As said in section 3.2.1, three types of launch were employed in the exper-imental activity: central launch, offset launch and overfilled launch. Central launch was obtained linking together the connectors of the laser single-mode pigtail and the MMF with an adapter. All the connectors used were angle-polished standard connectors (SC–APC) and all the adapters were the same used for SMF. Offset launch was obtained with a mode conditioning patch-cord connected to the RoF TX single-mode pigtail. This patch-patch-cord provides a launch of the optical power out of the MMF center with an offset between 10 and 16 µm [80]. Overfilled launch was obtained by using a mode scrambler [81] on a short multi-mode patch-cord. The mode scrambling was obtained by inducing periodic microbendings on a short part of the multi-mode patch-cord.
The results presented in this subsection show the impact of the three different types of launch on modal noise. The quantities under study are:
• σG: the standard deviation of the link gain, i.e. the standard deviation in dB of the received power at fc,1
• hC/HD2i : the mean value of the ratio in dB between the received power at fc,1 and the received power at 2fc,1
• hC/IM D3i : the mean value of the ratio in dB between the received power at fc,1 and the received power at 2fc,2− fc,1 or 2fc,1− fc,2 The mean value of the received power at fc,1 is not reported because it is slightly dependent from modal noise as also reported in (3.37a). The experimental results are compared with the simulations results coming from the model described in section 3.1. The mean value of C/HD2 and C/IM D3 in dB were calculated numerically on a simulated time behavior of all the received components, while σG was calculated through analytical formulas applying the approximation that leads to (3.37a) and (3.37b). Indeed, in this case it is,
σG ≈ 20
ln(10)ΓRF ≈ 20 log10(1 + ΓRF) (3.63) where Γ2RF is defined in (3.53).
Fig. 3.7 shows the standard deviation, σG, between 50 and 550 m. The theoretical and experimental curves were obtained using the RoF TX classi-fied as TX1 in 3.2.5, and the RoF RX classiclassi-fied as RX1 in 3.2.4. However, the considerations on the different types of launch are the same for all TXs and RXs used. The input power was chosen to have an OMI per carrier of 0.2. The gray line and crosses refer to central launch, the black line and cir-cles refer to offset launch, and the gray dashed line and triangles to overfilled launch. Lines refer to simulation results while markers refer to measurements.
Note that theoretical and experimental results are in good agreement. Note that overfilled launch and offset launch have σG values higher than central launch. In particular, at 525 m the difference is of about 1.5 dB with off-set launch and of about 2.5 dB with overfilled launch. The reason for this behavior can be explained with the help of the developed model.
3.2. EXPERIMENTAL AND THEORETICAL RESULTS
0 100 200 300 400 500 600
0 1 2 3 4 5
Fiber length (m) σ G (dB)
Figure 3.7: Comparison of measured (markers) and modeled (lines) values of σG for increasing fiber length using central launch (gray line and circle), offset launch (black line and cross) and overfilled launch (gray dashed line and triangle)
0 100 200 300 400 500 600 0
10 20 30 40 50 60
Fiber length (m)
<C/HD2> (dB)
(a)
0 100 200 300 400 500 600
0 20 40 60 80
Fiber length (m)
<C/IMD3> (dB)
(b)
Figure 3.8: Comparison of measured (markers) and modeled (lines) values of hC/HD2i (a) and hC/IM D3i (b) using central launch (gray line and circles), offset launch (black line and crosses) and over-filled launch (gray dashed line and triangles)
3.2. EXPERIMENTAL AND THEORETICAL RESULTS
All the three launches excite all the MMF modes, i.e. in (3.5) it is always
|Am| > 0 for all m. Hence, the difference between the three launches lies in the relative weights of the various Am. All the other model parameters are the same since we are using the same RoF TX and RoF RX, and MMF.
In the case of central launch, more than 99.9% of the optical power is dis-tributed just among the eight modes LP01 to LP04, each one taken in its two degeneracies (LP stands for linearly polarized [3]). These modes are invariant azimuthally, and therefore the electrical field is mostly concentrated in the central part of the MMF core. It is therefore in high percentage detected, regardless of the finite value of the photodiode surface SP D. This means that for these modes the scalar products bmn in (3.14) become relatively close to zero, reducing the impact of the modal noise on the variance of the received power in (3.39). The same effect is true for a not perfect central launch. In this case not only the eight azimuthally invariant modes, LP01 to LP04, are excited. Anyway, the additionally excited modes are still lower order modes which are as well confined in the central part of the MMF core.
In the case of offset launch, the 99.9% of the total power results dis-tributed among a set of more than 90 modes. Many pairs of modes (m, n) must now be considered in the evaluation of the variance of the received power in (3.39). Since most of these pairs refer to higher order modes the amplitudes of their electrical fields are not negligible in regions of the MMF core far from its center. This means that the correspondent scalar products bmn are not close to zero, and thus the variance of the received power gives relatively high values.
In the case of overfilled launch, the 99.9% of the total power results dis-tributed among all the set of 156 guided modes. Hence, most of the pairs of modes produces high bmn values. Moreover, since both low and high order modes are present, for most of the couples (m, n) the quantity ∆τmn can assume higher values compared to central and offset launch.
Fig. 3.8 presents the results for the mean value of C/HD2 and C/IM D3.
Indeed, central launch gives rise to higher values of hC/HD2i and hC/IM D3i with respect to offset launch and overfilled launch. At 300 m a difference of about 10 dB in hC/HD2i and hC/IM D3i is reported between central
Photodiode chip
(a) (b)
Figure 3.9: Schematic drawing showing the difference between TO-Can PDs with flat window (a) or ball lens (b)
launch and offset launch and of more than 20 dB between central launch and overfilled launch. The reason for this behavior is the same used to explain the difference in σG. I also underline that the previous results are valid in general also for different RoF TXs, RoF RXs and MMFs even if not reported here.
This demonstrates the better performance of central launch with respect to offset launch and overfilled launch. Hence, in the following I will always consider central launch technique.