1. Introduction

Transverse Anderson localization arises from the confinement of the electromagnetic waves in transverse plane and the beam propagation takes place in the longitudinal direction. To achieve this, the medium requires to be disordered in transverse (xy) plane and is invariant along the direction of the beam propagation (z direction) so that the refractive index contrast in such a quasi-2D random medium can easily satisfy the Ioffe–Regel criterion [1–3]. Even weak fluctuations in random 2D systems can cause transverse Anderson localization [4–6], but, this is rather challenging to achieve for a 3D case. Nonetheless, it has been demonstrated that one can still obtain the transverse Anderson localization despite the presence of a particular degree of randomness in the direction of the beam propagation [7,8]. The novel concept of transverse Anderson localization in a completely random 3D network has remarkably been revealed in a theoretical study before [9], and interestingly, it has been experimentally achieved for the first time using sound waves [10]. The first observation of the transverse Anderson localization of the light waves in a 3D random medium has been presented by our recently published work [11]. An optical waveguide, fabricated inside a triangular air hole between two fused silica walls, including a 3D disordered medium, made of phenol and dye solution along with naturally formed air bubbles, has been proposed to obtain a single mode Anderson localized cavity. The emission from the dye molecules coupled into a specific Anderson mode was shown to result in an enhanced spontaneous emission rate of the on-resonance quantum light sources with the localized optical mode by a factor of 6.8 [11]. Then, a multimode Anderson localization in a 3D random medium has been achieved using hyperbolic waveguides with different physical characteristics, which were produced in a deltoid-shaped microtube including a similar disordered waveguide medium [12]. The emission dynamics of the dye molecules coupled into particular Anderson modes, which trap the photons at specific resonant frequencies, are also analyzed. In these photonic systems, controlling the number of Anderson modes, sustained by the waveguide systems with slightly different photonic designs, were ensured by varying physical dimensions and optical properties of the optical structures [11,12].

In this paper, strong localization and suppression of multiple Anderson modes are successfully achieved by a single asymmetric optical waveguide in a more elegant and efficient way, which consists of a 3D disordered medium, made of rhodamine dye-doped phenol solution with air bubbles and Ag nanoparticles. The waveguide is formed inside a fused-silica material by drawing the mixture into an air hole via the capillary process. Naturally formed air inclusions and Ag nanoparticles both serve as the scattering centers for strong light confinements, which are detected as sharp resonant modes in the photoluminescence spectra. By changing the amount of Ag nanoparticles in the waveguide medium, the photonic system allows to control the number of modes available for the light emitters to be coupled. In conventional methods, scattering centers are made of materials of which the index of refraction is much higher than the surrounding medium [13]. However, in our case, the scattering centers are made of naturally self-assembled air bubbles. On the other hand, the main function of the additional Ag particles here in this structure is to boost the scattering strength of the 3D random medium.

Ag or Au particles are normally used to achieve the plasmonic effects in light–matter interacting systems if the size of the metal particles is much smaller than the emission wavelength of the source particles [14–17]. However, here in this work, the localized surface plasmon effect is eliminated since the Ag particle size is comparable to the emission wavelength; hence, they act as additional scattering centers.

Moreover, increasing the number of Ag nanoparticles in the waveguide to some extent also facilitates to restrict the light waves in more concentrated volume with enhanced quality factor (Q-factor) of the sustaining mode. Thus, the controllability of the degree of the disorder in the waveguide is ensured by changing the amount of Ag nanoparticles to manage the desired strong optical mode confinement to manipulate light–matter interaction. Additionally, time resolved experiments based on a single photon counting technique have been performed to analyze the changes of the radiative decay rate of the dye molecules, which are coupled into the Anderson localized cavities in the disordered waveguide. The fastest decay population from the fluorescence signal is referred to the emission from the quantum sources, which are on-resonant with the particular Anderson mode without spectral detuning. The radiative decay rate of the dye molecules is observed to be enhanced by up to a factor of about 10.1 through coupling into a specific Anderson localized cavity. Therefore, our experimental and numerical results demonstrate that the photon localization in the disordered waveguide can be controlled in a meticulous and predictable manner, which would pioneer for further studies to comprehend and use the Anderson localized modes in a 3D random network to manipulate light–matter interaction.

2. Experiment

2.1 Preparation of asymmetric optical waveguide

A V-shaped micro-hole inside a fused-silica optical fiber is filled with a guiding material of a 3D random network to form an asymmetrical optical waveguide with scattering centers. The disordered waveguide medium is made of 5 mM rhodamine dye-doped phenol solution with air bubbles and Ag nanoparticles. By drawing the mixture into the micro-hole at 40 °C via the capillary process, the material is confined at the edge of the V-shaped fused-silica walls. The disordered medium is formed while naturally self-assembled air bubbles are generated to function as scattering centers for Anderson localization of the electromagnetic waves, together with the Ag nanoparticles. After the phenol solution is crystallized at a refrigerator, a robust and stable optical waveguide is obtained. The details of the sample preparation are also reported in our previous work [11]. The cross-sectional area images of the asymmetrical optical waveguide are shown in Fig. 1(a) and 1(b), which are taken by the scanning electron microscopy (SEM) and the fluorescence microscopy, respectively. The bright spot shown in Fig. 1(b) indicates the dye-doped material, confined between the fused silica walls, which serves as a 3D random medium for transverse light localization. The sketch of the cross-sectional view of the disordered waveguide is also given in Fig. 1(c), which illustrates the index of refraction of the materials. It shows that the refractive index of the disordered medium (n_p= 1.19) is smaller than the surrounding fused silica fiber (n_f= 1.46) and greater than the air space (n_a= 1), forming both physically and optically an asymmetrical optical waveguide. The thickness (d) of the material confined between the fiber walls at the excitation surface is about 3 µm, based on the information given in Fig. 1(a) and 1(b); however, it exponentially becomes much thicker along the propagation direction.

 

Fig. 1. (a) SEM and (b) fluorescence microscopy images, (c) the sketch of the cross-sectional area of the V-shaped asymmetrical optical waveguide. (d) the sketch of the side view of the asymmetric optical waveguide with a 3D random medium.

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In our work, to enhance the scattering strength of the medium, the Ag nanoparticles with diameters ranging from 300 nm to 600 nm are controllably added to the mixture for strong light confinement and suppression of unwanted modes. A sketch of the side view for the asymmetric waveguide with a 3D disordered medium is given in Fig. 1(d). Both excitation and photoluminescence (PL) emission of the dye molecules are obtained from the same cross-sectional face of the waveguide, as displayed in Fig. 1(d). In such a 3D random medium of the waveguide, the electromagnetic waves are scattered from both air inclusions and Ag nanoparticles to constitute standing waves in a loop and they remain in the localized state in the transverse plane (xy-plane) when the beam width becomes comparable to the localization length [18,19]. Then, a quasi-optical cavity, which traps the photons at a certain frequency, is obtained to form transverse Anderson localization of light waves in a completely disordered 3D network. The guidance of the light localization is also provided by fused silica fiber along the z-axis.

2.2 Time-resolved experiments

The optical setup is designed to detect the Anderson modes in random media through photoluminescence (PL) spectra by a photo-spectrometer (Ocean Optics) and to measure their time-resolved fluorescence emission by Time Harp 200 PC-Board system (Picoquant, GmbH), simultaneously. The dye molecules embedded in the waveguide are optically excited at the wavelength of 515 nm, using a high-power pulsed laser with a repetition rate of 30 Hz and pulse duration of 1.2 ns (Flare NX 515-0.6-2 Coherent). The excitation field is focused on the disordered waveguide medium through a microscope objective (Nikon ELWD 100 X) and its intensity is adjusted by a reflective density filter. The fluorescence signal of the dye molecules is separated from the excitation signal using a dichroic beam splitter and a band pass filter and is collected by the same microscope objective. When the Anderson localized optical mode is observed in the PL spectra, then, a picosecond pulsed diode laser at the wavelength of 470 nm (LDH-D-C-470 Picoquant, GmbH) is used to obtain the time-resolved fluorescence signal. The emission signal is simultaneously directed to the photo-spectrometer and the single-photon avalanche photodiode after it is filtered at the resonant wavelength of a specific mode via a monochromator, which is interrogated to the optical setup before the detector.

3. Results and discussion

The PL spectra of the excited dye molecules coupled into Anderson localized cavities in the asymmetrical optical waveguide are obtained by collecting fluorescence signal from the transverse plane of the asymmetrical waveguide under high-power excitation, as shown in Fig. 1. The PL spectrum of the light sources confined in the random medium of the waveguide in which the scattering centers are naturally self-assembled air inclusions is shown in Fig. 2(a). It reveals that such a photonic system with a disordered medium sandwiched between the V-shaped fiber walls with a cross-sectional thickness of 3 µm at the excitation surface is designed to allow the guidance of at least three dominant optical modes that appear at the emission wavelengths of 567.2 nm, 569.5 nm and 571.6 nm. Therefore, the multiple scattering wave phenomenon is exploited in such a random network for light localizations through constructive interference of the electromagnetic waves to generate standing waves in three distinctive closed loops at random frequencies and locations in the optical waveguide. Two more samples with different Ag nanoparticle concentrations, prepared using the same asymmetric waveguide structure, are investigated during the experiments to understand the effect of the further increase in the scattering strength of the disordered medium on the localization dynamics of the Anderson modes. When 1.6 g/L Ag nanoparticles are added to the disordered waveguide medium, the scattering strength of the random structure enhances to allow the suppression of some of the guided Anderson localized modes. For example, as shown in the PL spectrum given in Fig. 2(b), the waveguide has provided mostly two distinctive Anderson modes. These two resonant optical modes are clearly observed at the emission wavelengths of 565.5 nm and 568.7 nm, which are attributed to be the emissions from the quantum light source coupled into the two specific Anderson localized cavities in the asymmetric optical waveguide. Then, 3.2 g/L of the Ag nanoparticles is added to the same mixture to further increase the scattering strength of the disordered medium. It results in the suppression of the majority of the localized modes and, on the average, the guidance of one single dominant Anderson mode. Figure 2(c) shows one of the single-mode PL spectrum results at 565.8 nm. Thus, experimental results confirm that as the degree of the disorder in such a waveguide medium is increased, by adding more Ag nanoparticles in the environment, many more undesired optical modes are suppressed, eventually leading the confinement of one single dominant optical mode only.

 

Fig. 2. The PL spectra of the dye molecules coupled into the Anderson localized cavities in the asymmetrical optical waveguide in which the scattering centers are randomly oriented (a) air inclusions, (b) air inclusions and 1.6 g/L Ag nanoparticles and c) air inclusions and 3.2 g/L Ag nanoparticles.

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The Q-factor of the resonant cavity is determined by Q = λ_c/Δλ_c in which λ_c and Δλ_c are the central wavelength and the spectral linewidth of the resonant optical mode, respectively [20]. The spectral linewidth of the Anderson localized mode shown in Fig. 2(c) is determined to be about 0.8 nm, yielding a Q-factor of 707. This value is significantly higher than the previously reported values for the Anderson localized modes generated in similar disordered waveguides, consisting of solely air inclusions [11,12]. Thus, it would be fair to claim that adding a certain amount of Ag nanoparticles into the waveguide allows to considerably enhance the Q-factor of the quasi-optical cavity. It is also proven from the PL spectra in Fig. 2(a) and 2(b) that each optical mode confined in the asymmetrical optical waveguide is observed to be spectrally stabilized and distant from each other and having a minimized mode competition, which can only be possible in the Anderson localized regime [21–23]. On the other hand, the stability and the efficiency of the Anderson localized cavity is more improved by adding more Ag nanoparticles into the waveguide medium to function as additional scattering centers, as shown by Fig. 2(c).

Such a spectral mode profile like a sharp lasing peak shown in Fig. 2(c) unveils that the generated quasi-optical cavity in the asymmetrical waveguide traps the photons at a specific resonant frequency, similar to a traditional photonic cavity with a moderate Q-factor. Although the traditional photonic cavities have been elegantly designed in countless ways to provide much higher Q-factors, nevertheless, they have also been demonstrated to be considerably susceptible to unavoidable inhomogeneities or fabrication imperfections [24–26]. On the other hand, in our case, the disorders of the system are exploited to control the light emission. More importantly, although our optical waveguide is designed to obtain multi-mode localizations, it also facilitates suppression of undesired optical modes and directing photons to be trapped by a single quasi-optical cavity through boosting the scattering strength of the medium. When the dye molecules are coupled into such Anderson localized cavity, a significant change occurs in the vacuum fluctuations and the localized density of states are naturally altered. This causes the radiative decay rate of the on-resonant quantum sources to change dramatically. A time resolved spectroscopy based on a single photon counting technique is used to directly probe the emission from the Anderson localized cavities.

The decay dynamics of the light sources, which are coupled into a transversely localized Anderson mode and in bulk, are shown in Fig. 3. The fluorescence lifetime of the dye molecules in bulk phenol with Ag nanoparticles is determined to be about 3.54 ns. The fluorescence emission signal of the light sources coupled into the resonant Anderson mode is determined by two exponential decay fits of 0.35 ns and 1.60 ns. The fastest decay rate of the multi-exponential decay curves is attributed to the on-resonant dye molecules with the specific Anderson localized mode. This method provides recording the fluorescence lifetime of the dye molecules that are best coupled into the specific Anderson mode without fine-tuning between the fluorescent molecules and the Anderson localized cavity. The enhancement factor of the radiative decay rate ($\varGamma $/$\varGamma $₀) is calculated by the ratio of the spontaneous emission rate of the light emitters coupled into the Anderson localized cavity ($\varGamma $) to that of the emitters in the bulk ($\varGamma $₀) [11]. According to this information, the radiative decay rate of the dye molecules is observed to be enhanced by a factor of about 10.1 through coupling into a specific Anderson localized cavity. This value is considerably higher than that of the quantum light sources, which are best coupled into an Anderson mode in a random medium of a similar optical waveguide in which the scattering centers are solely naturally self-assembled air inclusions only [11,12]. The improvement on the enhanced decay rate is basically due to the increased Q-factor of the quasi-optical cavity in the presence of the Ag nanoparticles and the suppressed modal interactions. Also, the confinement of the light waves in a much smaller region plays a significant role on the enhancement of the decay rate. Hence, the stronger scattering strength results in a stronger coupling of the dye molecules into the Anderson localized mode.

 

Fig. 3. The fluorescence decay curves of the light sources coupled into a transversely localized Anderson mode in the asymmetrical waveguide and in the bulk.

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In addition to all these, in the literature, cavity quantum electrodynamics experiments were performed by quantum dots and Anderson localized modes, generated in a disordered photonic crystal waveguide [27]. The emission rate of the quantum source coupled into the Anderson mode in the disordered medium was demonstrated to be enhanced by a factor of 15 by spectral tuning of a single quantum dot into a resonant Anderson localized cavity. Another statistical study reported an average Purcell factor of 4.5 ± 0.4 for the light emission of quantum light sources coupled into Anderson modes without spectral detuning in the disordered photonic crystal waveguides [28]. Although the photonic device proposed here in this work has not been produced by any advanced lithographic fabrication processes, the enhancement on the radiative decay rate through coupling of the quantum sources in such a 3D random medium is observed to be comparable to that of the previously recorded values obtained from sophisticated devices [27,28].

Statistical measurements of the decay dynamics for on-resonant quantum sources with specific Anderson modes, generated in the same asymmetric waveguide, are performed at the same experimental conditions. In each case, the Anderson localized cavities are detected and probed directly via a time resolved spectroscopy. The fluorescence lifetime of the on-resonant dye molecules with specific Anderson modes is determined to be ranging from 0.35 ns to 1.84 ns. The statistical distribution of the decay rate enhancement factors of the on-resonant quantum sources with specific modes in the same asymmetric disordered waveguide is graphed in Fig. 4. The variance of the enhancement factor of the radiative decay rate is calculated by Var($\varGamma $/$\varGamma $₀) =­ <($\varGamma $/$\varGamma $₀)²> - <($\varGamma $/$\varGamma $₀) > ², which is found to be equal to 6.5. This value, which reveals the random nature of the light localization in a 3D disordered medium, is observed to be higher than the previously recorded value for that of the Anderson modes generated in a V-shaped optical waveguide [11], and is comparable to the value for that of the Anderson modes formed in the disordered photonic-crystal waveguide [28].

 

Fig. 4. The statistical distribution of the decay rate enhancement factors of the on-resonant quantum sources with the specific Anderson modes in the same asymmetric disordered waveguide.

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In addition to all these, using a high-power excitation might cause generation of some non-linear effects due to excessive structural heating. However, during our measurements, any unusual patterns caused by such nonlinear effects are not observed. Nevertheless, the effects of non-linearity as a result of cavity interaction remains as a potential research topic.

Numerical calculations are performed by a 3D finite difference time domain (FDTD) technique to confirm the existence of the transverse Anderson localization and the changes of the localization dynamics of the optical modes in the presence of Ag nanoparticles. The exact geometry of the asymmetrical optical waveguide is used in the simulations. A dipole fluorescing at the emission wavelength of the rhodamine dye molecules is placed at the disordered medium of the waveguide. The air bubbles with various dimensions, ranging from nano to micro-scale, and Ag nanoparticles with diameters, ranging from 300 nm to 600 nm, are randomly oriented in a phenol medium of the waveguide. The filling fraction factors of air inclusions and Ag nanoparticles are chosen to be f = 0.40 and f = 0.30, respectively. The cross-sectional electric field intensity profiles for the waveguide in which the disordered medium is made of (i) air inclusions, (ii) Ag nanoparticles, and (iii) both air inclusions and Ag nanoparticles are shown in Fig. 5(a), 5(b), and 5(c), respectively. The random configuration of the air inclusions in the waveguide medium is observed to give rise to four distinctive localizations of the electromagnetic waves, as shown in Fig. 5(a). Although, in our experiments, it is not possible to exclude the air bubbles from the waveguide medium since they are naturally formed due to the capillary process, the random configuration of solely Ag nanoparticles in the same asymmetric waveguide is also simulated and a single extended mode is observed, as displayed in Fig. 5(b). The same air inclusion and Ag nanoparticle configurations, used in the simulations, regarding to the profiles given in Fig. 5(a) and 5(b), are both operated in the same waveguide medium to analyze the synergetic effects of the combined scattering centers on the formation of the Anderson localization. The electric field intensity distribution in such a disordered waveguide medium is shown in Fig. 5(c), which displays a single strongly confined Anderson mode, which drastically traps the photons at a particular frequency. It proves that using both air inclusions and Ag nanoparticles in the simulated waveguide yields a light localization in a more concentrated volume, as shown in Fig. 5(c).

 

Fig. 5. The cross-sectional electric field intensity profiles for the V-shaped asymmetrical optical waveguide in which the disordered medium is made of (a) air inclusions, (b) Ag nanoparticles (nps), and (c) both air inclusions and Ag nps.

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The mode volume values for randomly generated Anderson modes in the asymmetric waveguide are also obtained by FDTD calculations. Since changing the scattering center configuration causes a different electromagnetic wave localization for each time, the mode volume values are also observed to be changing from 0.12(λ/n)³ to 0.97(λ/n)³ for the Anderson localized cavities formed in the asymmetrical optical waveguide in which the disordered medium is made of both air inclusions and Ag nanoparticles.

To analyze the size effects of the Ag nanoparticles on the formation of Anderson localized modes, the simulations are repeated using Ag nanoparticles with different diameters and the same configuration. Figure 6 shows the cross-sectional electric field intensity profiles for the waveguide in which the disordered medium is made of Ag nanoparticles with different diameters of a_Ag= 150 nm, a_Ag= 200 nm, a_Ag= 250 nm and a_Ag= 350 nm while the same air inclusion configuration is included in all simulations. It is clearly observed that when the diameter of the Ag nanoparticles is gradually increased to the value of 350 nm, which is comparable to the emission wavelength of the dye molecules, light concentration in a smaller volume is achieved along with the suppression of the undesired optical modes, as shown by Fig. 6(d).

 

Fig. 6. The cross-sectional electric field intensity profiles for the V-shaped asymmetrical optical waveguide in which the disordered medium is made of air inclusions and Ag nanoparticles with different diameters of (a) a_Ag= 150 nm, (b) a_Ag= 200 nm, (c) a_Ag= 250 nm, and (d) 350 nm.

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Additionally, the filling fraction factor of the Ag nanoparticles is also investigated to better understand its impact on the localization dynamics of the Anderson modes. Figure 7 gives the cross-sectional electric field intensity profiles for the asymmetric optical waveguide in which the disordered medium is made of air inclusions with the same configuration and Ag nanoparticles with different filling fraction factors of f = 0.10, f = 0.20, f = 0.25, and f = 0.30; without changing the configurations of the remaining Ag nanoparticles. The majority of the Anderson modes is eliminated to enable guidance of a single dominant mode when the filling fraction factor of the Ag nanoparticles is gradually increased to the value of f = 0.30, as shown in Fig. 7(d). This result is in a very good agreement with the experimentally obtained results given in Fig. 2.

 

Fig. 7. The cross-sectional electric field intensity profiles for the asymmetrical optical waveguide in which the disordered medium is made of air inclusions and Ag nanoparticles with different filling fraction factors of (a) f = 0.10, (b) f = 0.20, (c) f = 0.25, and (d) f = 0.30.

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Investigations on photonic cavities have been a milestone to discover the quantum nature of the confined light sources, the physical dynamics of the optical modes and the effects of vacuum fluctuations [29–32]. The control of light emission based on these fundamentals of the physics has provided an outstanding insight in various photonics research and technologies, ranging from quantum information technologies [33,34], single photon sources [35], integrated circuits [36] to sensor and laser applications [37,38]. Hence, numerous sophisticated approaches have been developed to control light emission by engineering elegant photonic cavities with precisely controlled units at the nanoscale range [39]. However, it has also been demonstrated that it is not possible to eliminate the unavoidable imperfections of the materials that devices are made of and the fabrication processes, which are definitely known to reduce the efficiency of such devices [24–26]. Surprisingly, a pioneering concept was manifested that using a disorder as a scattering source for localization of the electromagnetic waves, referring to the Anderson localization, offers an alternative to highly-engineered photonic devices to control the light emission [40,41]. Since photonic crystal waveguides are quite eligible for efficient light localization, owing to their high-quality factors (Q-factors) and high sensitivity to fabrication imperfections, they have been successfully utilized for the purpose of generating strongly localized Anderson modes by lithographically calibrated number of additional disorders [42,43]. It is a well-known fact that such well-designed photonic devices offer ideal platforms for controlling light–matter interaction in disorder-induced Anderson localized cavities [27]. Nevertheless, it also requires advanced and high-cost lithographic fabrication techniques to produce such kind of sophisticated devices [44].

Instead of fabricating highly-engineered photonic crystal devices to control light–matter interaction, the fluorescence dynamics of nanosized light emitters in completely random 3D networks, made of highly diffusive particles like ZnO or TiO₂, were also reported to be modified due to fluctuations of the localized density of states, which accounts for the number of available modes at the emission wavelengths of the light emitters in strongly scattering dielectric matrix [45,46]. Quantum light sources embedded in 3D random media consisting of ZnO powders showed to result in a large Purcell enhancement due to strong localization of resonant optical modes in a very small volume [47]. The reduction of the localized density of the photon states was also demonstrated in another study through observation of the lengthening of the fluorescence lifetimes of nitrogen-vacancy color centers in diamond nanocrystals in a scattering medium consisting of a powder of TiO₂ particles [46]. Although these 3D random systems can be considered to be substantially efficient to probe the local environment of the quantum sources in random media, nonetheless, it is also quite challenging to obtain a stable and controllable system sustaining strongly confined optical modes that corresponds to the specific Anderson localized cavities which are available for the quantum light sources to be coupled as it is successfully achieved by lithographically controlled disordered photonic crystal waveguide studies [26].

Alternatively, transverse Anderson localization has been proposed for localization of electromagnetic waves in a more convenient manner without requiring a strongly disordered network like 3D random systems. Transverse Anderson localization was firstly demonstrated through random fluctuations via 2D photonic lattices by controlling the amount of the disorder in such a system [4]. The observation of strong light localization was shown by a longitudinally invariant optical fiber with a disordered transverse plane made of glass and polymer [48,49]. A stronger localization was also achieved through a higher refractive index contrast in a glass fiber, which was designed to have randomly oriented air holes in the transverse plane [50]. Then, for the first time, the observation of the transverse Anderson localization of the light waves in a 3D random medium was demonstrated by our recently published works [11,12]. In these studies, although the different optical waveguides were designed to efficiently obtain single and multi-mode Anderson localizations of the electromagnetic waves, nonetheless, here in this new work, a single asymmetric optical waveguide is proposed to obtain preferably single and multi-mode localizations.

In photonic systems with complex scattering mechanisms, it is still unclear how nonlinear interactions exactly affect the localizations of light waves. Thus, the research about understanding the nature of Anderson localized cavities with the proposed asymmetric optical waveguide, hosting Anderson localized states, aims to reveal the changes of the localization dynamics of the Anderson modes when the modal interactions are suppressed and all photons are routed into a single channel as the scattering strength of the random medium of the same optical waveguide is increased by adding extra Ag nanoparticles. In contrast to conventional photonic cavities, Anderson localized cavities, which are based on disordered gain media, where photons experience random multiple scatterings, are majorly multimode. In one hand, strong modal interactions are assumed to be eliminated, owing to strong light localizations in the Anderson localized regime; on the other hand, controlling the number of individual optical modes also alters the localization length of the quasi-optical modes [22]. In this work, although the waveguide medium is designed to support the guidance and localization of multi-modes, nonetheless, the suppression of some optical modes is achieved via increasing the degree of the waveguide medium’s disorder to demonstrate the effects of the suppressed modal interactions on the localization dynamics of the single dominant Anderson mode.

Time resolved experiments proves that suppression of some Anderson modes, that is, the inhibited modal interactions, significantly alters the localization dynamics of the single guided modes in this random photonic system. Therefore, here in this work, a superior photonic system is being introduced, using a V-shaped asymmetrical optical waveguide to suppress the undesired optical modes and obtain one single dominant Anderson localized mode only, together with the enhanced cavity properties. Localization dynamics of a single mode Anderson cavity, generated in such a disordered asymmetric waveguide, by suppressing modal interactions, is investigated for the first time through radiative decay rates of the fluorescent emitters coupled into such cavity. The Q-factor and the mode volume of the artificial Anderson localized cavity in concern is observed to be improved through suppressing the other Anderson modes in the same optical waveguide. A higher enhancement on the radiative decay rate of the dye molecules coupled into the single dominant Anderson mode is achieved by eliminating the other optical modes, which reveals that the transverse Anderson localization in a 3D random media is not only possible but also controllable in an elegant way. The results also assert that routing photons in one channel in the Anderson localized regime enhances the efficiency of the artificial Anderson localized cavity. In the context of transverse Anderson localization of light waves in a low refractive index system, such as in an asymmetric optical waveguide assembly introduced in this paper; it is envisaged as an original contribution to the field of Anderson localization, through analyses of the effects of the mode suppressions on the localization dynamic of the single guided mode. Since this multimode photonic device facilitates to controllably route the photons in isolated localized channels with enhanced optical device properties, by changing the concentration of Ag nanoparticles, a system like this can be improved to fabricate intelligent random lasers, which allow the suppression of undesired optical modes. It can also be proposed as a quantum switcher to preferably couple the single quantum emitters into an isolated localized optical channel through fine tuning of the Anderson localized mode, enabling the effective host media to produce single photon sources and quantum information processing.

4. Conclusions

In this paper, transverse Anderson localization of light waves in a 3D random network is accomplished by an asymmetrical optical waveguide, which consists of naturally formed air inclusions and Ag nanoparticles in rhodamine dye doped-phenol solution. The disorder level in the waveguide is ensured by changing the amount of the Ag nanoparticles to obtain the desired strong optical mode confinement with an enhanced Q-factor, by eliminating other undesired naturally generated optical channels that the photonic design allows. The time resolved spectroscopy is performed to investigate the changes of the radiative decay rate of on-resonant dye molecules with a particular Anderson mode in the disordered waveguide. The radiative decay rate of the dye molecules is observed to be enhanced by a factor of about 10.1 through coupling into the Anderson localized cavity. The photonic system proposed in this work is envisaged to pioneer investigation of the transverse Anderson localization of light waves in 3D disordered media to control optical modes and manipulate light–matter interaction.

Appendix

Details of the asymmetric optical waveguide

The effective refractive index (n_p) of the disordered waveguide medium is calculated by Bruggeman equation [51]. When the medium consists of phenol solution and air inclusions with a filling fraction factor of 0.40, the effective refractive index of the medium is calculated to be about 1.33. As the Ag nanoparticles with a filling fraction factor of 0.30 are added to the mixture, the effective refractive index of the disordered medium of the asymmetric waveguide is calculated to drop to about 1.19, mainly due to the real part of the refractive index of the Ag nanoparticles.

In the experiments, the filling fraction factors of the Ag nanoparticles in the asymmetric optical waveguide are calculated through the concentrations of the Ag nanoparticles and the physical dimensions of the air inclusions, Ag nanoparticles and the waveguide medium. Thus, the filling fraction factor of the Ag nanoparticles is changed from 0.15 to 0.30 as the nanoparticle concentration is increased from 1.6 g/L to 3.2 g/L during the experiments.

The SEM and brightfield optical images of the waveguide along the z-axis are given in Fig. 8(a) and 8(b), respectively. The waveguide length is adjusted to be about 1 cm, which is sufficient for allowing backscattering of the excited photons and transmitting the excitation beam along the waveguide. The angle of the V-shaped optical waveguide also affects the amount of disordered material confined at the excitation surface of the optical structure. The narrower angle of the V-shaped waveguide might cause an increase material thickness at the surface of the optical waveguide due to the capillary effect. The wedge angle is measured to be about 50° in the experiments.

 

Fig. 8. The SEM and brightfield optical images of the asymmetric optical waveguide along the z-axis.

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A.2 Details of the FDTD simulations

The exact 3D geometry of the asymmetrical optical waveguide is used in the simulations to obtain the numerical calculations of the transverse Anderson modes in a 3D random medium. The mesh grid size of the structure is chosen to be 0.5 nm. To account for the field leakage from the system, caused by the moderate Q-factors of the Anderson localized cavities and the absorptive nature of the Ag nanoparticles, perfectly matched layers are used at the borders of the asymmetric optical waveguide. Hence, the numerical calculations are performed throughout the entire area, including the real space and the perfectly matched layers to obtain the precise field distribution and optical mode volume of the Anderson localized cavities.

Numerical calculations are performed in 3D geometry of the asymmetric waveguide; nevertheless, the field distributions are obtained in xy-plane since the localizations are detected in the cross-sectional face of the optical waveguide and the guidance of the optical modes are observed along the longitudinal direction of the structures in the real experiments. However, the electric field intensity profiles for the waveguide in which the disordered medium is made of (i) air inclusions, (ii) Ag nanoparticles, and (iii) both air inclusions and Ag nanoparticles in zx plane are obtained and shown in Fig. 9(a), 9(b), and 9(c), respectively. Additionally, the electric field intensity profiles for the waveguide in which the disordered medium is made of (i) air inclusions, (ii) Ag nanoparticles, and (iii) both air inclusions and Ag nanoparticles in zy plane are also obtained and shown in Fig. 9(d), 9(e), and 9(f), respectively.

 

Fig. 9. The electric field intensity profiles for the waveguide in which the disordered medium is made of (a) air inclusions, (b) Ag nanoparticles, and (c) both air inclusions and Ag nanoparticles in zx plane. The electric field intensity profiles for the waveguide in which the disordered medium is made of (d) air inclusions, (e) Ag nanoparticles, and (f) both air inclusions and Ag nanoparticles in zy plane.

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Funding

Bŏaziçi University Research Fund (16761).

Acknowledgments

The author wants to thank Dr. Ekrem Yartaşı for his help in preparing the samples.

Disclosures

The author declares 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 author upon reasonable request.

References

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