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Abstract
Besides the scattering structures, the energy transfer (ET) process in the gain medium plays a significant role in the competition between coherent (comprising strongly coherent components) and incoherent (consisting of weakly coherent or “hidden” coherent components) modes of random lasers. In this study, bichromatic emission random lasers were successfully created using polydimethylsiloxane (PDMS) replicas with grooved structures that imitate the inner surface of abalone shells as scattering substrates. The influence mechanism of the ET process from the monomer to dimer in the Rhodamine 640 dye on the competition of random laser modes was thoroughly investigated from both spectral and temporal dimensions. It was confirmed that the ET process can reduce the gain of monomers while amplifying the gain of dimers. By considering the dominant high-efficiency ET processes, an energy transfer factor associated with the pump energy density was determined. Notably, for the first time, it was validated that the statistical distribution characteristics of the time sequence variations in the coherent random laser generated by dimers closely resemble a normal distribution. This finding demonstrates the feasibility of producing high-quality random number sequences.
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1. Introduction
As early as 1966, Basov et al. conducted experiments where they observed a type of non-resonant feedback mode of laser output, which they referred to as random modes [1]. Subsequently, Letokhov theoretically predicted that multiple scattering could also contribute to laser generation by providing feedback, resulting in multi-mode output. This theoretical insight played a crucial role in establishing the foundation for the development of random lasers [2]. In 1994, Lawandy et al. conducted the pioneering experimental observation of random lasers, confirming their existence [3]. Later, Wiersma et al. improved the random laser light diffusion model by considering the influence of multiple scattering and amplification in the medium [4]. Following these advancements, research on random lasers experienced a period of rapid development [5,6,7,8,9]. Random lasers heavily rely on the phenomenon of multiple scattering of photons in random media [10], including metallic nanoparticles [11,12,13], inorganic dielectric nanoparticles [14], liquid crystals [15], micro/nanostructures of butterfly wings [16,17], papilla hill [18] and wrinkle-like [19] scattering structures of leaves on replica polydimethylsiloxane (PDMS) flexible substrates. The different types of scattering particles and structures directly impact the transmission paths of photons, while the occurrence of coherent and incoherent feedback is dependent on whether the photon transmission paths form closed loops [20]. Random lasers hold significant potential for various applications in fields such as speckle-free laser imaging and display [21,22,23,24,25], information security [26], anti-counterfeiting measures [27,28], compact and integrated red-green-blue (RGB) light sources [29,30], super-resolution spectroscopy [31], and the differentiation of malignant and healthy tissues for diagnostic imaging [32]. Due to the inner surface of an abalone shell possesses a scattering structure akin to a grating, random lasers based on the structural characteristics of abalone shells also show promising potential in sensing applications [33].
In recent years, random lasers have demonstrated significant potential in generating random numbers. True random number generators (TRNGs) play a crucial role in secure communication, scientific simulations, random modeling, and cryptography [34]. Various methods have been employed for optical random number generation, including chaotic semiconductor lasers [35], fiber lasers [36], single photon measurements [37], quantum vacuum fluctuations [38], laser phase noise [39], amplified spontaneous emission [40], optical parametric oscillators [41], stimulated Raman scattering [42], and spontaneous Raman scattering [43]. These optical random number generators primarily rely on the temporal variation of signal intensity. Notably, chaotic semiconductor lasers have showcased remarkable progress. Kim et al. have developed chip-scale laser capable of generating massively parallel ultrafast random bits. This laser achieved a total bit rate of 254 Tbit/s and a single-channel rate of 2 Tbit/s [44]. However, research on random number generation using random lasers has been limited. Sznitko et al. verified the feasibility of generating random numbers by contrasting the intensity of dual-band random lasers [45]. In 2020, employing PDMS as the substrate, we initially replicated the papilla hill structure from the surface of a lotus leaf onto PDMS. This process enabled us to achieve a wavelength tuning of approximately 11 nm in a random laser, leveraging the flexibility inherent in PDMS [18]. In 2021, we first achieved dual-band incoherent and coherent random lasers based on replicated abalone shell structures [46]. Subsequently, in 2023, we harnessed incoherent random lasers to extract “hidden” coherent spectra, enabling a random number generation rate of 810 Tbit/s and a single-channel rate of 40 Tbit/s. The quality of the generated random numbers successfully passed the NIST SP800-22 testing standard [47]. To the best of our knowledge, this represents the current international record for the highest generation rate of random numbers.
Indeed, the bichromatic emission property can be achieved by blending different dyes [29] through the Förster resonance energy transfer (FRET) process. Alternatively, it can be accomplished using the same dye, such as Rhodamine 640 (Rh640), by utilizing energy transfer (ET) from monomer to dimer combined with scattering microstructures. This approach enables the realization of dual-band random lasers emitting at 620 nm and 650 nm [48,49]. In the case of solid Rh640 dye, the formation of aggregates occurs through a reabsorption and reemission process [14,50]. This process involves the collective ET from monomers and dimers to aggregates, resulting in dual-band random laser outputs at 620 nm and 700 nm [51]. Although the ET mechanism for dual-band transfer, particularly in the presence of abalone shell-like grating scattering structures, requires further investigation. Additionally, our previous work has demonstrated the potential of abalone shell random laser systems to generate high-quality and high-rate random numbers. However, increasing the spectral dimension significantly boosts the rate of random number generation. Nevertheless, the complexity of post-processing data arises due to the need to control incoherent random lasers with “hidden” coherent modes. Moreover, this method is not suitable for strong coherent random lasers. These factors limit the practical application of random laser spectrum-based random number generation. Currently, no reports exist on the generation of random numbers based on the temporal variations of random laser intensity. Therefore, demonstrating its feasibility is crucial, particularly in verifying the potential of temporal sequences in coherent random lasers (strongly coherent) and incoherent random lasers (weakly coherent or with “hidden” coherent components as mentioned below), to advance the practical development of random lasers in the field of random number generation. In this study, we examine the competition between coherent and incoherent modes of dual-band random lasers from an ET perspective. For the first time, we compare the temporal variations in random laser intensity for coherent and incoherent modes, and assess the potential application of their temporal sequences in random number generation.
2. Experiment setup
The experimental setup is illustrated in Fig. 1, which is a standard configuration commonly employed in random laser experiments, akin to the setup utilized in our previous works [46,47]. The pump source is a second harmonic Nd: YAG laser (Beamtech, SGR-10) with a pulse width of approximately 6.9 ns and a repetition rate of 10 Hz. The energy of the 532 nm laser is controlled using a combination of a half-wave plate and a polarizing beam splitter (PBS). The vertically polarized laser serves as an energy monitor, while the horizontally polarized laser is focused onto the random laser through a cylindrical lens with a focal length of 75 mm. The size of the 532 nm laser on the focal line is 0.1 cm × 1.0 cm. The scattering substrate of the random laser features a grating structure resembling the inner surface of an abalone shell, which needs to be replicated onto a flexible PDMS substrate. To create the PDMS solution, silicone rubber and crosslinking agent are mixed at a ratio of 10:1. The mixture is then degassed in a vacuum chamber for 1.5 hours before being poured onto the inner surface of the abalone shell. The solution is cured at 80°C for 3 hours to form a negative template. A thin film of HfO2 with a thickness of 30 nm is deposited on the surface of the negative template using atomic layer deposition, creating an anti-adhesive layer. Subsequently, the negative template is replicated with PDMS for the second time to generate the positive template. The spacing between the replicated groove structures ranges from 10 to 40 µm. For detailed preparation procedures, please refer to our previous work [46]. The advantages of using PDMS include its low optical transmission loss, surface smoothness that preserves the direction of light transmission, and excellent flexibility, enabling the creation of high-performance, low-threshold random lasers.
Fig. 1. Schematic diagram of the experimental setup. Inset: Photograph of the random laser spot. Please note that the actual random laser emits red light. While capturing the photograph with a camera, we employed a filter to eliminate the interference caused by the strong scattering of the 532 nm pump laser. However, this filter has high transmission in the blue wavelength range, resulting in the random laser spot appearing pink in the photograph (as pink light is produced by the mixture of blue and red light).
In our experiment, we utilized a Rh640 dye solution as the gain medium, with ethanol as the solvent, at concentrations of 1 mM, 3 mM, and 5 mM. To prevent excessive reabsorption of the Rh640 dye, which can hinder the generation of random lasers, we vertically pumped a 532 nm laser near the edge of the PDMS substrate. The resulting red random laser was emitted from the side, as illustrated in the inset of Fig. 1. We collected the random laser using a fiber connected to a spectrometer (Horiba Jobin Yvon, iHR320), and its spectrum was captured by a charge-coupled device (CCD). Additionally, we detected the waveform of the random laser using a photodetector (PD), and the temporal variations in random laser intensity were recorded using a high-speed oscilloscope (LeCroy WaveRunner 625Zi).
3. Results and discussion
The section has been organized into three subsections. In Section 3.1, we investigated the bichromatic emission characteristics of random laser spectra generated by varying concentrations of Rh640, and analyzed threshold properties through spectral intensity and linewidth. In Section 3.2, we delved into the physical mechanisms behind these characteristics, studying ET processes between monomers and dimers to understand their impact on random laser coherence. Section 3.3 examined how these ET processes influence temporal variations in coherent and incoherent random lasers, with an assessment of the feasibility of generating high-quality random numbers based on statistical distribution characteristics of random laser temporal sequences.
3.1 Random laser spectra
With the help of random laser spectrum, the threshold can be judged by the spectral line width, and the coherence of the random laser can also be decided by mode changes evident in the spectrum. At different concentrations of the Rh640 solution, the random laser exhibits distinct spectral characteristics, as depicted in Fig. 2. Moreover, the random laser demonstrates the tunable property of bichromatic emission. Figure 2(a) displays the random laser spectrum when the Rh640 solution concentration is 1 mM. As the pump energy density increases, the emission spectrum of the random laser predominantly centers around 627 nm in the short-wavelength band. Figure 2(b) illustrates the random laser spectrum at a concentration of 3 mM Rh640 solution, revealing bichromatic emission. The short-wavelength band is centered around 627 nm, while the long-wavelength band is centered around 648 nm. At low pump energy densities, the intensities of the bichromatic emission signals are approximately equal. However, as the pump energy density increases, the intensity of the long-wavelength band random laser becomes significantly stronger than that of the short-wavelength band. Additionally, the mode of the long-wavelength band random laser becomes more pronounced. When the Rh640 solution concentration is 5 mM, as shown in Fig. 2(c), the random laser spectrum exhibits a long-wavelength band centered around 650 nm.
Fig. 2. Random laser spectra obtained at different concentrations of Rh640 solution. (a) 1 mM. (b) 3 mM. (c) 5 mM.
To further confirm that the generated collimated light is indeed a random laser, we examine its threshold properties through spectral intensity and linewidth analysis. Piecewise linear fitting of spectral linewidth and intensity variations [13,23,25] is used to confirm the threshold for generating random laser. Figure 3(a) demonstrates the threshold properties of the short-wavelength band random laser at a concentration of 1 mM. At low pump energy density, the spectral signal is weak, and the linewidth is broad. However, as the pump energy density increases, the signal intensity grows rapidly, and simultaneously, the linewidth narrows significantly. Based on the inflection point in the graph, the threshold for generating the random laser can be estimated to be approximately 0.78 mJ/cm2. Figures 3(b) and 3(c) demonstrate that the thresholds for the long-wavelength band random laser in Rh640 solution concentrations of 3 mM and 5 mM are approximately 0.50 mJ/cm2 and 1.50 mJ/cm2, respectively.
Fig. 3. Threshold properties of random lasing at different concentrations of Rh640 solution. (a) 1 mM. (b) 3 mM. (c) 5 mM.
3.2 Energy transfer between monomer and dimer
The concentration of the Rh640 dye solution plays a crucial role in regulating the bichromatic emission properties of the random laser. By adjusting the concentration, we can observe different behavior. At low concentrations, the random laser primarily emits in the short-wavelength band. On the other hand, at high concentrations, the emission shifts to the long-wavelength band. Intermediate concentrations allow for the simultaneous appearance of a dual-band random laser. This bichromatic emission is a unique characteristic of the Rh640 dye. The Rh640 dye solution consists of both monomers and dimers. The monomers emit light at a wavelength of approximately 620 nm, while the dimers emit at around 650 nm [48]. These emission wavelengths correspond directly to the experimental results shown in Fig. 2. Importantly, there is a process of reabsorption and reemission that occurs between the monomers and dimers. This process is facilitated by the significant overlap between the emission cross-section of the monomers and the absorption cross-section of the dimers. However, no overlap exists between the absorption cross-section of the monomers and the emission cross-section of the dimers. This reabsorption and reemission process is similar to FRET [52], ultimately resulting in an ET process [48,49,51]. In this system, the monomers act as donors, while the dimers act as acceptors.
The ET process occurs unidirectionally from the monomers to the dimers, resulting in the bichromatic emission in Rh640 random lasers. Although the dimers have fewer particles and weaker fluorescence compared to the monomers, the presence of this unidirectional ET process leads to a significantly strong emission peak for the dimers [53]. With an increase in the energy density of the 532 nm pump, a larger number of monomers are excited to the high level. This intensifies the ET process between the excited monomers and the fundamental dimers [49], resulting in a rapid growth in the intensity of the long-wavelength band random laser. These findings are confirmed by the results presented in Fig. 2(b) and Fig. 2(c).
Actually, the concentration of Rh640 dye solution greatly impacts the efficiency of the ET process. A higher concentration of Rh640 dye promotes the formation of dimers, leading to increased energy absorption. The mechanism of the ET process can be revealed through the dual-band random laser spectrum, at a concentration of 3 mM, the random laser produced by the long-wavelength band is significantly stronger compared to the short-wavelength band. This indicates that most excited state monomers are transferring energy to the fundamental dimers. Furthermore, at a concentration of 5 mM, only the long-wavelength band random laser is observed, further confirming the high efficiency of the ET process at higher concentrations. At a concentration of 1 mM, only the short-wavelength band random laser generated by monomers is observed, and there is no contribution from long-wavelength band random laser generated by dimers. The significant mode changes in the behavior of the random laser at 3 mM and 5 mM concentrations demonstrate a strong coherent random laser effect. However, at 1 mM concentration, the random laser exhibits fewer coherent modes and smaller variations, indicating the predominance of incoherent random laser generation. It is important to note that in this paper, the term “incoherent random laser” does not solely refer to purely incoherent modes but rather represents random lasers with “hidden” or weaker coherent modes. Even at a low concentration of 1 mM Rh640 dye solution, dimers are still present, and the ET process occurs, although long-wavelength band random laser is not generated. This suggests that the efficiency of the ET process is reduced due to the limited number of dimers. Additionally, it indirectly suggests the existence of a higher threshold for coherent random laser generation, requiring sufficient gain to occur. Furthermore, the presence of the abalone shell grating introduces multiple scattering effects, leading to a direct competition between coherent and incoherent random laser modes, with one mode prevailing. The increased threshold for long-wavelength band random laser at high concentrations of Rh640 primarily arises from the gradual transition of fluorescence dimers (J-dimers) to non-fluorescence dimers (H-dimers) [51,54] as the concentration approaches a certain limit.
In the region where the 532 nm laser is used for pumping, both monomers and dimers are present, resulting in similar feedback provided by multiple scattering. However, the resulting modes of the random laser differ significantly. This observation demonstrates that the unidirectional nature of the ET process directly impacts the gain of monomer and dimer particles themselves, thus influencing the amplification or attenuation of the feedback generated by multiple scattering. Put simply, the ET process reduces the gain of monomers, which weakens the feedback and results in incoherent random laser generation, whereas the gain of dimers is amplified by the ET process, enhancing the feedback and leading to coherent random laser generation. To gain a deeper understanding of the influence of the ET process on the competition between coherent and incoherent modes in the dual-band random laser, a semi-quantitative evaluation of the ET process between monomers and dimers at a concentration of 3 mM is performed. It is widely recognized that laser intensity is exponentially related to gain, as indicated by Eq. (1) and Eq. (2).
Whereas ICRL represents the intensity of coherent random laser generated by dimers in the long-wavelength band, Gdimer represents the gain generated by excited-state dimers. IIRL stands for the intensity of incoherent random laser produced by monomers in the short-wavelength band, with Gmonomer denoting the gain generated by excited-state monomers.
By applying Eq. (1) and Eq. (2), we derive Eq. (3).
In Eq. (4), the difference in gain between dimers and monomers is associated with the ET process, where Ipump represents the energy density of the pump laser, and gET denotes the energy transfer factor related to the pump energy density. The relationship between ICRL/IIRL and gET is given by Eq. (5), as derived from Eq. (3) and Eq. (4).
It is important to clarify that ICRL and IIRL are not interrelated. Coherent and incoherent random lasers are independent under the same pump energy density [45,46], and their intensity ratio exhibits a wide range of distributions. In addition to intrinsic parameters such as the number of monomer and dimer particles, the ET process is also influenced by various external parameters of the random laser, including pump energy density, refractive index, multiple scattering, total gain length, and temperature, among others. Apart from the pump power density, all other external parameters can be fixed. The refractive index corresponds to the concentration of the Rh640 solution, with a selected random laser spectrum of 3 mM. Multiple scattering refers to the length of the microcavity formed by the grooves of the abalone shell. In our previous work [46], we achieved an average optical cavity length of 51.40 µm. The total gain length, determined mainly by the spot size of the pump laser and cylindrical lens, is 1 cm. The experiments were conducted at room temperature. Regarding intrinsic parameters, the fluctuation in the ET process between monomers and dimers results in intense mode competition between coherent and incoherent random lasers. As mentioned earlier, due to the unidirectionality of the ET process, efficient ET from monomers to dimers leads to a significant increase in the gain of dimers, while the gain of monomers decreases substantially. This ultimately leads to a much stronger intensity of coherent random lasers compared to incoherent ones during mode competition. To effectively study the influence of pump energy density on the ET process, we selectively chose data points with a higher ICRL / IIRL ratio under the condition of efficient ET from monomers to dimers, these data points were then fitted using an exponential model. This approach minimizes the impact of mode competition between coherent and incoherent random lasers under intrinsic parameters dominated by the ET process. In our analysis, we obtained an excellent fit with a correlation coefficient (R2) of 0.997, as depicted in Fig. 4. The fitted energy transfer factor, gET, was determined to be (0.128 ± 0.029) (mJ/cm2)-1. This result demonstrates the significant role of pump energy density in influencing the ET process. For enhancing the slope modification in Fig. 4, equates to ameliorating ET efficiency and achieving higher gET, it can be realized by augmenting the concentration of Rh640 solution.
Fig. 4. Fitting curve of the energy transfer relationship between monomers and dimers at a concentration of 3 mM Rh640 solution. It is worth noting that due to the significant mode competition between coherent and incoherent random lasers, we carefully selected data points where the ICRL/IIRL ratio was large, ensuring efficient energy transfer from monomers to dimers and minimizing the influence of mode competition within the random laser system.
3.3 Statistical properties of random laser’s time sequence variation
In our previous work [47], we accomplished a successful single-channel random number generation rate of 40 Tbit/s by extracting the coherent components that were “hidden” in the incoherent random laser spectra generated by monomers in the short-wavelength band. To further enhance the application of random lasers in random number generation, exploring the potential of temporal variations in random laser intensity is necessary. In this experiment, we present the spectra and waveforms of the 532 nm laser used in Fig. 5(a) and Fig. 5(b), respectively.
Figure 6 displays typical random laser spectra and corresponding waveforms obtained at different concentrations of Rh640 dye solution. The wavelength of the generated random laser falls within the range of 620 to 660 nm, precisely within the high-response detection region of Si-based photodetectors [55]. Consequently, the proposed scheme for generating random numbers based on random laser time sequence in this work proves highly convenient for laser signal detection. At a concentration of 1 mM, as shown in Fig. 6(a), there is minimal variation in the random laser modes produced by monomers in the short-wavelength band. The behavior mainly exhibits incoherent random laser characteristics, and the corresponding temporal variations shown in Fig. 6(b) are also relatively small. Figure 6(c) and Fig. 6(d) illustrate the random laser spectra and temporal variations generated by 3 mM Rh640 solution, respectively. The mode variations of coherent random lasers, produced by dimers in the long-wavelength band, are much more diverse and noticeably stronger than the incoherent random lasers in the short-wavelength band. The corresponding temporal variations are also predominantly influenced by coherent random lasers. At a concentration of 5 mM, the differences in coherent random laser modes become even more apparent, as depicted in Fig. 6(e). Furthermore, as observed in Fig. 6(f), the corresponding temporal variation amplitudes are significantly larger. In other words, the disparities in spectral modes between incoherent random lasers in the short-wavelength band and coherent random lasers in the long-wavelength band can also be reflected in temporal variations.
Fig. 6. Typical spectra and corresponding temporal variations of random lasing at different concentrations of the Rh640 solution. (a) Spectrum at 1 mM. (b) Temporal variation at 1 mM. (c) Spectrum at 3 mM. (d) Temporal variation at 3 mM. (e) Spectrum at 5 mM. (f) Temporal variation at 5 mM.
At the Rh640 dye concentration of 1 mM, the produced random laser is characterized as an incoherent random laser with a short wavelength. Due to the low concentration, there is a predominance of monomers over dimers in the dye solution, resulting in an indiscernible ET process. Moreover, the low gain at this concentration leads to the random laser operating in an incoherent mode with a limited number of modes, as evidenced by subtle fluctuations in temporal variation. As the Rh640 dye concentration increases, the ET process becomes more pronounced. At 3 mM, a robust long-wavelength coherent random laser and a weaker short-wavelength incoherent random laser emerge. At 5 mM, only long-wavelength coherent random lasers are predominantly observed. This escalation in dye concentration correlates with a significant increase in dimer formation. The heightened efficiency of the ET process amplifies the gain of dimers while diminishing that of monomers. Consequently, the increased gain facilitates the generation of coherent modes by dimers, resulting in a greater number of modes and rapid fluctuations in time sequences. Hence, the ET process plays a pivotal role in regulating mode competition within the random laser, directly influencing spectral and temporal variations observed in the random laser output.
To further assess the potential of temporal variations in generating random numbers using coherent and incoherent random lasers, we conducted a study on the statistical distribution of the time series. The quality of random numbers primarily relies on the statistical characteristics of the sources of randomness. As an example, we analyzed the time series data collected at a concentration of 5 mM. To mitigate the discrete influence of marginal data points, we selected the central 120 data points from the time series plot and sampled every 4 data points, which are represented by the red points in Fig. 7.
Fig. 7. Schematic diagram of data acquisition points (using the time series data collected at a concentration of 5 mM as an example). Selecting the central 120 data points from each temporal plot, sampling points were taken every four data points (in red).
We aggregated multiple time series plots collected at each concentration for sampling. For a more accurate comparison, we derived 500 data sampling points from concentrations of 1 mM, 3 mM, and 5 mM, respectively. The histograms depicting the intensity distribution of the sampling points are presented in Fig. 8(a) to Fig. 8(c). From Fig. 8(a), it is evident that the distribution of sampling points at a concentration of 1 mM is significantly uneven. In contrast, the distribution of sampling points at concentrations of 3 mM and 5 mM (excluding a few data points with large deviations) tends to resemble a normal distribution, as indicated by the red box in the figure. The distribution of the original data at a concentration of 5 mM appears to be the most favorable. It should be noted that due to the limited quantity of time series data obtained in the initial experiment using short-pulse pumped lasers, the results are relatively preliminary.
Fig. 8. Statistical characteristics of sampling points extracted from original data at different concentrations of the Rh640 solution. (a) 1 mM. (b) 3 mM. (c) 5 mM.
To eliminate any unwanted statistical biases, we can employ high-order finite difference on the original data. The calculation of the mth-order difference is demonstrated by Eq. (6),
Fig. 9. Statistical characteristics after applying 3th-order differential processing to the original data at different concentrations of the Rh640 solution. (a) 1 mM. (b) 3 mM. (c) 5 mM.
Sampling and statistical distribution of time series data for random laser intensity demonstrate its potential for generating random number sequences. Coherent random lasers in the long-wavelength band are more favorable for generating high-quality random number sequences compared to incoherent random lasers in the short-wavelength band. This is due to the amplification of the gain in the dimer through the ET process, resulting in a more diverse range of coherent modes and intense competition, leading to pronounced time series variations in intensity and a statistical distribution close to a normal distribution. Therefore, time series variations based on coherent random lasers have the capacity to generate high-quality random number sequences. On the other hand, the gain in the monomer is reduced by the ET process, resulting in an incoherent random laser with weak intensity, minimal mode changes, inconspicuous time series variations in intensity, and a significantly uneven statistical distribution. These characteristics indicate that the time series variation of the incoherent random laser is not suitable for generating high-quality random number sequences.
The spectrum of random lasers has shown immense potential in high-speed random number generation. However, the approach relying on time series in the intensity of random lasers still encounters a few challenges. Firstly, high-gain materials and high-scattering feedback structures are necessary to reduce the threshold of random lasers. Secondly, microsecond-level long pulse widths, or even continuous lasers, are required for pumping random lasers to ensure sufficient time series data for generating random number sequences. Lastly, coherent random lasers can be generated at low pump energy densities to guarantee the production of high-quality random number sequences.
4. Conclusion
A random laser was fabricated using PDMS engraved with the groove structure of the inner surface of an abalone shell as a scattering substrate and Rh640 dye solution as the gain medium, achieving bichromatic emission. With an increase in Rh640 dye concentration, more dimers are formed, and the ET process between excited monomers and fundamental dimers is enhanced under 532 nm pumped laser excitation. To further investigate the impact of ET processes on mode competition in coherent and incoherent random lasers, we conducted a semi-quantitative evaluation of ET processes between monomers and dimers at a 3 mM concentration. With a high-efficiency ET process, the influence of coherent and incoherent random laser mode competition is minimal, and the energy transfer factor related to pump energy density is determined. ET processes also directly affect the temporal variation of coherent and incoherent random laser intensities. By assessing the statistical distribution characteristics of random laser time series, we demonstrate that the data point distribution of coherent random lasers is closer to the normal distribution, indicating the feasibility of generating high-quality random number sequences. Once again, the ET process amplifies dimer gain, leading to intensified competition among coherent random laser modes, as evidenced by intricate temporal variations in random laser intensity.
Funding
National Natural Science Foundation of China (22173102, 21973093, 22203096, 61505210); Natural Science Foundation of Liaoning Province (2021-MS-021); Dalian Science & Technology Star Program (2018RQ02); State Key Laboratory of Laser Interaction with Matter (SKLLIM2010); Dalian Institute of Chemical Physics, Chinese Academy of Sciences (DICP I201931).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. R. V. Ambartsumyan, N. G. Basov, P. G. Kryukov, et al., “A laser with a nonresonant feedback,” IEEE J. Quantum Electron. 2(9), 442–446 (1966). [CrossRef]
2. V. S. Letokhov, “Quantum statistics of multi-mode radiation from an ensemble of atoms,” Sov. Phys. JETP 26, 1246–1251 (1968).
3. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, et al., “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994). [CrossRef]
4. D. S. Wiersma and Ad Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54(4), 4256–4265 (1996). [CrossRef]
5. H. Cao and Y. G. Zhao, “Random Laser Action in Semiconductor Powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999). [CrossRef]
6. D. S. Wiersma and S. Cavalieri, “A temperature-tunable random laser,” Nature 414(6865), 708–709 (2001). [CrossRef]
7. D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008). [CrossRef]
8. M. Leonetti, C. Conti, and C. Lopez, “The mode-locking transition of random lasers,” Nat. Photonics 5(10), 615–617 (2011). [CrossRef]
9. R. Sapienza, “Determining random lasing action,” Nat. Rev. Phys. 1(11), 690–695 (2019). [CrossRef]
10. D. Wiersma, “Laser physics: The smallest random laser,” Nature 406(6792), 133–135 (2000). [CrossRef]
11. J. Ziegler, C. Wörister, C. Vidal, et al., “Plasmonic nanostars as efficient broadband scatterers for random lasing,” ACS Photonics 3(6), 919–923 (2016). [CrossRef]
12. T. Zhai, X. Zhang, Z. Pang, et al., “Random laser based on waveguided plasmonic gain channels,” Nano Lett. 11(10), 4295–4298 (2011). [CrossRef]
13. X. Shi, Q. Chang, Y. Bian, et al., “Line Width-Tunable Random Laser Based on Manipulating Plasmonic Scattering,” ACS Photonics 6(9), 2245–2251 (2019). [CrossRef]
14. L. Ye, Y. Feng, Z. Cheng, et al., “Coherent Random Lasing from Dye Aggregates in Polydimethylsiloxane Thin Films,” ACS Appl. Mater. Interfaces 9(32), 27232–27238 (2017). [CrossRef]
15. Z. Wang, M. Cao, G. Shao, et al., “Coherent random lasing in colloidal quantum dot-doped polymer-dispersed liquid crystal with Low threshold and high stability,” J. Phys. Chem. Lett. 11(3), 767–774 (2020). [CrossRef]
16. H. Zhang, G. Feng, S. Wang, et al., “Coherent random lasing from liquid waveguide gain channels with biological scatters,” Appl. Phys. Lett. 105(25), 253702 (2014). [CrossRef]
17. S. Chen, J. Lu, B. Hung, et al., “Random lasers from photonic crystal wings of butterfly and moth for speckle-free imaging,” Opt. Express 29(2), 2065–2076 (2021). [CrossRef]
18. X. Li, H. Liu, X. Xu, et al., “Lotus-leaf-inspired flexible and tunable random laser,” ACS Appl. Mater. Interfaces 12(8), 10050–10057 (2020). [CrossRef]
19. V. S. Gummaluri, R. Gayathri, C. Vijayan, et al., “Bio-inspired wrinkle microstructures for random lasing governed by surface roughness,” Opt. Lett. 46(5), 1033–1036 (2021). [CrossRef]
20. F. Luan, B. Gu, A. S. L. Gomes, et al., “Lasing in nanocomposite random media,” Nano Today 10(2), 168–192 (2015). [CrossRef]
21. B. Redding, M. A. Choma, and Hui Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012). [CrossRef]
22. J. Tong, X. Shi, L. Niu, et al., “Dual-color plasmonic random lasers for speckle-free imaging,” Nanotechnology 31(46), 465204 (2020). [CrossRef]
23. Y. Zhang, J. Wang, L. Wang, et al., “Carbon dots with blue-to-near-infrared lasing for colorful speckle-free laser imaging and dynamical holographic display,” Adv. Mater. 35(31), 2302536 (2023). [CrossRef]
24. K. Wu, H. Zhang, Y. Chen, et al., “All-silicon microdisplay using efficient hot-carrier electroluminescence in standard 0.18µm CMOS technology,” IEEE Electron Device Lett. 42(4), 541–544 (2021). [CrossRef]
25. Z. Zhan, Z. Liu, J. Du, et al., “Thermally evaporated MAPbBr3 perovskite random laser with improved speckle-free laser imaging,” ACS Photonics 10(9), 3077–3086 (2023). [CrossRef]
26. Y. Bian, H. Xue, and Z. Wang, “Programmable Random Lasing Pluses Based on Waveguide-Assisted Random Scattering Feedback,” Laser Photonics Rev. 15(4), 2000506 (2021). [CrossRef]
27. M. Karl, J. M. E. Glackin, M. Schubert, et al., “Flexible and ultra-lightweight polymer membrane lasers,” Nat. Commun. 9(1), 1525 (2018). [CrossRef]
28. X. Shi, W. Song, D. Guo, et al., “Selectively visualizing the hidden modes in random lasers for secure communication,” Laser Photonics Rev. 15(10), 2100295 (2021). [CrossRef]
29. S. Chen, X. Zhao, Y. Wang, et al., “White light emission with red-green-blue lasing action in a disordered system of nanoparticles,” Appl. Phys. Lett. 101(12), 123508 (2012). [CrossRef]
30. T. Zhai, Z. Xu, S. Li, et al., “Red-green-blue plasmonic random laser,” Opt. Express 25(3), 2100–2106 (2017). [CrossRef]
31. A. Boschetti, A. Taschin, P. Bartolini, et al., “Spectral super-resolution spectroscopy using a random laser,” Nat. Photonics 14(3), 177–182 (2020). [CrossRef]
32. R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85(7), 1289–1291 (2004). [CrossRef]
33. A. Pospori, C.A.F. Marques, D. Sáez-Rodríguez, et al., “Thermal and chemical treatment of polymer optical fiber Bragg grating sensors for enhanced mechanical sensitivity,” Opt. Fiber Technol. 36, 68–74 (2017). [CrossRef]
34. J. D. Hart, Y. Terashima, A. Uchida, et al., “Recommendations and illustrations for the evaluation of photonic random number generators,” APL Photonics 2(9), 090901 (2017). [CrossRef]
35. A. Uchida, K. Amano, M. Inoue, et al., “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008). [CrossRef]
36. A. Theodosiou, R. Min, A. G. Leal-Junior, et al., “Long period grating in a multimode cyclic transparent optical polymer fiber inscribed using a femtosecond laser,” Opt. Lett. 44(21), 5346–5349 (2019). [CrossRef]
37. M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, et al., “Photon arrival time quantum random number generation,” J. Mod. Optic. 56(4), 516–522 (2009). [CrossRef]
38. C. Gabriel, C. Wittmann, D. Sych, et al., “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010). [CrossRef]
39. H. Guo, W. Tang, Y. Liu, et al., “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E 81(5), 051137 (2010). [CrossRef]
40. C. R. S. Williams, J. C. Salevan, X. Li, et al., “Fast physical random number generator using amplified spontaneous emission,” Opt. Express 18(23), 23584–23597 (2010). [CrossRef]
41. A. Marandi, N. C. Leindecker, K. L. Vodopyanov, et al., “All-optical quantum random bit generation from intrinsically binary phase of parametric oscillators,” Opt. Express 20(17), 19322–19330 (2012). [CrossRef]
42. P. J. Bustard, D. G. England, J. Nunn, et al., “Quantum random bit generation using energy fluctuations in stimulated Raman scattering,” Opt. Express 21(24), 29350–29357 (2013). [CrossRef]
43. M. J. Collins, A. S. Clark, C. Xiong, et al., “Random number generation from spontaneous Raman scattering,” Appl. Phys. Lett. 107(14), 141112 (2015). [CrossRef]
44. K. Kim, S. Bittner, Y. Zeng, et al., “Massively parallel ultrafast random bit generation with a chip-scale laser,” Science 371(6532), 948–952 (2021). [CrossRef]
45. L. Sznitko, T. Chtouki, B. Sahraoui, et al., “Bichromatic laser dye as a photonic random number generator,” ACS Photonics 8(6), 1630–1638 (2021). [CrossRef]
46. J. Li, X. Li, Y. Li, et al., “Dual-band random laser based on positive replica of abalone shell,” J. Lumin. 241, 118543 (2022). [CrossRef]
47. J. Li, J. Liu, D. Liu, et al., “Ultrafast random number generation based on random laser,” J. Lightwave Technol. 41(16), 5233–5243 (2023). [CrossRef]
48. M. A. F. de Souza, A. Lencina, and P. Vaveliuk, “Controlling bichromatic emission in scattering gain media,” Opt. Lett. 31(9), 1244–1246 (2006). [CrossRef]
49. R. Barbosa-Silva, A. F. Silva, A. M. Brito-Silva, et al., “Bichromatic random laser from a powder of rhodaminedoped sub-micrometer silica particles,” J. Appl. Phys. 115(4), 043515 (2014). [CrossRef]
50. F. S. De Vicente, L. X. Moreno, M. V. A. Prado, et al., “Tunable random lasing in dye-doped mesoporous silica SBA-15,” Phys. Rev. Mater. 5(2), 025203 (2021). [CrossRef]
51. A. L. Moura, R. Barbosa-Silva, C. T. Dominguez, et al., “Single bead near-infrared random laser based on silica-gel infiltrated with Rhodamine 640,” J. Appl. Phys. 123(13), 133104 (2018). [CrossRef]
52. T. Shen, H. Hu, W. Lin, et al., “Coherent Förster resonance energy transfer: A new paradigm for electrically driven quantum dot random lasers,” Sci. Adv. 6(41), eaba1705 (2020). [CrossRef]
53. P. Vaveliuk, A. M. de Brito-Silva, and P. C. de Oliveira, “Model for bichromatic laser emission from a laser dye with nanoparticle scatterers,” Phys. Rev. A 68(1), 013805 (2003). [CrossRef]
54. P. Innocenzi, H. Kozuka, and T. Yoko, “Dimer-to-monomer transformation of rhodamine 6 G in sol-gel silica films,” J. Non Cryst. Solids 201(1-2), 26–36 (1996). [CrossRef]
55. K. Xu, “Silicon electro-optic micro-modulator fabricated in standard CMOS technology as components for all silicon monolithic integrated optoelectronic systems,” J. Micromech. Microeng. 31(5), 054001 (2021). [CrossRef]
