1. Introduction

A photonic bandgap HC-PCF provides low loss air-guidance by photonic band gap (PBG) over a given range of optical frequencies (typically 50 to 70 THz). Thanks to the strong dual-confinement of laser and gas, ultra-long interaction length and limited optical bandwidth offered by the fibre, pure rotational stimulated Raman Scattering (SRS) in molecular H₂ gas has been favorably excited over the usually dominant vibrational resonance, with the pumping photons being almost-fully and selectively down-converted by ~18 THz to one single Stokes emission line. This near quantum-limit frequency-converter has been obtained in both the pulsed and CW regime with ultra-low pump power threshold [1,2]. Critically, the fibre can be made into a photonic microcell, by hermetically fusing a length of gas-filled HC-PCF to solid optical fibres, hence achieving compactness and portability whilst maintaining its unprecedented non-linear efficiency [3]. Despite these promising demonstrations, the tight restriction on the PBG transmission bandwidth has paradoxically been an impediment in capitalizing on the advantages of PBG HC-PCF in a number of applications. Indeed, whilst the narrow-band feature of the fibre optical transmission enables efficient conversion to the desired frequency by suppressing concomitant conversion to other unwanted frequencies, it is a limiting factor in generating emissions whose frequency-shift from the pumping laser is larger than the fibre bandwidth. Large-pitch HC-PCF [2,4] provides the necessary bandwidth for such applications; however, the conversion efficiency to the desired wavelength is reduced by the many additional lines that are generated concurrently with the Stokes order of interest, or by the excitation of other Raman resonances. Furthermore, by virtue of the nature of the optical guidance mechanism in large-pitch HC-PCF, the transmission loss is higher than those of PBG HC-PCF. This shortcoming is strongly felt in applications where it is highly desirable to transfer the excellent optical properties of readily available lasers such as Ti:Sapphire (~800 nm) or Nd:Yag lasers (~1064 nm) by effectively up- or down-converting them to a well targeted wavelength in spectral regions that are poorly covered by existing laser systems such as in the mid-IR.

The mid-IR, which spans from 2 μm and 25 μm, is today a manifest example of a spectral region where the need for compact, tunable laser sources is as pervasive as pressing. Indeed, because the vast majority of the gaseous chemical substances exhibit strong spectral signatures within the mid-IR, even a partial coverage of this spectral region is of timely importance in environmental and chemical sciences. Hitherto, the most promising laser technology for mid-IR coverage relies on quantum cascade lasers [5]. However, their multi-mode nature at higher optical output powers and their sensitivity to temperature are serious drawbacks compared to the benchmark lasers mentioned-above. Alternatives based on Raman down-conversion using erbium-doped fibre amplifiers and dispersion-tailored silica fibre were explored [6], but the strong mid-IR absorption resonance of the silica represents a strong limitation of such a scheme and the full conversion to a selected wavelength cannot be addressed. On the other hand, whilst the PBG HC-PCF is almost immune from material absorption, the coverage of the mid-IR spectral-band via efficient successive Stokes conversion from, e.g. a Nd:Yag laser source would require a HC-PCF with a bandwidth up to 3 times larger than what is achievable in today’s state-of-the-art PBG HC-PCF, and finding a way to avoid the power conversion being shared with other spectral components.

2. Taper design, fabrication and linear characterization

2.1 Design and linked theoretical background

Here, we break the seemingly opposing constraints of the PBG HC-PCF limited-bandwidth and the selective aspect of the frequency-conversion mentioned-above, by tailoring the bandgap spectral-location along the fibre length so to accommodate favorably two but only two Raman lines. This was made possible thanks to two length-scaling laws inherent to the PBG guidance mechanism and to the Raman process respectively. Firstly, in PBG fibres, any frequency, ν, of a PBG guided mode shifts linearly with the photonic crystal cladding’s pitch, Λ, so that an increase in the structure size would red-shift the PBG. In other words, the product $\nu \times \Lambda$ is a structural constant$K_{PBG}$ [7]. Consequently, one could shift the PBG spectral location by controlling the pitch. This can be practically obtained within a single fibre by judiciously tapering the HC-PCF, which then results in a PBG frequency-shift per unit length of${r_{PBG}=d\nu /dl)}_{PBG}=-\left(K_{PBG}^{}/{\Lambda }^2\right)\left(d\Lambda /dl\right)$.

Secondly, in SRS, when a pump laser with an optical frequency ${\nu }_0$excites appropriately a Raman resonance${\Omega }_R$, its frequency can be fully converted to that of the Stokes${\nu }_0-{\Omega }_R$after an appropriate propagation length $L_{SRS}$ [6]. Thus we can define a Raman-induced frequency shift per unit length as${r_{SRS}=d\nu /dl)}_{SRS}=-{\Omega }_R/L_{SRS}$. In the case of 7-cell HC-PCF and with negligible linear optical loss, the full conversion length is given by$L_{SRS}\approx \left(\left(9/4\right)\pi {\Lambda }^2/g\left(\nu \right)P\right)G$ [1], where $g\left(\nu \right)$ is the Raman gain coefficient, which we take to be constant and P is the pump power. G is the net gain, which for a maximum pump-Stokes conversion is set to be ~30 [1].

As a result, if the frequency-shift per unit length of the PBG-location is matched with that of the Raman cascade, the requirement could be fulfilled for the generation, with a quantum-limited conversion, of any given order of Stokes. Consequently, this scheme enables to fully convert a benchmark laser such as Ti: sapphire or Nd:Yag down to ~5 μm in the mid-IR [8,9], which is the limit set by the current PBG HC-PCF guided power overlap with the silica cladding. Figure 1A shows a schematic of the principle of this matched-cascade of PBG-shift and the Raman frequency-conversion. As the cascaded Stokes orders are generated at different points along the tapered fibre, the optical guidance window of the taper is also shifted such that it sequentially accommodates the locally generated Stokes whilst the depleted, and then useless, pumping lower order Raman component is no longer guided. A full conversion to the desired Stokes order is then in principle possible provided that $r_{PBG}=r_{SRS}$ is fulfilled throughout the tapered HC-PCF.

 

Fig. 1 Tapered PBG HC-PCF based Raman converter: A) Schematic impression of the matched cascade of Raman Stokes down-conversion and HC-PCF PBG red-shift. The transmission window is red-shifted along the tapered HC-PCF at a rate that matches the rate of the Raman conversion to higher order Stokes. B) Schematic of the experimental set-up. A microchip laser emitting at 1064 nm is coupled to a tapered HC-PCF filled with H₂. The transmission window of the taper is centered around 1064 nm at the input end, and around 1500 nm at the output end. The taper is either spliced at both ends or at the input end with the second end is attached to gas chamber for pressure optimization or for imaging the intensity profile of the output spectral components. λ/2 and λ/4 stand for half-wave plate and quarter-wave plate respectively; PBS: polarizing beam-splitter; MO: microscope objective; IF: interference filter. OSA: optical spectrum analyzer.

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This translates in a linear evolution of the pitch (i.e. the fibre diameter) with respect to the taper length L which is given by$\Lambda \left(L\right)={\Lambda }_0+\left(4{\Omega }_{R}gP/9\pi G{K}_{PBG}\right)L$. More conveniently, we can express this condition by the relative fractional change of the pitch along the taper$\left(\Lambda \left(L\right)-{\Lambda }_0\right)/{\Lambda }_0=\left({\Omega }_R/{\nu }_0\right)\left(L/L_{SRS}\right)$. Here, ${\Lambda }_0$and$\Lambda \left(L\right)$ are the fibre cladding pitch at the start of the taper and at a length L away from the start of the taper respectively. Consequently, if one desires a selective conversion to the n-th order Stokes with an initial pump laser with peak power P and a frequency ${\nu }_0$, the required taper length L so that the total PBG red-shift matches the required total Raman frequency conversion$n{\Omega }_R$is$L=\left(n/\left(1-n{\Omega }_R/{\nu }_0\right)\right)L_{SRS}$, which for ${\Omega }_R<<{\nu }_0$ simplifies to $L\approx n{L}_{SRS}$.

For the following experiment which is shown schematically in Fig. 1B, the targeted Raman transition is that of the rotational transition S₀₀(1) of molecular hydrogen (Ω_R~18 THz and$g~0.3cm/GW$) and is excited in similar fashion to that in [10]. As a proof-of-principle of the mentioned-above scheme, the HC-PCF taper is set to generate up to the fifth-order Stokes with a pump emitting at 1064 nm. Consequently, the total frequency-shift due to the Raman conversion (~90 THz) is almost twice the fibre bandwidth. This physically translates in increasing the pitch of the fibre (i.e. its outer diameter) by about 50% along the taper. Furthermore for the maximum pump coupling peak-power of ~1 kW that is experimentally available, the corresponding minimum Raman length is $L_{SRS}\approx 5m$ and hence the taper should be at least 25 m long. Furthermore, it is important to note that in the above estimations we ignored the fibre optical transmission loss and the dependence of the Raman coefficient g on wavelength and pump pulse-duration. A further requirement to achieve a high conversion to the targeted wavelength relates to the adiabatic condition of the taper. In order to ensure adiabatic propagation of the guided mode and hence minimize the power loss, the taper local length-scale which is given by$l_t\approx \left(3/2\right)\Lambda /\left(d\Lambda /dl\right)=\left(3/2\right)\Lambda \left({\nu }_0/{\Omega }_R\right)\left(L_{SRS}/{\Lambda }_0\right)$must be much larger than the coupling beat length$l_b=2\pi /\Delta \beta$, where$\Delta \beta$is the difference between the propagation constant of the fundamental and that of the second local higher-order mode [11]. For the case of a 7-cell PBG HC-PCF the beat length is of the order of 1 mm while taper local length is of the order of several metres, fulfilling thus the adiabaticity requirement.

2.2 Fabrication process

Once the required taper specifications are set, the fibre taper is then fabricated during the fibre drawing process following a method adapted from [12]. A 7-cell core defect HC-PCF’s cane, obtained by the usual stack and draw technique [13], is drawn down to an outer diameter of 118µm so that the fibre’s PBG is centered at 1064nm; the linear taper is then realized by decreasing the fibre drawing speed whilst keeping all other parameters constant so that the final outer diameter reaches 180µm, corresponding to a PBG centered at ~1550 nm. During the fibre draw, care was taken in calibrating the pressure in the preform cladding and core respectively so to avoid the holes collapsing and to keep the air-filling fraction constant throughout. Several fibre tapers have been fabricated, with length varying from 20m to 40m so to be tailored to different pump power thresholds required to start the Raman amplification.

2.3 Linear and structural characterization

The taper used here, presented schematically in Fig. 1, is ~40 m-long, and designed with r_PBG~2.6 THz/m corresponding to L _SRS~4.5 m for a coupled pump-peak power of 200 W. Figure 2 shows the physical properties of an identical tapered HC-PCF, whereby Figs. 2A and 2B present scanning-electron-micrographs (SEM) of the fibre cross-section at both ends of the taper in the same scale. No significant fibre structural deformations are observed, even though the pitch, core diameter and the outer diameter of the fibre are scaled up by more than 50% over ~40m. The linear expansion of these parameters is corroborated in Fig. 2C, which shows the measured variation within the taper length of both the pitch and core diameter from the SEMs of the cross-sections of ~2 m-long segments of the truncated fibre taper. The air-filling fraction from these SEMs was consistently measured to be 93% ± 0.5%, confirming the maintained integrity of the structure throughout the taper. This was also corroborated optically by recording the transmission spectra through six 6 m-long sections of a truncated fibre taper. This evolution is plotted in Fig. 2D where the central wavelength of the transmitted spectrum was shown to shift quasi-linearly from 1073nm to 1522nm with a slope of 2.6 THz/m. The PBG bandwidth, measured to be 35% of the central wavelength at each taper section, exhibits less than 1% relative variation as the structure is scaled up. This fabrication technique proves therefore effective for the control of the transmission position over ~100THz, with no foreseeable obstacles to scale this process up to the mid IR. Furthermore, the optical transmission loss was also measured for each 6-m long sections and found to be ~100 dB/km around 1064 nm and ~50 dB/km near 1550 nm, which is qualitatively consistent with the wavelength-scale ${\lambda }^{-3}$ of the PBG HC-PCF optical loss [14].

 

Fig. 2 Physical and optical properties of a tapered HC-PCF. (A) and (B) Scanning electronic micrograph (SEM) of a tapered HC-PCF at the input section (1064 nm end) and the output section (1550 nm end) respectively. (C): Measured fibre core-diameter and cladding pitch o a tapered HC-PCF at different length sections. (D) Central band gap wavelength (black) at the position of the taper and 3dB bandwidth (grey) along the tapered HC-PCF.

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3. Raman cascade generation

The experimental setup for the SRS generation and spectral evolution of each generated Raman component is presented in Fig. 1. The taper is filled with hydrogen using the method described in [10] before the “1064nm” end is spliced to a single mode fibre for ease of use. The “1550nm” end is either spliced after the gas-loading to form a photonic microcell [3], or kept in a gas cell in order to control hydrogen pressure and allow visualization of the near field pattern at the output of the fibre. A microchip diode-pumped solid state Nd:YAG laser (1064nm, 7kHz rep. rate, 0.8ns pulse-width and 50mW max average power) is coupled to the taper’s “1064nm” end through a half wave-plate, a polarizing beam splitter and a quarter wave-plate so as to control the coupled power and polarization of the incident pump. The output signal is collimated and sent to an optical spectrum analyzer. Furthermore, the near-field of each Stokes components emitted at the output of the taper is recorded on a camera using interference filters.

Figure 3 illustrates the properties of the spectral outputs recorded when a ~20 mW of a pump average-power is coupled to the taper. Figure 3A shows a linearly-scaled SRS transmitted spectrum through the first 1 m-long section of the hydrogen filled section. As expected, no significant Raman conversion occurred after such a short propagation-length. Conversely, the transmitted SRS-spectrum through the whole taper (Fig. 3B) shows an almost full conversion to the 3rd (S3) and 4th (S4) higher-order Stokes lines. It is noteworthy that both Stokes lines lay outside the transmission window of the input section of the taper. Furthermore, the measured output power shows a power conversion from the coupled-pump to S3 (1310 nm) and S4 (1419 nm) of 63%. This represents a quantum conversion to these two lines of ~82% with 56% of the total converted photons being in S4 and 44% in S3. In addition to S3 and S4, Fig. 3C, which replots Fig. 3B in dB-scale, shows that the spectrum contains a relatively strong S5 (1549 nm), which counts for 1.7% of the total output power (i.e. 1.2% of quantum conversion from the input); bringing thus the total quantum conversion into guided modes to more than 83%. An increase in the input power would clearly transfer this conversion to S5.

 

Fig. 3 Tapered HC-PCF Raman spectra: (A) and (B) present the typical Raman spectrum (solid lines) and the HC-PCF transmission spectrum (dashed lines) at the start and the end of the tapered HC-PCF. The dotted grey lines indicate the spectral location of the higher order Stokes. (C) Same spectrum as in (B) in dB. In addition to the 3rd, 4th and 5th order Stokes (S3, S4 and S5) which are supported by the end section of the taper, the spectrum contains, a significant amount of output power remaining in the pump and lower-order Stokes lines (P, S1 and S2). (D) Intensity profile of each of the spectral components of the taper output spectrum.

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In addition, Fig. 3C shows an intriguing feature because the output spectrum contains spectral lines at the frequency of the pump, S1 and S2, which lay well outside the transmission bandwidth of the taper output. The presence of such spectral components does necessarily contribute to the residual fraction of the “unconverted” photons. Indeed, the linear transmission-loss of the taper doesn’t count for all the conversion loss as it contributes only ~1% loss for each conversion. Furthermore, although one would expect that the decrease of the Raman gain coefficient with wavelength and the occurrence of a possible competing parametric process (e.g. four-wave mixing) would limit the maximum quantum conversion achievable, the previous reported results of SRS in HC-PCF show that these effects are negligible [1].

The presence of these residual peaks, also underline a physical mechanism specific to PBG HC-PCF. This is hinted in Fig. 3D, which shows the intensity profile of each of the transmitted spectral components. Whilst the modes at S3, S4 and S5 are guided in the fibre hollow-core as expected, the modes at the pump, S1 and S2 show a “doughnut”-shaped profile. This type of intensity distribution is associated in HC-PCF with surface modes (SM). These modes co-exist with core-guided modes inside the PBG; but, as illustrated in Fig. 3D, their field is primarily localized on the silica surround of the hollow-core [15,16].

The light coupling to these modes and their “survival” through the tapered HC-PCF is explained by their characteristic dispersion which is shown in Fig. 4 . The figure shows the calculated dispersion curves of the different supported modes by the PBG for the case of the input section of the tapered HC-PCF along with the density of photonic state (DOPS) of the fibre cladding structure to indicate the PBG boundaries. The core modes are labeled as HE₁₁ modes for the polarization-degenerate defect fundamental mode, and as HOM modes for the first quartet of higher order modes. One can distinguish the modes in the hollow-core from those in the silica core-surround by the gradient of their dispersion curves. The core modes have a dispersion gradient closer to the air-line, whilst the surface modes exhibit much sharper gradients, which are closer to that of the silica cladding modes. Furthermore, unlike a core-mode effective index, which is always less than 1, those of SM can take values much larger than 1. Because of these dispersion properties, surface modes have larger transmission-windows relative to a core mode. This elucidates the “survival” of the SM at the output of the taper. Also, the large difference in the dispersion gradient between the two classes of modes explains how light which is initially launched in HE₁₁ core-mode ends-up in a surface mode at the output of the taper. Under the influence of symmetry overlap between core and surface modes, an anti-crossing may occur at the crossing-point of their dispersion curves. This is illustrated in the inset of Fig. 4 whereby one of the polarization-degenerate HE₁₁ core-mode splits at ~1040 nm to form a single dispersion branch with a SM. As a result, the mode corresponding to this dispersion curve exhibits a field-intensity profile which adiabatically transfers from being located in the hollow-core (wavelength larger than 1040 nm) to being sited in silica surround when the wavelength decreases such as in the present taper. The experimental corroboration is given by Fig. 5A which shows the modal evolution of the observed Raman lines along the fibre transition through mapping their intensity profile.

 

Fig. 4 Guided mode dispersion curves and density of photonic states of the 1064 nm section of the tapered HC-PCF.

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Fig. 5 Modal and spectral evolution of the Raman cascade in the tapered HC-PCF. A) Near-field mapping of each Raman component along the tapered HC-PCF. The dashed lines indicate qualitatively the transmission window boundaries at each length B) Schematic of density of states (white stands for null density of state) and modal behavior along the tapered HC-PCF.

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This intensity profile cartography reconstructs the modal and spectral evolution of the whole process along the taper. It is achieved by repeatedly cutting 2m samples off the taper from the 1550nm end and recording at each increment the reconstructed near-field profile of all observed Raman lines using interference filters whilst keeping the gas pressure and input coupling constant (average power ~20 mW). Each row of the map is associated with a taper-section length and contains the intensity profile of the components of the transmitted spectrum through the taper-section. Similarly, to each spectral component is related a column, which contains the evolution of the mode intensity profile along the whole taper. The adiabatic transfer from the non-depleted power-fraction of spectral lines that were initially guided in the HE₁₁ modes into surface modes is illustrated by the sequential behavior in the modal evolution of P, S1, S2 and S3 lines. The sequence shows that as light propagates through the taper and experiences the PBG red-shift, the Bessel-like core-mode transforms into a“doughnut”-shaped surface mode, which continues to be guided beyond the PBG air-guidance of the taper-section (horizontal dashed-line in Fig. 5A). This is in agreement with the dispersion red-curve in Fig. 4. This point is further highlighted schematically in Fig. 5B, whereby it is easy to follow an individual Stokes lines as the PBG shifts along the length of the taper. Because the power-fraction in SM does not contribute to the general Raman process in H₂, this coupling between the fundamental mode and SM is a limiting factor in achieving a full conversion during the Raman cascade. However, this effect is minor and can be circumvented by increasing the input power so the pumping Raman line is depleted before the mode hybridization occurs. Furthermore, the novelty of such a mechanism in such a photonic structure deserves further investigations in its own right. According to the output spectrum (Fig. 3C), we have 0.047%, 0.04% and 0.45% of the input photons residing in the pump, S1 and S2 respectively. From this, we estimate the unconverted photon fraction due to this mechanism to 3.2%. This is deduced by considering the transmission loss of the SM of ~1dB/m [15] and their respective propagation length which can be deduced from Fig. 5A. Furthermore, because of the adiabatic coupling, half of the residual power of a non-depleted pumping spectral line is coupled and guided in the SM. This gives the total photon fraction that is lost as a result of the residual non-depletion of the spectral lines and the adiabatic coupling of their core-mode to the SM is 6.4%. Consequently, for a converter tailored to a fixed input power, the design of the HC-PCF tapering must take into account anti-crossing between core modes and SM so that the PBG frequency-shift closely follows the sequential generation of high-order-Stokes lines. More preferably, achieving a core-shape in view to remove the SM inside the PBG [17] would be a better solution.

In addition to the above mentioned adiabatic coupling between core-modes and SM, Fig. 5A shows another intriguing feature. The high-order Stokes lines are first initiated in higher order core-modes (HOM) instead of the fundamental mode HE₁₁. This peculiar effect is due to the characteristic shape of the PBG edges of the HC-PCF cladding whereby the HOM optical window position is slightly red-shifted relative to HE₁₁ transmission window. In other words the lower-frequency edge of the HOM and HE₁₁ correspond to different structural constant$K_{PBG}=\nu \times \Lambda$. For the case of the present HC-PCF, the HOM lower frequency edge occurs at$K_{PBG}=680.4\mu mTHz$, whilst this is equal to $700.2\mu mTHz$for the HE₁₁, corresponding thus to a spacing of$\Delta \left(\nu \times \Lambda \right)=19.8\mu mTHz$between the two modes. Consequently, as it is illustrated schematically in Fig. 5B, when light travels down the taper, the first available guided core-mode for the next higher-order-Stokes generation occurs in HOM, as the HE₁₁ is not yet guided. The lower propagation-loss HE₁₁ mode starts to be guided only after the HOM has propagated a distance$\Delta l\approx 1.7m$down the taper. This length is deduced from $\Delta \left(\nu \times \Lambda \right)$which is related to this length l by$\Delta \nu \approx r_{PBG}\Delta \nu /〈\Lambda 〉$, where the pitch is taken to be constant and equal to the average one which is ~4.5 μm. As a result of this short length relative to the Raman length and the relatively high loss figure of the HOM, which is typically ~15 times higher than for HE₁₁ modes [15], the converted Stokes will take place in the HE₁₁ mode soon after 1.7 m. It is noteworthy that because of the strong index-mismatch between the HOM and HE₁₁ modes, power coupling between these modes is impossible. This means that Raman conversions to the two modes are uncorrelated. Consequently, and similarly to the anti-crossing, this mechanism represents another mechanism of quantum conversion loss. Using the SRS coupled equations [18], we found that the photon fraction lost by this mechanism is ~1% per conversion on average, giving thus a total photon loss of 5%. Suppressing it could be achieved by designing a truly single-mode HC-PCF. The above results show that the linear transmission loss, the adiabatic core-mode and SM coupling, and the initial Raman conversion into HOM contribute almost evenly to the quantum conversion loss of 17%, and to which the conversion to the first anti-stokes (AS1) (see Fig. 5A) doesn’t contribute significantly.

4. Conclusion

To conclude, we reported on a new concept by which an SRS cascade is matched with a HC-PCF photonic band-gap frequency-shift. This was achieved by developing for the first time an ultra-long tapered HC-PCF filled with hydrogen. As a proof of concept, the matching of the two processes along the taper was used to down-convert, with a photon conversion (>82%) approaching the quantum-limit, a laser at 1064 nm to higher order-Stokes whose frequency-shift from the initial pump frequency represents more than twice the transmission bandwidth of the taper input. These results confirm that the tapered HC-PCF is an excellent candidate as universal optical converter. Furthermore, the results showed that via a judicious design of the tapered HC-PCF and choice of the Raman gas, such a photonic component can be tailored to act as a quantum-limited wavelength down-converter to any targeted wavelength. For example, by simply scaling up the transverse size of the presently reported taper so the input section guides at 1550 nm, and exciting it with an Erbium based laser, one could obtain with quantum conversion greater than 80% laser emission in the 2-3 μm range and with same spectral attributes of the pump laser. Furthermore, the use of such a taper with materials that are more mid-IR transparent than silica [19] (e.g. telluride glass) could extend the spectral coverage of such a converter down to 10 μm. Another interesting use of this tapered HC-PCF is Raman up-conversion whereby one could up-convert a benchmark laser in the visible to a sought-after wavelength in the UV. In addition to the obvious impact of such a device on laser-related applications, it is a unique platform for novel spatial modal dynamics such as the above adiabatic coupling between modes.