Based on complex spectral analysis of the optical field, the Optical Complex Spectrum Analyzer AP2441B/AP2443B is able to measure the chromatic dispersion and the group delay of a transmission line. This paper is dedicated to explain clearly the measurement method of two examples of a 13.2 km standard Single Mode Fiber (SMF) length using a 10 Gb/s modulated signal produced by a Mach Zehnder modulator and a 12.4 km SMF using an optical frequency comb generator. Optional software (OCSA04-Group delay and chromatic dispersion analysis) can be integrated in the equipment in order to display the group delay and the chromatic dispersion as function of the wavelength/frequency. For accuracy issues, the paper presents a solution by using averaging functions.

### Chromatic Dispersion calculation steps

### Phase difference measurement

### Experimental setup

The first step is to calculate the Chromatic Dispersion (CD) and the Group Delay of a transmission line is to compare the complex spectrum of a periodical optical signal (test

signal) measured before (back-to-back) and after transmission. The figure 1 shows the experimental setup of two CD calculation examples. In first example we measure the CD of of a 13.2 km standard Single Mode Fiber (SMF) length using a 10 Gb/s modulated signal produced by a Mach Zehnder modulator while the second example for a 12.4 km SMF using an optical frequency comb generator with 2.5 GHz repetition frequency.

Figure 1: Experimental setup of phase difference measurement before and after transmission using the Optical Complex Spectrum Analyzer, 10 Gb/s Mach Zehnder Modulator (example 1) and the Optical Comb Generator (example 2)

### Experimental results

Let us consider an optical signal whose spectrum is defined by the electromagnetic field amplitude A and phase Ф of its spectral components located at wavelength λ.

For each of these spectral components, the electromagnetic field propagating through a transparent medium can be written as :

Where An, ωn and Фn are respectively the amplitude, angular frequency and the optical phase of the nth mode in the optical spectrum. β is the propagation constant

defined in (1). Thus the nth mode optical phase variation induced by the transmission through a length L of such medium is quadratic:

Figures 2 and 3 depict the parabolic distribution of the optical phase difference (equation (7)) as function of the wavelength/frequency measured by the Optical Complex Spectrum Analyzer respectively related to the examples 1 and 2.

Figure 2: The optical phase as function of wavelength measured using a 10 Gb/s Mach Zehnder Modulator related to the Back-to-Back case (a) and after transmission (b), The resulting phase difference measurement (c)

Figure 3: The optical phase as function of wavelength measured using an Optical Frequency Comb generator related to the Back-to-Back case (blue trace) and after transmission (yellow trace), The resulting phase difference measurement (red trace)

### Group Delay and Chromatic Dispersion Calculation

Figure 4 and 5 show the linear distribution of the calculated Group Delay (equation (10)) as function of wavelength/frequency using the optical phase difference measurements. According to the equation (5), the Chromatic Dispersion, expressed in ps/nm, corresponds to the slope of the Group Delay variation. It is estimated by linear fit of the group delay points with respect to wavelength/frequency. As shown in figure 5, the chromatic dispersion is represented by a red point for each calculation section.

Figure 4: The calculated Group Delay as function of wavelength (blue trace) related to 13.242 km transmission line using a 10 Gb/s Mach-Zehnder modulator. The black trace corresponds to corresponding fit function.

Figure 5: The Group Delay as function of wavelength (blue trace) related to 12.4 km transmission line using a Comb generator. The Group Delay is calculated for three wavelength sections of the Phase difference curve (figure 3). The red points correspond to the calculated chromatic dispersion values relative to the three sections.

### Conclusion

The Apex Technologies Optical complex Spectrum Analyzer (OCSA) is a high efficient tool for measuring the Group Delay and the Chromatic Dispersion of transmission lines. By integrating the Optional software (OCSA04), you will not only be able to quickly analysis and display the Group Delay and Chromatic Dispersion of your transmission line but also to solve the accuracy issues through the use of the weighted linear fit function as well as the averaging function for the optical phase difference measurement before and after transmission.