty, São Paulo State University–UNESP, 14800-900, Araraquara, Brazil e Departamento de Física Aplicada II, Facultad de Ciencia y Tecnología, Universidad del País Vasco UPV/EHU, Apartado 644, Bilbao, Spain b
art ic l e i nf o
a b s t r a c t
Article history: Received 3 November 2014 Accepted 28 November 2014 Available online 8 December 2014
The photon statistics of the random laser emission of a Rhodamine B doped di-ureasil hybrid powder is investigated to evaluate its degree of coherence above threshold. Although the random laser emission is a weighted average of spatially uncorrelated radiation emitted at different positions in the sample, a spatial coherence control was achieved due to an improved detection configuration based on spatial filtering. By using this experimental approach, which also allows for fine mode discrimination and timeresolved analysis of uncoupled modes from mode competition, an area not larger than the expected coherence size of the random laser is probed. Once the spectral and temporal behavior of nonoverlapping modes is characterized, an assessment of the photon-number probability distribution and the resulting second-order correlation coefficient as a function of time delay and wavelength was performed. The outcome of our single photon counting measurements revealed a high degree of temporal coherence at the time of maximum pump intensity and at wavelengths around the Rhodamine B gain maximum. & 2015 Elsevier B.V. All rights reserved.
Keywords: Diffusive random lasers Photon statistics Coherence
1. Introduction Random lasing has developed into a sophisticated and exciting area of laser research which embraces a number of phenomena related to the emission of light by spatially inhomogeneous disordered materials: scattering, optical amplification, nonlinearity, and light localization. Analogous to traditional lasers, such random active media, the so-called random lasers (RLs), have a threshold where gain exceeds losses. Nevertheless, in these open sources of stimulated emission, multiple scattering provides feedback in place of a Fabry-Perot cavity. In fact, multiple scattering processes increase the dwell time of photons inside the material and allow enough amplification to compensate for absorption and light leakage through the boundaries creating gain saturation. Among RLs, those in which light undergoes diffusive motion within the gain media, presently known as diffusive random lasers (DRLs), are particularly attractive as the presence of strong modal interactions makes an analytical approach to the description of n Corresponding author at: Departamento de Física Aplicada I, Escuela Superior de Ingeniería, Universidad del País Vasco UPV/EHU, Alda. Urquijo s/n, 48013 Bilbao, Spain. Tel.: þ 34 946014044. E-mail address: [email protected] (J. Fernández).
http://dx.doi.org/10.1016/j.jlumin.2014.11.051 0022-2313/& 2015 Elsevier B.V. All rights reserved.
their multimode emission a very challenging task. Early theoretical treatments based on the diffusive approximation, were able to explain the overall narrowing of the emission spectra and the rapid increase of emission intensity at the frequency of maximum gain found in the pioneer RL experiments performed through a nonresonant feedback [1,2] in colloidal dye solutions [3]. Nevertheless, the spectral output of some DRLs contains, under certain conditions, multiple narrow spikes superimposed on the narrowed and featureless amplified spontaneous emission (ASE) band which have triggered a debate of different theoretical possible scenarios [4]. It is now broadly accepted that spikes can be attributed to randomly embedded localized spatial modes or modes of much larger spatial extension which can thus be more easily coupled from mode competition [5]. Depending on the material both may co-exist and provide a coherent RL mechanism. The presence of many spatially and spectrally overlapping modes in diffusive active systems gives rise to strong intermode couplings which determine their different statistical regime of fluctuations and spectral profiles [6]. In DRLs, complex nonlinear processes such as temporal oscillations [7,8] or spatial hole burning [9] may also appear. Türeci et al. recently proposed a theoretical framework based on the constant-flux (CF) states able to treat DRLs in the stationary regime [10–12]. Most experimental research on the RL response is
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performed under a quasi-stationary excitation condition (i.e. for a time much longer than the mode lifetime). By doing so, modes are continuously pumped and the intermode interaction enables one to reach a steady state. However, quasi-instantaneous excitation with a picosecond laser is required when exploring the behavior of such extremely leaky systems on the time scale. It is also remarkable that the experimental configuration critically affects the structure of the DRL emission spectra. Single-shot measurements, short-time pump pulse durations and tight focusing of pump light favor the observation of a spiky spectrum. When several emission shots are collected or long enough single excitation pulses are employed, the overlap between lasing spikes tends to average them into a smooth peak with an overall narrowing of the spectrum [4]. By controlling the shape of the pump, it is possible to incrementally excite larger numbers of spatially separated lasing modes, generating a reduction of the emission spectra spikiness with an increase of the intermode spectral correlation. This effect was accounted for by assuming a phase locking transition between modes [13]. On the other hand, only few studies have focused attention on the coherence in random lasing. Based on photon statistics [14–18], interferometry [19–22], double slit experiments [23] or speckle pattern measurements [24–26], the spatiotemporal coherence in random active media has been explored. Temporal coherence is a measure of the correlation of a light wave's phase along the direction of propagation. It tells us how monochromatic the source is, and it is quantified by its coherence time τC which can be roughly estimated by τC 1=Δν (Δν is the effective spectral width of the light). Attention can also be focused on the probability distribution of photon counts in a given time since photon statistics can also be an important determinant of the temporal coherence properties of a light beam [27]. Another essential characteristic of a light source is its spatial coherence which tells us how uniform the phase of the wavefront is and is often presented as a function of correlation versus absolute distance between observation points. In RLs, light is trapped through multiple scattering and the spatial modes are inhomogeneous and highly irregular. With external pumping, a large number of modes can lase simultaneously with uncorrelated phases, which accounts for the low spatial emission coherence of these unconventional lasers [28]. In such disorder media, laser light is the weighted sum of the light emitted from various spatial regions, so that light intensity from sample zones separated by more than a given coherence length becomes uncorrelated. A valid assumption for RLs lies in regarding a transversal coherence length of the same order of the transport mean free path [29]. The first approach to this research field was carried out on a Rhodamine 6G-titania system in a polymer matrix where a partially coherent emission was found [14]. However, Cao et al. demonstrated in a ZnO pellet that above threshold, light emitted from a disordered material structure with resonant feedback exhibits coherence properties characteristic of true laser light [15]. Both conflicting results evidence a heavy dependence of the temporal coherence properties of RLs on the specific system in question, and particularly, on their mode competition [30]. More recently, Redding et al. found significant variations of the spatial coherence properties of the RL emission of dye solutions containing nanoparticles, depending on scattering strength and the pump area. These observations were also qualitatively explained in terms of the number and characteristics of the active RL modes [23]. Note that the investigation about coherence in RLs is not only of theoretical interest [30–32], but also of practical importance. Since their spatial and temporal coherence characteristics are quite different from those of conventional lasers, RLs could be well suited for a host of applications in which they could outperform conventional lasers [28]. In particular, the versatility of RLs combined with their unique ability
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to provide controllable coherence and laser-level intensity, open the possibility of developing a new kind of illumination sources for specific imaging applications. In fact, the feasibility of RLs for fullfield imaging or time-resolved microscopy has already been reported [28,33]. The aim of this work is to explore the photon statistics of the RL emission of a Rhodamine B (RhB) doped di-ureasil hybrid powder which allows access to its coherence properties. In a recent work we have demonstrated the possibility of obtaining random lasing in such a disordered active material [34], and subsequently investigated the modal structure and modal oscillation dynamics of this DRL with a novel mode selection method based on spatial filtering [35]. This experimental approach (which combined a spectrometer with a streak camera) made it possible to separate individual lasing modes and follow their temporal evolution after single shots of 30 ps pulse duration at 532 nm. In the present work, the ability of an adequately positioned pinhole aperture to reduce the number of supported transverse modes is used to control the spatial coherence of the explored powder sample. In fact, a spatial filter with a diameter close to its transport length is used here to limit the detection area on the sample surface and select emission from a region close the coherence area. This detection configuration, which presumably provides high spatial coherence of the emitted light, allows us to assess the degree of temporal coherence of its RL emission while the streak camera operates in the photon counting mode. In fact, we measure its photon statistics above threshold within small wavelength and time intervals. In particular, the photon-number probability distribution and second-order correlation coefficient for a sampling time window smaller than the relaxation oscillation periods of the di-ureasil powder are analyzed to estimate the coherent component of its laser-like emission. Under these conditions, just few lasing modes might be supported, allowing for coherence sensing. In addition, we investigate the time and wavelength variation of the temporal coherence. For doing so, we fit the photon distribution histograms inferred by moving the sampling window along the time or wavelength axis, respectively, and calculate the above mentioned correlation coefficient. We find that a high degree of temporal coherence can be achieved at the time of maximum pump intensity and wavelengths around the gain maximum of the RhB dye. We believe this work enriches the knowledge of the emission nature of DRLs which are usually spatially incoherent, making it difficult to measure their temporal coherence alone.
2. Experimental methods The preparation of the laser powder, consisting of a RhB doped d-U(600) di-ureasil hybrid containing 1.23 1019 RhB molecules/cm3 (average particle size of 6.6 μm) was presented elsewhere [36]. The photon statistics study was carried out at room temperature with compressed powder (with a volume filling factor of 0.55) placed in a 6 mm high cylindrical quartz cell without a front window. The transport mean free path of the powder was around 14 μm at 630 nm [34]. Random lasing was achieved by optically exciting the powder with a 20 Hz frequency-doubled Nd: YAG laser with a pulse duration of 30 ps. The pump beam was focused to a spot size of 50 mm on the sample surface. The emission from the front face of the powder sample was collected with a (f ¼ 5 cm) lens placed at twice the focal length distance and imaged on a pinhole (∅¼15 μm) positioned at the same distance behind the lens. As lateral magnification is 1, this experimental arrangement allows selecting emissions from pumped areas as small as 15 μm, controlling the number of lasing modes, and thereby, the spatial coherence. To provide a time reference, a small portion of the pump pulse was collected together
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with the RL emission of the explored sample. Photon counting measurements were performed by exploiting the capabilities of a streak camera (C5680 Hamamatsu) coupled to an imaging spectrograph (Chromex A6365-01). In order to verify the single photon counting condition, extremely weak signals are required. Note that the photon counting acquisition mode of this detection system enables noise to be eliminated completely by searching for the optimal threshold value. It also helps to measure the photonnumber distribution, PðnÞ; for different time delays at different wavelengths. By measuring the number of photons within a wavelength, Δλ, and time interval, Δt, of a streak image, it is possible to obtain the corresponding photon number histogram and photon probability distribution. Vertical axis of the recorded streak images serves as the time axis whereas the horizontal one corresponds to the wavelength axis.
3. Results and discussion The onset of RL action in the explored di-ureasil sample (which is experimentally determined by the temporal shortening and spectral collapse of its emission output) is around 0.6 mJ/pulse when the pump laser was impinged on the powder surface with a spot size of 50 mm. The emission spectral profile changes sharply, by reducing the size of the regarded emitting area with a pinhole aperture, while the diameter of the gain medium is maintained. As an example, Fig. 1 shows the map surfaces of the RL emission pulse of single shot streak images measured under the mentioned focusing conditions at
0.8 mJ/pulse without any pinhole (a), and by using a spatial filter diameter of 15 mm (b). It also shows the RL time-integrated spectra and temporal profiles extracted over the whole streak images, in the XZ and YZ planes of these figures. In the absence of spatial filter, the superposition of overlapping modes leads to smooth spectral and temporal profiles with just a small fine structure on top of the ASE band. In contrast, Fig. 1(b) shows a clear fine structure which evidences the reduction of the lasing peaks density. In fact, we found isolated spikes originated from non-spatially overlapping cavities which enables us to characterize their temporal and spectral features. The outcome of our experiments reveals that the average spectral linewidth of the lasing spikes is 0.35 nm whereas the time traces of uncoupled lasing modes indicates that their average full width at half maximum is around 6 ps showing clear relaxation oscillations with periods in the 8–38 ps range. On the other hand, we observed that the system lases in different modes upon repeated identical excitation events. This result evidences that the frequency of the lasing peaks in the di-ureasil powder is not completely determined by the realization of static disorder, revealing an intrinsically stochastic RL behavior. Based on our findings, it is therefore reasonable to presume that this spatial filtering method, which efficiently limits the number of supported transverse modes, might be also used to control the spatial coherence of the powder sample. Account taken that in an RL the coherence length is supposed to be of the same order of the transport length, ( 14 mm in our diffusive scattering system), a high spatial coherence is expected to achieve when using a pinhole of a 15 mm diameter. In such a case, the measured RL emission would barely exceed the coherence area. Consequently, we restrict the discussion of the coherent nature of laser-like emission from our powder sample to its temporal coherence properties by measuring its photon statistics. In order to approach the subject of photon statistics of a photon stream, we shall remind that the photon-number distribution of a single-mode coherent emission with a constant intensity should follow a Poisson distribution, that is, PðnÞ ¼ 〈n〉n expð 〈n〉Þ=n!, where 〈n〉 ¼ ∑nPðnÞ is the average photon number. For a singlemode chaotic light, PðnÞ satisfies a Bose-Einstein distribution, that is, P ðnÞ ¼ 〈n〉n =½1 þ 〈n〉n þ 1 [27]. It should be stressed that the mentioned photon statistics only applies to single-mode radiation. It can be shown that multimode chaotic light tends to exhibit a Poissonian statistics if the number of modes is high [27]. The assumption of a single mode of the electric field requires considering monochromatic light during the measurement interval; that is, the detection time interval is much smaller than the coherence time of the source, τ{τC . If time intervals longer than τC are considered, the intensity fluctuations will be averaged out and consequently, the measured statistics again approaches the uncorrelated Poisson distribution. One possibility of reducing the number of supported lasing modes, and therefore, the ambiguity of whether an emission with a Poisson statistics is temporally coherent, would be to reduce the wavelength and time intervals used. By doing so, the coherent and incoherent components of the temporally and spectrally narrowed emission of the powder sample can be estimated, by fitting the probability distribution of photons to a linear combination of a Poisson and Bose-Einstein function: P ðnÞ ¼ α
Fig. 1. 3D map surfaces of the RL emission pulses measured without any pinhole (a) and with a Øpinhole ¼15 mm (b) at 0.8 mJ/pulse, by focusing the laser beam to a spot size of 50 mm on the sample surface. Spectral and temporal profiles extracted over the whole images are presented in the XZ and YZ planes of these figures, respectively.
〈n〉n expð 〈n〉Þ 〈n〉n þ ð1 α Þ n! ½1 þ 〈n〉n þ 1
ð1Þ
where α represents the weight of the coherent component of the fit. The count mean 〈n〉 ¼ ∑nPðnÞ must be previously determined from the experimental data of PðnÞ. Zacharakis et al. have previously used this analysis procedure for the statistical distributions of other RL systems [14,17]. Alternatively, light temporal coherence can be accurately inferred by evaluating the normalized second-order correlation
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function g ð2Þ ðτÞ which characterizes the properties of the optical intensity [27]. If τ c τ c , the intensity fluctuations at times t and t þ τ are uncorrelated with each other, and therefore, g ð2Þ ðτ c τc Þ ¼ 1: In contrast, if τ{τc there will be correlations between the fluctuations at both times. In the particular case of a perfectly coherent monochromatic source with a time-independent intensity, g ð2Þ ðτÞ ¼ 1 for all τ, while for a chaotic light (incoherent light) g ð2Þ ð0Þ ¼ 2 with the value of g ð2Þ ðτÞ decreasing towards unity for τ c τc . Account taken that the normalized second-order correlation coefficient, g ð2Þ ð0Þ of a photon count distribution is given by [37]: 2 〈 Δn 〉 〈n〉 ð2Þ g ð2Þ ð0Þ ¼ 1 þ 〈n〉n we have studied the nature of the emitted light in the powder sample by calculating this correlation coefficient. The same approach was previously followed in Ref. [15] in order to determine the coherence properties of the RL action in a ZnO pellet. The reliability of our set up for photon counting has been previously checked by measuring the photon statistics of the coherent laser beam used for pumping. The columns in Fig. 2 show the measured photon count probability distribution of the laser reflection coming from an optical delay line by using a wavelength interval Δλ ¼ 0:9 nm and sampling time Δt ¼ 32:8 ps at the time of maximum intensity of the laser pulse. The red line through the histogram is the best fit of Eq. (1) to these experimental data. The dashed blue and green lines show, respectively, the Poisson and Bose-Einstein distributions for the same count mean. As can be observed, the measured distribution is very close to the Poisson statistics. In fact, the weight of the Poisson part of the fitting formula is 1.08 and the value of g ð2Þ ð0Þ calculated by using the data of P(n) is 0.97. This Poisson-shaped distribution at the pulse center thus reveals the coherence of the excitation source. We have then analyzed the photon-number distributions from the sample emission while pumped at 3 mJ/pulse, that is, above threshold. Photon counting of the studied powder was done at different time delays with a wavelength interval of 0.9 nm and within a sampling time window of 32.8 ps. Only smaller or slightly larger detection time intervals than the time period of relaxation oscillations (which is between 8 and 38 ps in our DRL), might support just few lasing modes for coherence sensing. Apart from the RL pulse contribution presented in Fig. 3, the explored image contains the laser reflection signal which provides the time reference. In fact, the time origin was set at the barycenter of the excitation pulse. The vertical rectangle in Fig. 3 shows the studied area of the image when the photon statistics is analyzed versus the time delay. This rectangle is centered at 601.3 nm close to the gain maximum of the RhB dye in the employed hybrid host. Fig. 4 shows as an example, the photon distribution histograms of
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Fig. 3. Streak image of the RL emission of the powder sample recorded at 3 mJ/pulse. The vertical and horizontal white rectangles represent the regions under examination when the coherence properties of the RL emission are explored as a function of the delay time and wavelength, respectively. The vertical rectangle is centered at 601.3 nm whereas the horizontal one is centered at a 1.2 ps delay time.
rectangles centered at a time delay of 1.2 ps (a) and 27.9 ps (b) together with their corresponding fits. Again in this case the Poisson and Bose-Einstein distributions for the resulting average photon number are depicted with dashed lines. The comparison between the mentioned photon distributions reveals the pure temporal coherence of the RL emission of the hybrid powder at 1.2 ps and its incoherent character at 27.9 ps. Fig. 5 shows the reduction of the coherence percentage (red dots) and the enhancement of the second-order correlation coefficient (blue squares) as one moves away from the pumping pulse center (vertical region of Fig. 3). Note that under our experimental conditions, coherent emission is the main emission contribution within a time window of around 40 ps. Zacharakis et al. showed in previous works that at short time delays, the photon-count distribution of the RL emission of a polymeric scattering gain medium is characteristic of coherent light, even though not pure (coherent percentage between 0.51–0.75 are reported). Nevertheless, as time delay increases, the Poisson-shaped distribution is lost and is replaced by the Bose-Einstein distribution characteristic of incoherent light [17]. According to these authors, the coherence of the random lasing light is destroyed by the intense scattering undergone by the photons during their propagation outwards the pumping volume and from the competition of different lasing modes from different microcavities. The time needed in their RL samples for the total loss of coherence, and therefore coherent percentages close to zero, was around 100 ps. On the other hand, Fig. 6 shows the coherence parameters of the sample emission pumping at 3 mJ/pulse in a wavelength range between 597–611 nm and at a 1.2 ps delay time (see horizontal rectangle of Fig. 3). As can be observed, the photon statistics around the maximum gain corresponds, in most cases, to an almost pure Poisson distribution (α 1 and g ð2Þ ð0Þ 1) revealing the coherence of the resulting RL emission. The same conclusion was drawn within the same spectral range by using a larger wavelength interval, Δλ ¼ 2:3 nm.
4. Summary and conclusions
Fig. 2. Measured photon count probability distribution of the pump laser at the time of maximum intensity together with the best fit to Eq. (1) (solid red line). Dashed blue and green lines represent the Poisson and Bose-Einstein distributions for the measured count mean.
In this work we show how to exploit a mode selection method based on spatial filtering in order to constrain the number of detected lasing modes in a diffusive random laser, and therefore, characterize the spectral and temporal response of those uncoupled from mode competition. The explored sample was a di-ureasil hybrid matrix powder doped with Rhodamine B, where lasing spikes with an average spectral linewidth of 0.35 nm, and full width at half maximum of around 6 ps, were found. Temporal profiles of uncoupled lasing modes of such disordered active media show clear relaxation oscillations with periods in the 8–38 ps range. It is important to highlight that not only the spectral profile, but
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Fig. 4. Measured photon count probability distributions of the RL emission at 1.2 ps (a) and 27.9 ps (b) time delays. Solid red lines represent the best fits of Eq. (1) to these distributions. Dashed blue and green lines correspond to the Poisson and Bose-Einstein distributions for the measured count mean. The best fit line at 1.2 ps in (a) is superimposed on the Poisson distribution (blue line) whereas at 27.9 ps (b) it matches the Bose-Einstein distribution (green line).
from its photon statistics. The dependence of the computed photon statistics on time delay and wavelength, shows values of the coherent percentage and of the second-order correlation coefficient close to 1, both at the time of maximum pump intensity and around the gain maximum of the Rhodamine B dye in the employed hybrid host. This result is an experimental evidence of the high degree of temporal coherence achieved in our diffusive random laser.
Acknowledgements Fig. 5. Dependence of the coherent percentage α (red dots) and of the coefficient gð2Þ ð0Þ (blue squares) on the time delay, obtained by using Δλ¼ 0.9 nm and Δt¼ 32.8 ps from the RL emission shown in Fig. 2. The time origin was set at the excitation pulse center. The studied image region was indicated in Fig. 2 by the vertical rectangle centered at 601.3 nm.
This work was supported by the Spanish Government under project FIS2011-27968, by the Basque Country Government (IT-659-13) and Saiotek (S-PE11UN072), and by the Fundação para a Ciência e a Tecnologia (FCT, Portugal), FEDER and COMPETE, under contract Pest-C/CTM/LA0011/2013. SGR acknowledges the financial support from the Research Association MPC for a postdoctoral appointment. References [1] [2] [3] [4] [5]
Fig. 6. Dependence of the coherent percentage α (red dots) and of the coefficient gð2Þ ð0Þ (blue squares) on the wavelength obtained by using Δλ ¼0.9 nm and Δt¼ 32.8 ps from the RL emission shown in Fig. 2. The studied image region was indicated in Fig. 2 by the horizontal rectangle centered at 1.2 ps.
also the degree of coherence measured in a diffusive random laser, strongly depends on the spatial mode selection attained in the experiment. Here, the control of the spatial coherence was made by limiting the detected region on the explored sample surface to nearly the spatial coherence area of its laser-like emission. For doing so, a spatial filter with an aperture close to the transport length of the explored sample was used. Assuming a high spatial coherence under this detection configuration, the present work explores the temporal coherence of the random laser emission of this diffusive scattering system from its photon statistics. We thus performed single photon counting measurements above threshold, and assessed the photon probability distributions obtained within a wavelength interval Δλ ¼0.9 nm, and sampling time window Δt¼32.8 ps. Account taken of the relaxation oscillation periods found in the explored di-ureasil powder, just few lasing modes might thus be supported which is a crucial requirement to evaluate the coherent nature of a light beam
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Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Coherence characteristics of random lasing in a dye doped hybrid powder S. García-Revilla a,b, J. Fernández a,b,n, M. Barredo-Zuriarrain a, E. Pecoraro c,d, M.A. Arriandiaga e, I. Iparraguirre a, J. Azkargorta a, R. Balda a,b a
Departamento de Física Aplicada I, Escuela Superior de Ingeniería, Universidad del País Vasco UPV/EHU, Alda. Urquijo s/n, 48013, Bilbao, Spain Material Physics Center CSIC-UPV/EHU and Donostia International Physics Center, 20018, San Sebastián, Spain c Instituto de Telecomunicações, University of Aveiro, 3810-193, Aveiro, Portugal d Institute of Chemisty, São Paulo State University–UNESP, 14800-900, Araraquara, Brazil e Departamento de Física Aplicada II, Facultad de Ciencia y Tecnología, Universidad del País Vasco UPV/EHU, Apartado 644, Bilbao, Spain b
art ic l e i nf o
a b s t r a c t
Article history: Received 3 November 2014 Accepted 28 November 2014 Available online 8 December 2014
The photon statistics of the random laser emission of a Rhodamine B doped di-ureasil hybrid powder is investigated to evaluate its degree of coherence above threshold. Although the random laser emission is a weighted average of spatially uncorrelated radiation emitted at different positions in the sample, a spatial coherence control was achieved due to an improved detection configuration based on spatial filtering. By using this experimental approach, which also allows for fine mode discrimination and timeresolved analysis of uncoupled modes from mode competition, an area not larger than the expected coherence size of the random laser is probed. Once the spectral and temporal behavior of nonoverlapping modes is characterized, an assessment of the photon-number probability distribution and the resulting second-order correlation coefficient as a function of time delay and wavelength was performed. The outcome of our single photon counting measurements revealed a high degree of temporal coherence at the time of maximum pump intensity and at wavelengths around the Rhodamine B gain maximum. & 2015 Elsevier B.V. All rights reserved.
Keywords: Diffusive random lasers Photon statistics Coherence
1. Introduction Random lasing has developed into a sophisticated and exciting area of laser research which embraces a number of phenomena related to the emission of light by spatially inhomogeneous disordered materials: scattering, optical amplification, nonlinearity, and light localization. Analogous to traditional lasers, such random active media, the so-called random lasers (RLs), have a threshold where gain exceeds losses. Nevertheless, in these open sources of stimulated emission, multiple scattering provides feedback in place of a Fabry-Perot cavity. In fact, multiple scattering processes increase the dwell time of photons inside the material and allow enough amplification to compensate for absorption and light leakage through the boundaries creating gain saturation. Among RLs, those in which light undergoes diffusive motion within the gain media, presently known as diffusive random lasers (DRLs), are particularly attractive as the presence of strong modal interactions makes an analytical approach to the description of n Corresponding author at: Departamento de Física Aplicada I, Escuela Superior de Ingeniería, Universidad del País Vasco UPV/EHU, Alda. Urquijo s/n, 48013 Bilbao, Spain. Tel.: þ 34 946014044. E-mail address: [email protected] (J. Fernández).
http://dx.doi.org/10.1016/j.jlumin.2014.11.051 0022-2313/& 2015 Elsevier B.V. All rights reserved.
their multimode emission a very challenging task. Early theoretical treatments based on the diffusive approximation, were able to explain the overall narrowing of the emission spectra and the rapid increase of emission intensity at the frequency of maximum gain found in the pioneer RL experiments performed through a nonresonant feedback [1,2] in colloidal dye solutions [3]. Nevertheless, the spectral output of some DRLs contains, under certain conditions, multiple narrow spikes superimposed on the narrowed and featureless amplified spontaneous emission (ASE) band which have triggered a debate of different theoretical possible scenarios [4]. It is now broadly accepted that spikes can be attributed to randomly embedded localized spatial modes or modes of much larger spatial extension which can thus be more easily coupled from mode competition [5]. Depending on the material both may co-exist and provide a coherent RL mechanism. The presence of many spatially and spectrally overlapping modes in diffusive active systems gives rise to strong intermode couplings which determine their different statistical regime of fluctuations and spectral profiles [6]. In DRLs, complex nonlinear processes such as temporal oscillations [7,8] or spatial hole burning [9] may also appear. Türeci et al. recently proposed a theoretical framework based on the constant-flux (CF) states able to treat DRLs in the stationary regime [10–12]. Most experimental research on the RL response is
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performed under a quasi-stationary excitation condition (i.e. for a time much longer than the mode lifetime). By doing so, modes are continuously pumped and the intermode interaction enables one to reach a steady state. However, quasi-instantaneous excitation with a picosecond laser is required when exploring the behavior of such extremely leaky systems on the time scale. It is also remarkable that the experimental configuration critically affects the structure of the DRL emission spectra. Single-shot measurements, short-time pump pulse durations and tight focusing of pump light favor the observation of a spiky spectrum. When several emission shots are collected or long enough single excitation pulses are employed, the overlap between lasing spikes tends to average them into a smooth peak with an overall narrowing of the spectrum [4]. By controlling the shape of the pump, it is possible to incrementally excite larger numbers of spatially separated lasing modes, generating a reduction of the emission spectra spikiness with an increase of the intermode spectral correlation. This effect was accounted for by assuming a phase locking transition between modes [13]. On the other hand, only few studies have focused attention on the coherence in random lasing. Based on photon statistics [14–18], interferometry [19–22], double slit experiments [23] or speckle pattern measurements [24–26], the spatiotemporal coherence in random active media has been explored. Temporal coherence is a measure of the correlation of a light wave's phase along the direction of propagation. It tells us how monochromatic the source is, and it is quantified by its coherence time τC which can be roughly estimated by τC 1=Δν (Δν is the effective spectral width of the light). Attention can also be focused on the probability distribution of photon counts in a given time since photon statistics can also be an important determinant of the temporal coherence properties of a light beam [27]. Another essential characteristic of a light source is its spatial coherence which tells us how uniform the phase of the wavefront is and is often presented as a function of correlation versus absolute distance between observation points. In RLs, light is trapped through multiple scattering and the spatial modes are inhomogeneous and highly irregular. With external pumping, a large number of modes can lase simultaneously with uncorrelated phases, which accounts for the low spatial emission coherence of these unconventional lasers [28]. In such disorder media, laser light is the weighted sum of the light emitted from various spatial regions, so that light intensity from sample zones separated by more than a given coherence length becomes uncorrelated. A valid assumption for RLs lies in regarding a transversal coherence length of the same order of the transport mean free path [29]. The first approach to this research field was carried out on a Rhodamine 6G-titania system in a polymer matrix where a partially coherent emission was found [14]. However, Cao et al. demonstrated in a ZnO pellet that above threshold, light emitted from a disordered material structure with resonant feedback exhibits coherence properties characteristic of true laser light [15]. Both conflicting results evidence a heavy dependence of the temporal coherence properties of RLs on the specific system in question, and particularly, on their mode competition [30]. More recently, Redding et al. found significant variations of the spatial coherence properties of the RL emission of dye solutions containing nanoparticles, depending on scattering strength and the pump area. These observations were also qualitatively explained in terms of the number and characteristics of the active RL modes [23]. Note that the investigation about coherence in RLs is not only of theoretical interest [30–32], but also of practical importance. Since their spatial and temporal coherence characteristics are quite different from those of conventional lasers, RLs could be well suited for a host of applications in which they could outperform conventional lasers [28]. In particular, the versatility of RLs combined with their unique ability
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to provide controllable coherence and laser-level intensity, open the possibility of developing a new kind of illumination sources for specific imaging applications. In fact, the feasibility of RLs for fullfield imaging or time-resolved microscopy has already been reported [28,33]. The aim of this work is to explore the photon statistics of the RL emission of a Rhodamine B (RhB) doped di-ureasil hybrid powder which allows access to its coherence properties. In a recent work we have demonstrated the possibility of obtaining random lasing in such a disordered active material [34], and subsequently investigated the modal structure and modal oscillation dynamics of this DRL with a novel mode selection method based on spatial filtering [35]. This experimental approach (which combined a spectrometer with a streak camera) made it possible to separate individual lasing modes and follow their temporal evolution after single shots of 30 ps pulse duration at 532 nm. In the present work, the ability of an adequately positioned pinhole aperture to reduce the number of supported transverse modes is used to control the spatial coherence of the explored powder sample. In fact, a spatial filter with a diameter close to its transport length is used here to limit the detection area on the sample surface and select emission from a region close the coherence area. This detection configuration, which presumably provides high spatial coherence of the emitted light, allows us to assess the degree of temporal coherence of its RL emission while the streak camera operates in the photon counting mode. In fact, we measure its photon statistics above threshold within small wavelength and time intervals. In particular, the photon-number probability distribution and second-order correlation coefficient for a sampling time window smaller than the relaxation oscillation periods of the di-ureasil powder are analyzed to estimate the coherent component of its laser-like emission. Under these conditions, just few lasing modes might be supported, allowing for coherence sensing. In addition, we investigate the time and wavelength variation of the temporal coherence. For doing so, we fit the photon distribution histograms inferred by moving the sampling window along the time or wavelength axis, respectively, and calculate the above mentioned correlation coefficient. We find that a high degree of temporal coherence can be achieved at the time of maximum pump intensity and wavelengths around the gain maximum of the RhB dye. We believe this work enriches the knowledge of the emission nature of DRLs which are usually spatially incoherent, making it difficult to measure their temporal coherence alone.
2. Experimental methods The preparation of the laser powder, consisting of a RhB doped d-U(600) di-ureasil hybrid containing 1.23 1019 RhB molecules/cm3 (average particle size of 6.6 μm) was presented elsewhere [36]. The photon statistics study was carried out at room temperature with compressed powder (with a volume filling factor of 0.55) placed in a 6 mm high cylindrical quartz cell without a front window. The transport mean free path of the powder was around 14 μm at 630 nm [34]. Random lasing was achieved by optically exciting the powder with a 20 Hz frequency-doubled Nd: YAG laser with a pulse duration of 30 ps. The pump beam was focused to a spot size of 50 mm on the sample surface. The emission from the front face of the powder sample was collected with a (f ¼ 5 cm) lens placed at twice the focal length distance and imaged on a pinhole (∅¼15 μm) positioned at the same distance behind the lens. As lateral magnification is 1, this experimental arrangement allows selecting emissions from pumped areas as small as 15 μm, controlling the number of lasing modes, and thereby, the spatial coherence. To provide a time reference, a small portion of the pump pulse was collected together
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with the RL emission of the explored sample. Photon counting measurements were performed by exploiting the capabilities of a streak camera (C5680 Hamamatsu) coupled to an imaging spectrograph (Chromex A6365-01). In order to verify the single photon counting condition, extremely weak signals are required. Note that the photon counting acquisition mode of this detection system enables noise to be eliminated completely by searching for the optimal threshold value. It also helps to measure the photonnumber distribution, PðnÞ; for different time delays at different wavelengths. By measuring the number of photons within a wavelength, Δλ, and time interval, Δt, of a streak image, it is possible to obtain the corresponding photon number histogram and photon probability distribution. Vertical axis of the recorded streak images serves as the time axis whereas the horizontal one corresponds to the wavelength axis.
3. Results and discussion The onset of RL action in the explored di-ureasil sample (which is experimentally determined by the temporal shortening and spectral collapse of its emission output) is around 0.6 mJ/pulse when the pump laser was impinged on the powder surface with a spot size of 50 mm. The emission spectral profile changes sharply, by reducing the size of the regarded emitting area with a pinhole aperture, while the diameter of the gain medium is maintained. As an example, Fig. 1 shows the map surfaces of the RL emission pulse of single shot streak images measured under the mentioned focusing conditions at
0.8 mJ/pulse without any pinhole (a), and by using a spatial filter diameter of 15 mm (b). It also shows the RL time-integrated spectra and temporal profiles extracted over the whole streak images, in the XZ and YZ planes of these figures. In the absence of spatial filter, the superposition of overlapping modes leads to smooth spectral and temporal profiles with just a small fine structure on top of the ASE band. In contrast, Fig. 1(b) shows a clear fine structure which evidences the reduction of the lasing peaks density. In fact, we found isolated spikes originated from non-spatially overlapping cavities which enables us to characterize their temporal and spectral features. The outcome of our experiments reveals that the average spectral linewidth of the lasing spikes is 0.35 nm whereas the time traces of uncoupled lasing modes indicates that their average full width at half maximum is around 6 ps showing clear relaxation oscillations with periods in the 8–38 ps range. On the other hand, we observed that the system lases in different modes upon repeated identical excitation events. This result evidences that the frequency of the lasing peaks in the di-ureasil powder is not completely determined by the realization of static disorder, revealing an intrinsically stochastic RL behavior. Based on our findings, it is therefore reasonable to presume that this spatial filtering method, which efficiently limits the number of supported transverse modes, might be also used to control the spatial coherence of the powder sample. Account taken that in an RL the coherence length is supposed to be of the same order of the transport length, ( 14 mm in our diffusive scattering system), a high spatial coherence is expected to achieve when using a pinhole of a 15 mm diameter. In such a case, the measured RL emission would barely exceed the coherence area. Consequently, we restrict the discussion of the coherent nature of laser-like emission from our powder sample to its temporal coherence properties by measuring its photon statistics. In order to approach the subject of photon statistics of a photon stream, we shall remind that the photon-number distribution of a single-mode coherent emission with a constant intensity should follow a Poisson distribution, that is, PðnÞ ¼ 〈n〉n expð 〈n〉Þ=n!, where 〈n〉 ¼ ∑nPðnÞ is the average photon number. For a singlemode chaotic light, PðnÞ satisfies a Bose-Einstein distribution, that is, P ðnÞ ¼ 〈n〉n =½1 þ 〈n〉n þ 1 [27]. It should be stressed that the mentioned photon statistics only applies to single-mode radiation. It can be shown that multimode chaotic light tends to exhibit a Poissonian statistics if the number of modes is high [27]. The assumption of a single mode of the electric field requires considering monochromatic light during the measurement interval; that is, the detection time interval is much smaller than the coherence time of the source, τ{τC . If time intervals longer than τC are considered, the intensity fluctuations will be averaged out and consequently, the measured statistics again approaches the uncorrelated Poisson distribution. One possibility of reducing the number of supported lasing modes, and therefore, the ambiguity of whether an emission with a Poisson statistics is temporally coherent, would be to reduce the wavelength and time intervals used. By doing so, the coherent and incoherent components of the temporally and spectrally narrowed emission of the powder sample can be estimated, by fitting the probability distribution of photons to a linear combination of a Poisson and Bose-Einstein function: P ðnÞ ¼ α
Fig. 1. 3D map surfaces of the RL emission pulses measured without any pinhole (a) and with a Øpinhole ¼15 mm (b) at 0.8 mJ/pulse, by focusing the laser beam to a spot size of 50 mm on the sample surface. Spectral and temporal profiles extracted over the whole images are presented in the XZ and YZ planes of these figures, respectively.
〈n〉n expð 〈n〉Þ 〈n〉n þ ð1 α Þ n! ½1 þ 〈n〉n þ 1
ð1Þ
where α represents the weight of the coherent component of the fit. The count mean 〈n〉 ¼ ∑nPðnÞ must be previously determined from the experimental data of PðnÞ. Zacharakis et al. have previously used this analysis procedure for the statistical distributions of other RL systems [14,17]. Alternatively, light temporal coherence can be accurately inferred by evaluating the normalized second-order correlation
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function g ð2Þ ðτÞ which characterizes the properties of the optical intensity [27]. If τ c τ c , the intensity fluctuations at times t and t þ τ are uncorrelated with each other, and therefore, g ð2Þ ðτ c τc Þ ¼ 1: In contrast, if τ{τc there will be correlations between the fluctuations at both times. In the particular case of a perfectly coherent monochromatic source with a time-independent intensity, g ð2Þ ðτÞ ¼ 1 for all τ, while for a chaotic light (incoherent light) g ð2Þ ð0Þ ¼ 2 with the value of g ð2Þ ðτÞ decreasing towards unity for τ c τc . Account taken that the normalized second-order correlation coefficient, g ð2Þ ð0Þ of a photon count distribution is given by [37]: 2 〈 Δn 〉 〈n〉 ð2Þ g ð2Þ ð0Þ ¼ 1 þ 〈n〉n we have studied the nature of the emitted light in the powder sample by calculating this correlation coefficient. The same approach was previously followed in Ref. [15] in order to determine the coherence properties of the RL action in a ZnO pellet. The reliability of our set up for photon counting has been previously checked by measuring the photon statistics of the coherent laser beam used for pumping. The columns in Fig. 2 show the measured photon count probability distribution of the laser reflection coming from an optical delay line by using a wavelength interval Δλ ¼ 0:9 nm and sampling time Δt ¼ 32:8 ps at the time of maximum intensity of the laser pulse. The red line through the histogram is the best fit of Eq. (1) to these experimental data. The dashed blue and green lines show, respectively, the Poisson and Bose-Einstein distributions for the same count mean. As can be observed, the measured distribution is very close to the Poisson statistics. In fact, the weight of the Poisson part of the fitting formula is 1.08 and the value of g ð2Þ ð0Þ calculated by using the data of P(n) is 0.97. This Poisson-shaped distribution at the pulse center thus reveals the coherence of the excitation source. We have then analyzed the photon-number distributions from the sample emission while pumped at 3 mJ/pulse, that is, above threshold. Photon counting of the studied powder was done at different time delays with a wavelength interval of 0.9 nm and within a sampling time window of 32.8 ps. Only smaller or slightly larger detection time intervals than the time period of relaxation oscillations (which is between 8 and 38 ps in our DRL), might support just few lasing modes for coherence sensing. Apart from the RL pulse contribution presented in Fig. 3, the explored image contains the laser reflection signal which provides the time reference. In fact, the time origin was set at the barycenter of the excitation pulse. The vertical rectangle in Fig. 3 shows the studied area of the image when the photon statistics is analyzed versus the time delay. This rectangle is centered at 601.3 nm close to the gain maximum of the RhB dye in the employed hybrid host. Fig. 4 shows as an example, the photon distribution histograms of
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Fig. 3. Streak image of the RL emission of the powder sample recorded at 3 mJ/pulse. The vertical and horizontal white rectangles represent the regions under examination when the coherence properties of the RL emission are explored as a function of the delay time and wavelength, respectively. The vertical rectangle is centered at 601.3 nm whereas the horizontal one is centered at a 1.2 ps delay time.
rectangles centered at a time delay of 1.2 ps (a) and 27.9 ps (b) together with their corresponding fits. Again in this case the Poisson and Bose-Einstein distributions for the resulting average photon number are depicted with dashed lines. The comparison between the mentioned photon distributions reveals the pure temporal coherence of the RL emission of the hybrid powder at 1.2 ps and its incoherent character at 27.9 ps. Fig. 5 shows the reduction of the coherence percentage (red dots) and the enhancement of the second-order correlation coefficient (blue squares) as one moves away from the pumping pulse center (vertical region of Fig. 3). Note that under our experimental conditions, coherent emission is the main emission contribution within a time window of around 40 ps. Zacharakis et al. showed in previous works that at short time delays, the photon-count distribution of the RL emission of a polymeric scattering gain medium is characteristic of coherent light, even though not pure (coherent percentage between 0.51–0.75 are reported). Nevertheless, as time delay increases, the Poisson-shaped distribution is lost and is replaced by the Bose-Einstein distribution characteristic of incoherent light [17]. According to these authors, the coherence of the random lasing light is destroyed by the intense scattering undergone by the photons during their propagation outwards the pumping volume and from the competition of different lasing modes from different microcavities. The time needed in their RL samples for the total loss of coherence, and therefore coherent percentages close to zero, was around 100 ps. On the other hand, Fig. 6 shows the coherence parameters of the sample emission pumping at 3 mJ/pulse in a wavelength range between 597–611 nm and at a 1.2 ps delay time (see horizontal rectangle of Fig. 3). As can be observed, the photon statistics around the maximum gain corresponds, in most cases, to an almost pure Poisson distribution (α 1 and g ð2Þ ð0Þ 1) revealing the coherence of the resulting RL emission. The same conclusion was drawn within the same spectral range by using a larger wavelength interval, Δλ ¼ 2:3 nm.
4. Summary and conclusions
Fig. 2. Measured photon count probability distribution of the pump laser at the time of maximum intensity together with the best fit to Eq. (1) (solid red line). Dashed blue and green lines represent the Poisson and Bose-Einstein distributions for the measured count mean.
In this work we show how to exploit a mode selection method based on spatial filtering in order to constrain the number of detected lasing modes in a diffusive random laser, and therefore, characterize the spectral and temporal response of those uncoupled from mode competition. The explored sample was a di-ureasil hybrid matrix powder doped with Rhodamine B, where lasing spikes with an average spectral linewidth of 0.35 nm, and full width at half maximum of around 6 ps, were found. Temporal profiles of uncoupled lasing modes of such disordered active media show clear relaxation oscillations with periods in the 8–38 ps range. It is important to highlight that not only the spectral profile, but
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P(n)
P(n)
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Fig. 4. Measured photon count probability distributions of the RL emission at 1.2 ps (a) and 27.9 ps (b) time delays. Solid red lines represent the best fits of Eq. (1) to these distributions. Dashed blue and green lines correspond to the Poisson and Bose-Einstein distributions for the measured count mean. The best fit line at 1.2 ps in (a) is superimposed on the Poisson distribution (blue line) whereas at 27.9 ps (b) it matches the Bose-Einstein distribution (green line).
from its photon statistics. The dependence of the computed photon statistics on time delay and wavelength, shows values of the coherent percentage and of the second-order correlation coefficient close to 1, both at the time of maximum pump intensity and around the gain maximum of the Rhodamine B dye in the employed hybrid host. This result is an experimental evidence of the high degree of temporal coherence achieved in our diffusive random laser.
Acknowledgements Fig. 5. Dependence of the coherent percentage α (red dots) and of the coefficient gð2Þ ð0Þ (blue squares) on the time delay, obtained by using Δλ¼ 0.9 nm and Δt¼ 32.8 ps from the RL emission shown in Fig. 2. The time origin was set at the excitation pulse center. The studied image region was indicated in Fig. 2 by the vertical rectangle centered at 601.3 nm.
This work was supported by the Spanish Government under project FIS2011-27968, by the Basque Country Government (IT-659-13) and Saiotek (S-PE11UN072), and by the Fundação para a Ciência e a Tecnologia (FCT, Portugal), FEDER and COMPETE, under contract Pest-C/CTM/LA0011/2013. SGR acknowledges the financial support from the Research Association MPC for a postdoctoral appointment. References [1] [2] [3] [4] [5]
Fig. 6. Dependence of the coherent percentage α (red dots) and of the coefficient gð2Þ ð0Þ (blue squares) on the wavelength obtained by using Δλ ¼0.9 nm and Δt¼ 32.8 ps from the RL emission shown in Fig. 2. The studied image region was indicated in Fig. 2 by the horizontal rectangle centered at 1.2 ps.
also the degree of coherence measured in a diffusive random laser, strongly depends on the spatial mode selection attained in the experiment. Here, the control of the spatial coherence was made by limiting the detected region on the explored sample surface to nearly the spatial coherence area of its laser-like emission. For doing so, a spatial filter with an aperture close to the transport length of the explored sample was used. Assuming a high spatial coherence under this detection configuration, the present work explores the temporal coherence of the random laser emission of this diffusive scattering system from its photon statistics. We thus performed single photon counting measurements above threshold, and assessed the photon probability distributions obtained within a wavelength interval Δλ ¼0.9 nm, and sampling time window Δt¼32.8 ps. Account taken of the relaxation oscillation periods found in the explored di-ureasil powder, just few lasing modes might thus be supported which is a crucial requirement to evaluate the coherent nature of a light beam
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