Royal Society Publishing

Hollow-core photonic bandgap fibre: new light guidance for new science and technology

F Benabid

Abstract

We review the progress made on the fabrication and applications of hollow-core photonic crystal fibres (HC-PCFs). The mechanism of the light guidance in these fibres is described along with their dispersion properties. We review the HC-PCF fabrication, the different results achieved in the fields of laser-induced particle guidance, low-threshold stimulated Raman scattering in hydrogen (vibrational and rotational), laser frequency metrology and quantum optics. Finally, we show the different new prospects opened up by these fibres.

Keywords:

1. Introduction

Since the advent of quantum mechanics and the demonstration of the wave nature of matter, solid-state physics borrowed a great number of concepts and analytical tools from optics. However, we had to wait almost 100 years to witness a ‘conceptual transfer’ from the field of solid-state and quantum mechanics to optics, a process which began in the late 1970s with the development of photonic band structure. This gave rise to the proposal, in the late 1980s, of the photonic bandgap by John (1987) and Yablonovitch (1987). Among the fields that emerged as a consequence of the mentioned work is that of photonic crystal fibres (PCFs); optical fibres whose cladding exhibits a two-dimensional periodic array of air holes1 and in which guidance is partially or totally based on photonic bandgaps with possible light confinement in a low-index defect (e.g. hollow core). Since its conceptual prediction by Russell in 1991 (Russell 2003) and its subsequent theoretical demonstration by Birks et al. (1995), hollow-core photonic crystal fibre (HC-PCF) represents by far the most advanced two-dimensional photonic bandgap structure, where the light transmission length-scale is now of the order of kilometres (Mangan et al. 2004).

In addition of being a unique platform in exploring the properties of the emerging physics of photonic bandgap, HC-PCF, thanks to its ability of guiding light through air or gas-phase material rather than glass, opens new prospects in various fields. As a matter of fact, groundbreaking results have already been demonstrated in areas as varied as nonlinear optics (Benabid et al. 2002a, 2004, 2005a; Ouzounov et al. 2003), laser-induced guidance (Benabid et al. 2002b) and quantum optics (Benabid et al. 2005b; Ghosh et al. 2005). When the hollow core of the fibre is filled with an active gas, it offers an unprecedented length where a laser field can interact with a gas-phase material in a diffractionless fashion, thus contrasting with the intrinsic diffractive nature of free space laser beams, which prevents most focused laser beams from travelling even a few centimetres (limited by the Rayleigh range). As a result, the power required for generating stimulated Raman scattering (SRS) in hydrogen has been lowered by a factor of more than one million while exhibiting a near quantum-limited conversion (Benabid et al. 2004), and quantum effects such as electromagnetically induced transparency (EIT) are made possible in molecular gases (Benabid et al. 2005b; Ghosh et al. 2005). For example with acetylene-filled HC-PCF, EIT was observed over the absorption grid of a whole branch located at the telecommunication band, opening very compelling prospects in optical telecommunications and slow light applications. Finally, and seeking to add to the HC-PCF scientific novelty, a compactness and integrability which will be of great interest for technological implementations, all the results mentioned earlier have been reproduced in all fibre devices, thanks to the recently developed HC-PCF-based gas cell (Benabid et al. 2005c). Furthermore, and as the first demonstration of HC-PCF applications, micro-sized particles have been guided by laser pressure through the hollow core of the fibre over a distance 100 times longer than previously reported (Benabid et al. 2002b) and with today's transmission performance one could envisage transporting with intrusion-free micro-objects such biological cells over hundreds of metres.

This paper presents the progress made in the understanding of the guidance mechanism in HC-PCF, in the fabrication of these fibres and, finally, in the different applications including laser-induced particle guidance, SRS, laser frequency metrology and quantum optics. In §2, we review the properties of a HC-PCF that guides by a photonic bandgap and of another that does not show any bandgap and yet exhibits experimentally a 3 dB loss length of 10 m. In §3, we review the fabrication technique for HC-PCFs. In §4, we review results on the levitation of micro-sized dielectric particles and guidance in a HC-PCF, we present results on low-threshold SRS generation in two different HC-PCFs filled with hydrogen gas and experimental observations of EIT in acetylene-filled HC-PCF. Finally, we present the new gas cell based on HC-PCF and as a demonstration of its vast potential, we describe an all-fibre laser stabilization unit using acetylene-filled HC-PCF.

2. Guidance mechanisms

One of the most interesting PCFs, with no counterpart in conventional fibre, is the HC-PCF (Cregan et al. 1999). Since its core index is lower than the effective index of the cladding, guidance via total internal reflection is impossible. The light in HC-PCF is instead confined and guided in the core exclusively by the surrounding photonic structure, which is made up of a periodic array of air holes in glass (Russell 2003). Depending on this structure, the light can be guided via ‘out-of-plane’ photonic bandgap (Birks et al. 1995) with extremely low loss over a relatively narrow bandwidth. The concept of ‘out-of-plane’ photonic bandgap refers to a situation where a given two-dimensional photonic structure exhibits forbidden frequencies for optical waves whose wavevector component β over the third dimension (non-periodicity plane) is not necessarily nil. In the first reported results on out-of-plane bandgap guidance by Birks et al. (1995), β was a variable parameter like the frequency and the manner the authors presented their results—a band diagram relating the propagation constant to the frequency illustrates very well the fruitful cross between guided-optics and solid-state physics.

(a) Bandgap guidance

Guidance in the air via a photonic bandgap has the potential for transmission with losses much lower than that in the glass, which is fundamentally limited by the Rayleigh scattering. However, until now and despite the huge progress in the transmission performance of HC-PCF, the lowest loss figure reported of 1.7 dB km−1 (Mangan et al. 2004) is still higher than the typical loss value in standard single-mode conventional optical fibre of approximately 0.2 dB km−1.

Among the fundamental effects causing the loss in HC-PCF is confinement loss, caused by the finite number of rows of air holes but also to the width of the bandgap, which is inherent to the lattice structure of the cladding. Consequently, finding a lattice that can be fabricated and exhibits the largest bandgap is of paramount importance. To date, the triangular lattice; a circular array of air holes packed in a triangular arrangement shows to be the most promising, as its fabrication is relatively easy and the numerical modelling results do not seem to show any better alternative.

In figure 1a, we show the projected band diagram centred on the dispersion curve of the vacuum (vertical red line) for such a triangular lattice with different air hole diameters D, while keeping the pitch Λ (spacing between the air holes) fixed. The colours indicate the density of states (DOS) of the modes supported by the structure. The DOS values are normalized to that of silica bulk material (Hedley et al. 2003; Pottage et al. 2003). The bandgap corresponds to DOS=0 and is depicted in white. For D/Λ=90% and below, the band structure exhibits several narrow bandgap in confirmation with the results in Birks et al. (1995); as the D/Λ increases, the bandgaps located in the higher frequency region (relatively to =9 for D/Λ=90%) tend to shrink and eventually disappear, while the bandgap at ∼9 follows a clear trend: it gets wider and wider and its location shifts to the higher frequencies (figure 1b). Figure 1c shows the evolution of the bandwidth2 of this bandgap with D/Λ, and indicates sort of a cut-off value for D/Λ, above which the bandwidth widens at a very fast rate as D/Λ is increased, e.g. an increase of D/Λ from 94 to 96% doubles the bandwidth. Moreover, the band diagram for D/Λ=100%, shown for pure academic purposes as its fabrication is impossible, indicates that the above-mentioned bandgap is owing to the glass features located at the interstitials of the stacked air holes. It is noteworthy that the location frequency shift and the widening of the bandgap trend continue for D/Λ>100% (i.e. smaller interstitial features). The sensitivity of the width of this bandgap to the air-filling fraction partly explains the dramatic drops reported recently (Venkataraman et al. 2002; Mangan et al. 2004) in the transmission loss of HC-PCF based on this structure. Moreover, the bandwidth for D/Λ=96% spans over 1.15 units of normalized frequency. Based on this, one would expect transmission with less than 0.1 dB km−1 loss figure being possible (Xu & Yariv 2003). However, experimentally for fabricated fibres with high air-filling fraction (greater than 80%), such as those reported in the fibres in Venkataraman et al. (2002) and Mangan et al. (2004), the structure gets slightly distorted during the draw ending by air holes with an overall hexagonal shape with curved corners instead of being circular (see figure 2; Mortensen & Nielsen 2004). Consequently, the air-filling fraction can be higher than the upper limit of approximately 91% in a perfect triangular lattice and hence having the bandgap shifted to higher frequency regions, however its bandwidth is narrower. This could be explained by a stronger ‘crosstalk’ between the interstitial features and the hexagon's strands.

Figure 1

Evolution of the band structure with the air-filling fraction. (a) Band structure for a triangular lattice with different D/Λ (the air-filling fraction is deduced from Embedded Image). (b) The evolution of the edges and the centre of the lowest frequency bandgap as D/Λ increases. (c) The evolution of the bandwidth with D/Λ.

Figure 2

Index profile of a ‘real’ triangular structure (a) and its corresponding band structure (b).

However, recent findings (Smith et al. 2003) have shown that the transmission performance is presently limited, not by the width of the bandgap or irregularities along the fibre but mainly, if one excepts the surface roughness scattering effects, by anti-crossing between modes mainly localized on glass surrounding the core (which we call for simplicity surface modes) and the mode confined in the core. Figure 3 shows the dispersion curve (figure 3a) for the fundamental-like mode (figure 3b(ii)) for a HC-PCF with a core formed by removing the seven central holes and a cladding with a triangular lattice with D/Λ=96% (figure 3b(i)). At the region indicated by the rectangle, the surface modes cross the fundamental core mode, resulting in a mode splitting (figure 3c). The spatial profile evolution of one surface mode and the core mode (figure 4(b)) near one anti-crossing region (figure 4(c)) illustrates the coupling between the two modes. Away from the anti-crossing point, the field is mostly confined in the core; as one approaches the anti-crossing point, the amount of field in the surface mode increases and starts to overlap with the core region to the point that the two modes are indistinguishable at the anti-crossing point. As the two modes pass the anti-crossing point, the mode, which was confined in the core, is coupled to the surface mode and vice versa with the surface mode. Figure 4(c) shows the spectrum of the group velocity of the core mode (defined here as ∂(βΛ)/∂()). The effect of coupling with the surface modes appears as a division of the spectrum into several regions. In the same figure, the DOS along the dispersion line is plotted. Note that the anti-crossing regions for such a structure and its corresponding core shape (figure 2b) do not lie inside the bandgap but in a region exhibiting low DOS compared to that of silica (DOS<1). For the present fabricated fibres, these crossings lie inside the bandgap region and are responsible for a large part of the present transmission loss (Smith et al. 2003). Consequently, the challenge for future improvement in these fibres is to optimize the core shape. The effect of these anti-crossings on the transmission loss and dispersion spectra of a fabricated HC-PCF is illustrated in figure 5. The fibre cladding has a triangular lattice (figure 2) and which the scanning electron micrograph (SEM) is shown in figures 9e and 14a and has been drawn to have its bandgap centred on approximately 1064 nm. Figure 5c shows the transmission spectrum of a length of fibre of 20 m (curve A) and 150 m (curve B), respectively. For the shorter piece of fibre, the signature of the coupling with surface modes on the transmission spectrum takes the form of strong absorption peaks located on the short-wavelength side with respect to the bandgap central wavelength. Consequently, the observed spectrum narrowing with a longer fibre length is dominated by the loss via coupling to the surface modes. The mechanism by which light is leaked out could be either via intrinsic loss of the surface mode or via coupling of the latter to a continuum of leaky modes (West et al. 2004). The transmission spectrum also shows some narrowing on the long-wavelength side; this is owing to the fact that the fundamental mode is not any longer supported (i.e. reached the bandgap edge) and only remains in the higher-order mode. It is worth noting the presence of small absorption peaks in the region of 1050–1070 nm in both the 150 m long fibre transmission spectrum and the loss spectrum. These are likely to be owing to higher-order and weakly coupled surface modes. The effect of the latter is clearly evident on the spectrum of the group delay and the group velocity dispersion as shown in figure 5a, where the anti-crossing between the core-mode and the surface modes is readily apparent.

Figure 3

(a) The band structure where the bandgap region is depicted in white and the dispersion of fundamental-like mode in the thick black line. (b) Dispersion properties of (i) the fundamental-like mode in a HC-PCF with a perfect triangular lattice with D/Λ=96%. The dielectric profile of a region of the super-cell used to solve the propagation modes (ii) and the near-field of the fundamental-like mode at =10.5. (c) Close-up of the dispersion line that shows the four splitting owing to coupling between the fundamental-like mode confined in the core and the surface modes.

Figure 4

Spatial modes evolution near an anti-crossing region. (a) The mode splitting around an anti-crossing region showing the dispersion of the fundamental-like mode and of one surface mode. (b) Modal plots of the core mode and the surface mode at different points near the anti-crossing region. Note that the scale in the first two plots (from the left) in bottom row and the last two in the top row are magnified by a factor 10 for visibility. (c) Group velocity and the DOS plot along the dispersion line of the core mode.

Figure 5

Effects of surface modes on the transmission and dispersion spectra of HC-PCF with a bandgap centred around 1064 nm. (a) The group delay and GVD, (b) the loss spectrum, and (c) transmission spectrum after a length of 20 m (curve A) and 150 m (curve B).

(b) Low density of state guidance

Moderately low-loss guidance can be obtained in certain HC-PCFs, even without a bandgap. One of the most intriguing HC-PCFs is one with a kagomé lattice in the cladding as reported in Benabid et al. (2002a) (figure 6a(iii)). The lattice consists of fine silica webs arranged in a kagomé lattice and surrounded by air. It has a relatively higher transmission loss in comparison with a bandgap HC-PCF but with an extremely large bandwidth, spanning several octaves, as shown by the loss spectrum (figure 6a(i)) and illustrated by the bright white colour of the guided mode (figure 6a(ii)). The calculated band diagram of the kagomé lattice does not show any significant bandgap. However, the structure exhibits low DOS over the normalized frequency range of 26–40 (Benabid et al. 2003; Hedley et al. 2003).

Figure 6

Properties of the HC-PCF with the kagomé lattice. (a) Transmission and loss spectrum (i), output end of the fibre when illuminated with white light source (ii), and the SEM of the fibre (iii). (b) The band diagram of the Kagomé structure (i), calculated mode profile for =26 (ii), and calculated mode with t/Λ=5% (iii).

This range corresponds to the transmission spectrum of the fibre indicating a possible correlation. Moreover, well-confined modes were found in low-DOS regions in both the kagomé HC-PCF (figure 6b(i)) and the triangular HC-PCF described earlier, as it is illustrated in figures 3 and 4.

3. Fabrication procedure of hollow-core photonic crystal fibre

The fabrication of all PCFs, independently of their cladding structure, follows common core-procedure (Knight et al. 1996). It is based on drawing a tube (usually made of silica) with a chosen wall thickness to hundreds of approximately 1 m long and approximately 1 mm diameter capillaries (figure 7a). The latter are then stacked by hand to the desired structure (figure 7b) to form what we call a ‘stack’. The stack is then fused and drawn to approximately 1 m long and a few millimetres diameter ‘canes’ (figure 7c). Finally, each cane is drawn into a fibre (figure 7d). This procedure has proven to be sufficient to draw efficiently all kind of solid-core PCFs along with the early HC-PCFs that have relatively low air-filling fraction (figure 8a). However, as the air-filling fraction gets higher than 80%, which is required to most hollow-core bandgap guiding fibres, the preservation of the integrity of the fibre structure becomes problematic as the effects of surface tension and the spatial variation of viscosity during the fibre drawing become important especially when one wants to ‘jacket’ the fibre (figure 9b,c).

Figure 7

Schematic of the fabrication procedure of HC-PCFs.

Figure 8

Schematic of the pressurization procedure of HC-PCF.

Figure 9

SEM of different HC-PCFs presented in chronological order. (a) The first fabricated HC-PCF (Cregan et al. 1999) exhibiting an air-filling fraction of approximately 40% and transmission loss of a few 100 dB m−1. (b) A HC-PCF exhibiting approximately 60% of air-filling fraction and a transmission loss of approximately 10 dB m−1. (c) A HC-PCF with an air-filling fraction greater than 70% when drawn with a jacket using the conventional stack-draw technique (expansion of the core and distortion of the cladding structure). (d) A jacketed HC-PCF (air-filling fraction greater than 87%) drawn using the modified stack-draw technique (Benabid & Knight 2002). (e) A HC-PCF from BlazePhotonics.

The HC-PCF could be seen as a periodic set of thin tubes of silica. These thin silica tubes witness, by virtue of surface tension, a pressure directed inward and consequently the tube tends to collapse. In order to contour-balance this effect, we exert an equal pressure directed outward by loading the tube with a gas flow (Benabid & Knight 2002). Given the fact that the surface tension depends on the diameter of the collapsing tube, we pressurize the core, the cladding and the interface between the jacket and the stack with different pressures (figure 8). With the above-mentioned technique, we managed to draw jacketed HC-PCFs with extremely high air-filling fraction (greater than 87%) while keeping a high level of the fibre integrity. These techniques then led to the state-of-the-art HC-PCF made by BlazePhotonics (Mangan et al. 2004).

4. Multi-facetted applications of hollow-core photonic crystal fibre

The key parameters in many of the applications involving laser–matter interactions, whether it is gas-phase material such as in nonlinear and quantum optics, and laser frequency metrology applications or micro-scaled particles for particle/atom guidance purposes are (i) diffraction-free propagation of light, (ii) low power loss, and (iii) light confinement in very small area. This can be summarized by maximizing the following dimensionless figure-of-merit (Benabid et al. 2002a) fom=λ(Leff/Aeff). Here, Leff is the effective constant-intensity interaction length, Aeff is the effective cross-sectional area and λ is the vacuum wavelength. A number of conventional approaches such as tight-focusing a laser beam or using a fibre capillary have been used to enhance this figure; however, their figure-of-merit is orders of magnitude lower than what one could achieve with HC-PCF as is illustrated in figure 10, making it an excellent host for all kind of applications involving strong interaction of laser with matter in general and gases in particular. In the subsequent sections are experimental results illustrating the huge improvements a HC-PCF could bring to a lot of above-mentioned fields.

Figure 10

Figure-of-merit for a capillary fibre, a focused laser beam and four HC-PCFs with different loss figures. At a bore radius of 5 μm, the HC-PCF with the lowest transmission loss (approx. 2 dB km−1) exhibits a figure-of-merit more than 10×106 times better.

(a) Particle guidance

Ashkin (1970) demonstrated that small particles could be propelled and suspended against gravity using only the force of radiation pressure. The use of the radiation pressure principle provides a useful means for non-intrusive manipulation of microscopic objects, e.g. biological objects, particles, etc. However, these applications are intrinsically limited by the diffraction of the laser beam to micrometre length-scales, as strong lateral confinement requires tight beam focusing. Overcoming this limitation is of particular interest in many areas where transportation of micro-sized objects over longer distances is required. For stable guidance, including cornering, one requires constant beam intensity focused to a small spot over many Rayleigh lengths, so that a hollow optical waveguide is a natural approach. Unlike glass capillaries, where the maximum guiding length one can hope for is, for example, a few millimetres for a laser power of 100 mW (Renn et al. 1999), in a HC-PCF, the guidance length can be many times longer. In Benabid et al. (2002b), we demonstrated particle guidance in HC-PCF over a length of 150 mm with only 80 mW laser power. The transverse (gradient) force in our fibre would be sufficient to easily support the particle against the force of gravity (if the fibre were horizontal) or to steer the particle around sharp corners (if the fibre were bent). Such a strong gradient force with a comparable laser power would only be attainable over a distance of 0.6 mm using a focused beam in free space, or over 12 mm using a standard capillary fibre.

The experimental setup is described in Benabid et al. (2002b). A collimated cw argon-ion laser operating at 514.5 nm is focused and directed vertically upwards into a HC-PCF. The particles are held on a vibrating glass plate located in the focused beam just below the fibre. The HC-PCF is held vertically above the glass plate. The length of the HC-PCF used in our experiments varied from 100 to 200 mm. The two steps of the experiment, namely the levitation of the particle from the glass plate and the guidance in the air-core of the fibre are monitored using two CCD cameras equipped with telescopes and connected to a monitor, a PC and a video recorder.

Figure 11b shows the output face of the fibre when the input face is illuminated with white light. It has core diameter of 20 μm, a pitch of 3–4 μm and an air-filling factor of approximately 70%. At our wavelength of 514.5 nm, loss was measured to be 10 dB m−1. Figure 12 shows a frame sequence of polystyrene with a size-standard of 5 μm diameter being levitated and guided over a 1 mm section of 150 mm long HC-PCF localized at about 4 cm from the input end of the fibre at a speed of 1 cm s−1. Despite the high loss figure of 10 dB m−1 of the HC-PCF used here in comparison with the actual standard transmission length of these fibres, the guidance length achieved with the 80 mW laser power represents an improvement of more than 1 order magnitude. With loss below 10 dB km−1, the possible guidance lengths would increase to a few 100 m.

Figure 11

(a) The transmission spectrum of the HC-PCF used here for particle levitation. (b) The micrograph of the exit end of an approximately 5 cm long HC-PCF as it is seen from a microscope.

Figure 12

A sequence of a polystyrene particle (pointed out by an arrow) being levitated in air and guided into a HC-PCF. Each frame corresponds to a captured scene size of 2.5×2.5 mm2. Each frame corresponds to a captured scene size of 0.9×0.9 mm2.

(b) Low-threshold stimulated Raman scattering

The way light is guided in a HC-PCF makes an excellent candidate for nonlinear optical interactions where long interaction length, low linear transmission losses and small mode diameters are simultaneously required. This dramatically contrasts with conventional techniques, which are all compromises. One such field where HC-PCF has brought a dramatic progress is SRS in molecular gases, where conventional techniques require high power lasers (1 MW) to reach the Raman threshold. In the following sections, we present results on the generation of vibrational SRS in hydrogen using a kagomé HC-PCF with a pump threshold 100 times lower than any previously reported in single- or multi-pass cells, and rotational SRS using a bandgap HC-PCF with thresholds some one million lower than its corresponding experiments and with photon conversion reaching almost the quantum limit.

(i) Vibrational stimulated Raman scattering

The experimental setup is described in detail in Benabid et al. (2002a). A Q-switched Nd: YAG laser, operating at 532 nm with a pulse duration of 6 ns, is coupled to the lowest-order air-guided mode of the HC-PCF filled with hydrogen and with an initial length of approximately 1 m. The HC-PCF had a cladding with a kagomé structure mentioned in §2. Its transmission bandwidth covers the whole visible–IR (VIS–IR) range with a minimum value of approximately 1 dB m−1 at 1307 nm.

Figure 13d shows the near-field pattern of the transmitted energy of the pump (532 nm), Stokes (683 nm) and anti-Stokes (approx. 435 nm) through a hydrogen-filled HC-PCF. The threshold level of the coupled energy was measured for the different fibre lengths we cut and found to be 0.8 μJ for Stokes (i.e. approx. 133 W of peak power). As the Stokes power increases with the increasing of input power, an anti-Stokes component appears. The measured threshold for the latter is 3.4 μJ. Despite the absence of an optimization study, a photon conversion efficiency to the Stokes of approximately 30% is obtained for a length of 32 cm and a coupled energy of 4.5 μJ. Moreover, for a fibre length and coupled power where the Stokes has not yet suffered from the loss, the ratio Stokes–anti-Stokes reaches a maximum of approximately 5%.

Figure 13

(a) The loss spectrum of the Kagomé HC-PCF. (b) The SEM of the fibre. (c) The end face of the fibre as it is illuminated by a white light source. (d) The near-field pattern of the pump, the Stokes and the anti-Stokes, respectively.

(ii) Rotational stimulated Raman scattering

Here, we use the same principle to generate rotational SRS in H2. However, unlike in the preceding section, the fibre used here guides via a photonic bandgap, hence exhibiting a narrower bandwidth but much lower transmission loss (see figure 13). These features make it ideal for applications (e.g. LIDAR, single frequency converters) where occurrence of additional Raman lines, owing to either Raman cascade or wave mixing, can be highly undesirable and where extremely high conversion is needed. The experimental setup used here is basically identical to the one reported in Benabid et al. (2002a), except that the pump signal was delivered by a passively Q-switched frequency-doubled Nd: YAG microchip laser with a maximum output energy of 2 μJ, and is circularly polarized in order to have higher gain coefficient and to eliminate Stokes–anti-Stokes coupling (Venkin et al. 1985). The fibre has a diameter of 7.2 μm and its cladding has a triangular structure with a pitch of approximately 3 μm and had an initial length of 35 m. Its transmission spectrum is approximately 150 nm wide, centred around 1064 nm (figure 14).

Figure 14

(a) SEM of the HC-PCF. (b) Transmission loss spectrum of the fibre. The vertical arrows show the location of the pump (P), the first Stokes (S) and the anti-Stokes (AS).

Figure 15 shows the evolution of the ratio of the transmitted average power to that of the coupled one as the latter increases for the pump (1064 nm) and the first Stokes (1135 nm), respectively. The transmitted spectrum through 3 m long fibre is also shown for two different coupled energy values, showing the near depletion of the pump and almost full conversion to the first Stokes. The lowest threshold energy was approximately 3 nJ (approx. 3.9 W peak power) and observed for a fibre length of 35 m (figure 15a). This value is more than one million times lower than the lowest value reported in conventional experiments for rotational SRS generation (Heeman and Godfried 1995; Perrone et al. 1997; Tomasi et al. 2001).

Figure 15

Evolution of the ratio of transmitted average power over that of the coupled average power for the pump (open circles) and the Stokes (solid circles) in the case of a fibre length of (a) 35 m and (b) 2.9 m. (c) The transmitted spectrum for two different values of coupled energy through 3 m long fibre.

The threshold level increased as the fibre length was reduced in agreement with the theoretical prediction. For fibre lengths shorter than 3 m, the ratio of the Stokes power to that of the coupled one reached a maximum of 86%, corresponding to a photon conversion of 92%. This corresponds to a photon conversion efficiency of 92%, which is to our knowledge the highest ever reported.

(c) Electromagnetically induced transparency in acetylene-filled HC-PCF

Another field where the figure-of-merit mentioned above plays a key role is quantum optics. An example of the many phenomena in this field is EIT (Harris 1997). This refers to an effect that, in a medium driven by a control laser, a probe laser whose frequency is near an otherwise absorbing transition will experience a narrow transparency window at the centre of the absorption profile. In addition, the transparency is accompanied with a very sharp change in dispersion. These features find compelling applications in topics as various and varied as ultraslow light (Hau et al. 1999) and light storage (Liu et al. 2001), laser cooling (Aspect et al. 1988), nonlinear optics (Jain et al. 1996) and atomic clocks (Motomura et al. 2004). They are indeed the driving motives behind the extensive study of EIT since its first experimental demonstration (Boller et al. 1991) and the growing endeavours and proposals presently undertaken aimed at finding ways to implement it in all-optical switching and signal processing in optical communication as well as in building blocks for quantum computing and teleportation.

Despite the consensus on the potential of EIT mentioned earlier, experiments have been restricted to atomic vapours (e.g. Rb), and few studies have addressed the occurrence of EIT in molecular systems (e.g. Qi et al. 1999). Molecular systems have a number of distinctive features that could not only broaden our fundamental understanding of EIT-related phenomena by offering new test grounds, but also would open new technological prospects. For instance, many molecular systems exhibit quantized and spectrally resolvable vibrational and regularly spaced rotational–vibrational transitions which cover the whole VIS–IR spectrum. An appropriate combination of two transitions could form a three-level system in the Λ, V or cascade configurations where electromagnetically induced transparencies could in principle occur. Figure 16 schematically illustrates this in the case of rotational transitions between two vibrational states in a parallel band of a linear molecule (Brown 1998). The figure clearly shows that for a control laser, which is on resonance with an absorption line (e.g. P(J+1), J being the rotational quantum number), one could observe transparencies with a probe laser tuned around either the line R(J−1), thus forming a Λ interaction configuration, or the R(J+1) line, forming a V interaction scheme. Consequently, the R-branch could be used as a comb of transparencies spanning several THz for future devices such as all-optical routers in telecommunications. In this case, molecules such as acetylene and hydrogen cyanide are the natural choice, since their ν1+ν3 and 2ν1 bands, respectively, offer a comb of stable and regularly spaced ro-vibrational overtone transitions covering the whole telecommunications wavelength range and are already used as grids of frequency standards (Nakagawa et al. 1996). Using the very same absorption lines as a grid of ‘transparency windows’ at which light could propagate with controllable group velocity is a highly attractive prospect.

Figure 16

Schematic illustration of the energy level diagram of rotational transitions between two vibrational states (v and v′). The rotational transitions in the P-branch correspond to transitions accompanied by an excess of one unit of angular momentum, i.e. ΔJ=−1, and in R-branch to transitions with ΔJ=+1. With this system, a combination of control-probe lasers resonant with P(J+1)−R(J−1) forms Λ interaction and P(J+1)−R(J+1) forms a V interaction, developing a comb of transparencies over the spectrum covered by the R-branch.

The hurdles thus far to the observation of EIT in gas-phase molecules are twofold. On one hand, the strength of the typical molecular transition dipole moments is orders of magnitude smaller than their atomic vapour counterparts (e.g. in Rb, the effective dipole moment is approximately 60 Debye, while it is only a few milli-Debye for the ν1+ν3 band of acetylene). On the other hand, low intensities in coherent interactions are often required in order to avoid power broadening and frequency shifts, which result in an unfavourably low signal-to-noise ratio. This drawback is particularly felt in molecular systems where even the simplest molecules are open systems, in that every excited molecular ro-vibrational level is radiatively coupled to many more energy levels than any atomic excited state, thus necessitating extremely long interaction lengths. Fortunately, and as we saw it earlier, this requirement can be satisfied in HC-PCF (Cregan et al. 1999).

The experiments were performed using acetylene gas (12C2H2) under a pressure ranging from 1 to 10−3 mbar. The gas is kept at room temperature and is contained in a HC-PCF. The latter was preliminarily spliced at one end to a single-mode fibre (SMF) using the procedure described in Benabid et al. (2005c) (splice loss approx. 1 dB) and evacuated before being filled with acetylene through its second end which is hermetically attached to a gas chamber (Benabid et al. 2002a). The pressure of the acetylene-filled HC-PCF is then brought to equilibrium at pressures of 0.1–1 mbar (using a mechanical vacuum pump) and 0.1–0.001 mbar (using an adsorption vacuum pump). The fibre has a bandgap centred on 1550 nm, exhibits a linear loss of 5–10 dB km−1 in the range 1450–1700 nm and has a 20 μm core diameter (inset of figure 17). The choice of a larger core in comparison with the fibre used in Benabid et al. (2005c) is motivated by the need to reduce the collision rate of the gas with the inner wall, which is likely to be one of the dominant sources of decoherence, given the confined geometry of the interaction zone. The control beam is tuned around the P(J+1) line corresponding to the transition Embedded Image, where J is the rotational quantum number of the vibrational state and physically can take any value from 0 to 27, covering thus all the strong absorption lines of the P-branch of the overtone ν1+ν3 band. For each laser control coupled to a P(J+1) line, the probe is swept around R(J−1) (i.e. Embedded Image transition) for Λ interaction scheme, and R(J+1) (i.e. Embedded Image transition) for V-type interaction.

Figure 17

Schematic of the experimental setup. PD, photodetector; IF, interference filters; S, splice between the HC-PCF and a solid SMF; FPC, fibre polarization controller; EDFA, erbium-doped fibre amplifier; and ECDL, external cavity diode laser. The inset on the left-hand side is a SEM of the HC-PCF used as the acetylene cell.

The experimental setup is shown schematically in figure 17. The probe beam is delivered from a commercial tunable external cavity diode laser (ECDL). This beam is coupled to a fibre system consisting of an isolator and the 10% port of a 90/10 coupler. The control beam, from a second ECDL, is amplified by an approximately 1 W erbium-doped fibre amplifier (EDFA). It passes through a polarization controller and is coupled to the 90% port of the 90/10 coupler where it is combined with the probe beam. The combined beams pass through a circulator and finally enter the acetylene-filled HC-PCF. The role of the circulator is first to avoid feedback to the laser sources and secondly to monitor the input beams via their residual reflection at the HC-PCF/SMF splice. At the output of the HC-PCF, the control beam is filtered out using interference filters, leaving mainly the probe beam to be transmitted and detected.

The measurements were carried out for three different fibre lengths (approx. 1, 2 and 5 m) and under different pressures. Figure 18 shows the transmission of the spectrum of the probe field when the coupling beam is off (figure 18a) and when an approximately 500 mW coupling field is copropagating with the probe field.

Figure 18

Measured and theoretical transmission trace of R(11) line in the absence of control beam (a) and in the presence of approximately 800 mW control power (b). The operating pressure range is 10−2–10−3 mbar and length of fibre is approximately 2 m.

5. All-fibre gas cell based on hollow-core photonic crystal fibre

In §4c, we have demonstrated the high adding value in efficiency; however, the setups involved were relatively cumbersome as the fibre needs to be permanently attached to a gas or vacuum chamber. In order to add to this efficiency a compactness and an integrability value, we spliced a gas-filled HC-PCF at both ends to standard solid SMFs (figure 19a,b; see Benabid et al. (2005c) for more details). The net result is an all-fibre transportable gas cell (figure 19d). With this gas cell, filled with the appropriate filling gas, we have reproduced all the above experimental demonstrations mentioned in §4c but with an all-fibre device. Another device is a self-contained laser frequency stabilization unit.

Figure 19

(a) SEMs of side view of HC-PCF spliced to an SMF. (b) End of a HC-PCF cleaved at the junction of the splice. The recess, which creates an air-gap of a few tens of micrometres between the fibre cores, is owing to the action of surface tension during fusion. (c) SEM of the same piece as in (a) and (b) cleaved a few millimetres from the splice, showing clearly the preservation of the microstructure integrity. (d) Photograph of a 5 m hydrogen HC-PCF-based gas cell, showing its size compared to a match.

(a) Acetylene-filled hollow-core photonic crystal fibre-based laser frequency stabilization

Acetylene is suitable as frequency standard for the optical communications wavelength range (Quinn 2003), offering a comb of stable and regularly spaced overtone absorptions in the vicinity of 1.55 μm. It exhibits Doppler-free saturation linewidths of less than 1 MHz (Nakagawa et al. 1996) and is remarkably insensitive to external perturbations (Swann & Gilbert 2000). Figure 20a is a plan of our all-fibre frequency stabilization system. A simple side-locking technique was used to lock the laser frequency to one of the shoulders of a selected absorption line (MacAdam et al. 1992). The setup consisted of a tunable ECDL source, an isolator, fibre couplers and a length of acetylene-filled HC-PCF. The laser output, after passing the isolator, is split into three beams using two fused taper couplers. The first (the locking) beam passes through the gas cell (control cell) and is then sent to the photodetector (PD1 in figure 20a). The second (reference) beam is monitored at an identical detector PD2. The reference and locking signals from PD1 and PD2 are sent to a difference amplifier, the output of which is fed to a locking circuit based on (MacAdam et al. 1992). To avoid possible artefacts in the control system (Wieman & Hollberg 1991), an independent means of testing/discriminating the absolute frequency was achieved by passing the third (out-of-loop) beam through a second HC-PCF gas cell (the monitor cell). This resulted in a frequency stabilization and testing system that was completely fibre based. Using this system, we were able to lock the laser to different acetylene absorption lines. Figure 20b shows the detected transmission at 1530.43 nm (P9 absorption; Swann & Gilbert 2000) from the locking and monitor cells as the laser frequency is swept through 2 GHz. Figure 20c shows the frequency fluctuations of the laser when it is free running and when the locking loop is closed. The closed-loop frequency fluctuations exhibit an RMS frequency deviation of approximately 310 kHz over a 1 min integration time. The residual noise exhibits a white noise spectrum with an Allan variance of Embedded Image for an averaging time of 1≤τ≤25.6 s and is limited by the electronic noise of our detection system (PD3 in figure 20a).

Figure 20

(a) Experimental setup. (b) Spectrum of the transmitted signal from the locking and monitor cell when the laser frequency is swept around P9 line. (c) Frequency fluctuation as read from the monitor cell.

6. Conclusion

In conclusion, we reviewed the progress made on the development of HC-PCF and its implementation in application as varied as nonlinear optics, quantum optics and laser metrology. All these experimental demonstrations were reproduced in an all-fibre, ultra-compact, high performance, easy-to-use and unconditionally stable gas-laser devices. The commercial availability of a wide range of all-fibre components (e.g. lasers, phase-modulators, power-attenuators, isolators, Bragg-gratings and beam-splitters) makes complex systems easy to design and construct. It is now possible to imagine miniature laser-gas devices, occupying a tiny volume and containing minute amounts of gas, with everyday applications in fields such as colour conversion of laser light (perhaps, using a built-in diode pump laser) and the measurement and stabilization of laser frequency. It is also possible to use such a gas cell as transportable atomic clock or a host for laser cooling. The unique features of HC-PCFs make these gas-laser devices of extreme efficiency as it is demonstrated. The impact in these and many other laser-related fields is likely to be deep and lasting.

Acknowledgments

The author would like to thank Tom Hedley and David Bird for providing the computer code for the band diagram and mode solver. He is also thankful to Francois Couny, Phil Light, Philip Russell, Tim Birks, Jonathan Knight and Greg Antonopoulos.

Footnotes

  • One contribution of 23 to a Triennial Issue ‘Mathematics and physics’.

  • Though, this array could be made by arbitrary materials with different refractive indices, we limit our definition of PCF in the present paper to those made by silica and air.

  • Here, the bandwidth is taken along the vacuum dispersion line.

References

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