La Unidad didáctica desde el enfoque constructivista

The induced periodic refractive index change in a fibre Bragg grating causes back-reflection of wavelengths which satisfy the Bragg condition (Equation 1-3). The result is a peak in the reflection spectra or a dip in the transmission

spectra at λm when broadband light propagates down the fibre, as shown in

Figure 1-7. For an ideal fibre Bragg grating, a narrow peak is observed in the reflection spectrum which corresponds to a reflectance R equal to 1 (or 100%)

at λ_m. Conversely, an ideal fibre Bragg grating would have a narrow dip in the transmission spectrum corresponding to a transmittance T equal to 0 at λ_m. The grating spectral width, λsw, is commonly defined as the full width at half

maximum (FWHM) of the reflectance peak or transmission dip at λm.

Figure 1-7. Optical spectra of an ideal FBG measured in (a) reflection and (b) transmission.

(a) (b) Wavelength R ef lec ta nc e R λ_m λ_sw 0 1 Wavelength Tra ns m itta nce T λ_m λ_sw 0 1

In practice, fibre grating spectra exhibit losses on the short wavelength side of reflectance peaks known as side lobes or cladding mode losses [80] that are due to inefficient back-reflections from the grating. These losses can be undesirable in certain applications and can be minimised by using fibres with a depressed cladding region surrounding the core [85].

As can be noted in the Bragg condition in Equation 1-3, different harmonic wavelengths of order m will be back-reflected from a Bragg grating. In 1993,

Xie et al. [83] reported the first observation of second-order diffraction

(~½ λ_B) from fibre Bragg gratings written in germanosilicate fibres doped with various photosensitivity enhancing elements. The tested samples were evidently type I and IIA gratings, fabricated using a prism interferometer (see section 1.4.2) and a frequency doubled XeCl pumped dye laser operating at 243 nm. Xie et al. correlated the growth of the second-order reflectance peaks with the saturation of the Bragg reflectance peak growth. Hill and Meltz [86] reported the observation of second-order Bragg reflection lines at about one- half the fundamental Bragg wavelength and at other shorter wavelengths for higher order modes. These observations were attributed to strongly saturated gratings whose refractive index variations are no longer sinusoidal along the length of the fibre. In such a case, the peak index regions would be flattened, whereas the valleys in the perturbation index distribution would be sharpened, giving rise to the new harmonics in the Fourier spatial spectrum of the grating. Hill and Meltz did not give details of the fabrication conditions of the fibre grating in which the higher-order reflection lines were observed. Malo et al. [51] reported the observation of sharp transmission dips in the spectrum of a fibre grating that occurred at 1535, 1030, 770 and 620 nm (see Figure 1-8). The fibre grating was produced using a phase mask of period

Λ_pm = 1.06 µm and single high fluence pulse from a KrF excimer laser operating at 249 nm. The phase mask was reportedly designed to suppress the zeroth-order to <5% so that ~80% of the diffracted light was contained in the ± 1 order diffracted beams.

Figure 1-8. Transmission spectrum of a phase-mask-written type II FBG measured over the range 600 to 1600 nm (after [51]).

As discussed in section 1.5.2, the period of a fibre grating written only by the ± 1 orders of a phase mask is equal to half the period of the phase mask. Since

a grating with a period Λpm/2 cannot efficiently reflect light at wavelengths

1030 and 620 nm, Malo et al. attributed all the reflections to a photoimprinted grating with a period Λpm, equal to the period of the phase

mask. This attribution was supported by the observation, using an optical microscope, of refractive index perturbations that were highly localised on the core-cladding boundary and had a period equal to the phase mask inside the core of a type II fibre grating. The authors reasoned that fibre gratings produced using a phase mask and low-fluence multiple-pulses have a period

Λ_pm/2 but single, high-fluence pulse exposure conditions result in gratings with a period Λ_pm. It was also suggested that a weak grating with period Λ_pm/2 may exist but was not detected since the spatial resolution of the microscope viewing system was near its limit.

Mihailov et al. reported the production of fibre gratings in standard SMF-28 and all-silica-core fibre using an ultrafast femtosecond and picosecond infrared (IR) source at 800 nm [87, 88]. Researchers in the same group have analysed the interference patterns formed behind different phase masks using a pulsed IR source and in 2004 reported spatial separation of the ± 1st

diffracted orders from the zeroth and ± 2nd _{at positions greater than 1.3 mm}

from a Λpm = 3.213 μm phase mask when using a femtosecond pulsed IR

source [89]. When the fibre is placed several millimetres behind the phase mask, the time of arrival at the fibre of each diffracted order pair is different causing a spatial separation of the order pairs, defined as group velocity walk- off [90]. Two-beam interference patterns with a pitch half that of the phase mask can be produced by exploiting the short pulse duration of a femtosecond laser source and the group velocity walk-off of the diffracted phase mask orders along an axis perpendicular to the phase mask. This is not possible for longer pulse sources because the pulse duration is such that there would be much more overlap at large distances from the phase mask.

When the fibre is placed at distances greater than 1.3 mm from a

Λpm = 3.213 μm phase mask and it is irradiated with a femtosecond pulsed IR

source, the resultant gratings are formed by the interference of only the ± 1st

orders with a period equal to half that of the phase mask, i.e. Λ = 1.6065 μm. Referring to Equation 1-3, a reflection at 1550 nm corresponds to the third harmonic reflection from such a grating. Gratings fabricated using this technique reportedly exhibit high reflectivity and strong cladding mode suppression at 1550 nm [91].