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The experimental set-up for this measurement is shown in Fig. 4.1. Both ends of a length of fibre are stripped of coating and cleaved (as described in Section 4.2.2). Light is launched into one end of the fibre and the other end is firmly secured at one end of a long translation rail in a rotating fibre chuck. The fibre is positioned so that the centre of the beam diverging from the end of the fibre is aligned parallel to the translation rail. It is important that the fibre remains in the same orientation for the duration of the measurement. It is also essential that the cleaved bare fibre end is of excellent quality to ensure that the far-field image is representative of the fibre mode. A rotating optical chopper is mounted on the translation rail and is positioned so that the blades cut the diverging beam at 90o_{. The distance} between the centre of the chopper and the centre of the beam, x, (shown in the insert in Fig. 4.1) is recorded. The light that passes through the optical chopper is then focused onto a large area photo-diode using a large diameter lens (diameter ≈10 cm). This lens must

θ

x

_(a)

Detector Large diameter lens

Translation rail

z

∆

t

Figure 4.1: Experimental set-up to measure mode field diameter

be far enough away from the end of the fibre to ensure that the optical chopper has at least 5 cm of translation, but it must also be close enough to the end of the fibre to ensure that the tails of the far-field light emitted by the fibre are captured by the lens. Similarly, the gaps between the blades of the optical chopper must be sufficiently large to allow the beam to pass unhindered in the ‘on’ state of the chopper.

An oscilloscope connected to the photo-diode displays a (nearly) square wave, the sides of which are slightly rounded due to the time taken for the chopper blade to cut through the beam (See Fig. 4.1). It is this transit time that we wish to record. We define the beam width, w, as the distance between the peak intensity (shown as Io on Fig. 4.2) and the

point at which the intensity drops to 1/e2 _{of its maximum. Here we choose to measure this} distance between the points−w/2 andw/2 across the beam, which corresponds to intensity levels ofIo/

√

eeither side of the maximum intensity, Io, as shown in Fig. 4.2.

If we then define t₁ and t₂ to be the times at which the leading edge of the chopper blade is at a position of r = −w/2 andr =w/2 respectively, then the time taken for the blade to cut through the width of the beam,w, is given by ∆t=t₂−t₁. At timest₁ and

o

I

t

r

I(r)

e

I

t

Figure 4.2: Experimental set-up to measure mode field diameter

These percentages are given by:

R_∞ −w/2I(r)dr R_∞ −∞I(r)dr = 0.84 R_∞ w/2I(r)dr R_∞ −∞I(r)dr = 0.16 (4.1) By setting the low and high clip levels on the oscilloscope to these percentages, the rise time of the signal equals the time taken for the blade to cut through the beam (∆t).

The width of the beam w (defined as the 1/e2 _{width, or the distance between I =} −Io/

√

eand I =Io/

√

e) is then given by ∆t × v, where v is the speed of the chopper at the centre of the beam and is given by:

v= 2πxf

n , (4.2)

wherex is the distance between the centre of the chopper and the centre of the beam,f is the frequency of the chopper andnis the number of gaps in the chopper (In Fig. 4.1n= 4). Although this assumes that the speed of the chopper blade is a constant value across the width of the beam, the error introduced by this assumption is small. By recording ∆tand hence w, as a function of distance from the fibre end (z), the far-field angle of divergence

θ ≈ dw/dz is determined by the gradient of w graphed against z. A sample set of data from the measurement of one of our holey fibres at 1064 nm is shown in Fig. 4.3. The angle of divergence is ≈0.047 radians, which corresponds to an AFM_eff of 170 µm2_{. Note that in} order to determine the far-field divergence it is not necessary to know the distance from the fibre end to the chopper, only the relative distance between each width measurement is required. Ideally, somewhere between 5−10 measurements of the beam width should be taken, separated by approximately 0.5−1 cm depending on the level of divergence. Assuming that the fibre orientation remains the same, a variation of ≈ 1% in the beam

width is observed for repeat measurements. This corresponds to a variation of≈2−3% in the final AFM_eff for repeat measurements.

Figure 4.3: Example data from a MFD measurement of a large-mode-area holey fibre

Once the far-field divergence of the fibre has been determined, the spot-size of the fibre mode, wo = w(z = 0), can be calculated using the following equations. For a Gaussian

beam there is a simple relationship betweenθ and wo. This is given by:

w(z) = λ z π wo (4.3) θ= d w(z) dz = λ π wo (4.4) wo = _{π θ}λ (4.5)

For a circularly-symmetric Gaussian modal field, the effective area defined in [135] reduces to:

which is used here for all measured values. As mentioned above, this is a simplification for the holey fibres considered here, which have slightly hexagonal-shaped modes, but both theoretical calculations and direct measurements of the near-field mode profile show this to be a reasonable approximation. In fact, theoretical modelling shows that the spot size varies by≈5−10% in different angular directions and by averaging repeated measurements taken for several different angular orientations of the fibre, we find that a more representative value of effective area can be obtained. Including all sources of error, such as those arising from imperfect cleaves and alignment, in addition to that mentioned above, we estimate at most a 5% variation in repeat effective area measurements for a given fibre.

4.3.3 Discussion

The method described here is best suited to large-mode-area fibres, which possess small angles of divergence (limited by the diameter of the lens and the aperture size of the optical chopper as discussed above) and is restricted to single-mode fibres in which the field profile can be well approximated by a Gaussian function. This requirement means that it is important to ensure that no cladding or higher-order modes are present at the measurement end of the fibre. Any cladding modes will act to offset the zero level of the transverse intensity profile, making the mode appear smaller. The presence of higher-order modes will also cause the effective area measurement to be underestimated by introducing a much higher angle of divergence. Indeed, we have found that even a very low level presence of a higher-order mode can greatly perturb the measurement. Cladding modes can be stripped from the fibre trivially, since they are typically very sensitive to bending and can be completely removed with quite a gentle bend. Bending the fibre can also be used to filter out higher-order modes, if there is a sufficient differential between the bend loss of the fundamental and the first higher-order mode.