Photoluminescence of Rhodamine from Nano-Confinement Inside 3D Sculptured Coatings

1. Introduction

Birefringence and optical activity (birefringence for circularly polarised light) are useful material properties, which originates form the material structure defined at the molecular/atomic level. The very same properties can be engineered via larger structural building blocks at the nanoscale, e.g., via 3D control of nanofilm coating using glancing angle deposition (GLAD). Folding of growth by fast change deposition angle and azimuthal rotation around the normal axis to the surface, 3D structures endowed with form birefringence and optical activity can be formed. Shadowing during film formation by GLAD also induces porosity, which becomes a key advantage for the performance of GLAD coatings under high-power laser irradiation, where rapid local heating occurs. Local rapid heating typically causes coating failure, and GLAD coatings exhibit higher tolerances under such extreme conditions due to their porosity. The GLAD coatings can achieve highly controlled thicknesses comparable to the wavelength of light $\sim 1\mu$m or thicker, which makes them suitable for polarisation active functions such as waveplates $\lambda /2$, $\lambda /4$. Furthermore, zero-order waveplates can be made with micrometre-thick GLAD coatings with various isotropic materials, e.g., evaporated/sputtered SiO₂[1,2,3]. Releasable micrometer-thin waveplates can be made out of alumina on Cu mirror surface for optomechanical applications [4]. 3D nanofilms can also find applications in spectral-spatial filtering applications due to strongly expressed Fano resonances [5,6] and they can be formed on nano-structured surfaces [7].

How porosity affects the stability of 3D sculptured GLAD coatings needs a better understanding. It is previously shown that the porous GLAD films do not have increased surface defect absorption in the case of SiO₂ films as determined by synchrotron IR micro-spectroscopy [8]. Nanogaps of 10-20 nm in the GLAD coatings are formed during a fast folding of the angle of deposition. These nanogaps lie between the nano-walls and extend through the entire height of the 3D coating, usually 1-2 $\mu$m thick. Apart from micro-optical and polarisation optics applications, such 3D coatings can be used in photo-catalysis applications, in particular, LaF₃-graphene composite showed efficient water splitting and H₂ generation under UV illumination [9]. Different phases of water films in nano-confinement were predicted [10] while production of a well controlled structures with 3D nanogaps and nano-channels is in high demand for water desalination and filter applications [11,12].

To understand how nanogap porosity interacts with an aqueous film, rhodamine 6G (RhD6G) was chosen due to its high quantum yield [13], strong sensitivity of its fluorescence lifetime to the local environment, and well-characterised dipole orientation [14,15], making it an ideal dye for studying nanoscale interactions. Here, we investigate the orientational properties of RhD6G in aqueous solution under nano-confinement, when RhD6G enters between the nanoplanes of a form-birefringent LaF₃ micro-film deposited by GLAD, using fluorescence lifetime imaging microscopy (FLIM). Light LaF₃ localisation inside nanogaps of the structure was further analysed with numerical modelling.

2. Experimental: Samples and Methods

2.1. 3D Sculptured Micro-Film Coatings

Anisotropic sculptured coatings were fabricated using the serial bi-deposition technique, which involves periodic ${180}^{\circ }$ rotation of the substrate around its normal axis. This approach produces vertically aligned, elliptical columnar structures, thereby inducing birefringence. The LaF₃ films with a thickness of 1 $\mu$m were deposited at ${60}^{\circ }$ angle of inclination on two fused silica samples using thermal evaporation. One of the samples was additionally covered with a dense capping layer to close the open voids. Figure 1 shows scanning electron microscopy (SEM) images of LaF₃ films.

2.2. Method: Fluorescence-Lifetime Imaging Microscopy

Fluorescence-lifetime imaging microscopy (FLIM) was used to determine the influence of nano-porosity of 3D sculptured coating of LaF₃ on the lifetime of rhodamine 6G (RhD6G). Aqueous solution of RhD6G at low concentration $5\times {10}^{-6}$ mol was used to avoid dimer formation. An automatic pipette was used to dispense a 20 $\mu$l drop of rhodamine solution onto the substrates. Excitation of RhD6G was made with an LED with emission centred at 470 nm (Figure 2a).

FLIM data acquisition and analysis were carried out with a commercial setup (LIFA, Lambert Instruments, Groningen, The Netherlands). The numerical aperture of the objective lens was $NA=0.1$, wavelength of excitation $\lambda =470$ nm. The diameter of the focus on the sample was $2w_0=1.22\lambda /NA=5.7\mu$m, and the depth of focus (DoF; double the Rayleigh length) was $2z_R=2\pi w_0^2/\lambda =110\mu$m. A sample, which was $d\simeq 1.2\mu$m 3D sculptured porous LaF₃ film, was positioned at the optimised height inside DoF for maximum fluorescence.

FLIM allows to detect spatial (orientation, translation) changes of emitting molecule, its transition dipole moment (TDM; Figure 3a). Molecule is excited along the selected orientation $\mathbf{n}\Vert {\mathbf{X}}_{\mathbf{1}}$ with linearly polarised LED illumination, and two fluorescent intensities at cross-polarised orientations are measured $I_{\Vert }$ and $I_{\perp }$ Figure 3b. Excitation selects those dye molecules which have TDM aligned with polarisation according to its projection $M_{TDM}cos\theta$.

The second-rank order parameter for angle $\theta$: $P_2\left(\theta \right)=[3\langle {cos}^2\theta \rangle -1]/2$, where $\langle ...\rangle$ marks the average. By measuring fluorescence intensities at perpendicular and parallel polarisations with respect to the selected orientation (along $\mathbf{n}\Vert {\mathbf{X}}_{\mathbf{1}}$), the second order parameter $P_2$ or fluorescence anisotropy can be obtained:

$$P_2\left(\theta \right)={\displaystyle \frac{I_{\Vert }-I_{\perp }}{I_{\Vert }+2I_{\perp }}}.$$

(1)

Estimation of the molecule’s (or chain’s) second order momentum $P_2$ is carried out considering three angles between the measured transition dipole moment $\theta$, the chain axis ${\alpha }_M$ and mutual orientation between polarisation and chain $\phi$ (Figure 3a): $P_2\left(\theta \right)=P_2\left({\alpha }_M\right)\times P_2\left(\phi \right)$:

$$P_2\left(\phi \right)\equiv {\displaystyle \frac{P_2\left(\theta \right)}{P_2\left({\alpha }_M\right)}}={\displaystyle \frac{I_{\Vert }-I_{\perp }}{I_{\Vert }+2I_{\perp }}}\times {\displaystyle \frac{2}{3\langle {cos}^2\theta \rangle -1}}.$$

(2)

The TDM can be classified into two (parallel or perpendicular) anisotropies depending on the relation of $\phi$ to the magic angle $54.7^{\circ }$ (the denominator is zero in Eqn. 2). Notably, the same formalism described above for fluorescence applies to the absorption dichroism.

Anisotropy of the measured fluorescence intensity at two perpendicular orientations $I_{\Vert ,\perp }$ is fast changing $r\left(t\right)$, when emitting objects are rotating and translating (from the pre-selected orientation defined by the linear polarisation of the excitation. This can analytically be defined, considering the simplest exponential decay, as:

$$r\left(t\right)=(r_0-r_{\infty })e^{-{\displaystyle \frac{t}{\varsigma }}}+r_{\infty },$$

(3)

where $r_0$ and $r_{\infty }$ are the initial and final anisotropies, respectively, $\varsigma ={\displaystyle \frac{\eta V}{RT}}$ (for spherical molecules) is the depolarisation rate constant dependent upon the temperature T, the viscosity of solution $\eta$ and the volume of excited species V. This temporal dependence of emitted anisotropy corresponds to the instantaneous second order parameter $P_2\left(\theta \right)$ (Eqn. 1). The Perrin equation reveals the time dependence of rotational deactivation for a spherical rotor ${\displaystyle \frac{r_0}{r}}=1+{\displaystyle \frac{\tau }{\varsigma }}$, where $\tau$ is the fluorescence lifetime.

It is noteworthy that depolarisation of emission from absorption is inherently related to the orientation of the corresponding absorption and emission transition dipole moments. The Kasha’s rule states that emission occurs from the single vibrationally relaxed lowest excited state of the corresponding spin multiplicity $S_1,S_2,...$, while absorption/excitation TDM can have a different orientation with respect to the molecule axis in the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) transition. The offset in the TDMs of absorbance and emission is an effective anisotropy, which is the largest for the parallel/co-linear. It is defined by $r_0={\displaystyle \frac{2}{5}}\times {\displaystyle \frac{3{cos}^2\beta -1}{2}}$, where the $\beta$ is the angle between the TDMs of absorption and emission [16]. Hence, there is no anisotropy $r_0=0$ at the magic angle $\beta =54.7^{\circ }$, the maximum $r_0=0.4$ at $\beta =0^{\circ }$ and the minimum $r_0=-0.2$ at $\beta ={90}^{\circ }$.

The frequency domain realisation of FLIM is based on the temporal modulation of the excitation and on the synchronised detection of the phase-shifted signal applicable to liquid [17] as well as solid state samples [18]. The frequency-domain approach was utilised to determine the lifetime from the phase $\psi$ and modulation m of the fluorescence signal with an optical modulation frequency of 35MHz. The typical phasor presentation: $B=mcos\psi$ and $A=msin\psi$. The phasor method is well-suited to measure fluorescence lifetime changes due to dye-nanoparticle dye-environment interactions in solutions.

3. Results and Discussion

3.1. Optical Properties of 3D Sculptured Films

The width of porous channels in 3D sculptured coating of LaF₃ is $20-30$ nm, and they are extending throughout the entire height of the surface structure as shown in Figure 1. The nanogaps were open on the surface in the sample without the 100 nm cap layer. This pattern of nanogaps made the effective surface tension different, and the surface energy was approximately twice larger along the slow axis when compared with the fast axis (aqueous solution of RhD6G droplet spreading is shown in Figure 2b).

The 3D sculptured coating has a form birefringence with extraordinary refractive index smaller than that of ordinary $n_e<n_o$, i.e., $\Delta n\equiv n_e-n_o<0$. Figure 4 shows the transmittance spectrum $T\left(\lambda \right)$ for two linearly polarised beams along fast and slow axes. A clear separation of the interference pattern is discernible. The thickness of LaF₃ film is $d=1.2\mu$m, at $\lambda =300$ nm, and the retardance $|\Delta n|d\approx 0.2\lambda$. This corresponds to high birefringence $|\Delta n|=0.05$. The birefringence is approximately 3 times lower in the long wavelength region at 800 nm.

The form birefringence depends to the volume fraction of material f and can be calculated from the known isotropic refractive index of LaF₃ for light’s E-field oscillating along the extraordinary (along optical axis) and ordinary directions in the same way as for laser inscribed bulk nanogratings [19]:

$$n_e=\sqrt{{\displaystyle \frac{n_1^2{n}_2^2}{(1-f)n_2^2+f{n}_1^2}}};n_o=\sqrt{(1-f)n_1^2+f{n}_2^2},$$

(4)

where $n_{1,2}$ are the refractive indices of environment (air) and material (LaF₃), respectively. Figure 5 shows Eqns. 4 for two wavelengths of 300 nm and 800 nm. At low porosity $\sim 93\%$ (correspondingly high volume fraction $f\approx 0.93$), a high birefringence $|\Delta n|\simeq 0.05$ can be achieved. This corresponds to nanogaps between nano-walls of LaB₃ only tens-of-nm wide in GLAD coatings investigated here. Useful virtue for application is the low wavelength dependence of form birefringence $\Delta n\left(\lambda \right)\simeq Const$. This analysis of form birefringence is only qualitatively applicable to the 3D sculptured GLAD coatings, which have a more complex structure. The experimentally measured retardance (Figure 4) and numerical simulations (Figure 5) are in agreement.

3.2. Fluorescence-Lifetime Imaging Microscopy

The phasor analysis is used to determine the lifetime $\tau$ (Figure 6). This approach involves first measuring the reference phasor (lifetime standard), then measuring the sample. By using the reference sample, instrumental corrections for phase lag and demodulation can be made, allowing finally the coordinates $(A,B)$ of the measured sample to be obtained. The intersection point with the semicircle contains information about the lifetime (phase) of the sample with the background removed. The lifetime (phase) $\tau ={\displaystyle \frac{A}{B\omega }}$, where $\omega =2\pi \times 35$ MHz is the modulation frequency. Phasors with the end point on the semi-circle correspond to the single-exponential decay [20,21,22,23]. To determine the anisotropy decay parameters, the FLIM-phasors under polarised-excitation/orthogonal-polarised detection conditions were measured and analysed as previously described [24]. Table 1 summarises the results of the photophysical parameters of RhD6G dye as a droplet on the surface of un-capped 3D sculptured film (wet condition) and after absorption within the structure (dry condition, which is $\sim 4$ hours from droplet deposition). As a droplet on a non-porous substrate, the RhD6G has a lifetime close to 4 ns and exhibited a rotational correlation time of 0.2-0.3 ns, consistent with free rotation of the dye molecules in an aqueous environment [17]. These values were obtained for the RdH6G on a capped sample, when the dye (wet condition) was not permeating the porous GLAD film.

After RhD6G droplet filled the nanogaps, quenching of the lifetime was observed, and the anisotropy decay exhibited complex dynamics (phasor ends are inside the semi-circle in Figure 6). In the context of a free and immobilised model of dye molecules, in the permeated (and also surface adsorbed) state, the majority of dye was rotationally immobile with the free state undergoing motion on the nanosecond time-scale. Of particular note, the photophysics of the dye was orientation-independent in the wet state (as expected) but strongly dependent on the orientation after filling into nanogaps of permeable coating. A tentative explanation is that the dye-material interaction is orientation dependent, with a greater extent of quenching and rotational hindrance in one direction relative to the orthogonal direction.

In the dried state ($\sim 4$ hours), the portion of rotationally hindered state was $>57\%$ (Table 1). The larger rotation hindrance $\sim 89\%$ was for the orientation along the gaps of the form-birefringence structure, i.e., along the ordinary axis (larger refractive index $n_o$) as compared with the extraordinary orientation (with index $n_e$). A possible explanation is by larger portion of dye molecules are aligned to the vertical walls of the LaF₃ nano-planes. Apparently, a small part of dye molecules are still able undergo orientational changes (or re-emit after charge transfer to the neighbouring molecules with different orientation [25]).

For the capped dried conditions, there was no fluorescence anisotropy on linear polarisation of excitation at 470 nm along ordinary and extraordinary orientations, nor measurable rotation dephasing since molecules were immobilised in random orientation (not shown for brevity).

Lifetime quenching could be due to an increase in radiative rate due to refractive index increase (Strickler-Berg relation)[26], but also possible non-radiative rate enhancement due to a change in environment (interaction with material). These mechanisms need further investigation. To elucidate light intensity enhancement inside nanogaps of form-birefringent structures, a numerical study was carried out and discussed next.

3.3. Toy Model: Dipole in a Birefringent Cage

Numerical modelling by finite difference time domain (FDTD) was carried out for qualitative understanding of light excitation and dipole emission in a generic form-birefringent structure. This toy-model has a gap of 20 nm and the same width of LaF₃ plains (duty cycle of 0.5 corresponding to the strongest form birefringence; Figure 5).

By using the dipole source in FDTD simulations, one can visualise light enhancement in the close proximity (Figure 7). The dipole source is fundamentally different from a plane wave: it is not normalised to a fixed incident field amplitude, but instead injects power via a point electric dipole moment. As a result, the near-field ${\left|E\right|}^2$ can become very large and does not represent a normalised incident intensity. The effect of the structure on a dipole emitter is evaluated through the emitted power ratio (i.e., the Purcell factor or local density of states (LDOS) enhancement) by comparing the dipole-emitted power with and without the structure, rather than using field intensity monitors. The field maps are therefore used only to illustrate the spatial redistribution of the electromagnetic field and do not represent emission enhancement.

For visualisation of field enhancement, a $\lambda =470$ nm dipole was placed at the centre of the 20-nm-wide groove of the form-birefringent structure at mid-height of 25 nm. This $\lambda =470$ nm is the wavelength of RhD6G excitation, however the qualitatively same result of field enhancement (emitted power ratio) was also for the Stokes-shifted fluorescence at $\sim 570$ nm (not shown for brevity). Figure 7c,d enhancement or Purcell factor maps visualise a very fast decay of enhancement from the position of Y-polarised dipole placed at $(x,y,z)=(0,0,25)$ nm. Enhancement decay along the x-direction (the equatorial direction of y-polarised dipole) is approximately by one order of magnitude in every next well of the structure (Figure 7c). In the direction along the dipole axis (along the y-direction), a similar very fast decay of enhancement was observed. The enhancement was well localised inside the centre groove where the dipole was placed (Figure 7c). This is consistent with the E-field decay from a dipole in a free space which has the axial and equatorial distributions: $E_{dip}^{ax}\sim 2\times dipole/y^3$ and $E_{dip}^{eq}\sim dipole/x^3$, both polarised along the dipole, i.e., y-polarised where the dipole momentum is defined by the two charges $\pm q$ separated by $y_d$ as $\mathbf{dipole}=q{\mathbf{y}}_{\mathbf{d}}$ with dipole orientation from negative to positive $-\to +$. Hence, the local intensity, which is $E^2$, has a very steep decay $1/x^6$ (equatorial) or $1/y^6$ (axial) and has a smaller amplitude in the equatorial direction by a factor of $2^2$ as compared with the axial (Figure 7b). This scaling is for a dipole in free space, while the addition of the structure and high refractive index walls in close proximity facilitates further localisation of emission inside the groove via a slot-wave-guiding mechanism. The Figure 7c,d shows enhancement (the emitted power ratio) for the total field, which has a more complex polarisation pattern if separated into the constituent contributions $E^2=E_x^2+E_y^2+E_z^2$ (not shown here, however is always available in the FDTD field monitors).

Next, let us estimate the field enhancement for the dipole in the form-birefringent structure at the perpendicular direction (along $n_e$ fast axis). Figure 8 shows E-field enhancement maps (proportional to the Purcell’s factor) along the fast- and slow-axis (x- and y-axis, respectively). Strong light localisation inside the gap is evident, as well as strong dependence of intensity decay from the dipole source. As expected, stronger light localisation inside the nanogap was for the dipole along the fast-axis $n_e$ (Figure 8) as compared with the slow-axis $n_o$ (Figure 7). The higher light localisation inside nanogaps for the E-field (dipole or plane wave source) oriented perpendicular to the interface is based on the boundary condition for the normal component of displacement $D={\epsilon }_0\epsilon E$, where ${\epsilon }_0$ is the permittivity of free space and $\epsilon \equiv n^2$ is the permittivity of material. At the interface LaF₃-air(gap), $D_n^{LaF3}=D_n^{air}$ or $E_n^{LaF3}\times n_{LaF3}^2=E_n^{air}\times n_{air}^2$. For intensity in air nanogap, this reads $|E_n^{air}{|}^2=\left[{\displaystyle \frac{n_{LaF3}}{nair}}\right]4\times |E_n^{LaF3}{|}^2\equiv n_{LaF3}^4|E_n^{LaF3}{|}^2$. The intensity enhancement by a factor $1.6^4\simeq 6.6$ times is expected for $n_{LaF3}\simeq 1.6$. The tangential components of the E-field are equal on both sides of the interface (no enhancement); see Supplement for plane wave illumination of the same structure as in Figure 7Figure 8. Redistribution of light preferentially into nanogaps can explain the higher damage threshold of 3D sculptured coatings in high intensity laser beams [27].

Analysis of FDTD results for a dye-dipole emitting inside the form-birefringent structure predicts a stronger fluorescence (shorter lifetime due to the Purcell enhancement) in the extraordinary orientation along the $n_e$ (fast-axis) due to larger E-field localisation inside nanogaps. However, the observed tendency in experiments for the dried sample (${90}^{\circ }$ in Table 1) is that a shorter fluorescence lifetime (if it is due to the Purcell enhancement) is for the excitation orientated along the slow-axis $n_o$-direction. This could be explained by the preferential alignment of flat RhD6G molecules preferentially along the walls of the form-birefringent GLAD structure. For such orientation, a stronger E-field perpendicular to the walls does not excite dyes (oriented along the walls). Further studies are needed to test this hypothesis when different form-birefringent structures are filled with the dye solution. Separation of orientation due to absorbing dipoles induces dichroism, which can be distinguished from the orientation of the birefringent host as demonstrated earlier [28] and is made available as a freeware data analysis tool [29]. This four-polarisation analysis of orientation has inherent super-resolution capability [30,31].

4. Conclusions and Outlook

Rhodamine 6G aqueous solution dropped onto form-birefringent 3D sculptured GLAD coatings showed the absence of rotational anisotropy of fluorescence, similarly as in solution. Shortening of fluorescence/photoluminescence lifetime by $\sim 10\%$ was observed from the dye-permeated (in liquid form) structure; however, there was no rotational hindrance of dye molecules. When dried, a strong rotational hindrance $89\%$ was observed for the orientation along the ordinary optical axis (fast-axis), and the hindrance was smaller $57\%$ for the extraordinary direction (fast axis). Light intensity distribution inside a nano-structure with a form-birefringence was numerically modelled using plane wave illumination and a dipole source. Nanoscale localisation of light intensity due to dipole nature $I\sim 1/radiu{s}^6$ and boundary conditions for E-field allows efficient energy deposition inside the region of lower refractive index (nanogaps).