Grating-based uniform full-cycle fibre coupler OADM

This is a novel symmetric design that that relies on the positioning of the grating between the two 50%-50% points of a full-cycle (2π) coupler. The theoretical performance and design parameters of this device are analysed in this section. Figure 8.15 shows schematically the principle of operation of this device. A full-cycle coupler is obtained when the total phase difference between the coupler even and odd eigenmodes along the coupler is 2π. The power evolution along the length of a full-cycle coupler, illustrated schematically in Figure 8.15b), has two points where

the power is equally distributed between the individual waveguides (50-50% points) or equivalently where the total phase difference between the coupler eigenmodes is

π/2 and 3π/2 respectively. In a symmetric coupler these points are located symmetrically relatively to the centre of the coupler and the distance between them is designated L3dB. The grating is written symmetrically along the coupler waist and

its length, LG, should be optimised so that the reflection points in the grating

coincide with the 50-50% points of the coupler and therefore it is necessary that LG=L3dB+2Zpen. It sould be pointed out that L3dB=LC/2 for ideal couplers with no

tapered regions and constant coupling strength.

Figure 8.15 – Principle of operation of a symmetric add-drop multiplexer based on the inscription of a Bragg grating in the waist of a full-cycle (2π) coupler. a) Device representation. b) Drop operation: a channel launched in port 1 is dropped to port 2 and the rest of the channels are transmitted to port 3.

8.3.2.1 Optimising for the penetration depth

The operation of this device depends critically on the exact placement of the grating so that its two effective reflection points coincide with the 50-50% points of the coupler. For the same gratings as illustrated in Figure 8.3, the grating length that is required for matching the reflection points with the 50-50% points of the coupler is shown in Figure 8.16, for different distances between the coupler reflection points.

For a symmetric 30mm long uniform full-cycle coupler the distance between the two 50-50% points of the coupler is half the coupler length (15mm) and for an effective index modulation of ∆n=2x10-4 the required grating lengths are LG≈17.6mm and

LG≈27.3mm, for uniform and sine2 apodisation profiles, respectively (represented in

Figure 8.3 by the dashed lines). The required length for a Blackman apodised grating is greater than the coupler length and therefore not possible with an index modulation of∆n=2x10-4. 0 5 10 15 20 25 30 0 5 10 15 20 25 30

Reflection points difference, L3dB(mm)

G ra tin g le ng th ,L G (m m ) Uniform Blackman Sin 2_(x)

Figure 8.16 – Grating length, LG, required for different distances between the reflection points of the coupler, L3dB. Black line: Uniform apodisation. Blue line: Blackman apodisation. Red line: Sine2apodisation.

The spectral responses of a 30mm long full-cycle coupler, with both a 27.3mm long sine2apodised grating and a 17.6mm long uniform grating written in the waist, are shown in Figures 8.17a) and 8.17b), respectively. Light is launched in port 1 and the power arriving at each one of the ports is calculated. The ports are represented by: P11– Thin red line; P21– Thick red line; P31– Thick black line; P41– Thin black

line. The second subscript in Pij refers to the input port (j) and the first subscript

-60 -50 -40 -30 -20 -10 0 -0.50 -0.25 0.00 0.25 0.50 Wavelength detuning (nm) P ow er (d B ) P11 P21 P31 P41 LC=30mm a) -60 -50 -40 -30 -20 -10 0 -0.50 -0.25 0.00 0.25 0.50 Wavelength detuning (nm) P ow er (d B ) P11 P21 P31 P41 LC=30mm b)

Figure 8.17– Spectral response of a uniform 30mm long full-cycle coupler with a grating length optimised for the penetration depth inscribed in its waist. a) LG=27.3 sine2 apodised grating. b) LG=17.6mm uniform grating.

For optimised symmetric operation, the performance of this device is shown to be poor in terms of out of band back-reflection and light leakage through the drop port. As shown previously, this effect is due to the high dispersion at the edges of the grating bandwidth. For DWDM networks, these high cross-talk values could be suppressed by using two isolators placed at each the input and drop ports. However this requirement reduces the cost effectiveness of the device. Alternatively, this device could be employed to route signals with large channel spacing where the out of band cross-talk is small. Due to the large difference in the coupler eigenmodes (double the case of a similar length half-cycle coupler), the overlap between the individual gratings affecting the even and odd eigenmodes is smaller giving rise to shorter available bandwidths. This effect is more pronounced for apodised gratings where the bandwidth is reduced, as shown in Figure 8.17a). The main advantages of this device are the large grating lengths required for optimising the couplers that allow for higher device isolation due to the large reflectivity of the grating and the symmetric operation (under optimised conditions), in contrast with the previous case of the half-cycle coupler. Variation of the coupler length and maximum effective index modulation do not improve further the performance of the device. There is always a compromise between the optimisation of the penetration depth at the resonant wavelength and the high penetration depths at the edges of the grating bandwidth. The increased coupler length requires a longer grating and, therefore, the device performance is scaled accordingly.

8.3.2.2 Sensitivity to the determination of the coupler 50-50% points

The amount of back-reflected power due to the incorrect determination of the 50- 50% points of the coupler is analysed for a uniform grating placed in the waist of a uniform full-cycle coupler. Generally, it is assumed that the positions of these optimum reflection points of the coupler are at LC/4 and 3LC/4, which is true only

for the case of uniform couplers. The tapering of the coupler waist due to fabrication irregularities and especially the tapered coupler region at both ends, influence the location of these points within the coupler, as shown in Figure 4.10. In fact, for the coupler profile illustrated in Figure 4.9, that was determined by measuring the power evolution during the coupler fabrication, and using expression (4.13), the distance between the 50-50% coupler points is L3dB=18.6mm increasing by 3.6mm relative to

the case of a uniform full-cycle coupler. The effect of the error in the grating length on the amount of back-reflected light at the centre wavelength is shown in Figure D1 in appendix D. Optimally the error in the grating length should be less than 1mm for less than -20dB of back-reflected light to be achieved and therefore, the determination of the exact 50-50% points of the coupler is critical. This issue was tackled by developing a non-destructive method for characterising fibre couplers in Chapter 9 that allows the determination of the 50-50% points with an accuracy of less than 1mm, which could be further improved by suitable optimisation. It is shown that for a full-cycle coupler the 50-50% points are identified even for couplers presenting tapered waists and long transition regions.

8.3.2.3 Conclusions

The operation of this device is symmetric but the out-of-band crosstalk and back- reflections are very high. Its employment in DWDM systems where the optical channels are tightly spaced would only be possible with the use of optical isolators at the input and add ports that would increase its total cost. However, this device could be used to route channels with large spacing between them without the need

for optical isolators. The performance of this device relies on the correct grating length and determination of the 50-50% positions in the coupler.