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Abstract
Intrinsic properties of a polyethylene glycol nanofiber are utilized for the first time to dynamically modify the spontaneous emission rate of encapsulated boradiazaindacene dye molecules with fluorescence lifetime imaging. Nanofibers, fabricated by the electrospinning technique, are exposed to relative humidity up to 80%. The spontaneous emission rate of the confined boradiazaindacene is observed to inhibit and enhance the nanofibers’ swelling. The Purcell factor is determined to demonstrate an oscillatory behavior resulting from the distinct characteristics of the mode volume, and the step-like increase of the quality factor of the nanofiber cavity due to the changes in the refractive index and fiber diameter.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
One of the most sophisticated methods to make a connection between the atomic physics and the macroscopic electrodynamics is the study of inhibition or enhancement of the spontaneous emission rate of the fluorescent nanoparticles confined in nano or micro-cavities. For the situations where the wavelength of the emitter is comparable to the cavity size, the photo physical properties of the dye molecules are highly affected since the vacuum states of the emitter are significantly altered by the cavity confinement. Such a change is measured by the Purcell factor [1]. Therefore, the rate of the spontaneous emission can be controlled by modifying the emitter’s environmental photonic conditions, which result in the changes of the local density of the electromagnetic states (LDOS) [2]. This modification has become more of an issue for the evolution of the many types of the photonic and optoelectronic devices in numerous fields such as illumination, photonics, lasers, solar cells, and quantum information processing systems [3–8].
Innumerable studies have been accomplished to modify and investigate the dynamics of the spontaneous emission rate of the individual emitters like quantum dots or organic dye molecules confined in different types of nano or micro cavities with various dimensions [9–16]. Especially, photonic crystals and micro pillar cavities have been commonly used to manipulate the light and matter interactions to construct devices based on the fundamentals of quantum electrodynamics [17–24]. Polymer nanofibers seem to have a great potential in offering a substantial alteration of the vacuum fluctuations of the emitters arising from their suitable dielectric properties [25, 26]. These nanostructures have been extensively practiced in numerous biomedical applications over the last two decades due to the similarity between different forms of some nanofiber types and human tissues. Polyethylene Glycol (PEG) is known to be one of these biocompatible polymers [27]. Besides being a significant and important commercial nanomaterial for many chemical, biological and biotechnological applications [28], PEG is also employed in various quantum devices as anchoring or insulating agent between two different substances due to its distinct polymeric chain, crystallinity and flexibility [29]. In addition, the most important feature of the PEG is being a very hydrophilic material [30]. This unique property of the PEG makes it to be almost indispensable for controlling its physical parameters by exposing it to the humid air.
In this work, PEG’s hydrophilic material properties are utilized for the first time to alter the spontaneous transition rate of the Boradiazaindacene (BODIPY) dye molecules, which are doped in PEG nanofibers. The dye-doped nanofibers are produced by electrospinning, which is an efficient and cost-effective technique to fabricate almost uniform nanofibers with desired diameters, ranging from several hundreds of nanometers to micrometer scale. The physical mechanism affecting the spontaneous emission rate of the encapsulated BODIPY dye molecules within a single nanofiber is investigated through studying inhibition and enhancement in their lifetimes using a time resolved fluorescence lifetime imaging method. Nanofibers are excited with 470 nm picosecond light source while they are exposed to relative humidity (RH) from 40% up to 80%. Results show that the inhibition and enhancement occurring in the spontaneous emission rate of the dye molecules exhibit an oscillatory manner, arising from the humidity induced variations in the refractive index and diameter of the PEG nanofibers upon swelling. Varying the RH alters the spontaneous emission rate of the dye molecules almost periodically, which directly affects the Purcell factor to demonstrate a similar characteristic between 1.25 and 2.52. This oscillatory behavior of the Purcell factor, originating from the distinct characteristics of the single nanofiber cavity’s mode volume and the steep increase of the quality factor, are also due to the humidity induced changes in the index of refraction and the fiber diameter. Such dynamical mechanism might be a useful candidate as an optical switch for the environments where the relative humidity is desired to be stringently controlled.
2. Spontaneous emission rate
The spontaneous emission rate of a fluorescent molecule (Γ) from its initial state (|i ˃) to its final state (|f >) is given by the Fermi’s Golden rule [31] as
where H is the Hamiltonian of the atom-field interaction, ρ(ω) is the local density of the electromagnetic states that signifies the density of the vacuum fluctuations for an optical medium of the index of refraction n per unit energy at the angular frequency ω, which is given by [10]where V is the mode volume calculated by integrating the field intensity over a volume and normalizing it to the maximum field intensity defined as [32]It is possible to manipulate the spontaneous emission rate given in Eq. (1) via modifying the density of the optical modes. By placing the fluorescent molecule in a photonic cavity, one could modify the vacuum fluctuations and consequently change the spontaneous emission rate of the emitter, which is determined by the Purcell factor Fp [1] as
where Γ0 is the spontaneous emission rate in bulk, λ is the wavelength of the emitter, n is the refractive index of the cavity, and Ԛ is the cavity’s quality factor, which is given by [33]where r = (n-nc)/(n + nc) is the reflectance, which depends on the refractive indices difference between the optical cavity and its surrounding medium of refractive index nc.In this paper, a BODIPY dye doped PEG nanofiber is excited by the laser beam of 470 nm through the lateral surface of the nanofiber as depicted in Fig. 1(a). The nanofiber with cross-sectional diameter d is considered to be infinitely long. It is made of PEG (n = 1.443) and is surrounded by an air cladding (nc = 1), which allows guiding light from the excited dye molecules to be confined in the nanofiber. The nanofiber is exposed to the humid air to perturb the cavity’s photonic density of states. Since the localized density of the electromagnetic states are modified with the nanofiber’s swelling, the spontaneous emission rate is rapidly inhibited and enhanced as the RH takes different values.
Fig. 1 (a) Excitation of the BODIPY doped nanofiber (b) Electric field distributions of the BODIPY dye molecules confined in a single PEG nanofiber for 40% and 80% relative humidity values.
Figure 1(b) shows the calculated electric field patterns of the fluorescing BODIPY dye molecules in a single nanofiber using the specific refractive index and diameter values for the certain RH values of 40% and 80%. The electric filed distributions are calculated using FDTD method. As shown in Figs. 1(a) and 1(b), the nanofiber is taken parallel to z-axis, with the fiber length of 8 μm, which is taken to be much longer than the fiber diameter by a factor of about 16 to perform numerical calculations. This figure is the evidence of the changes in the density of the optical modes corresponding to the given parameters for the particular RH values, which elucidates the modification of the spontaneous emission rate of the encapsulated dye molecules.
3. Experiment
3.1 Preparation of the dye doped PEG nanofibers
BODIPY dye embedded PEG based nanofibers are prepared using electrospinning, a widely used method for producing nanofibers from polymers [27]. The BODIPY dye used here is a bromide-containing derivative, namely, 4,4-difluoro-1,3,5,7-tetramethyl-8-[(10-bromodecyl)]-4-bora-3a,4a-diaza-s-indacene, synthesized according to previously reported literature procedure [34]. A solution of PEG (100 g, MW = 100000g/mol) and the BODIPY dye (1.0 mg) are dissolved in a mixture of 1:8 H2O: isopropyl alcohol (0.9 mL). The solution was fed by a syringe pump (New Era Pump Systems, Inc., New York, USA) to a blunt needle (diameter 0.8 mm) at a flow rate of 0.01 mL/min. A voltage of 15kV using a high voltage power supply (Spellman, SL Series, USA) was applied to the tip of the needle and ejected fibers were collected on a grounded aluminum plate at a horizontal distance of 15 cm. Electrospinning with these parameters yields uniform bead-free nanofibers. The polymeric nanofibers are stored in a desiccator to prevent any damage from humidity prior to the experiments.
3.2 Time resolved fluorescence lifetime and fluorescence intensity measurements
Time resolved fluorescence lifetime measurements and fluorescence intensity measurements are performed with a TimeHarp 200 PC-Board system (Picoquant, GmbH) and a fiber optic spectrometer (USB-4000-VIS-NIR Ocean Optics), respectively. The confocal fluorescence lifetime imaging measurement (FLIM) setup used in our experiments is given in Fig. 2.
A pulsed diode laser emitting at the wavelength of 470 nm with a repetition frequency of 10 MHz (LDH-D-C-470 Picoquant, GmbH) is used as an excitation source and is launched in a single mode optical fiber (Thorlabs, S405-HP) to obtain a pure single mode Gaussian beam illumination. A microscope objective with 0.70 numerical apertures and a working distance of 10.1 mm (Nikon ELWD 100 X) is used in confocal microscopic measurements, that is, to focus the excitation light reflecting from the dichroic mirror onto the sample and to collect the emission of the dye molecules confined in the nanofibers in concern. An optical bandpass filter is employed to completely eliminate the excitation beam. A pinhole with a diameter of 75 μm is inserted into the focal plane to obtain FLIM images with a high resolution. A 3D piezo scanner (Piezo System, NV40-3CLE), which provides a scanning range of 100 × 100 μm2, and SCX 200 (Picoquant, GmbH) as a controller of the fluorescence lifetime imaging are operated to scan the network formed by the electro spun nanofibers. It is well known that the electrospinning nanofibers randomly intersect together during their production. For our samples, the smallest possible volume of nanofibers are grown onto the surface of a piece of a microscope slide, which is scanned using the FLIM method over an area of 50 × 50 μm2. This allows us to study a region that contains only single fibers. A humidity chamber is mounted to the Piezo Scanner as shown in Fig. 2. Saturated KNO3 solution is inserted to the chamber to increase the RH of the environment from 40% to 80%. A nanofiber sample is grown on a microscope slide by electrospinning and is inserted to a humidity chamber, which is then excited from the back side of the microscope slide with the laser beam of 470 nm. A commercially available humidity sensor is placed nearby the nanofiber sample in the humidity chamber. When a specific humidity value is reached, the sample is scanned by the piezo system. During the changes in the humidity level, optical and physical properties of the nanofibers are in situ monitored by the FLIM technique to trace the modification of the spontaneous emission rate. Fluorescence lifetimes of the BODIPY dye molecules confined in nanofibers are determined by SymPhoTime software (Picoquant, GmbH). The FluoFit computer program is used for multi-exponential decay fitting.
The decay of the fluorescence intensity I(t) at time t is obtained from the time domain data to get the fluorescence lifetimes as
where τi represents the fluorescence lifetime of the ith component and Ai is its corresponding decay amplitude. The fractional impact of the components to the total intensity is given byThe intensity decay is analyzed using the average intensity lifetime or the average amplitude lifetime. The amplitude average lifetime is calculated from
The intensity average lifetime is calculated from
4. Results and discussion
PEG nanofibers encapsulating the dye molecules are imaged through changes in the decay rates of the fluorescence from the excited sample. In this technique, the fluorescence lifetimes and the fluorescence intensities of the BODIPY molecules are determined for each pixel to obtain a fluorescence lifetime and an intensity map of the sample. Thus allows monitoring the humidity induced optical and physical changes of the photonic environment. The emission intensity is observed to decrease very slightly, by about 6%, when the humidity goes from 40% up to 80%. For the initial (40%) and final (80%) relative humidity values, the FLIM images of the nanofibers are shown in Fig. 3.
The diameter of the nanofiber increases while the index of refraction shows a decrease due to the water absorption when the RH is raised. Figure 3(a) shows the FLIM images of two separate BODIPY doped PEG nanofibers at 40% RH. The average nanofiber diameter is measured to be 366 nm. The corresponding index of refraction of PEG is taken to be 1.443 as measured in Ref [35]. It is worth noticing that as the radial optical path-length of the nanofiber monotonically increases in a linear manner up to 76% RH levels, a sudden phase transition is observed to occur between 76 and 79% RH values, causing a steep jump in the refractive index and the diameter of the PEG nanofiber. Thereupon, the average diameters of the single nanofibers shown in Fig. 3(a) are seen to enlarge up to approximately 510 nm, as seen in Fig. 3(b), and the refractive index of the PEG becomes 1.441 as the 80% RH is reached (see Table 1). Although the changes in the index of refraction and the diameter of the nanofibers for RH values up to 76% slightly change, this causes a considerable amount of variations in the LDOS of the emitter’s photonic environment for the specified relative humidity values. Spontaneous emission rate is analyzed from 40% to 80% to elucidate this significant change.
Table 1. The average diameter and refractive index of the PEG nanofibers with respect to the RH values.
Figure 4(a) shows absorption, photoluminescence emission of BODIPY. Figure 4(b) shows the fluorescence lifetime decay curves acquired from the excitation of the BODIPY molecules in a single PEG nanofiber for the relative humidity values of 40% and 80%. A substantial change is noticeably seen in the characteristics of these two curves. The fluorescence lifetime of the BODIPY molecules in the bulk PEG is measured from the lifetime decay parameters to be 4.98 ns, which refers to the spontaneous emission rate of Γ0 = 0.20 ns−1. For the relative humidity values of 40%, 50%, 60%, 70% and 80%, the parameters of the decay populations of the dye molecules confined in a single nanofiber are determined by the three exponential decay fit, minimizing the χ2 parameter. Non-single exponential decays of the BODIPY molecules might be attributed to the slightly varied size distribution along the nanofiber. Thus, the dye molecules are localized with different density of electromagnetic states causing a distinctive distribution of non-radiative decay rates. Consequently, the photonic effects on the averaged lifetime of the BODIPY molecules in a single nanofiber is considered.
Fig. 4 (a) Absorption and photoluminescence emission of BODIPY. (b) Fluorescence decay curves of BODIPY molecules in PEG nanofibers for 40% and 80% RH values.
As summarized in Table 2, the amplitude averaged fluorescence lifetime of the dyes in a single nanofiber is measured as 1.98 ns at 40% RH, which is attributed to the spontaneous emission rate of 0.51 ns−1. As the relative humidity is increased to 50%, the averaged lifetime of the emitter becomes 3.87 ns causing a sudden decrease in the spontaneous emission rate of 0.26 ns−1. For the RH value of 60%, the fluorescence lifetime of the dye molecules is determined as 2.03 ns, which corresponds to a sharp increase in the spontaneous emission rate of 0.49 ns−1. When the RH is measured as 70%, the fluorescence lifetime of the BODIPY is determined as 3.86 ns, which is exactly the same as that of the spontaneous emission rate value obtained at 50% RH. The emitter lifetime is measured to be 4.01 ns at 80% RH, corresponding the spontaneous emission rate of 0.25 ns−1, which is almost similar to that of 50% RH. Accordingly, it is observed throughout the humidity rage from 40% to 80% that the spontaneous emission rate shows a strong inhibition and enhancement occurring in a periodic behavior since the optical and physical properties of the photonic environment of the dye molecules are altered with an increase of each 10% RH. However, this periodic behavior is corrupted for the RH value of 80% because of the certain phase transition of the PEG material, which leads to a significant amount of variation in the PEG nanofiber. As there are multiple rises and falls occurring in the spontaneous emission rate between 76% and 79% RH, the final experimental Γ factor is measured to be approximately the same as that of the one obtained at 70% RH.
Table 2. Fluorescence decay parameters of BODIPY molecules in PEG nanofiber for different RH values.
Figure 5 shows the distribution of the decay times as histograms for each humidity value given in Table 2.
Modification of the spontaneous emission rate of the BODIPY dye molecules induced by the electromagnetic resonance is conventionally expressed by the Purcell factor as described by Eq. (4). The experimental data presented in Table 1 and Table 2 are used in Eq. (4) to calculate the Purcell factor for the doped BODIPY dye molecules in a single nanofiber shown in Fig. 3. Figure 6 shows the experimental and calculated Purcell factor versus humidity for a single nanofiber, which demonstrates a characteristics of an oscillatory step function.
Fig. 6 Calculated and measured Purcell factors of the dye molecules confined in nanofiber corresponding to the RH values.
The Purcell factor is experimentally measured via the ratio of the spontaneous emission rates (Γ/Γ0) to be 2.52 at the RH level of 40%, for the amplitude weighted average lifetimes. When the RH is increased to 50%, the Purcell factor is observed to suddenly fall to 1.29. It takes values of 2.45 and 1.29 when the relative humidity is 60% and 70%, respectively, as indicated with red dot points in Fig. 6. It exhibits sudden rises and falls as the RH is varied up to 80%, giving a corresponding Purcell factor of 1.25. These periodic variations in the Purcell factor is attributed to the fluctuations in the LDOS in the cavity originating from the changes of the diameter and the refractive index of the PEG nanofiber upon swelling. More sudden up and down jumps in the Purcell factor are expected to be observed in the rapidly varying phase transition region of the PEG nanofiber for the humidity levels between 75% and 80%. However, the Purcell factor of such often fluctuating jumps would be almost the same as those of the experimental data shown in Fig. 6. Additionally, it is clearly seen from Fig. 6 that this good agreement between the measured and calculated Purcell factors confirms that the spontaneous emission rate of the embedded dye molecules is strongly affected by the photonic environment of the cavity. Thus, the variation pattern of the Purcell factor is due to the dyes’ electromagnetic field playing a fundamental role on the spontaneous emission rate, which is inversely proportional to the mode volume and linearly proportional to the quality factor of the nanofiber cavity.
The quality factor Q and the mode volume V directly affect the Purcell factor as their relations are described by Eq. (4). In our experiments, swelling induced changes in the diameter and the refractive index of the single PEG nanofiber principally modify the Q factor and the mode volume of the photonic environment, and hence the Purcell factor changes. Figure 7(a) shows the Q factor versus relative humidity, by making use of the determined diameter and refractive index values, given for specific RH values, in Table 1, using Eq. (5). For the initial RH value of 40%, the Q factor is calculated as 2.35 and it increases linearly up to a value of 76% RH. A significant steep jump of Q factor occurs between the RH values of 76% and 79% due to the substantial amount of the swelling of the PEG nanofiber. After this swelling induced phase transition in the PEG’s physical structure, Q factor starts to gradually increase in a more moderate manner, reaching a value of 3.12 for the 80% RH. Figure 7(b) demonstrates the mode volume behavior versus RH, which is obtained from the calculations using the experimental data presented in Table 1 and Ref [34] for the swelling induced fiber diameter and index of refraction, respectively. For 40% RH, the mode volume is determined as 0.06(λ/n)3 for the emitter wavelength of λ = 510 nm, which is the central emission wavelength of the confined BODIPY molecules in a single nanofiber shown in Fig. 3. As seen in Fig. 7(b), sharp rises and falls occur in the mode volume values as a result of the variations in the dipole’s electromagnetic field since the optical dimensions of the nanofiber cavity are altered as the RH increases. Demonstrating a similar characteristics like that of the Purcell factor given in Fig. 6, the mode volume reaches 0.21(λ/n)3 as the relative humidity of the environment is 80%. The data presented in Fig. 7 are used to obtain the calculated values of the Purcell factor shown in Fig. 6.
Fig. 7 (a) Q factor versus relative humidity (b) Mode volume of the dye molecules confined in PEG nanofiber with respect to the changing RH values.
As stated above, the reason for the oscillatory step profile shown in Fig. 6 is due to the mode volume, given by Fig. 7(b). Such oscillation profile is due to both index of refraction and diameter of the nanofiber. Figure 8 describes the mode volume as a function of the fiber diameter and the index of refraction. Figure 8(a) shows the mode volume versus fiber diameter by taking the index of refraction constant, i.e., n = 1.443. Figure 8(b) shows the mode volume versus the index of refraction for a constant fiber diameter, i.e., d = 366 nm. It is obviously seen that the dominant parameter affecting the oscillatory step profile of the mode volume, and hence the Purcell factor, is the change in the fiber diameter rather than the index of refraction, causing the value of the mode volume to fluctuate by about 200%, as d is increased from 366 nm to 510 nm; whereas the change due to the refractive index is just 12%, as the index of refraction decreases from 1.443 to 1.411. This oscillatory behavior is envisaged to be due to the emitter’s coupling into the radiative modes, in addition to the guided HE11 mode, since our d/λ takes values between 0.7 and 1. As described in Ref [12], if d/λ is sufficiently small, between 0.15 and 0.19, the field amplitude inside the nanowire gradually increases but remains almost uniform; thus, no oscillatory behavior is observed in the Purcell factor since the maximum spontaneous emission is coupled into the fundamental guided HE11 mode. However, if d/λ ratio is greater than 0.19, the dye emission couples into a continuum, called the radiative modes, and additionally into other guided modes, the total spontaneous emission rate shows an oscillatory manner, because the screening effect becomes maximum in the vicinity of the wire axis since the field amplitude turns out to be position dependent inside the nanowire. In Ref [16], an infinitely long InP nanowire is made in contact with a Si/ SiO2 substrate to suppress the radiative modes in favor of the guided modes for various d/λ values, ranging from 0.16 to 0.20. The oscillatory behavior would have been observed in this study if d/λ scale were extended to further values up to 0.35 as studied in Ref [12]. A similar oscillatory behavior is observed for high quality micropillar cavities in Ref [19]. where the occurrence of the oscillation is related to a coupling of the propagating Bloch modes at Bragg mirror interfaces.
Although various studies have been accomplished to modify the spontaneous emission rate manipulating the photonic environments of the many types of cavities ranging from photonic crystals to micro pillars, in this study, the intrinsic properties of the PEG polymer are utilized for the first time to alter the photo physical properties of the dielectric environment surrounding the dye molecules. In previous studies, a high Q factor with great reflecting structures and different types of geometric constructions for the dielectric cavities are obtained to strongly alter the spontaneous emission rate giving rise to a high Purcell factor. For example, high-index contrast of the micro-pillars using Bragg mirrors can increase the efficiency of the enhanced spontaneous emission providing with the presence of a high Q factor [21, 23, 36]. Photonic crystal nano-beam cavities have also been widely used with the Q factor reaching as high as 7.5x105 together with small mode volumes that enable different photonic applications to be revealed [22]. Ultra-high-Q and small mode volume toroid micro cavities on a chip have been demonstrated successfully to achieve a high Purcell factor of 2x105 [37]. Nevertheless, in our work, a nanofiber is considered to be infinitely long and the Q factor is solely due to the difference between the refractive indices of the PEG polymer and the air cladding for a given fiber diameter. This causes the resonator to have a low finesse and consequently a low Q factor. However, such a low Q factor is sufficient to allocate the fluorescent light from the excited dye molecules to be confined into the cylindrical cavity, and a slight humidity induced change in the refractive index of the nanofiber would not lead to any critical amount of modifications in our Q factor. On the other hand, the main variation in the Purcell factor, as seen in Fig. 6, is attributed to the changes in the density of the electromagnetic states via humidity induced changes in the mode volume. In other words, the mode volume obtained in Fig. 7(b) is both refractive index and fiber diameter dependent, which has transmitted its step-like periodic characteristics onto the Purcell factor as seen in Fig. 6. Minimizing the mode volume to (λ/2n)3 is quite an important fundamental limit for various essential studies in the field of quantum electrodynamics as well as for many photonic device applications, ranging from the optical switches [38] to ultra-small lasers [39], strengthening the non-linear effects and shrinking the size of the photonic devices. Our dielectric nanofiber cavity offers a mode volume as low as 0.06(λ/n)3 and reaches to a value as high as 0.21(λ/n)3. Thus, the mode volume could be easily adjusted via changing the relative humidity in the vicinity of the nanofiber in concern to deploy it as an optical switch.
The preparation of the dye doped PEG single nanofibers using electrospinning technique and modifying the refractive index and the diameter of the nanofiber via increasing the RH of the medium provide a simple and cost effective method to control the spontaneous emission of an emitter. The length of the nanofiber we use might be fabricated to be a few micrometers, with both-ends-coated with some highly reflecting materials such as gold or silver, for the benefit of a better nanofiber cavity to yield a high Q factor. Thus would consequently improve the signal to noise ratio of the measured Purcell factor. The mode volume, the electric field distribution, and the spontaneous emission rate for such a system can be analyzed as a future work.
This work might pioneer using single polymer nanofibers for the inhibition and enhancement of the spontaneous emission through the evolution of the photonic devices. Furthermore, this modification of the spontaneous emission of the dye molecules confined inside the PEG nanofibers could provide an insight for various biomedical and biotechnological applications.
5. Conclusion
Spontaneous emission rate of the BODIPY dye doped PEG single nanofibers, exposed to relative humidity, is in situ investigated by the confocal fluorescence lifetime imaging microscopy. It is observed that the spontaneous emission rate of the dye molecules is enhanced and inhibited periodically for particular RH values, yielding the experimental Purcell factor to oscillate between 1.25 and 2.52 for the humidity rage from 40% to 80%. Our results reveal that using optical properties of suitable materials could be promising candidates for achievement of the inhibition and enhancement of the spontaneous emission rate in appropriate optical nano-cavities. Controlling of the spontaneous emission rate dynamically could encourage researchers in the field of quantum electrodynamics to improve desired photonic structures that might take crucial parts in different optoelectronic and light wave based photonic devices such as photonic switches, lasers, illuminations, solar cells, and quantum information systems.
Funding
Boğaziçi University (10522).
Acknowledgments
Miss Belkıs Gökbulut wants to express her gratitude to Boğaziçi University Research Fund for the financial support provided.
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