The interesting results obtained for SSMF-to-PD case at 1550 nm can be extended to
the same case operating at 850 nm using as source a SM VCSEL. As explained in detail
in Chapter 2 the major problem of such type of link is related to the bi-modal propagation
at 850 nm of SSMF which contributes to generate output power fluctuations on the receiver
side, especially for low size photo-detector. The model developed in Chapter 2 shows the
importance of having perfect alignment between connectors (if more than one long fiber is
used) and between the final fiber pigtail and detector. Especially for low size
photo-detector this can be a serious problem, and optical power fluctuations, relative to the mean
optical power, can be strong. In particular, the effects of modal noise in such case have been
shown in detail in Section 2.3 of Chapter 3 when the 10×10 µm^{2} SiGe HPT has been used
as photo-detector for LTE transmissions. For this last case the fluctuation of the RF gain, for
which the standard deviationσ_{G} can reach several dB, can lead to fluctuations of SNR and
successively to fluctuations of EVM.

As described by the model shown in Sections 2.2 and 2.3 of Chapter 2, σ_{G} is directly
pro-portional to the relative variation of the received RF modulating power, as happen also for
the optical power. Indeed, reducing the fluctuation of the optical power the effect on the RF
fluctuations reduces as well. The mean value and fluctuation of the optical power ∆P_{opt} in
case of the two modes propagation in SSMF at 850 nm is expressed as follows:

µ_{opt} =P_{0}

A^{2}_{1}b_{11}+A^{2}_{2}b_{22}

(4.1)

∆Popt(t) =P0[2A1A2b12cos(∆β(t))] (4.2) whereP0is the total initial optical power,Ai is weight of the i–th mode such thatP

iA^{2}_{i} =
1 and ∆β_{12}(t) is the difference in time of the phase of the two modes which is supposed varying
in time. The expression of the standard deviationσopt can be then computed as:

σ_{opt}=
q

var(∆P_{opt}) =
q

<∆P_{opt}^{2} >=

= 2P_{0}A_{1}A_{2}b_{12} (4.3)

so that the expression of the relative optical power variation Γopt can be expressed as:

Γopt= σ_{opt}
µopt

= 2A1A2b12

A^{2}_{1}b_{11}+A^{2}_{2}b_{22} (4.4)
which can be expressed as percentage of the average power value µopt. As explained
in Chapter 2, b_{ii} represents the power loss of the i–th mode due to the finite area S_{P D}
and its value contributes to the mean value µopt. The term b12 instead, represents the
non-orthogonality of the modes generated by the finite areaS_{P D}. Indeed, ifS_{P D} → ∞thenb21= 0
because of the orthogonality property of modes in electromagnetic waveguide and because no

fluctuation is present (see Eq. (4.2)). However ifS_{P D} assumes finite values, especially of the
same order of the area occupied by the optical field within the optical fiber, then a minimum
misalignment between the fiber and the center of symmetry of the photodiode surface will
giveb_{21}>0 and consequently ∆P_{opt}(t)6= 0. A possible theoretical behavior for different sizes
of photodiode is shown in Figure 4.6.

-6 -4 -2 0 2 4 6

Fiber Misalignment ( m) 0

5 10 15 20

opt (%)

Model for 10 m PD

Model for 17 m PD

Figure 4.6: Example of theoretical behavior of Γopt for different PD diameter sizes.

To measure the optical powerP_{opt}and its fluctuations due to modal noise the setup shown
in Figure 4.4 has been utilized taking the switch (S) in position (B). For this case, the 850 nm
SM VCSEL already coupled to a pigtail of 9 micron single mode fiber provided by Optowell^{R}
has been employed. Then, 30 meters of SSMF have been inserted in a climatic chamber to
force controlled temperature variations of maximum slope of±1^{◦}C/min. The optical power
is measured for a time period of one hour with a sampling period of one second. An example
of measurement of ∆Popt(t) =Popt(t)−µopt, whereµopt =< Popt(t)>, is shown in Figure 4.7.

0 1000 2000 3000

Time (s) -0.05

0 0.05

0 10 20

T (°C)

T (°C)

Figure 4.7: Example of Time measurements of ∆P_{opt} for 10 µm diameter photo-detector.

To evaluate the impact of fluctuations on optical power received, the parameter Γ_{opt}
defined in Eq. (4.4) is considered. Figure 4.7 shows also the typical temperature behavior
of each measurement performed. Both rise and fall slopes are tested in order to improve the
statistical validation.

As first test, the 10 µm PD and the polymer-based structure have been tested at constant temperature and for different fiber positions. The result is presented in Figure 4.8.

-20 -10 0 10 20

X position ( m) 0

20 40 60 80 100

Coupling Efficiency (%)

10 m PD

Polymer structure

Figure 4.8: Coupling efficiency of 10 micron photodiode with and without the polymer coupling structure.

Therefore as first result, the polymer-based structure results to be stronger to misalign-ment than the simple butt–coupling of 10 micron PD confirming also in this case the results obtained in 1550 nm case.

Taking as reference the results obtained in Figure 4.8, the nanopisitioner is used to locate the optical fiber and change the alignment with the structure tested. A maximum misalign-ment of ±10µm has been considered for both situations. Figure 4.9 shows the behavior of Γopt measured in both conditions.

The theoretical model described above is used to fit the measurements. The parameters
consider for the model are obtained considering the LP_{01} and LP_{11} modes of a SSMF and
considering the respective amplitude coefficients having almost the same weight (A1 'A2).

Moreover a relative Γ_{opt} floor is considered which takes into account possible fluctuations due
to connectors misalignment. For the case of the polymer structure, an equivalent diameter
of 17µm is considered. The results show a big tolerance of the polymer-based structure on
fiber misalignment, together with an higher average optical coupling efficiency, confirming the
measurements performed with ∆T '0^{◦}C/min of Figure 4.8.

-10 -5 0 5 10

Figure 4.9: Relative optical power variation Γ for 10µm diameter PD with and without the polymer-based coupling structure.