Differential Mode Group Delay (DMGD)
in Few Mode Fibers (FMF)
Microwave Interferometric Technique for
Characterizing Few Mode Fibers
Abstract—We propose and experimentally demonstrate a simple and accurate technique for measuring differential
mode group delay (DMGD) in few mode fibers (FMF). A frequency-swept microwave signal is modulated on a filtered
optical incoherent source. The microwave signals carried on different fiber modes experience different time delays andinterfere with each other in the photodetector. Optical interference between propagating fiber modes is avoided bythe use of an incoherent optical source. A mathematical model is established to analyze the interference pattern andextract the DMGD values. A 456-m two-mode fiber and a 981-m FMF, which supports four LP modes, are measured.
The measurement covers the whole C-band and the results coincide well with those obtained by the time-of-flightmethod and the numerical simulations. A precision of ±0.002 ps/m is achieved. [1]Introduction:
Few mode fibers (FMF) have been recently employed in mode division multiplexing (MDM) which isconsidered to be a promising solution for scaling the data-carrying capacity of networks. Differentialmode group delay (DMGD) is an important parameter of FMFs and should be carefully chosen in fiberdesign.

Project Layout
Since the core has a higher index of refraction than the cladding, light will be confined to the core if theangular condition for Total Internal Reflectance is met. The fiber geometry and composition determine
the discrete set of electromagnetic fields, or fiber modes, which can propagate in the fiber. Figure 1 (a)illustrates a step-index fiber having a uniform core of radius (a) with one index of refraction (ncore), and a
uniform cladding with a smaller index of refraction (ncladding). The OptiFiber profile layout is shown in Fig.
1 (b).

Figure 1: (a) A cross section plane view through a step-index fiber and (b) OptiFiber Profile layout.

FMF Design
The fiber parameter (V) that plays an important role in determining the cut-off condition of the
propagating modes is given by:
𝑉=2𝜋𝑎
𝜆𝑁𝐴,

where λ is the operating wavelength and NA is the numerical aperture. The numerical aperture is ameasure of the acceptance angle of the fiber. It is very important because it determines how strongly afiber guides light, and so how resistant it is to bend-induced losses. It is given by:
22
𝑁𝐴 = √𝑛𝑐𝑜𝑟𝑒− 𝑛𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔.

The following table summarizes the propagating modes according to the fiber parameter (V).
Fiber parameter (V)V < 2.405
2.405<V<3.832
3.832<V<5.136
5.136<V<5.520
5.520<V<6.380

Modes
LP01
LP01, LP11
LP01, LP11, LP02, LP21
LP01, LP11, LP02, LP21, LP31
LP01, LP11, LP02, LP21, LP31, LP12

Table 1: The existing propagating modes for a given range of V parameter.

1. FMF supports 2-modes
Numerical simulations were performed assuming a step index profile with a NA of 0.17 and core diameterof 15 μm [1].
Design Fiber Profile:Core refractive index
ncore=1.4569 ; 0 < r < 7.5 µm

Cladding refractive index
ncladding=1.44692; 7.5 µm < r < 62.5 µm

Calculating Fiber Modes:

From the parameters of this fiber the Vparameter is, V=3.78, which determinesthat the fiber should support 2 modes.
The numerical calculations show thatindeed the fiber supports two guided
modes: LP01, LP11.

1. FMF supports 4-modes
Numerical simulations were performed assuming a step index profile with a NA of 0.116 and core
diameter of 16.4 μm [1].
Design Fiber Profile:Core refractive index
ncore=1.4569 ; 0 < r < 8.2 µm

Cladding refractive index
ncladding=1.45245; 8.2µm < r < 62.5 µm

Calculating Fiber Modes:

From the parameters of this fiber the Vparameter is, V=5.16, which determinesthat the fiber should support 5 modes.
The numerical calculations show thatindeed the fiber supports five guided
modes: LP01, LP11, LP02, LP21 and LP31. LP31
is not further analyzed in the simulations
because it is very close to cut-offconditions.

Results
In order to calculate Differential Mode Group Delay (DMGD) at different wavelengths:
1- The propagation mode is selected. (Either for the fundamental mode or the higher modes).

2- The group delay at different wavelengths is extracted.

FMF supports 4-modes
Fundamental
Mode LP01

HigherMode LP02

HigherMode LP11

HigherMode LP21

FMF supports 2-modes
Fundamental
Mode LP01

HigherMode LP113- DMGD are then calculated between each higher mode and the fundamental mode.

λ (µm)
1.530
1.532
1.534
1.536
1.538
1.540
1.542
1.544
1.546
1.548
1.550
1.552
1.554
1.556
1.558
1.560

FMF supports 4-modes
LP11−LP01 (ps/m)
LP02−LP01 (ps/m) LP21−LP01 (ps/m)
4.424
8.068
8.886
4.429
8.046
8.886
4.433
8.023
8.886
4.437
8.000
8.886
4.442
7.977
8.886
4.446
7.953
8.885
4.450
7.929
8.884
4.455
7.905
8.884
4.459
7.880
8.883
4.4637.855
8.882
4.467
7.829
8.881
4.471
7.803
8.880
4.475
7.777
8.878
4.480
7.750
8.877
4.484
7.723
8.875
4.488
7.696
8.873

FMF supports 2-modes
LP11−LP01 (ps/m)
1.926
1.922
1.918
1.915
1.911
1.907
1.903
1.899
1.895
1.891
1.887
1.883
1.879
1.875
1.871
1.867

4-DMGD is finally plotted at different wavelengths.

Figure 2: (a) Simulated DMGD for four mode fiber and (b) Experimental results [1].

Figure 3: (a) Simulated DMGD for two mode fiber and (b) Experimental results [1].

Figures 2 and 3 demonstrate that the experimental results [1] agree with the simulated DMGD for the twoand four mode fibers.

References[1]

Lixian Wang, Cang Jin, Younès Messaddeq, and Sophie LaRochelle, “Microwave InterferometricTechnique for Characterizing Few Mode Fibers,” IEEE PHOTONICS TECHNOLOGY LETTERS, 26 (17),1695 -1698, 2014.