Study of Optical Fibre Dispersion and Measuring Methods

  • Iraj Sadegh Amiri
  • Masih Ghasemi
Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)


Generally, the design of apparatus configuration plays fundamental and deterministic role over acquired outcome. For any suggested model, there would be many devices available in the laboratory that meet our required expectation on the quantity of proposed variables or parameters. However, some of the devices do not meet the desired reliability, stability or accuracy quality. For the intent of this book, in addition of the above qualities, the response time of measuring device is quite a significant factor. In the following sections, important features and characteristics of active or passive elements will be investigated to exploit them in implementing the design for characterizing dispersion of the optical field.

3.1 Overview

Generally, the design of apparatus configuration plays fundamental and deterministic role over acquired outcome. For any suggested model, there would be many devices available in the laboratory that meet our required expectation on the quantity of proposed variables or parameters. However, some of the devices do not meet the desired reliability, stability or accuracy quality. For the intent of this book, in addition of the above qualities, the response time of measuring device is quite a significant factor. In the following sections, important features and characteristics of active or passive elements will be investigated to exploit them in implementing the design for characterizing dispersion of the optical field.

3.2 Dispersion Measurement Methods

This section first starts to study the available methods on measuring chromatic dispersion before going on more details about experimental device to find out the compatibility of device and method of measurement. The common techniques for measuring dispersion can be classified into some groups:
  1. 1.

    Time of flight (TOF)

  2. 2.

    Modulation phase shift (MPS)

  3. 3.

    Temporal interferometric

  4. 4.

    Spectral interferometric


3.2.1 Time of Flight

In this technique, two mechanisms can be employed to predict second-order dispersion parameter. First is by measuring the span of variable time delay between consecutive pulses at different wavelength, and the second is by measuring amount of widening of the pulse at the beginning and end of fibre [1]. The formula to determine dispersion is expressed in Eq. (3.1) [2]. The parameters Δt, Δλ, λ0 and D(λ0) are effective group delay, pulse wavelength bandwidth, centre of wavelength and chromatic dispersion coefficient for above equation.
$$ D\left({\lambda}_0\right)=\frac{\varDelta t}{L\varDelta \lambda \left({\lambda}_0\right)} $$

The serious problem associated with this technique is about length of fibre. For the short length of fibre, the measured dispersion could not be accurate because the given delay is not enough to distinguish the time difference between pulses. However, for long length (above several km), it is possible to measure dispersion on the order of 1 ps/nm.

3.2.2 Modulation Phase Shift

The MPS technique exploits the variation of phase of radio-frequency (RF) modulation envelope, while the wavelength is changed. The component for providing variable wavelength laser is usually tuneable laser with resolution bandwidth in the range of 1 nm. For implementing RF modulation, an external modulator is employed. The RF envelope and laser applied to external modulator and at the receiver amplify before detection by optical detector. If the RF envelope is considered as baseline, then by comparing the phase and amplitude of recovered data with detected optical envelope, it is possible to measure group delay over a wavelength Δλ. The following formula is used for calculation of group delay from obtained phase data:
$$ \varDelta {T}_{\mathrm{g}}=\frac{\varDelta \varPhi}{360}\times \frac{1}{f_{\mathrm{m}}} $$
where the first parameter ΔΦ represents RF phase shift and the second parameter shows frequency of applied sine wave. To calculate chromatic dispersion, usually the ratio of group delay to the difference wavelength is used.
$$ D=\frac{\varDelta {T}_{\mathrm{g}}}{\varDelta \lambda} $$

Practically, to achieve higher precision in the range of 1 ps/nm-km, the length of fibre at this method must be tens of metres [2]. The other significant limitation factor is about accuracy for different length of fibres [2]. Measured dispersion for long length fibre could be constant with acceptable tolerance value, but for short section of fibre, it would not be acceptable. This is due to the fact that the uniformity for the long length of fibre is considerably changed compared with short length of fibre.

3.2.3 Temporal Interferometric

This technique can be implemented by using a wideband source and the variable path. For measuring dispersion on short fixed length of fibre, the variable air path is employed to produce a temporal interferogram (Fig. 3.1) between it and fixed length of fibre which is under the test. The wideband source is utilized by two temporal interferometry arms [3, 4, 5, 6, 7, 8, 9]. One arm is known as reference and the other one is unknown test past. This arm is moving at constant speed, and it is possible to plot the output intensity as function of time. By applying Fourier transform, it is possible to extract the pattern of phase spectral information that is usable for calculating dispersion. The second derivation of this phase spectral gives the dispersion information indirectly.
Fig. 3.1

Sample temporal interferogram

3.2.4 Spectral Interferometric

This technique is also used for measuring dispersion in short length of fibre. Here the spectral interferogram can be extracted from wavelength domain. There is no need to move one arm because both arms are fixed, so this method offers more stable result rather than temporal interferometric. Two types of spectral interferometric are general case that called unbalance and special case that called balance. In special case it is possible to measure the dispersion directly, so the achieved result is more reliable than all above.

3.3 Apparatus

In the following sections, the main features and abilities of devices are inspected. Tuneable laser, coupler, digital oscilloscope, external modulator, single-mode fibre, polarization controller, coupler, laser diode, power supplier and function generator would be studied in advance. Most of the information in the following sections are taken from factory’s data sheet and might be unique for specific product. As a result due to available tolerance on device for different products, the achieved results would have minor differences on measured values rather than desirable values.

3.3.1 Tuneable Laser Source (TLS)

The block diagram structure of tuneable laser model AQ8201-13 for presenting the operation and controlling process is illustrated in Fig. 3.2 [10].
Fig. 3.2

The connectivity and functionality of each part in tuneable laser module AQ8201-13

As it shows in above figure, in block number one, the signal control from the frame is managed by the controller block. Block number 2 provides the ability of changing wavelength by using pulse motor. In block 3, based on the position of the switch, the laser would be on or off. In block 4, sub-multi-assembly (SMA) connector is used as an input port for modulation signal.

Block 5 is the final stage interface that the laser beam is radiated out. Block 6 is sort of circuit for driving the optical module. Since the output laser intensity is the function of temperature, block 7 is responsible for controlling temperature. Thus, the intensity amplitude of laser at the normal condition is approximately stable and constant. For manual controlling purpose and conducting the input data from the frame, the module interface in block 8 is employed.

The driver circuit for dealing with the pulse motor (related with changing wavelength in block 2) is the task of block 9. The considerable features of AQ8201-13 are gathered in the following (Table 3.1):
Table 3.1

AQ8201-13 main features [10]

Wavelength range

1460–1580 nm

Wavelength resolution

10 pm

Optical output level in the range 1520–1580

+10 dBm

Operating temperature

23 ± 5


−145 dB/Hz

Optical connector


3.3.2 Polarization Controller (PC)

The main purpose of using PC for this experiment is related with involving external modulator. It is required to adjust the polarization state of laser in the fibre before it enters to the external modulator. The birefringence phenomenon helps for controlling polarization and can be applied by coiling fibre.

The induced retardation is corresponding with two factors, first the length of fibre and the second inverse of bending radius. The FPC 560 is one of the popular polarization controllers and classified as “BAT EAR” controllers because it uses some holders at specific diameters and is adjustable for certain number of fibre turns in order to induce retardation.

Each paddle in Fig. 3.3 can make effective retardation corresponding to the number of fibre turns at specific diameter (if the paddle diameter is too small, the bending loss could happen). For FPC560, the first, the second and the third paddles make λ/4, λ/2 and λ/4 retardation, respectively. By changing the angle of first paddle, the input polarization state converts into linear polarization state, and the third state would convert it into the arbitrary output polarization state at a fixed wavelength. Since the polarization state is a function of wavelength, the high peak power can be achieved due to polarization rotation. Figure 3.4 depicts how lower wavelengths and higher number of loop retardation take the greater values compared with higher wavelengths [11].
Fig. 3.3

BAT EAR” polarization controller

Fig. 3.4

Retardation vs. wavelength for 1, 3 and 6 fibre loops per paddle. The fibre clad diameter is 80 μm

Main specifications for FPC560 are as follows:
  • Paddle material: Black Delrin

  • Loop diameter: 2.2″ (56 mm)

  • Paddle rotation: ±117.5°

  • Foot print (W × L): 1.0″ × 12.5″

3.3.3 Lithium Niobate (LiNbO3 ) Electro-optic Modulator (EOM)

The light characteristics can handle many applications such data transmission, sensor, measuring, etc. One of the popular devices that can help to exploit these characteristics is optical modulator. Since light has many variable parameters to manipulate by optical modulator, there are many types of modulators such as phase modulator, intensity modulator, etc. [12].

Since debating about available types of modulator is beyond the scope of this book, just Mach-Zehnder which is employed for this experiment would be studied. Mach-Zehnder modulator is usually categorized as interferometric modulators and in terms of application mostly used for optical data transmission. The employed modulator for this experiment is called “F10”, or “low drive voltage 10–12.5 Gb/s modulator small form factor chirp-free”, that it represents the main features of this modulator.

The “small form factor” expression is usually used for those components that have the capability of enhancing port density, and also their packaging must support small form factor (SFF) technology. “Low drive voltage” shows the fact it requires very low voltage to operate at very high-speed transmission.

This modulator is chirp-free; in other words, it means after modulation, there is no change in frequency of optical signal induced by modulator with time. Figure 3.5 shows different modulation schemes using LiNbO3 [13].
Fig. 3.5

Pattern of z-transect LiNbO3 waveguide. (a) Phase modulator, (b) intensity modulator and (c) directional coupler

Electro-optic coefficient provides the ratio of electrical to optical conversion. There are many types of electro-optic coefficients, and r33 provides the highest among of them [14]. In the condition that the electrodes were placed on top of the waveguide arm in Z-transect wafer and X-transect wafer was placed on both sides of the branches, the amount of changing in refractive index is calculated in Eq. (3.4) [13]:
$$ \varDelta {n}_{\mathrm{e}}=0.5\cdot {n}_{\mathrm{e}}\cdot {r}_{33}\cdot {E}_{\mathrm{z}} $$
where r33 is the highest electro-optic coefficient (pm/Volt), ne is the effective refractive index of material and Ez is the propagated electric field in Z-direction in terms of Volt/cm. Consecutively, the other critical parameter which is called half-wave voltage is studied. The electro-optic crystal is a medium that its refractive index can be changed by applied electric field. This crystal is part of Pockels cell (electro-optic device) device. The half-wave voltage Vπ (Eq. 3.5) is the required voltage that must be applied to Pockels cell for changing phase as π radian.
$$ {V}_{\pi }=\frac{\lambda \cdot g}{L_{\mathrm{m}}\cdot {n}_{\mathrm{e}}^3\cdot {r}_{33}\cdot \varGamma\;} $$
where λ is defined wavelength operation, g is electrode gap length (μm), Lm shows the modulator length (cm) and Γ is called confinement factor [13]. The following Tables 3.2 and 3.3 provide more details about electro-optic modulator.
Table 3.2

General operating conditions

Operating case temperature (Top)

−5 to +75 °c

Storage temperature

−40 to +85 °c

Maximum top variation rate

1 °c/min

RF input power (electrical)

25 dBm (AC coupled)

Optical input power

20 dBm (continuous wave)

Table 3.3

Specific operating conditions

Operating wavelength

1525–1605 nm

Optical insertion loss (2)

5 dB

RF Vπ voltage

3.8–5 V at 1 kHz

Bias Vπ voltage

5.5–6 V at 1 kHz

Optical return loss

45 dB

DC optical extinction ratio

20–24 dB

Chirp, alpha parameter


3.3.4 Signal Generator

The microwave source for the external modulator is produced by PM5191 function generator. It has capability to produce different waves like sine and square form. The frequency domain also covers the range between 0.1 MHz and 2 MHz. Accuracy and stability are the essential factors for produced sine wave that fulfils with this synthesizer/function generator. Another important feature of PM5191 is remote programmability using GPIB port. All front panel functions can be programmed remotely, and all settings and status data can be called and recalled through the remote controller. Some major features about the function generator are as follows:

Sine wave

0.1 MHz–2.147 MHz

Square wave

0.1 MHz–2.147 MHz

Phase noise

<−80 dBc/Hz

Signal to noise ratio (SNR)

≥55 dBc

Long-term drift

<0.3 ppm within 7 h

Max resolution

0.1 MHz

Voltage peak-to-peak open circuit (for both sine wave and square wave)

0–30 V

Rise and fall time for square wave

<35 ns

Duty cycle


3.3.5 Optical-to-Electrical Converter (O/E)

In the field of optic, for the application of measuring signal and further analysis, sometimes it is required to convert optical form into microwave form. For the purpose of this work, Agilent 11982A is utilized by means of PIN photodetector to convert optic signal to electric form. For optical application, the PIN photodetector can support bandwidths of the order of tens of gigahertz [14]. After detection process, the produced electrical signal needs to be amplified by very low-noise amplifier due to high attenuation during conversion. The amplified electrical signal is suitable to use with measuring instrument such as digital oscilloscope or spectrum analyser. In frequency domain, the optical characteristics of laser beam such as intensity modulation, distortion and laser intensity noise can be displayed by spectrum analyser, and the effect of laser modulation is measurable. Another important capability of the 11982A is changing display oscilloscope unit to watt unit in order to measure optical power. For this purpose it is enough to enter the reciprocal of the responsivity in oscilloscope’s probe attenuation field. Considerable features of the O/E 11982A are as follows [15]:

Wavelength range

1200–1600 nm

Bandwidth optical

DC to 15 GHz

Bandwidth electrical

DC to 11 GHz

Input return loss

23 dB

Conversion gain (accuracy of provided value)


Maximum safe optical input power (average)

10 mW

Temperature range

0 °C–+55 °C

3.3.6 Optical Multimetre

To monitor the measured optical power and wavelength metre simultaneously, the OMM-6810B is applied for this experiment. This model is used for general laboratory purpose and can be used for laser diode and any other laser source. It also supports GPIB/IEEE 488.2 interface which enables us to measure two important parameters, optical power and wavelength, automatically. More considerable experiment features are as follows [16]:

Range linear power

0.000–999.99 W

Range log power

−99.999–99.999 dBm/dB

Range wavelength

190–30,000 nm


Meets ANSI/IEEE Standard 488.1–1987


Meets ANSI/IEEE Standard 488.2–1987

Operating temperature

10–40 °C

3.3.7 Digital Signal Oscilloscope

The “DSO1022a”, from, has been employed to analyse the converted optical signal to microwave signal in time domain. This device supports two input RF channels. Automatic measurement function provides the feasibility of 22 automatic measurements. As shown in Fig. 3.6a, b, most of the voltage components and time components can be measured by DSO1022a [17].
Fig. 3.6

(a) Measurable voltage components and (b) measurable time components between two channels in DSO1022a

Noticeable features of the DOSC can be summarized as follows:
  1. 1.

    Displaying automatic measurements for three parameters at the same time.

  2. 2.
    Automatically measuring ten parameters of voltage.
    1. (a)

      Maximum voltage

    2. (b)

      Minimum voltage

    3. (c)

      Peak-to-peak voltage

    4. (d)

      Top voltage

    5. (e)

      Base voltage

    6. (f)

      Amplitude voltage

    7. (g)

      Average voltage

    8. (h)

      Root mean square voltage

    9. (i)

      Over shoot

    10. (j)


  3. 3.
    Automatically measuring 12 parameters of time.
    1. (a)


    2. (b)


    3. (c)

      Rise time

    4. (d)

      Fall time

    5. (e)

      + pulse width

    6. (f)

      Pulse width

    7. (g)

      + duty cycle

    8. (h)

      Duty cycle

    9. (i)

      Delay A–B, rising edges

    10. (j)

      Delay A–B, falling edges

    11. (k)

      Phase A–B, rising edges

    12. (l)

      To calculate the delay between source one and source two, the conversion formula (3.6) is applied to the phase A–B, rising edges:

    $$ \mathrm{Phase}=\frac{\mathrm{Delay}}{\mathrm{Source}\;1\;\mathrm{Period}}\times {360}^{{}^{\circ}} $$
    1. (m)

      Phase A–B, falling edges

  4. 4.

    Using cursor measurements for the purpose of measuring in the selectable area for both time and amplitude axes. This cursor can be set in manual, automatic and track mode. Manual mode lets the user to adjust the cursors manually. Automatic mode adjusts the cursors by the digital oscilloscope for the most recent displayed voltage or time measurements automatically. Track mode lets the user to adjust one or two cross hair cursors manually in order to track the points of wave form in both horizontal and vertical axes.

  5. 5.
    DSO1022a provides the ability of saving oscilloscope screen in terms of graphical or sampling data at two locations:
    1. (a)

      Internal storage

    2. (b)

      External storage

  6. 6.
    Trigger mode is activated when it is supposed the data is captured and stored. This mode includes some subfunctions. When the subfunctions are chosen properly, the unstable or blank screen is converted into preselected wave form. In the first trigger point, the oscilloscope captures enough data to draw the waveform in the left of the trigger point, and when the next trigger condition takes place, the process of collecting data would be continued to the right of the trigger point. Subfunctions of trigger mode:
    1. (a)

      Edge: to take place when the trigger input passes through a specified voltage level with the specific slope

    2. (b)

      Pulse: to search certain width pulses between other pulses

    3. (c)

      Video: to trigger on lines for standard video waveforms

    4. (d)

      Pattern: to trigger on patterns from all input channels

    5. (e)

      Alternate: to trigger on non-synchronized signals

  7. 7.
    Main features and environmental conditions of DSO1022a are collected as follows:
    1. (a)

      Bandwidth 200 MHz

    2. (b)

      Time base accuracy: ±50 part per million (ppm) from 0 °C to 30 °C

    3. (c)

      Trigger sensitivity for both channels: ≥5 mV/div – 1 div from DC to 10 MHz and 1.5 div from 10 MHz to full bandwidth

    4. (d)

      Peak detection: 4 ns

    5. (e)

      Coupling: AC, DC, ground

    6. (f)

      DC vertical gain accuracy : 2–5 mV/div – ±4.0% full scale


3.3.8 SMF 28

Single-mode optical fibre “SMF-28” has set the standard for value and performance for telephone, cable television, submarine and utility network applications. It is widely used in the transmission of voice, data and/or video services. It is manufactured to the most demanding specifications in industry. The following specifications can be considered as main features of SMF-28:
  • Versatility in 1310–1550 nm applications

  • Cable cut-off wavelength < 1260 nm

  • Core diameter 8.2 μm

  • Numerical aperture: 0.14

  • Effective group index of refraction: 1.4682 at 1550 nm

  • Attenuation: <0.22 at 1550 nm

  • Zero-dispersion wavelength: 1313 nm

3.4 Summary

At the first and second sections of this chapter, some methods of dispersion measurement have been studied as a start point; consecutive sections review basics and main features of laboratory’s apparatus. In the third section, a set of optical devices such as external modulator and measuring devices such as digital oscilloscope and so on are reviewed in advance. Since one of the main outcomes of this book is auto-measuring and remote controlling the capable devices, it is essential to know their functions.


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Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Iraj Sadegh Amiri
    • 1
    • 2
  • Masih Ghasemi
    • 3
  1. 1.Computational Optics Research Group, Advanced Institute of Materials ScienceTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Applied SciencesTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Institute of Microengineering and NanoelectronicsUniversiti Kebangsaan MalaysiaSelangorMalaysia

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