**2. Photonic crystal fibers**

The authors of the paper in 1996 [3] were looking for photonic bandgap guidance in the defect core of the PCF with a core size of ~4.6 μm. The reason for the absence of photonic bandgap guidance in a solid-core PCF with air holes in the cladding only became clear a few years later. To their surprise, they observed very broadband single-mode guidance from 458–1550 nm (extended to 337-1550 nm in [4]). A conventional single-mode step-index optical fiber would become multimode at shorter wavelength. Even more surprising, the diffraction angle of the output beam was smaller at shorter wavelengths, indicating a smaller fiber numerical aperture at short wavelength.

#### **2.1. Fundamental space-filling mode of photonic crystal cladding**

In a follow-on paper [4] the initial observation of the "endlessly single-mode" nature of photonic crystal fibers was explained by the dispersive nature of the cladding, which can be viewed as a composite of two materials, i.e. silica and air. The effective refractive index of the composite cladding was identified for the first time as the effective index of the fundamental mode of the composite cladding, referred to as the *fundamental space-filling mode (FSM)*. In the extreme case of conventional optical fibers with an infinite cladding, the effective index of the fundamental space-filling mode becomes the refractive index of the cladding. In PCFs with air holes, the cladding index ncl, i.e. the effective index of the fundamental space-filling mode, is lower than the refractive index of the background glass nb due to the existence of the air holes, i.e. ncl<nb. The core index nco is the same as the index of the background glass, nco=nb. Funda‐ mental optical guidance in PCFs can, therefore, in principle, be understood in a similar way to that in conventional optical fibers (see Figure 1).

This paper [4] established the principle for understanding the basic guidance properties of PCFs. In conventional optical fibers, the refractive indexes of core and cladding are only weakly dependent on wavelength due to material dispersion. This is also expected of the core refractive index of a PCF. The refractive index of the composite photonic crystal cladding, however, behaves very differently. At the long wavelength extreme, i.e. λ→∞, the wavelength is much larger than the air holes and the fundamental space-filling mode will occupy all areas

**Figure 1.** Refractive index of photonic crystal fiber cladding.

propagation of a higher-order mode in a specially designed multimode fiber [11, 12]. It is argued that perturbations mostly have anti-symmetry in optical fibers and promote mode coupling mostly between modes of opposite symmetries. The mode spacing between a radially symmetric LP0n mode and its nearest neighbor modes with opposite symmetry is, in fact, larger for higher order modes. These higher-order modes are also more resistant to bendinduced mode compression. A special fiber design facilitates the ease of mode conversion to

In this chapter, we will give a brief introduction to the key approaches to effective mode area scaling which have shown great promise for future high power fiber lasers. Basic concepts are

The authors of the paper in 1996 [3] were looking for photonic bandgap guidance in the defect core of the PCF with a core size of ~4.6 μm. The reason for the absence of photonic bandgap guidance in a solid-core PCF with air holes in the cladding only became clear a few years later. To their surprise, they observed very broadband single-mode guidance from 458–1550 nm (extended to 337-1550 nm in [4]). A conventional single-mode step-index optical fiber would become multimode at shorter wavelength. Even more surprising, the diffraction angle of the output beam was smaller at shorter wavelengths, indicating a smaller fiber numerical aperture

In a follow-on paper [4] the initial observation of the "endlessly single-mode" nature of photonic crystal fibers was explained by the dispersive nature of the cladding, which can be viewed as a composite of two materials, i.e. silica and air. The effective refractive index of the composite cladding was identified for the first time as the effective index of the fundamental mode of the composite cladding, referred to as the *fundamental space-filling mode (FSM)*. In the extreme case of conventional optical fibers with an infinite cladding, the effective index of the fundamental space-filling mode becomes the refractive index of the cladding. In PCFs with air holes, the cladding index ncl, i.e. the effective index of the fundamental space-filling mode, is lower than the refractive index of the background glass nb due to the existence of the air holes, i.e. ncl<nb. The core index nco is the same as the index of the background glass, nco=nb. Funda‐ mental optical guidance in PCFs can, therefore, in principle, be understood in a similar way

This paper [4] established the principle for understanding the basic guidance properties of PCFs. In conventional optical fibers, the refractive indexes of core and cladding are only weakly dependent on wavelength due to material dispersion. This is also expected of the core refractive index of a PCF. The refractive index of the composite photonic crystal cladding, however, behaves very differently. At the long wavelength extreme, i.e. λ→∞, the wavelength is much larger than the air holes and the fundamental space-filling mode will occupy all areas

and from the LP0n mode using a *long period grating* (LPG).

222 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

introduced and the latest developments are also discussed.

**2.1. Fundamental space-filling mode of photonic crystal cladding**

to that in conventional optical fibers (see Figure 1).

**2. Photonic crystal fibers**

at short wavelength.

of the cladding equally. In this case, the refractive index of the FSM can be obtained by averaging the square of the refractive index of the composite photonic crystal cladding, i.e. ncl 2 =nb 2 (1-F)+nair2 F=nb 2 -F(nb 2 -nair2 ) where F is the area fraction of air; and nair is the refractive index of air. The effective NA of the PCF for λ→∞ is, therefore, F1/2(nb 2 -nair2 ) 1/2. At the short wavelength extreme, i.e. λ→0, the wavelength is much smaller than the pitch of the air holes and the fundamental space-filling mode is mostly in the region with high refractive index, i.e. the background glass. In this case, the cladding index is the refractive index of the background glass nb. The effective NA of a PCF at λ→0 trends to zero. The guidance of a PCF still gets weaker at large λ, as in a conventional optical fiber, due to the inverse wavelength dependence of the normalized frequency V. In addition, its guidance also gets weaker at short wavelengths due to the diminishing NA, which also limits the growth of V and leads to the "endlessly singlemode" nature of the PCFs with small air holes. Guidance of PCF will, therefore, diminish at both long and short wavelength ends, possessing two bend-induced cut-off edges.

#### **2.2. Single mode and multimode regime of photonic crystal fibers**

In conventional fibers, a mode is guided when the effective mode index neff is between the core and cladding index, i.e. nco>neff>ncl. The mode cut-off can be identified when neff=ncl. The second-order mode cuts off in a step-index fiber at V=2.405. In the first reported work on determining the single-mode regime of PCFs with a 1-cell core, i.e. one hole missing at the defect core, by Birks et al [4], a somewhat arbitrary equivalent step-index core radius equaling *pitch*Λ, i.e. center-to-center hole separation, was used to calculate the V value. Work by Saitoh [13] using a *finite element model* (FEM) to determine nFSM and the condition neff=ncl to determine the second-order mode cut-off, put the effective step-index core radius to be Λ/31/2 for a onecell core. Later work by Saitoh [14] determined the effective step-index core radius to be Λ for a 3-cell core and 21/2Λ for a 7-cell core.

The optical waveguide equation allows the scaling of all parameters measured in the length scale by the same factor. For PCF, the most convenient scaling factor is 1/Λ. The second-order mode cut-off is typically plotted as a normalized wavelength λ/Λ versus normalized hole diameter d/Λ plot. This is shown for PCFs with 1-cell, 3-cell and 7-cell core in Figure 2 [14]. For each of the curves, the area above the curve is in the single-mode regime, i.e. the wave‐ lengths above the second-order mode cut-off wavelength, and, below it, multimode regime. The "endlessly single-mode" nature of PCFs can be easily identified in Figure 2. When d/ Λ<0.424, 0.165 and 0.046 respectively for 1-cell, 3-cell and 7-cell core PCFs, the PCFs will remain in the single-mode regime for all wavelengths. It is worth noting that Figure 2 is for PCFs with infinite cladding. For PCFs with finite cladding, guidance is weaker and the second-ordermode cut-off is expected to happen at slightly shorter wavelengths. The curves in Figure 2 are expected to move downwards slightly. It needs to be noted as discussed earlier, that the PCFs are too weak to guide any light at long and short extremes of wavelength. The critical bend radius at the short wavelength edge is determined to be dependent on pitch Λ and wavelength λ such that [4]

$$\mathcal{R}\_c \ll \frac{\Lambda^3}{\lambda^2} \tag{1}$$

The critical bend radius at the short length edge increases in proportion to 1/λ<sup>2</sup> as wavelength decreases. This relation was verified experimentally for the critical bend radius at 3dB excessive bend loss [4]. It comes directly from the dispersive nature of the photonic crystal cladding.

**Figure 2.** The second-order mode cut-off determined by neff=nFSM (dots) and V=2.405 (solid lines) using core radius ρ=Λ/31/2, Λ and 21/2Λ respectively for 1-cell, 3-cell and 7-cell cores [14].

#### **2.3. Waveguide loss of photonic crystal fibers**

PCFs are intrinsically leaky, i.e. there is always a finite waveguide loss for each mode in a PCF with a finite cladding. The waveguide loss can be found by calculating the imaginary part of the effective mode index using a numerical mode solver. When plotting the waveguide loss versus wavelength, the slope is expected to change around cut-off. This can also be used to determine the second-order-mode cut-off. This was done for a 1-cell core PCF [15]. The results are consistent with those in [13].

In conventional optical fibers, the fully enclosed core and cladding boundary ensures that waveguide loss is zero for all guided modes, i.e. those that satisfy the conditions for total internal reflection at the boundary. For the open structure of PCFs with a finite cladding, all modes are leaky with finite waveguide losses. At the extreme of an infinite number of layers, the waveguide losses are zero. The waveguide losses are lower for larger air holes and can be substantially lowered by increasing the number of air-hole layers. In practice, the waveguide loss can be made below other material and process related losses. By employing appropriate polishing, etching and dehydration processes, a PCF with a loss 0.28dB/km at 1550nm has been demonstrated [16]. For applications in fiber lasers where a length of not more than a few tens of meters is used, the waveguide loss does not present any problem if appropriate designs are used.

### **2.4. Modeling of photonic crystal fibers**

lengths above the second-order mode cut-off wavelength, and, below it, multimode regime. The "endlessly single-mode" nature of PCFs can be easily identified in Figure 2. When d/ Λ<0.424, 0.165 and 0.046 respectively for 1-cell, 3-cell and 7-cell core PCFs, the PCFs will remain in the single-mode regime for all wavelengths. It is worth noting that Figure 2 is for PCFs with infinite cladding. For PCFs with finite cladding, guidance is weaker and the second-ordermode cut-off is expected to happen at slightly shorter wavelengths. The curves in Figure 2 are expected to move downwards slightly. It needs to be noted as discussed earlier, that the PCFs are too weak to guide any light at long and short extremes of wavelength. The critical bend radius at the short wavelength edge is determined to be dependent on pitch Λ and wavelength

224 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

Rc∝ Λ3

decreases. This relation was verified experimentally for the critical bend radius at 3dB excessive bend loss [4]. It comes directly from the dispersive nature of the photonic crystal

**Figure 2.** The second-order mode cut-off determined by neff=nFSM (dots) and V=2.405 (solid lines) using core radius

PCFs are intrinsically leaky, i.e. there is always a finite waveguide loss for each mode in a PCF with a finite cladding. The waveguide loss can be found by calculating the imaginary part of the effective mode index using a numerical mode solver. When plotting the waveguide loss versus wavelength, the slope is expected to change around cut-off. This can also be used to determine the second-order-mode cut-off. This was done for a 1-cell core PCF [15]. The results

In conventional optical fibers, the fully enclosed core and cladding boundary ensures that waveguide loss is zero for all guided modes, i.e. those that satisfy the conditions for total

ρ=Λ/31/2, Λ and 21/2Λ respectively for 1-cell, 3-cell and 7-cell cores [14].

**2.3. Waveguide loss of photonic crystal fibers**

are consistent with those in [13].

The critical bend radius at the short length edge increases in proportion to 1/λ<sup>2</sup>

<sup>λ</sup><sup>2</sup> (1)

as wavelength

λ such that [4]

cladding.

Due to the complexity of the geometrical structures of PCFs, numerical models are typically used to find mode properties including the effective mode index, waveguide loss and effective mode area. For any numerical mode solvers, electric and magnetic fields are described by an expansion series. Eigenvalue equations are then established by requiring the fields to satisfy all boundary conditions. These equations are typically expressed as a set of linear equations, which can be solved for complex effective mode index. The more complex a waveguide design is, the larger is the number of linear equations. The waveguide dispersion can be calculated from the real part of the complex effective mode index. The waveguide loss can be obtained from the imaginary part of the complex effective mode index. Electric and magnetic fields can be calculated once the effective mode index is determined. The most common and flexible numerical mode solver is a *finite element mode solver* (FEM). This is commercially available from COMSOL (*http://www.comsol.com/*). A FEM is capable of handling practically any design. It can, however, be computationally very demanding. If only circular boundaries are involved, a Multipole mode solver is a good option [17, 18]. It is based on the decomposition of fields into circular Bessel series, which are the most accurate and efficient method for modeling circular boundaries. For non-commercial research and teaching purposes, it can be downloaded from the University of Sydney website (*http://sydney.edu.au/science/physics/cudos/research/mofsoft‐ ware.shtml*). A plane wave expansion method can also be used. This, however, assumes an infinite cladding and, therefore, cannot determine the waveguide loss.

#### **2.5. Mode area scaling with photonic crystal fibers**

The first demonstration of a large-core PCF was performed by Knight el at [5]. The 1-cell PCF with relative hole diameter d/Λ≈0.12 and a core diameter of 2ρ=22.5μm, provided robust single-mode guidance at 458nm. According to Figure 2, a 1-cell PCF with d/Λ<0.424 is expected to be single-mode over its entire wavelength range. It is, therefore not surprising that the PCF was single mode at 458nm. The critical bend radius was measured to be 50cm at 458nm and 4cm at 1.55μm [5]. This fiber is expected to have a critical bend radius of ~10cm at 1μm using equation 1.

Considering the wavelength scalability of the waveguide equation, this 1-cell PCF with 2ρ/ λ≈50 can be scaled by a factor of ~2.2 to a ~50μm core diameter to operate at 1μm. The critical bend radius for this single-mode PCF with 50μm core diameter is expected to be ~1.1m at 1μm according to equation 1! A similarly scaled 1-cell PCF with a core diameter of 30μm will have a critical bending radius of ~24cm. This is probably close to the practical limit of coiled singlemode 1-cell PCFs. Above a core diameter of ~40μm, 1-cell single-mode PCF can only be used in a straight configuration in practice. The single-mode operation of PCFs with large core diameters comes at the cost of weak guidance as a result of the diminishing effective NA. This fundamentally limits the use of single-mode PCFs with large cores in coiled configurations. If PCFs are allowed to operate in the few-moded regime, coiled PCFs with slightly larger core diameters are possible. For high average power fiber lasers with outputs exceeding kW, effective thermal management becomes increasingly critical. Long fiber lengths of many meters are required. The constraint of not being able to coil the fibers can become a major issue considering the additional space constraints.

#### **2.6. Rare-earth-doped glass for large-core photonic crystal fibers**

The diminishing NA of PCFs with large cores also has additional implications, as realized by the authors of [5]. To fabricate rare-earth-doped large-core PCFs, the core refractive index needs to be accurately controlled at levels far below the very small effective index difference between the core and cladding in order not to disturb the guidance properties of the PCFs. This requires much improved techniques for the fabrication of the active core in large-core PCFs.

The first ytterbium-doped large-core PCF with 15μm core diameter was reported in 2001 at Bath University [19]. The effective mode area at 1μm was ~100μm2 . The laser operated in single mode with poor efficiency. The key advance was the use of a repeated stack-and-draw process to achieve a uniformly doped core with a refractive index close to silica. Conventional fabrication techniques for rare-earth doped silica fibers result in significant non-uniformity in refractive index across the core as well as a raised refractive index above silica. Due to the weak guidance in large-core PCFs, any index non-uniformity across the core can lead to mode distortion. It also requires the refractive index of the core to be very close to the silica back‐ ground in PCFs. The authors of [19] fabricated ytterbium-doped glass with low doping levels. The doped glass is surrounded by some undoped silica glass. The glass is stacked and drawn twice before being finally incorporated into the core of a PCF. The resulting PCF has an ytterbium-doped core which consists of 425 original doped glass sections. The dimension of each of the original doped glass sections is much smaller than the wavelength of light and the core of the PCF, therefore, appears to be homogeneous to light at the operating optical wavelength. The doped core is also heavily diluted by the addition of silica glass (90%), leading to an average refractive index close to that of silica [20]. In the same paper, it was pointed out that rare-earth-doped glass with a higher index can be stacked and drawn with undoped glass with a low index to achieve a better match to that of silica background [20].

#### **2.7. Double-clad photonic crystal fibers with high NA air-clad for pump guidance**

The concept of a composite air-glass clad with a high air-filling fraction to provide a high NA pump guide in a double-clad fiber was first proposed in 1999 at what was then then Lucent Technologies [21]. The high pump NA can enable a significant improvement in pump coupling especially from low brightness multimode diode lasers for a given pump waveguide dimen‐ sion. In conventional double-clad fibers, low-index polymer coatings are typically used to form the pump cladding. The air-clad pump isolates high pump powers from the polymer coatings, leading to potentially improved reliability.

according to equation 1! A similarly scaled 1-cell PCF with a core diameter of 30μm will have a critical bending radius of ~24cm. This is probably close to the practical limit of coiled singlemode 1-cell PCFs. Above a core diameter of ~40μm, 1-cell single-mode PCF can only be used in a straight configuration in practice. The single-mode operation of PCFs with large core diameters comes at the cost of weak guidance as a result of the diminishing effective NA. This fundamentally limits the use of single-mode PCFs with large cores in coiled configurations. If PCFs are allowed to operate in the few-moded regime, coiled PCFs with slightly larger core diameters are possible. For high average power fiber lasers with outputs exceeding kW, effective thermal management becomes increasingly critical. Long fiber lengths of many meters are required. The constraint of not being able to coil the fibers can become a major issue

The diminishing NA of PCFs with large cores also has additional implications, as realized by the authors of [5]. To fabricate rare-earth-doped large-core PCFs, the core refractive index needs to be accurately controlled at levels far below the very small effective index difference between the core and cladding in order not to disturb the guidance properties of the PCFs. This requires much improved techniques for the fabrication of the active core in large-core

The first ytterbium-doped large-core PCF with 15μm core diameter was reported in 2001 at

mode with poor efficiency. The key advance was the use of a repeated stack-and-draw process to achieve a uniformly doped core with a refractive index close to silica. Conventional fabrication techniques for rare-earth doped silica fibers result in significant non-uniformity in refractive index across the core as well as a raised refractive index above silica. Due to the weak guidance in large-core PCFs, any index non-uniformity across the core can lead to mode distortion. It also requires the refractive index of the core to be very close to the silica back‐ ground in PCFs. The authors of [19] fabricated ytterbium-doped glass with low doping levels. The doped glass is surrounded by some undoped silica glass. The glass is stacked and drawn twice before being finally incorporated into the core of a PCF. The resulting PCF has an ytterbium-doped core which consists of 425 original doped glass sections. The dimension of each of the original doped glass sections is much smaller than the wavelength of light and the core of the PCF, therefore, appears to be homogeneous to light at the operating optical wavelength. The doped core is also heavily diluted by the addition of silica glass (90%), leading to an average refractive index close to that of silica [20]. In the same paper, it was pointed out that rare-earth-doped glass with a higher index can be stacked and drawn with undoped glass

. The laser operated in single

considering the additional space constraints.

PCFs.

**2.6. Rare-earth-doped glass for large-core photonic crystal fibers**

226 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

Bath University [19]. The effective mode area at 1μm was ~100μm2

with a low index to achieve a better match to that of silica background [20].

**2.7. Double-clad photonic crystal fibers with high NA air-clad for pump guidance**

The concept of a composite air-glass clad with a high air-filling fraction to provide a high NA pump guide in a double-clad fiber was first proposed in 1999 at what was then then Lucent Technologies [21]. The high pump NA can enable a significant improvement in pump coupling The first such fiber was demonstrated in 2000, where the pump cladding was mostly air except for a single connecting element [22]. The measured pump NA over 1m was below 0.2. The fiber was passive and there was no laser demonstration in this first attempt. The first claddingpumping demonstration in an active fiber with an air-clad pump guide and a conventional core design was in 2001 at Southampton University [23]. The measured NA of the pump guide with air-cladding was 0.4-0.5. In a separate demonstration from Southampton University later in the same year, a conventional core with a very low NA together with a photonic crystal cladding was used in combination with a pump guide with air-cladding [24]. The core guidance came from a combination of the raised core index and the photonic crystal cladding. Cladding pumping with a low brightness laser diode at 915nm (100μm core with a NA=0.22) was demonstrated with a slope efficiency of 70% relative to the absorbed pump power. The measured pump NA over a short length (~10cm) was 0.3-0.4. NA over much longer fiber length as in a fiber laser is expected to be lower. The first true active double-clad photonic crystal fibers with a pump air-cladding was demonstrated in 2003 with a measured pump NA of 0.8 at 1μm [20].

The theoretical basis for the high NA of optical waveguides formed by air-cladding was established in [25]. It had been understood previously that the effective index of a glass and air composite can be obtained by the effective index of the fundamental space filling mode. An example of high NA air-clad used in double-clad fibers is shown in Figure 3 from [25]. In such air-glass composites, the glass webs can be considered as slab waveguides. The separa‐ tions between the webs are typically far enough that the webs can be considered as isolated. In this case, the effective index of the glass-air composite cladding can be well approximated by that of the fundamental slab waveguide mode. This can be easily calculated. The resulting pump NA is only dependent on the ratio of the web width w and wavelengthλ. This is plotted in Figure 3(c), showing that a small w/λ is critical for high NA.

**Figure 3.** (a) High NA air-clad from [25], (b) close-up of the high NA air-clad, and (c) NA of air-clad waveguide based on slab waveguide model plotted against the ratio of waveguide width w and wavelength λ.

### **2.8. Progress of active large-core photonic crystal fibers**

Since 2003, the group at Friedrich-Schiller-University Jena has been playing a significant role in the development large-mode-area photonic crystal fibers with pump air-clad. In their first work in collaboration with then Crystal Fibre A/S, now NKT Photonics, an ytterbium-doped PCF with effective mode area of ~350μm2 and mode field diameter (MFD) of 21μm was demonstrated [26] (see Figure 4). The 3-cell PCF had a hole diameter d=2μm and pitch Λ=11.5, giving an d/Λ=0.18. The core diameter was 28μm. A relatively small circular area of 9μm was doped in the 3-cell core. The doped area had a high ytterbium-doping level of ~0.6 at%. It was further co-doped with aluminum and fluorine to provide an index merely 2×10-4 above the silica background. The PCF with the raised index in the doped area was simulated, showing that the fiber guides the second-order mode, which is, however, close to cut-off. The fiber had a 150μm pump guide with an air clad. The webs in the air clad were ~50μm long with a thickness of ~390nm, giving w/λ=~0.4 at 976nm. The measured pump NA was 0.55, slightly below the NA=0.68 predicated by the slab model in Figure 3. The fiber had an outer glass diameter of 450μm and was coated with standard acrylic coating. Due to the high doping level, the fiber has a pump absorption of ~9.6dB/m at 976nm. An impressive slope efficiency of 78% was demonstrated with respect to the launched pump power.

Figure 4 SEM image of the air‐clad ytterbium‐doped large‐mode‐area photonic crystal fiber in [26]. **Figure 4.** SEM image of the air-clad ytterbium-doped large-mode-area photonic crystal fiber in [26].

In a subsequent paper in 2003 [27], the fiber in [26] and a new fiber with narrower pump air‐clad were studied with the FEM for temperature distributions in the fiber at various thermal loads in the core, considering both convective and radiative heat transportation by air at the fiber surface. The results show that, in the case of natural cooling, the thermal transportation is mainly limited by the heat transfer at the fiber surface. The air‐clad impedes heat flow, especially when the width of the air clad is large. A narrower pump air‐clad is advantageous, especially in actively cooled fiber lasers. In a subsequent paper in 2003 [27], the fiber in [26] and a new fiber with narrower pump airclad were studied with the FEM for temperature distributions in the fiber at various thermal loads in the core, considering both convective and radiative heat transportation by air at the fiber surface. The results show that, in the case of natural cooling, the thermal transportation is mainly limited by the heat transfer at the fiber surface. The air-clad impedes heat flow, especially when the width of the air clad is large. A narrower pump air-clad is advantageous, especially in actively cooled fiber lasers.

In 2004, the bar was raised in a collaborative work between Friedrich Schiller University Jena and Crystal Fibre A/S [28]. Their 7-cell fiber has an effective area of ~1000μm2 and MFD of ~35μm (see Figure 5). Core diameter is ~40μm. Hole diameter d is 1.1μm and the pitch Λ is 12.3μm, giving a d/Λ=0.09. The fiber has a pump guide diameter of 170μm and a measured pump NA of 0.62 at 950nm. The pump absorption is ~13dB/m at 976nm. The pump air-clad is

Figure 5 Microscope image of the air‐clad ytterbium‐doped single‐mode PCF and close‐up to the 40‐μm core formed by seven missing air holes [28].

Figure 6 Microscope image of a rod‐type photonic crystal fiber and close‐up view of the inner cladding and core regions.

To further mitigate bend loss, a rod‐type PCF was developed in 2005 [29] (see Figure 6). The rod had an outer diameter of 1.7mm so that it cannot be bent. A 48cm long length was used in the demonstration. The relative hole diameter was increased to d/=0.33. This reduces bend sensitivity. This larger d/ in a 7‐cell core PCF, however, puts this fiber firmly in the multimode regime (see Figure 2). The pump guide was reduced to a hexagon with flat‐ to‐flat dimension of 117m and corner‐to‐corner dimension of 141m, similar to earlier fibers. The ytterbium

multimode regime for a 7‐cell PCF (see Figure 5). This helps to ease bend loss in the weakly guided fiber.

In 2004, the bar was raised in a collaborative work between Friedrich Schiller University Jena and Crystal Fibre A/S [28]. Their 7‐cell fiber has an effective area of ~1000m2 and MFD of ~35m (see Figure 5). Core diameter is ~40m. Hole diameter d is 1.1m and the pitch is 12.3m, giving a d/=0.09. The fiber has a pump guide diameter of 170m and a measured pump NA of 0.62 at 950nm. The pump absorption is ~13dB/m at 976nm. The pump air‐clad is much narrower for more efficient heat diffusion. It is worth noting that the fiber is in the

especially in actively cooled fiber lasers.

especially in actively cooled fiber lasers.

Figure 4 SEM image of the air‐clad ytterbium‐doped large‐mode‐area photonic crystal fiber in [26].

Figure 4 SEM image of the air‐clad ytterbium‐doped large‐mode‐area photonic crystal fiber in [26].

In a subsequent paper in 2003 [27], the fiber in [26] and a new fiber with narrower pump air‐clad were studied with the FEM for temperature distributions in the fiber at various thermal loads in the core, considering both convective and radiative heat transportation by air at the fiber surface. The results show that, in the case of

In a subsequent paper in 2003 [27], the fiber in [26] and a new fiber with narrower pump air‐clad were studied with the FEM for temperature distributions in the fiber at various thermal loads in the core, considering both convective and radiative heat transportation by air at the fiber surface. The results show that, in the case of

**2.8. Progress of active large-core photonic crystal fibers**

228 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

was demonstrated with respect to the launched pump power.

PCF with effective mode area of ~350μm2

especially in actively cooled fiber lasers.

especially in actively cooled fiber lasers.

Since 2003, the group at Friedrich-Schiller-University Jena has been playing a significant role in the development large-mode-area photonic crystal fibers with pump air-clad. In their first work in collaboration with then Crystal Fibre A/S, now NKT Photonics, an ytterbium-doped

demonstrated [26] (see Figure 4). The 3-cell PCF had a hole diameter d=2μm and pitch Λ=11.5, giving an d/Λ=0.18. The core diameter was 28μm. A relatively small circular area of 9μm was doped in the 3-cell core. The doped area had a high ytterbium-doping level of ~0.6 at%. It was further co-doped with aluminum and fluorine to provide an index merely 2×10-4 above the silica background. The PCF with the raised index in the doped area was simulated, showing that the fiber guides the second-order mode, which is, however, close to cut-off. The fiber had a 150μm pump guide with an air clad. The webs in the air clad were ~50μm long with a thickness of ~390nm, giving w/λ=~0.4 at 976nm. The measured pump NA was 0.55, slightly below the NA=0.68 predicated by the slab model in Figure 3. The fiber had an outer glass diameter of 450μm and was coated with standard acrylic coating. Due to the high doping level, the fiber has a pump absorption of ~9.6dB/m at 976nm. An impressive slope efficiency of 78%

Figure 4 SEM image of the air‐clad ytterbium‐doped large‐mode‐area photonic crystal fiber in [26].

In a subsequent paper in 2003 [27], the fiber in [26] and a new fiber with narrower pump airclad were studied with the FEM for temperature distributions in the fiber at various thermal loads in the core, considering both convective and radiative heat transportation by air at the fiber surface. The results show that, in the case of natural cooling, the thermal transportation is mainly limited by the heat transfer at the fiber surface. The air-clad impedes heat flow, especially when the width of the air clad is large. A narrower pump air-clad is advantageous,

**Figure 4.** SEM image of the air-clad ytterbium-doped large-mode-area photonic crystal fiber in [26].

Figure 5 Microscope image of the air‐clad ytterbium‐doped single‐mode PCF and close‐up to the 40‐μm core formed by seven missing air holes [28].

In 2004, the bar was raised in a collaborative work between Friedrich Schiller University Jena and Crystal Fibre A/S [28]. Their 7-cell fiber has an effective area of ~1000μm2 and MFD of ~35μm (see Figure 5). Core diameter is ~40μm. Hole diameter d is 1.1μm and the pitch Λ is 12.3μm, giving a d/Λ=0.09. The fiber has a pump guide diameter of 170μm and a measured pump NA of 0.62 at 950nm. The pump absorption is ~13dB/m at 976nm. The pump air-clad is

Figure 6 Microscope image of a rod‐type photonic crystal fiber and close‐up view of the inner cladding and core regions.

To further mitigate bend loss, a rod‐type PCF was developed in 2005 [29] (see Figure 6). The rod had an outer diameter of 1.7mm so that it cannot be bent. A 48cm long length was used in the demonstration. The relative hole diameter was increased to d/=0.33. This reduces bend sensitivity. This larger d/ in a 7‐cell core PCF, however, puts this fiber firmly in the multimode regime (see Figure 2). The pump guide was reduced to a hexagon with flat‐ to‐flat dimension of 117m and corner‐to‐corner dimension of 141m, similar to earlier fibers. The ytterbium

multimode regime for a 7‐cell PCF (see Figure 5). This helps to ease bend loss in the weakly guided fiber.

In 2004, the bar was raised in a collaborative work between Friedrich Schiller University Jena and Crystal Fibre A/S [28]. Their 7‐cell fiber has an effective area of ~1000m2 and MFD of ~35m (see Figure 5). Core diameter is ~40m. Hole diameter d is 1.1m and the pitch is 12.3m, giving a d/=0.09. The fiber has a pump guide diameter of 170m and a measured pump NA of 0.62 at 950nm. The pump absorption is ~13dB/m at 976nm. The pump air‐clad is much narrower for more efficient heat diffusion. It is worth noting that the fiber is in the

In a subsequent paper in 2003 [27], the fiber in [26] and a new fiber with narrower pump air‐clad were studied with the FEM for temperature distributions in the fiber at various thermal loads in the core, considering both convective and radiative heat transportation by air at the fiber surface. The results show that, in the case of natural cooling, the thermal transportation is mainly limited by the heat transfer at the fiber surface. The air‐clad impedes heat flow, especially when the width of the air clad is large. A narrower pump air‐clad is advantageous,

and mode field diameter (MFD) of 21μm was

40‐μm core formed by seven missing air holes [28]. In 2004, the bar was raised in a collaborative work between Friedrich Schiller University Jena and Crystal Fibre Figure 5 Microscope image of the air‐clad ytterbium‐doped single‐mode PCF and close‐up to the 40‐μm core formed by seven missing air holes [28]. **Figure 5.** Microscope image of the air-clad ytterbium-doped single-mode PCF and close-up to the 40-μm core formed by seven missing air holes [28].

much narrower for more efficient heat diffusion. It is worth noting that the fiber is in the multimode regime for a 7-cell PCF (see Figure 5). This helps to ease bend loss in the weakly guided fiber. A/S [28]. Their 7‐cell fiber has an effective area of ~1000m <sup>2</sup> and MFD of ~35m (see Figure 5). Core diameter is ~40m. Hole diameter d is 1.1m and the pitch is 12.3m, giving a d/=0.09. The fiber has a pump guide diameter of 170m and a measured pump NA of 0.62 at 950nm. The pump absorption is ~13dB/m at 976nm. The pump air‐clad is much narrower for more efficient heat diffusion. It is worth noting that the fiber is in the In 2004, the bar was raised in a collaborative work between Friedrich Schiller University Jena and Crystal Fibre A/S [28]. Their 7‐cell fiber has an effective area of ~1000m <sup>2</sup> and MFD of ~35m (see Figure 5). Core diameter is ~40m. Hole diameter d is 1.1m and the pitch is 12.3m, giving a d/=0.09. The fiber has a pump guide

multimode regime for a 7‐cell PCF (see Figure 5). This helps to ease bend loss in the weakly guided fiber.

Figure 6 Microscope image of a rod‐type photonic crystal fiber and close‐up view of the inner cladding and core regions. **Figure 6.** Microscope image of a rod-type photonic crystal fiber and close-up view of the inner cladding and core re‐ gions.

To further mitigate bend loss, a rod‐type PCF was developed in 2005 [29] (see Figure 6). The rod had an outer diameter of 1.7mm so that it cannot be bent. A 48cm long length was used in the demonstration. The relative hole diameter was increased to d/=0.33. This reduces bend sensitivity. This larger d/ in a 7‐cell core PCF, however, puts this fiber firmly in the multimode regime (see Figure 2). The pump guide was reduced to a hexagon with flat‐ to‐flat dimension of 117m and corner‐to‐corner dimension of 141m, similar to earlier fibers. The ytterbium To further mitigate bend loss, a rod-type PCF was developed in 2005 [29] (see Figure 6). The rod had an outer diameter of 1.7mm so that it cannot be bent. A 48cm long length was used in the demonstration. The relative hole diameter was increased to d/Λ=0.33. This reduces bend sensitivity. This larger d/Λ in a 7-cell core PCF, however, puts this fiber firmly in the multimode regime (see Figure 2). The pump guide was reduced to a hexagon with flat-to-flat dimension of 117μm and corner-to-corner dimension of 141μm, similar to earlier fibers. The ytterbium doping level was also increased compared with earlier fibers. The increased doping level and reduced pump guide led to a high pump absorption of ~30dB/m at 976nm. The fiber was used to demonstrate power extraction of ~250W/m. Figure 6 Microscope image of a rod‐type photonic crystal fiber and close‐up view of the inner cladding and core regions. To further mitigate bend loss, a rod‐type PCF was developed in 2005 [29] (see Figure 6). The rod had an outer diameter of 1.7mm so that it cannot be bent. A 48cm long length was used in the demonstration. The relative hole diameter was increased to d/=0.33. This reduces bend sensitivity. This larger d/ in a 7‐cell core PCF, however,

The rod-type PCF was further developed with the demonstration of a 19-cell PCF with a core diameter of 60μm, effective mode area of ~2000μm2 and MFD of 75μm in 2006 [30] (see Figure puts this fiber firmly in the multimode regime (see Figure 2). The pump guide was reduced to a hexagon with flat‐ to‐flat dimension of 117m and corner‐to‐corner dimension of 141m, similar to earlier fibers. The ytterbium

multimode regime. The effective mode area was ~4500m2 and MFD was ~75m.

power of 4.5MW and pulse energy of 4.3mJ with M2

3 Leakage channel fibers

7). The fiber had a d/Λ=0.19, again firmly in the multimode regime (19-cell PCF not shown in Figure 2). The pump guide was 175μm in diameter. The pump air-clad had a web thickness of 400nm, which was 10μm long. The measured pump NA was 0.6 at 975nm, fairly close to the 0.67 NA predicted by the slab model (see Figure 3). The pump absorption is ~30dB/m at 976nm. The rod diameter is ~1.5mm. A 58cm long fiber was used to demonstrate 55W/m power extraction. In the same paper, a passive 100μm core fiber was also demonstrated. The 19-cell fiber had a d/Λ=0.2, again in the multimode regime. The effective mode area was ~4500μm2 and MFD was ~75μm. led to a high pump absorption of ~30dB/m at 976nm. The fiber was used to demonstrate power extraction of ~250W/m. The rod‐type PCF was further developed with the demonstration of a 19‐cell PCF with a core diameter of 60m, effective mode area of ~2000m2 and MFD of 75m in 2006 [30] (see Figure 7). The fiber had a d/=0.19, again firmly in the multimode regime (19‐cell PCF not shown in Figure 2). The pump guide was 175m in diameter. The pump air‐clad had a web thickness of 400nm, which was 10m long. The measured pump NA was 0.6 at 975nm, fairly close to the 0.67 NA predicted by the slab model (see Figure 3). The pump absorption is ~30dB/m at 976nm. The rod diameter is ~1.5mm. A 58cm long fiber was used to demonstrate 55W/m power extraction. In the same paper, a passive 100m core fiber was also demonstrated. The 19‐cell fiber had a d/=0.2, again in the doping level was also increased compared with earlier fibers. The increased doping level and reduced pump guide led to a high pump absorption of ~30dB/m at 976nm. The fiber was used to demonstrate power extraction of ~250W/m. The rod‐type PCF was further developed with the demonstration of a 19‐cell PCF with a core diameter of 60m, effective mode area of ~2000m2 and MFD of 75m in 2006 [30] (see Figure 7). The fiber had a d/=0.19, again firmly in the multimode regime (19‐cell PCF not shown in Figure 2). The pump guide was 175m in diameter. The pump air‐clad had a web thickness of 400nm, which was 10m long. The measured pump NA was 0.6 at

975nm, fairly close to the 0.67 NA predicted by the slab model (see Figure 3). The pump absorption is ~30dB/m at

doping level was also increased compared with earlier fibers. The increased doping level and reduced pump guide

Figure 7 Microscope‐image of the extended‐mode‐area rod‐type photonic crystal fiber, SEM‐picture of the micro‐ structured region and measured near‐field intensity profile of the 60μm core fiber [30]. **Figure 7.** Microscope-image of the extended-mode-area rod-type photonic crystal fiber, SEM-picture of the microstructured region and measured near-field intensity profile of the 60μm core fiber [30].

The demonstration of a 100m active 19‐cell PCF finally came in 2006 [6]. The pump guide had a diameter of

290m. The rod diameter was 1.5mm. A 90cm long fiber was used to amplify 1ns pulses at 9.6kHz to record peak power of 4.5MW and pulse energy of 4.3mJ with M2 =1.3. The demonstration of a 100μm active 19-cell PCF finally came in 2006 [6]. The pump guide had a diameter of 290μm. The rod diameter was 1.5mm. A 90cm long fiber was used to amplify 1ns pulses at 9.6kHz to record peak power of 4.5MW and pulse energy of 4.3mJ with M2 =1.3. Figure 7 Microscope‐image of the extended‐mode‐area rod‐type photonic crystal fiber, SEM‐picture of the micro‐ structured region and measured near‐field intensity profile of the 60μm core fiber [30]. The demonstration of a 100m active 19‐cell PCF finally came in 2006 [6]. The pump guide had a diameter of 290m. The rod diameter was 1.5mm. A 90cm long fiber was used to amplify 1ns pulses at 9.6kHz to record peak

=1.3.

with a mode area of ~700m2 was demonstrated in 2005 [31] (see left figure in Figure 8). The pitch was 12.3m with a d/ of 0.2. In the weakly guided PCFs, the polarization modes on slow and fast axis have different bend Figure 8 SEM image of the single polarization PCF with an effective area of ~700m2 [31] (left) and 2300m2 (right) [32]. **Figure 8.** SEM image of the single polarization PCF with an effective area of ~700μm2 [31] (left) and 2300μm2 (right) [32].

Polarization‐maintaining (PM) PCFs have also been developed by introducing stress elements. A PM 7‐cell PCF

losses. This enables single‐polarization operation where the polarization mode on the slow axis is still guided while polarization mode on the fast axis suffers high bend loss. Another single‐polarization 19‐cell PCF was demonstrated in 2008 with a mode area of ~2300m2 (right figure in Figure 8) [32]. The corner‐to‐corner distance of the core was 70μm. The pitch was 11m with a d/ of 0.1. 3 Leakage channel fibers A 2D micro‐structured cladding, which is made possible by the stack‐and‐draw technique developed for Polarization‐maintaining (PM) PCFs have also been developed by introducing stress elements. A PM 7‐cell PCF with a mode area of ~700m2 was demonstrated in 2005 [31] (see left figure in Figure 8). The pitch was 12.3m with a d/ of 0.2. In the weakly guided PCFs, the polarization modes on slow and fast axis have different bend losses. This enables single‐polarization operation where the polarization mode on the slow axis is still guided while polarization mode on the fast axis suffers high bend loss. Another single‐polarization 19‐cell PCF was demonstrated in 2008 with a mode area of ~2300m2 (right figure in Figure 8) [32]. The corner‐to‐corner distance of the core was 70μm. The pitch was 11m with a d/ of 0.1. Polarization-maintaining (PM) PCFs have also been developed by introducing stress elements. A PM 7-cell PCF with a mode area of ~700μm2 was demonstrated in 2005 [31] (see left figure in Figure 8). The pitch Λ was 12.3μm with a d/Λ of 0.2. In the weakly guided PCFs, the polarization modes on slow and fast axis have different bend losses. This enables singlepolarization operation where the polarization mode on the slow axis is still guided while polarization mode on the fast axis suffers high bend loss. Another single-polarization 19-cell

photonic crystal fibers, enables new designs which do not possess the closed core‐and‐clad boundaries of conventional optical fibers. When a mode is guided in a conventional optical fiber, total internal reflection everywhere around the closed core‐and‐clad boundary, traps light entirely in the core, leading to zero waveguide

A 2D micro‐structured cladding, which is made possible by the stack‐and‐draw technique developed for photonic crystal fibers, enables new designs which do not possess the closed core‐and‐clad boundaries of conventional optical fibers. When a mode is guided in a conventional optical fiber, total internal reflection everywhere around the closed core‐and‐clad boundary, traps light entirely in the core, leading to zero waveguide PCF was demonstrated in 2008 with a mode area of ~2300μm2 (right figure in Figure 8) [32]. The corner-to-corner distance of the core was 70μm. The pitch Λ was 11μm with a d/Λ of 0.1.
