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Understanding the emission pattern produced by focused laser beam excitation of perylene square single crystals
Chemical Physics Letters 667 (2017) 284–289
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
Understanding the emission pattern produced by focused laser beam excitation of perylene square single crystals Ken Takazawa National Institute for Materials Science, 3-13 Sakura, Tsukuba 305-0003, Japan
a r t i c l e
i n f o
Article history: Received 12 September 2016 In final form 16 October 2016 Available online 3 November 2016
a b s t r a c t Square single crystals of perylene (a-crystals) exhibit a peculiar emission pattern when excited by a focused laser beam. Fluorescence spots are observed at the point of excitation and at four edges, with the lines connecting the excitation point and edge emissions being perpendicular to the edges irrespective of the excitation position. Two different mechanisms explaining this emission pattern have been proposed so far. Our newly designed experiment and analysis revealed that the involved mechanism features a combination of the waveguide effect and total internal reflection by crystal edges. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction The electronic excited state of an organic crystal composed of aromatic molecules is generally a Frenkel exciton state, and the fluorescence/luminescence properties of such crystals are governed by the excitons and their dynamics. In addition to determining the crystal’s fluorescence spectrum, excitons can also influence the spatial distribution of the fluorescence intensity throughout the crystal. Frenkel excitons propagate through the crystal, and thus, fluorescence can occur at positions outside of the area illuminated by the excitation light. The propagation length of a singlet exciton is typically on the nanometer scale [1], whereas that of long-lived excitons, such as H-aggregate excitons [2] and triplet excitons [3], can reach the micrometer scale. A single crystal of perylene (Fig. 1a) is a typical example of a crystal whose excited state is the Frenkel exciton state. The use of perylene and its derivatives in various electronic and optoelectronic applications, including electroluminescence diodes and solar cells, has attracted substantial interest, and excitons play an important role in these devices [2,4]. Single perylene crystals can be grown using solution-phase or sublimation processes and exhibit two polymorphic forms—the so-called a- and b-crystals—both of which possess monoclinic P21/c symmetry [5]. a-Crystals contain four molecules per unit cell and exhibit a dimeric structure (Fig. 1b), whereas b-crystals contain two molecules per unit cell and are monomeric. Because of the differences in their crystal structures, the exciton properties of these crystals differ. In both crystals, delocalized free excitons are generated by optical excitation at a wavelength of 400 nm and relax to self-trapped excitons (STEs) because of strong exciton-phonon interaction [6–12]. Thus, E-mail address: [email protected] http://dx.doi.org/10.1016/j.cplett.2016.10.083 0009-2614/Ó 2016 Elsevier B.V. All rights reserved.
fluorescence from the STE state is substantially red-shifted with respect to the excitation wavelength. Because the energy of the STEs differs between these two types of crystals, a-crystals exhibit orange fluorescence peaking at 600 nm, and b-crystals display green fluorescence peaking at 550 nm [13]. In addition, a- and b-crystals also have different morphologies: a-Crystals exhibit a square plate form, whereas b-crystals possess a rhombic plate form [13]. Therefore, these two crystal types can be easily identified by their fluorescence color (orange or green) and shape (square or rhombic). Liao et al. reported a peculiar emission pattern of square acrystals produced by excitation with a focused laser beam [14]. The emission pattern reproduced by us is displayed in Fig. 1c–f. Fig. 1c and d shows an optical micrograph and a fluorescence microscopy image of a square a-crystal (102 lm 102 lm), respectively, with a thickness of a few hundred nanometers. When the center of the crystal was excited with a focused beam at 405 nm (408 nm in Ref. [14]), bright orange emission spots (or lines) were observed at the four crystal edges and the excited position (Fig. 1e). Interestingly, the directions from edge emissions to the excited position are perpendicular to crystal edges. When the laser spot was moved away from the center, the edge emissions also moved, maintaining the perpendicularity of the above directions to the crystal edges (Fig. 1f). Liao et al. recorded edge emission spectra by varying the distance between the edge and the laser spot and observed that the edge emission intensity gradually decreased with increasing distance. Based on these observations, they concluded that the observed emission pattern was attributed to the waveguide mechanism. Namely, the fluorescence radiation from the STE states generated at the laser spot is confined within the crystal and guided in directions perpendicular to the edges.
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Fig. 1. (a) Chemical formula of perylene. (b) Structure of perylene a-crystals, with black bars representing individual molecules. Optical micrograph (c) and fluorescence microscopy image (d) of an a-crystal. Fluorescence microscopy images were obtained by exciting the central (e) and an off-center position (f).
They claimed that perylene crystals provide an opportunity to investigate such anisotropic waveguiding in organic crystals. Recently, Tanaka et al. proposed a different interpretation of this emission pattern [15]. They recorded fluorescence microscopy images of a- and b-crystals excited by the focused laser beam at 408 nm and observed an emission pattern similar to that in Fig. 1e and f. By investigating the intensity distribution of this pattern, the authors found the edge emission intensity to be as high as or higher than that of the excited position. Their theoretical analysis of the intensity distribution showed that the edge emission should be weaker than that at the excited position if the former is caused by the waveguide mechanism. Therefore, the waveguide mechanism was concluded to be inconsistent, and another one was proposed instead. In this mechanism, the excitation laser beam is
scattered at the irradiation spot, reaching the crystal edges. The free excitons produced at the edges by the scattered laser light are relaxed to STEs that cause fluorescence. The radiative transition from the STE to the ground state is forbidden in bulk crystal [14]. However, the symmetry at the crystal edges is lowered compared to that in bulk crystal, enhancing the radiative transition. Consequently, the fluorescence intensity at the edges can exceed that at the excited position. They also considered the exciton propagation mechanism, in which the free excitons generated by laser excitation propagate through the crystal to the edges, relax to STEs, and emit orange fluorescence at the edges. However, they concluded that the free excitons cannot reach the crystal edges within their lifetime.
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In this study, we conclusively demonstrate that the edge emission of perylene a-crystals occurs via the waveguide mechanism. In this mechanism, the fluorescence from STEs generated at the laser spot is confined within the crystal and guided to the crystal edges. We also reveal that the fluorescence emitted by the STEs propagates not only perpendicularly to the crystal edges but also radially. Using a simple analysis, we explain why the fluorescence appears to propagate only perpendicularly to the edges. The emission pattern of an organic crystal can be influenced by various mechanisms, such as exciton propagation [3,16,17], the waveguide effect [18,19], and polariton propagation [20,21]. The techniques developed in this study facilitate identifying the mechanism responsible for the observed pattern.
2. Results and discussion Initially, spatially resolved fluorescence microscopy was used to record spectra at the excitation position and at the crystal edge of the square a-crystal by varying the distance between the edge and the laser spot (X) (Fig. 2a). The top spectrum in Fig. 2b was recorded at the laser spot and showed broad fluorescence peaking at 600 nm, which is characteristic for an a-crystal. The edge emission spectra were recorded by varying X from 3 to 41 lm (lower spectra). The spectral features of the edge emission spectra are nearly identical to that of the excited position and do not change with X. However, the spectral intensity gradually decreases with increasing X. These data are essentially identical to those previously reported by Liao et al. [14]. However, the decrease of spectral intensity with increasing X can be rationalized by both mechanisms, i.e., the waveguide mechanism and the scattered laser light mechanism. Thus, no conclusions regarding the edge emission mechanism can be drawn from the data. It should be noted that the edge emission intensities (lower spectra) are higher than that of the excited position (top spectrum) even for the maximal X value of 41 lm. This feature was observed by Tanaka et al. and formed the basis of the scattered laser light mechanism [14]. We conducted this measurement for ten crystals and observed that for some of them the edge emission intensity was indeed higher than that of the excited position. For the other crystals, the edge emission was of similar or lower intensity than that of the excited position. This variation in intensity distribution may be attributed to the difference in the thickness and perfection of the crystals. To reveal the mechanism responsible for the observed emission pattern, it is straightforward to extract the propagating light from the crystal and determine whether it is fluorescence or scattered excitation laser radiation. It is possible to mechanically introduce defects (scratches or cracks) into a crystal by using a sharp glass or metal tip attached to a micromanipulator [22,23] and observe the light leaking from the defects. However, the symmetry around such defects may be lowered, possibly enhancing radiative transitions in these regions. Therefore, the observation of light leaked from the defects does not provide conclusive evidence on the mechanism of the edge emission. Hence, it is necessary to extract the propagating light without lowering the crystal symmetry. Herein, we used evanescent coupling between the crystal and glass microspheres dispersed on the crystal. The propagating light can be evanescently coupled to the glass microspheres on the crystal surface, exciting their whispering-gallery modes [24]. This enables us to observe light emission from the spheres and identify whether the light is fluorescence or scattered laser radiation (Fig. 3a). Microspheres of 3–10 lm diameter were dispersed on a square a-crystal (Fig. 3b). When the crystal was excited with a laser spot, orange light (i.e., the fluorescence emission from the STE) was emitted at the perimeters of the microspheres, indicating that the fluorescence propagating in the crystal was coupled to the
Fig. 2. (a) Schematic representation of spatially resolved fluorescence microscopy. (b) Spatially resolved fluorescence microscopy spectra of the excited position (top) and of the edge (below). X represents the distance between the excited position and the edge.
microspheres (Fig. 3c and the lower A–C panels). This result confirms that the edge emission mechanism is due to waveguiding. Importantly, the microspheres located outside the triangular area defined by the laser spot and the edge emission (indicated by dashed lines) emitted orange light (lower A and C panels). This implies that the fluorescence generated at the laser spot propagates not only in the directions perpendicular to the edges, but also radially. These results provide additional evidence that the edge emission cannot be attributed to the exciton propagation mechanism, which was rejected by Tanaka et al. based on the exciton lifetime [15]. Indeed, propagating excitons in the crystal could potentially be trapped at the contact between the crystal surface and the sphere and relax to STEs; in this case, the orange fluorescence would arise from the STEs coupled in the sphere. However, if the excitons propagate radially from the laser excitation spot and reach the edges, fluorescence would not be emitted from a certain
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strongly dependent on the numerical aperture (NA) of the objective lens. Fig. 4 shows fluorescence microscopy images of the same crystal (32 lm 32 lm) recorded using objective lenses with different NAs (0.45, 0.55, 0.80, and 0.95). For a small NA of 0.45, the edge emission had a small width and was spot-like; however, its width increased with increasing NA, changing from spot-like to line-like. These results indicate that the increasing deviation of the propagation direction from the perpendicular to the edge leads to a decreased output angle of the fluorescence at the crystal edge. Based on the above experimental observations, we analyzed the propagation of fluorescence within a crystal using a simple model depicted in Fig. 5a. In our model, the center of a square crystal (2L 2L) is excited by a laser beam. The fluorescence generated at the excited position propagates radially and reaches the crystal edge with an incident angle of h. When h is smaller than the critical angle given by
sin hc ¼ nair =n
ð1Þ
where nair and n are the refractive indices of air and the crystal, respectively, the fluorescence leaks out from the crystal edge, giving rise to edge emission. On the other hand, when h is greater than hc, the fluorescence is totally reflected at the edge and cannot leak out from the crystal. We think that this total internal reflection is the reason why fluorescence seems to propagate only in the direction perpendicular to the edge. To prove this more quantitatively, we analyzed the images shown in Fig. 4 based on our model. The critical angle hc can also be expressed as
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin hc ¼ D= L2 þ D2
ð2Þ
where D is the half-width of the edge emission (see Fig. 5a). We measured D and L for the images shown in Fig. 4 and evaluated sin hc using Eq. (2). The values of sin hc plotted in Fig. 5b (red dots and lines) steadily increase with NA. Subsequently, n was evaluated using the equation obtained by combining Eqs. (1) and (2), which is given by
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi nair =n ¼ D= L2 þ D2 :
Fig. 3. (a) Scheme of evanescent coupling between light propagating within a crystal and a microsphere. (b) Optical micrograph of an a-crystal with microspheres dispersed on its surface. (c) Upper panel: fluorescence microscopy image of a crystal with dispersed microspheres obtained using focused laser excitation. The area surrounded by dashed lines is determined by the excited position and the edge emission. Lower panels: magnified images of areas A, B, and C in the upper panel.
portion of the edge, as experimentally observed; instead, it would occur along the entire length of the edge. Subsequently, we focused on the question why fluorescence seems to propagate in the two orthogonal directions perpendicular to the crystal edges. We found that the edge emission width was
ð3Þ
The values of n obtained using Eq. (3) are plotted in Fig. 5b as a function of NA (black dots and lines). For a small NA of 0.45, n equaled 5.3, which is too large for the refractive index of an organic crystal. The values of n decreased with increasing NA, being equal to 1.84 for NA = 0.95, which is consistent with the refractive index of a perylene crystal [15,25]. Here, we summarize our investigations into the emission pattern of perylene crystals. Exciting these crystals with a laser beam produces free excitons, which immediately relax to STEs. The fluorescence generated by the transition from the STE state to the ground state radially propagates within the crystal via the waveguide mechanism and reaches the crystal edges. Fluorescence with an incident angle smaller than the critical angle hc leaks out from the edges, generating edge emission, while that with an incident angle greater than the critical angle is totally reflected at the edges. Thus, the generated fluorescence pattern looks as if fluorescence propagates only in the two directions perpendicular to the crystal edge. This mechanism also explains the emission pattern observed by exciting the off-center position with a laser beam (Fig. 1f). However, the emission pattern is not solely determined by the total internal reflection at the edges. The width of the edge emission is strongly dependent on the NA value of the objective lens used. When a small NA lens is employed, the observed edge emission width is much narrower than that determined by the critical angle. This point requires particular attention to elucidate the observed emission pattern.
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Fig. 4. Fluorescence microscopy images of the same crystal recorded by objective lenses with NAs of 0.45 (a), 0.55 (b), 0.80 (c), and 0.95 (d).
The reaming question is why the edge emission intensity for some crystals is higher than that at the excited position. Tanaka et al. performed model calculations and showed that in case of the waveguide mechanism the edge emission should be weaker than the fluorescence at the excited position [15]. In their model, a circular thin plate consisting of uniformly distributed point light sources spherically radiating light is embedded in a circular twodimensional waveguide. They calculated the intensity of light detected at the position of the light source and at the waveguide edge. A possible origin of the discrepancy between the result of their model calculation and our conclusion is that the emission from the point light source is not spherically isotropic, but anisotropic. However, an elaborate analysis considering the arrangement of transition dipoles and exciton dynamics is needed to prove such anisotropy, and will be included in our future work. 3. Conclusions In conclusion, we investigated the mechanism involved in the genesis of the emission pattern of square a-perylene crystals that is produced by focused laser excitation. We revealed that the emission observed at four edges of the crystal is explained by the waveguide mechanism, with fluorescence generated at the laser spot being confined within the crystal and guided to its edges. Furthermore, we explained why fluorescence seems to propagate in the direction perpendicular to the crystal edge. The fluorescence emitted from the laser spot propagates radially, leaking out from the crystal edges for edge incident angles smaller than the critical
angle, thus giving rise to edge emission. On the other hand, light with an incident angle greater than the critical angle is totally reflected. This behavior yields an emission pattern that looks as if fluorescence propagates only in the two directions perpendicular to the crystal edge. The experimental techniques and model analysis used in this work can be used to study the mechanism of light or exciton propagation in organic crystals. 4. Experimental section Sample preparation. Perylene was purchased from Tokyo Kasei (Japan) and was used without further purification. An approximately 10 mM solution of perylene in acetone or chloroform was drop-cast on a glass substrate (microscope cover glass), and the solvent was allowed to evaporate at ambient conditions, yielding single perylene crystals on the substrate. The majority of crystals produced by this process were a-crystals, with very few bcrystals obtained. The crystal size ranged from a few to a few hundred micrometers, and the thickness was from a few tens to a few hundred nanometers, as measured by atomic force microscopy (data not shown). Dispersion of glass microspheres on perylene crystals was conducted by spin-coating an aqueous suspension of glass microspheres (Polyscience, 3–10 lm diameter) on the sample. Fluorescence microscopy. Fluorescence microscopy images were recorded using an epi-illumination microscope (Olympus) equipped with a motorized stage (Prior). The output of a continuous wave diode laser (k = 405 nm) was coupled to the microscope,
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the excitation spot in a direction parallel to the slits by changing the distance between the laser spot and the edge (X). Acknowledgement This work was supported by JSPS KAKENHI [grant Number 15K04705]. References
Fig. 5. (a) Scheme of the light propagation path within a crystal. (b) Plots of sin hc (left ordinate) and n (right ordinate) as a function of NA.
directed to the sample by a dichroic mirror (Omega Optical), and focused onto the sample with an objective lens (Olympus, 20– 100). The fluorescence from the sample was collected by the same objective lens, and the image was captured by a color CCD camera (Jenoptik). In spatially resolved fluorescence microscopy, the fluorescence was imaged onto the entrance slits of an imaging monochromator (Acton Research, SpectraPro 2150) through a long-pass filter (Omega Optical) to block the excitation laser. The light that passed through the slits was recorded by a liquid-nitrogen-cooled backilluminated CCD camera (Princeton Instruments, Spec10, 1340 400 pixels). The captured image was spectrally and spatially resolved along the horizontal and vertical axes of the camera, respectively. A square crystal was positioned by translating and rotating the sample in such a way that the fluorescence at the excitation spot and the edge emission passed through the entrance slits (Fig. 2a). The spectra at both positions were obtained by extracting horizontal cross-sections of the image recorded by the CCD camera. The spectral and spatial resolutions were 0.4 nm and 1 lm, respectively. These spectra were recorded while moving
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Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
Understanding the emission pattern produced by focused laser beam excitation of perylene square single crystals Ken Takazawa National Institute for Materials Science, 3-13 Sakura, Tsukuba 305-0003, Japan
a r t i c l e
i n f o
Article history: Received 12 September 2016 In final form 16 October 2016 Available online 3 November 2016
a b s t r a c t Square single crystals of perylene (a-crystals) exhibit a peculiar emission pattern when excited by a focused laser beam. Fluorescence spots are observed at the point of excitation and at four edges, with the lines connecting the excitation point and edge emissions being perpendicular to the edges irrespective of the excitation position. Two different mechanisms explaining this emission pattern have been proposed so far. Our newly designed experiment and analysis revealed that the involved mechanism features a combination of the waveguide effect and total internal reflection by crystal edges. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction The electronic excited state of an organic crystal composed of aromatic molecules is generally a Frenkel exciton state, and the fluorescence/luminescence properties of such crystals are governed by the excitons and their dynamics. In addition to determining the crystal’s fluorescence spectrum, excitons can also influence the spatial distribution of the fluorescence intensity throughout the crystal. Frenkel excitons propagate through the crystal, and thus, fluorescence can occur at positions outside of the area illuminated by the excitation light. The propagation length of a singlet exciton is typically on the nanometer scale [1], whereas that of long-lived excitons, such as H-aggregate excitons [2] and triplet excitons [3], can reach the micrometer scale. A single crystal of perylene (Fig. 1a) is a typical example of a crystal whose excited state is the Frenkel exciton state. The use of perylene and its derivatives in various electronic and optoelectronic applications, including electroluminescence diodes and solar cells, has attracted substantial interest, and excitons play an important role in these devices [2,4]. Single perylene crystals can be grown using solution-phase or sublimation processes and exhibit two polymorphic forms—the so-called a- and b-crystals—both of which possess monoclinic P21/c symmetry [5]. a-Crystals contain four molecules per unit cell and exhibit a dimeric structure (Fig. 1b), whereas b-crystals contain two molecules per unit cell and are monomeric. Because of the differences in their crystal structures, the exciton properties of these crystals differ. In both crystals, delocalized free excitons are generated by optical excitation at a wavelength of 400 nm and relax to self-trapped excitons (STEs) because of strong exciton-phonon interaction [6–12]. Thus, E-mail address: [email protected] http://dx.doi.org/10.1016/j.cplett.2016.10.083 0009-2614/Ó 2016 Elsevier B.V. All rights reserved.
fluorescence from the STE state is substantially red-shifted with respect to the excitation wavelength. Because the energy of the STEs differs between these two types of crystals, a-crystals exhibit orange fluorescence peaking at 600 nm, and b-crystals display green fluorescence peaking at 550 nm [13]. In addition, a- and b-crystals also have different morphologies: a-Crystals exhibit a square plate form, whereas b-crystals possess a rhombic plate form [13]. Therefore, these two crystal types can be easily identified by their fluorescence color (orange or green) and shape (square or rhombic). Liao et al. reported a peculiar emission pattern of square acrystals produced by excitation with a focused laser beam [14]. The emission pattern reproduced by us is displayed in Fig. 1c–f. Fig. 1c and d shows an optical micrograph and a fluorescence microscopy image of a square a-crystal (102 lm 102 lm), respectively, with a thickness of a few hundred nanometers. When the center of the crystal was excited with a focused beam at 405 nm (408 nm in Ref. [14]), bright orange emission spots (or lines) were observed at the four crystal edges and the excited position (Fig. 1e). Interestingly, the directions from edge emissions to the excited position are perpendicular to crystal edges. When the laser spot was moved away from the center, the edge emissions also moved, maintaining the perpendicularity of the above directions to the crystal edges (Fig. 1f). Liao et al. recorded edge emission spectra by varying the distance between the edge and the laser spot and observed that the edge emission intensity gradually decreased with increasing distance. Based on these observations, they concluded that the observed emission pattern was attributed to the waveguide mechanism. Namely, the fluorescence radiation from the STE states generated at the laser spot is confined within the crystal and guided in directions perpendicular to the edges.
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Fig. 1. (a) Chemical formula of perylene. (b) Structure of perylene a-crystals, with black bars representing individual molecules. Optical micrograph (c) and fluorescence microscopy image (d) of an a-crystal. Fluorescence microscopy images were obtained by exciting the central (e) and an off-center position (f).
They claimed that perylene crystals provide an opportunity to investigate such anisotropic waveguiding in organic crystals. Recently, Tanaka et al. proposed a different interpretation of this emission pattern [15]. They recorded fluorescence microscopy images of a- and b-crystals excited by the focused laser beam at 408 nm and observed an emission pattern similar to that in Fig. 1e and f. By investigating the intensity distribution of this pattern, the authors found the edge emission intensity to be as high as or higher than that of the excited position. Their theoretical analysis of the intensity distribution showed that the edge emission should be weaker than that at the excited position if the former is caused by the waveguide mechanism. Therefore, the waveguide mechanism was concluded to be inconsistent, and another one was proposed instead. In this mechanism, the excitation laser beam is
scattered at the irradiation spot, reaching the crystal edges. The free excitons produced at the edges by the scattered laser light are relaxed to STEs that cause fluorescence. The radiative transition from the STE to the ground state is forbidden in bulk crystal [14]. However, the symmetry at the crystal edges is lowered compared to that in bulk crystal, enhancing the radiative transition. Consequently, the fluorescence intensity at the edges can exceed that at the excited position. They also considered the exciton propagation mechanism, in which the free excitons generated by laser excitation propagate through the crystal to the edges, relax to STEs, and emit orange fluorescence at the edges. However, they concluded that the free excitons cannot reach the crystal edges within their lifetime.
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In this study, we conclusively demonstrate that the edge emission of perylene a-crystals occurs via the waveguide mechanism. In this mechanism, the fluorescence from STEs generated at the laser spot is confined within the crystal and guided to the crystal edges. We also reveal that the fluorescence emitted by the STEs propagates not only perpendicularly to the crystal edges but also radially. Using a simple analysis, we explain why the fluorescence appears to propagate only perpendicularly to the edges. The emission pattern of an organic crystal can be influenced by various mechanisms, such as exciton propagation [3,16,17], the waveguide effect [18,19], and polariton propagation [20,21]. The techniques developed in this study facilitate identifying the mechanism responsible for the observed pattern.
2. Results and discussion Initially, spatially resolved fluorescence microscopy was used to record spectra at the excitation position and at the crystal edge of the square a-crystal by varying the distance between the edge and the laser spot (X) (Fig. 2a). The top spectrum in Fig. 2b was recorded at the laser spot and showed broad fluorescence peaking at 600 nm, which is characteristic for an a-crystal. The edge emission spectra were recorded by varying X from 3 to 41 lm (lower spectra). The spectral features of the edge emission spectra are nearly identical to that of the excited position and do not change with X. However, the spectral intensity gradually decreases with increasing X. These data are essentially identical to those previously reported by Liao et al. [14]. However, the decrease of spectral intensity with increasing X can be rationalized by both mechanisms, i.e., the waveguide mechanism and the scattered laser light mechanism. Thus, no conclusions regarding the edge emission mechanism can be drawn from the data. It should be noted that the edge emission intensities (lower spectra) are higher than that of the excited position (top spectrum) even for the maximal X value of 41 lm. This feature was observed by Tanaka et al. and formed the basis of the scattered laser light mechanism [14]. We conducted this measurement for ten crystals and observed that for some of them the edge emission intensity was indeed higher than that of the excited position. For the other crystals, the edge emission was of similar or lower intensity than that of the excited position. This variation in intensity distribution may be attributed to the difference in the thickness and perfection of the crystals. To reveal the mechanism responsible for the observed emission pattern, it is straightforward to extract the propagating light from the crystal and determine whether it is fluorescence or scattered excitation laser radiation. It is possible to mechanically introduce defects (scratches or cracks) into a crystal by using a sharp glass or metal tip attached to a micromanipulator [22,23] and observe the light leaking from the defects. However, the symmetry around such defects may be lowered, possibly enhancing radiative transitions in these regions. Therefore, the observation of light leaked from the defects does not provide conclusive evidence on the mechanism of the edge emission. Hence, it is necessary to extract the propagating light without lowering the crystal symmetry. Herein, we used evanescent coupling between the crystal and glass microspheres dispersed on the crystal. The propagating light can be evanescently coupled to the glass microspheres on the crystal surface, exciting their whispering-gallery modes [24]. This enables us to observe light emission from the spheres and identify whether the light is fluorescence or scattered laser radiation (Fig. 3a). Microspheres of 3–10 lm diameter were dispersed on a square a-crystal (Fig. 3b). When the crystal was excited with a laser spot, orange light (i.e., the fluorescence emission from the STE) was emitted at the perimeters of the microspheres, indicating that the fluorescence propagating in the crystal was coupled to the
Fig. 2. (a) Schematic representation of spatially resolved fluorescence microscopy. (b) Spatially resolved fluorescence microscopy spectra of the excited position (top) and of the edge (below). X represents the distance between the excited position and the edge.
microspheres (Fig. 3c and the lower A–C panels). This result confirms that the edge emission mechanism is due to waveguiding. Importantly, the microspheres located outside the triangular area defined by the laser spot and the edge emission (indicated by dashed lines) emitted orange light (lower A and C panels). This implies that the fluorescence generated at the laser spot propagates not only in the directions perpendicular to the edges, but also radially. These results provide additional evidence that the edge emission cannot be attributed to the exciton propagation mechanism, which was rejected by Tanaka et al. based on the exciton lifetime [15]. Indeed, propagating excitons in the crystal could potentially be trapped at the contact between the crystal surface and the sphere and relax to STEs; in this case, the orange fluorescence would arise from the STEs coupled in the sphere. However, if the excitons propagate radially from the laser excitation spot and reach the edges, fluorescence would not be emitted from a certain
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strongly dependent on the numerical aperture (NA) of the objective lens. Fig. 4 shows fluorescence microscopy images of the same crystal (32 lm 32 lm) recorded using objective lenses with different NAs (0.45, 0.55, 0.80, and 0.95). For a small NA of 0.45, the edge emission had a small width and was spot-like; however, its width increased with increasing NA, changing from spot-like to line-like. These results indicate that the increasing deviation of the propagation direction from the perpendicular to the edge leads to a decreased output angle of the fluorescence at the crystal edge. Based on the above experimental observations, we analyzed the propagation of fluorescence within a crystal using a simple model depicted in Fig. 5a. In our model, the center of a square crystal (2L 2L) is excited by a laser beam. The fluorescence generated at the excited position propagates radially and reaches the crystal edge with an incident angle of h. When h is smaller than the critical angle given by
sin hc ¼ nair =n
ð1Þ
where nair and n are the refractive indices of air and the crystal, respectively, the fluorescence leaks out from the crystal edge, giving rise to edge emission. On the other hand, when h is greater than hc, the fluorescence is totally reflected at the edge and cannot leak out from the crystal. We think that this total internal reflection is the reason why fluorescence seems to propagate only in the direction perpendicular to the edge. To prove this more quantitatively, we analyzed the images shown in Fig. 4 based on our model. The critical angle hc can also be expressed as
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin hc ¼ D= L2 þ D2
ð2Þ
where D is the half-width of the edge emission (see Fig. 5a). We measured D and L for the images shown in Fig. 4 and evaluated sin hc using Eq. (2). The values of sin hc plotted in Fig. 5b (red dots and lines) steadily increase with NA. Subsequently, n was evaluated using the equation obtained by combining Eqs. (1) and (2), which is given by
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi nair =n ¼ D= L2 þ D2 :
Fig. 3. (a) Scheme of evanescent coupling between light propagating within a crystal and a microsphere. (b) Optical micrograph of an a-crystal with microspheres dispersed on its surface. (c) Upper panel: fluorescence microscopy image of a crystal with dispersed microspheres obtained using focused laser excitation. The area surrounded by dashed lines is determined by the excited position and the edge emission. Lower panels: magnified images of areas A, B, and C in the upper panel.
portion of the edge, as experimentally observed; instead, it would occur along the entire length of the edge. Subsequently, we focused on the question why fluorescence seems to propagate in the two orthogonal directions perpendicular to the crystal edges. We found that the edge emission width was
ð3Þ
The values of n obtained using Eq. (3) are plotted in Fig. 5b as a function of NA (black dots and lines). For a small NA of 0.45, n equaled 5.3, which is too large for the refractive index of an organic crystal. The values of n decreased with increasing NA, being equal to 1.84 for NA = 0.95, which is consistent with the refractive index of a perylene crystal [15,25]. Here, we summarize our investigations into the emission pattern of perylene crystals. Exciting these crystals with a laser beam produces free excitons, which immediately relax to STEs. The fluorescence generated by the transition from the STE state to the ground state radially propagates within the crystal via the waveguide mechanism and reaches the crystal edges. Fluorescence with an incident angle smaller than the critical angle hc leaks out from the edges, generating edge emission, while that with an incident angle greater than the critical angle is totally reflected at the edges. Thus, the generated fluorescence pattern looks as if fluorescence propagates only in the two directions perpendicular to the crystal edge. This mechanism also explains the emission pattern observed by exciting the off-center position with a laser beam (Fig. 1f). However, the emission pattern is not solely determined by the total internal reflection at the edges. The width of the edge emission is strongly dependent on the NA value of the objective lens used. When a small NA lens is employed, the observed edge emission width is much narrower than that determined by the critical angle. This point requires particular attention to elucidate the observed emission pattern.
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Fig. 4. Fluorescence microscopy images of the same crystal recorded by objective lenses with NAs of 0.45 (a), 0.55 (b), 0.80 (c), and 0.95 (d).
The reaming question is why the edge emission intensity for some crystals is higher than that at the excited position. Tanaka et al. performed model calculations and showed that in case of the waveguide mechanism the edge emission should be weaker than the fluorescence at the excited position [15]. In their model, a circular thin plate consisting of uniformly distributed point light sources spherically radiating light is embedded in a circular twodimensional waveguide. They calculated the intensity of light detected at the position of the light source and at the waveguide edge. A possible origin of the discrepancy between the result of their model calculation and our conclusion is that the emission from the point light source is not spherically isotropic, but anisotropic. However, an elaborate analysis considering the arrangement of transition dipoles and exciton dynamics is needed to prove such anisotropy, and will be included in our future work. 3. Conclusions In conclusion, we investigated the mechanism involved in the genesis of the emission pattern of square a-perylene crystals that is produced by focused laser excitation. We revealed that the emission observed at four edges of the crystal is explained by the waveguide mechanism, with fluorescence generated at the laser spot being confined within the crystal and guided to its edges. Furthermore, we explained why fluorescence seems to propagate in the direction perpendicular to the crystal edge. The fluorescence emitted from the laser spot propagates radially, leaking out from the crystal edges for edge incident angles smaller than the critical
angle, thus giving rise to edge emission. On the other hand, light with an incident angle greater than the critical angle is totally reflected. This behavior yields an emission pattern that looks as if fluorescence propagates only in the two directions perpendicular to the crystal edge. The experimental techniques and model analysis used in this work can be used to study the mechanism of light or exciton propagation in organic crystals. 4. Experimental section Sample preparation. Perylene was purchased from Tokyo Kasei (Japan) and was used without further purification. An approximately 10 mM solution of perylene in acetone or chloroform was drop-cast on a glass substrate (microscope cover glass), and the solvent was allowed to evaporate at ambient conditions, yielding single perylene crystals on the substrate. The majority of crystals produced by this process were a-crystals, with very few bcrystals obtained. The crystal size ranged from a few to a few hundred micrometers, and the thickness was from a few tens to a few hundred nanometers, as measured by atomic force microscopy (data not shown). Dispersion of glass microspheres on perylene crystals was conducted by spin-coating an aqueous suspension of glass microspheres (Polyscience, 3–10 lm diameter) on the sample. Fluorescence microscopy. Fluorescence microscopy images were recorded using an epi-illumination microscope (Olympus) equipped with a motorized stage (Prior). The output of a continuous wave diode laser (k = 405 nm) was coupled to the microscope,
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the excitation spot in a direction parallel to the slits by changing the distance between the laser spot and the edge (X). Acknowledgement This work was supported by JSPS KAKENHI [grant Number 15K04705]. References
Fig. 5. (a) Scheme of the light propagation path within a crystal. (b) Plots of sin hc (left ordinate) and n (right ordinate) as a function of NA.
directed to the sample by a dichroic mirror (Omega Optical), and focused onto the sample with an objective lens (Olympus, 20– 100). The fluorescence from the sample was collected by the same objective lens, and the image was captured by a color CCD camera (Jenoptik). In spatially resolved fluorescence microscopy, the fluorescence was imaged onto the entrance slits of an imaging monochromator (Acton Research, SpectraPro 2150) through a long-pass filter (Omega Optical) to block the excitation laser. The light that passed through the slits was recorded by a liquid-nitrogen-cooled backilluminated CCD camera (Princeton Instruments, Spec10, 1340 400 pixels). The captured image was spectrally and spatially resolved along the horizontal and vertical axes of the camera, respectively. A square crystal was positioned by translating and rotating the sample in such a way that the fluorescence at the excitation spot and the edge emission passed through the entrance slits (Fig. 2a). The spectra at both positions were obtained by extracting horizontal cross-sections of the image recorded by the CCD camera. The spectral and spatial resolutions were 0.4 nm and 1 lm, respectively. These spectra were recorded while moving
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