We characterize the spontaneous emission of dye that is introduced into the central core of a tapered photonic crystal fiber. Since the photonic crystal period in the fibre cladding varies along the taper, the transmission and spontaneous emission spectra over a wide range of relative frequencies can be observed. The spontaneous emission spectra of the fibre transverse to the fiber axis show suppression due to partial band-gaps of the structure, and also enhancement of spontaneous emission near the band edges. We associate these with van Hove features, as well as finite cluster size effects.
© 2006 Optical Society of America
Photonic crystals (PCs) have many potentially important applications, such as the manipulation of the spontaneous emission of atoms . However this application has received relatively little interest, in part because of the difficulty of the associated experiments and theory. Previous work on spontaneous emission in PCs  has concentrated mostly on changes in the spontaneous emission lifetime in PCs with a high refractive index contrast, and thus well-developed band gaps, over a relatively narrow range of wavelengths. The work  by Fujita et al., for example, shows the spectral dependence of the redistribution of spontaneous light emission into the third (unconfined) dimension in a 2D photonic crystal semiconductor structure. Louvion et al.  used near-field optical probes to observe the coupling of quantum well emission to 2-D photonic crystal microcavities in InP.
In contrast, here we investigate spontaneous emission in a two-dimensional PC with modest refractive index variations, using a photonic crystal fibre (PCF). Our investigation is most closely related to the work of Cregan et al. , in which the spontaneous emission pattern from Er3+ doped PCF was measured in a cone around the fiber axis. Here, rather, we measure the transverse radiation patterns, and use tapering to provide a wider range of effective frequencies. We do so by infiltrating the hollow PCF core with a Rhodamine 6G (R6G) dye solution, which emits in the 500–600 nm wavelength range, and exciting the dye optically. The dye emission is monitored in the plane transverse to the fibre axis.
PCFs are designed to support modes that travel parallel to the longitudinal axis–thus they have band gaps for radiation with wave vectors that are almost parallel to the fiber axis, with only a small transverse component. These gaps for predominantly longitudinal propagation provide no guiding in the plane orthogonal to the axis. The in-plane band structure of the lattice in the PCF cladding (Fig. 1) shows that even to have partial transverse gaps in the visible part of the spectrum, the lattice period d needs to be well below 1 µm, substantially less than the actual period d=1.6 µm. To provide at least the partial gaps in the transverse plane as required we gradually tapered the fiber down [6–10] reducing its outer diameter by a factor of four. It has been shown [7–9] that the periodic lattice in the PC scales similarly. The tapering has two advantages: the first is that reduction of the period shifts the in-plane bandgap to shorter wavelength, within the emission band of R6G. The second arises from the gradual variation of the fiber diameter (and hence d). This gradual variation ensures that the relative frequency ωd/(2πc)=d/λ varies considerably along the PCF taper, even though the actual wavelength range is limited.
We compare the results of our measurements with calculations based on the Local Density of States (LDOS) ρ(ω,r) [11–13], and transverse directional emission calculations, reported to our knowledge for the first time here for photonic crystal fibre. The LDOS, a generalization of the usual density of states, has a spatial dependence at frequency ω which embodies the modal fields at that frequency; for example at a field node, ρ(ω,r)=0, even though the Density of States does not vanish. We investigate the angular- and polarization-dependence of the emission spectra [14–16] and find evidence of both enhanced and suppressed emission near and within partial gaps.
2. Experimental geometry
We used commercial air-guiding photonic bandgap fiber AIR-6-800 from Crystal Fibre. The cladding of this PCF has a period of d=1.6 µm, with relative air hole size a/d=0.4. The hollow core has a diameter of approximately 6 µm, and the fiber’s outer diameter is 125 µm. This fiber provides photonic band gap guiding for wavelengths from 760–800 nm. The fiber was tapered using the technique of Mägi et al . Figure 2 shows the cross section of the PCF that was tapered down by a factor 4, with the untapered fiber cross-section shown in the inset. Some damage is attributed to the cleaving of the tapered fibre. The relative increase in size of the central hole as compared to the outer micro-structure was due to over-pressuring  during tapering induced by the sealed ends on the PCF. To reduce the expansion, the pressure in the central hole would have to be reduced relative to the outer holes, whilst tapering. This was not possible here as access to the central hole was needed for fluid filling.
In the first experiments, we characterize the PCF’s reflection and transmission spectra using the geometry shown in Fig. 3, in a way similar to the work of Mägi et al. : light is incident from the single mode fiber (SMF) on the left, and is collected by the SMF on the right to measure the transmission. Between these two fibers is the tapered PCF, which can rotate around its axis to allow different crystallographic directions to be probed. The PCF is characterized at different positions along the taper, corresponding to different lattice constants, resulting in a large variation of the relative frequency d/λ.
In the second, more crucial set of experiments we selectively introduce Rhodamine 6G in methanol solution into the core of the PCF. The experimental geometry is as in Fig. 3 except that the left-hand PCF carries the light from a continuous wave frequency-doubled Nd:YAG laser to excite the dye. The orange light emitted by the dye is collected by a short length of SMF and thence to a polarizer and spectrometer.
Figure 4(a) shows the reflection versus wavelength taken at different positions along the taper. The various spectral features do not line up because the PCF period varies along the taper. We analyzed these results by first transforming the variable on the horizontal axis to the relative frequency d/λ. We then superimposed all traces, corresponding to data taken along the entire length of the taper. The large quantity of data thus obtained improves the statistical significance of our results. An example of such a data set is shown in Fig 4(b), which gives the transmission versus d/λ for the light propagating through the PCF in the ΓM direction with TE-polarized light. The vertical lines show the edges of the photonic band-gaps from Fig. 1. Note that the first gap around d/λ=0.5 appears clearly in all traces. However, the second gap just below d/λ=1.0 shows up less clearly as it is more sensitive to structural disorder and because the background intensity is generally lower at this frequency. Similar results were obtained for TM polarization and for propagation in the ΓK direction.
The emission spectra for ΓM and ΓK directions and TE and TM polarizations were analyzed in a similar manner, after normalizing the spectra with the dye emission from a hollow-core capillary without photonic crystal structure. The increasing baseline in Fig. 5 accounts for the increasing dye volume as the taper diameter increases. The resulting emission spectra, shown in the lower part of Fig. 5, exhibit suppressed emission features associated with partial bandgaps. However, in addition, enhanced emission inside the high-energy edge of the first bandgap is observed, with a similar, though weaker peak on the low frequency side. The origin of these two latter features, which only appear in emission and do not show up in transmission or reflection measurements, is discussed in Section 4.
4. Modeling and discussion
The emission spectra depend on both the LDOS, which determines the emission strength, and the emission pattern, which determines its directionality. Our modeling gives the far-field emission spectra (Fig. 5), which we compare to measurement, and the near-field emission pattern (Fig. 6 and multimedia files TM and TE), which we employ to understand the emission spectra. The modeling used a multipole method  to calculate the two-dimensional Green tensor in the PCF geometry in Fig. 6. (No account was taken of variation in the fiber cross-section due to air-hole collapse during tapering). Strictly speaking the point-like species of the dye require the three-dimensional Green tensor, which involves a Fourier integral over the propagation constant in the direction of the PCF axis, β. However, when the observation point is in the far-field and in the same plane transverse to the PCF axis as the dye, the method of stationary phase can be used to approximate the Fourier integral. The only stationary phase point is β=0, at which the three-dimensional Green tensor reduces to the two-dimensional Green tensor.
The emission patterns in Fig. 6 and in the multimedia files are depicted using the squared-amplitude of the Poynting vector, normalized to its free-space value. As in the experiment, radiating sources are spread evenly across the core. The emission intensity is presented using a color scale with red indicating enhanced emission and blue indicating suppressed emission. As the angle-integrated emission flux is proportional to the LDOS, the average emission intensity on the boundary of the defect is an indication of the LDOS modification. The emission’s directionality is then determined by noting that the PCF is configured with the x-axis in the ΓK direction and the y-axis in the ΓM direction.
Around a relative frequency of d/λ=0.5, the band structure shows a partial bandgap for ΓM (TE and TM) and ΓK (TE only), which is seen to correspond to a dip in the measured and calculated emission. In addition, both the modeling and the experiments (Fig. 5) predict emission enhancements near the low- and high-energy sides of the bandgap. Similar emission patterns are seen in ΓK and TE polarization at the frequencies of the two peaks in the TE emission spectrum of Fig. 5. In both cases, the LDOS is significantly enhanced. The peaks in the emission spectrum, therefore, are not entirely due to the emission being focused in the ΓM direction. Nonetheless, a degree of focusing in the ΓM direction does occur, and this is why two peaks occur in Fig. 5, but not in the corresponding spectra for ΓK. The first peak coincides with the saddle point of the first band, located at the M point of the band structure in Fig. 1. We therefore attribute this peak to a van Hove singularity [16, 17]. To verify that the peak is due solely to the periodicity of the PCF, we varied the size of the PCF in the modeling and removed the defect, but did not observe any change to the peak. The second peak lies well within the TE band gap. The frequency of this peak shifts in the modeling when the size of the core region is varied and disappears when it is removed. We therefore attribute the second peak to a defect state associated with the core.
In conclusion, we have investigated the transverse emission of dye infiltrated in the central core of a tapered PCF. Since we only measure the emission in the plane transverse to the fiber axis, a two-dimensional theoretical analysis is sufficient. This is in contrast to earlier work by Cregan et al.  in which emission measurements in a cone around the fiber axis necessitate a three-dimensional analysis. Such an analysis is more complex, with results that are more difficult to interpret. We not only observed emission suppression at wavelengths corresponding to a partial gap in the two-dimensional band structure of the lattice, but also observed enhanced emission close to the gap edges. Thus the effect of the photonic crystal cladding is more than simply an optical filter. We associate the low-frequency feature with a saddle point in the (two-dimensional) band structure, while the high-frequency feature is associated with finite size effects. Neither of these two features appears in transmission or reflection measurements, illustrating that the emission is sensitive to the local density of states (LDOS) of the structure, rather than the density of states (DOS). However, even the LDOS does not encapsulate directional emission information, so the experimental results provided here may well point to the need for the development of density of states functions incorporating both spatial information (strength of radiation from a source placed at a particular point) and directional information (ability of radiation to escape in a particular direction).
This work was produced with the assistance of the Australian Research Council (ARC) under the ARC Centres of Excellence Program. CUDOS (the Centre for Ultra-high bandwidth Devices for Optical Systems) is an ARC Centre of Excellence. The authors thank Dr Mike Steel for useful discussions. David Fussell’s present address is the School of Physics, Queens University, Kingston, Ontario, Canada K7L 3N6.
References and links
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