CD Chromatic dispersion in ps/nm: change of group delay over wavelength: CD=dGD/dλ DGD Differential group delay in ps: difference in propagation time between two orthogonal polarization
Modulation phase shift method
General
The measurement setup for characterizing the group delay (GD) properties of optical components is illustrated in Figure 1, with a comprehensive description of the system's various components and their functions provided in sections 5.1.2 to 5.1.13.
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Detector (D1) Phase comparator generator RF
Figure 1 – MPS measurement method apparatus
Variable wavelength source VWS
The variable wavelength source (VWS) is a polarized light source capable of selecting and tuning specific output wavelengths across a defined range It ensures power stability at all operating wavelengths to prevent significant errors in phase comparators The combined accuracy and repeatability of the VWS and wavelength monitor are precise to 3 pm within the measuring range, while the absolute wavelength accuracy meets the specifications of the device under test Additionally, the source's linewidth is maintained at less than 100 MHz.
The VWS must have a tuning range that encompasses the entire spectral region of the device, ensuring that the source remains free from mode hopping throughout this range Additionally, the output power of the system is crucial for optimal performance.
VWS shall be sufficient to provide enough signal to ensure good comparison of the phase
The minimum increment of the wavelength of the VWS should be adjusted to one tenth of expected GDR period of the DUT.
Tracking filter (optional)
The tracking filter is essential for DUT measurements when the VWS and detector's dynamic range falls short of 40 dB due to the DUT's shape and the broadband source's spontaneous emission (SSE) It must effectively track the VWS to maximize SSE suppression and transmitted power during scans across the measurement area Additionally, the filter's spectral shape should ensure sufficient out-of-band attenuation to achieve a dynamic range of 40 to 50 dB at the transmission detector.
Reference branching device RBD1, RBD2
The RBD configuration can be either 1 × 2 or 2 × 2, with the latter requiring one port to be terminated for a return loss exceeding 50 dB It is essential for the splitting ratio of the RBD to remain stable across wavelengths and to be insensitive to polarization, with polarization sensitivity of transmission attenuation limited to less than 0.1 dB or one-tenth of the device's wavelength dependency Additionally, the directivity must exceed the maximum return loss by at least 10 dB, and the split ratio should ensure adequate dynamic range for measuring the transfer function and sufficient power for the wavelength monitor's proper operation.
Wavelength monitor (optional)
In this test procedure, the wavelength accuracy of the source needs to be closely monitored
For accurate measurements, a wavelength monitor is essential if the tuning accuracy of the VWS is inadequate This method requires measuring the spectral peak of any input signal within the device's bandwidth to an accuracy of 3 pm Suitable wavelength monitors include optical wavelength monitors or gas absorption cells, like acetylene cells When using a gas absorption cell, the VWS must have sufficient wavelength accuracy to resolve the absorption lines and maintain linearity between them.
Included under this specification, is the wavelength repeatability of the VWS + monitor It should be understood by the operator that if the test apparatus has 0,1 ps of ripple with a
30 pm period, then a random 3 pm wavelength variation from reference scan to device scan can result in as much as 0,03 ps of GD noise.
Device under test DUT
This document outlines a testing method that utilizes a single "input-output" path for measurement This approach can be extended to create a measurement system that accommodates an m x n device The device can be connected using either pigtails or connectors.
Due to the high sensitivity of this measurement setup to reflections, it is crucial to ensure that the measurement system does not introduce any reflections, as this could interfere with the detection of reflections in the Device Under Test (DUT).
The performance of DWDM components is often influenced by temperature variations, necessitating that these devices be maintained at a constant temperature during measurement procedures The accuracy of these measurements can be affected by the precision of the heating or cooling systems used For instance, if a device exhibits a temperature sensitivity of 0.01 nm/°C and is kept within ±1 °C of a set temperature, the resulting spectral measurements will carry a total uncertainty of 0.02 nm due to temperature fluctuations.
Detectors D1, D2
The optical detectors include an optical detector, necessary electronics, and a connection to an optical fiber While the use of an optional detector (D2) is not mandatory, it offers valuable correction for any instability in the group delay (GD) of the instrument setup between the modulator and the detector.
DUT between Step 3 and Step 4 of 6.1.3 The optical connection may be a receptacle for an optical connector, a fibre pigtail, or a bare fibre adapter The back-reflection from detectors
To minimize D1 and D2, the preferred choice is to utilize an APC connector, which contributes approximately 0.03 dB.
PDL to the measurement if terminated in air
The detectors must possess adequate dynamic range and sensitivity to effectively measure the specified range based on the power level from the modulated source Additionally, the linearity of the detectors is essential for accurately representing the modulated signal.
The detector shall transfer the optical modulation phase to the RF output phase with good stability and little dependence on the optical signal level
During the measurement sequence, it is essential to ensure that when a detector is disconnected and reconnected, the coupling efficiency for both measurements is preserved to at least the accuracy level of the mated connector.
RF generator
The RF Generator delivers an electrical signal that is used for driving the intensity modulator
The signal is sent to the phase comparator in detectors D1 and D2 as a reference signal An RF Generator creates a waveform featuring a single dominant Fourier component, such as sinusoidal wave modulation Generally, a sinusoidal signal with a frequency between 100 MHz and 3 GHz is utilized It is essential for the RF generator to maintain adequate frequency accuracy and stability to ensure the required measurement precision, as the frequency serves as the time base for GD measurement.
Amplitude modulator
The amplitude modulator utilizes the RF generator's modulated signal to create equivalent amplitude modulation on a continuous wave optical signal It effectively transforms the RF modulated signal into a modulated optical signal, ensuring sufficient linearity for optimal sinusoidal modulation Additionally, the modulation amplitude must align with the dynamic range of the detector system for effective performance.
Phase comparator
The phase comparator, integrated within detectors D1 and D2, is responsible for comparing the phase of the modulated optical signal with the RF reference signal Commonly, a network analyzer or lock-in amplifier serves as the phase comparator This process employs phase sensitive detection to isolate the signal component at a designated reference frequency and phase.
Noise signals at frequencies other than the reference frequency are rejected and do not affect the phase measurement The RF signal level shall not affect the phase measurement.
Temporary joints TJ1, TJ2
Temporary joints are specified to connect the test input signal to the device under test to the device output to the transmission detector (D1)
Temporary joints, such as connectors and splices, are commonly used, but alternative methods like vacuum chucks and micromanipulators can also be effective To maintain optimal performance, it is crucial that all joints achieve a back-reflection level of less than -50 dB, given their high sensitivity to back reflections.
Polarization controller (optional)
The modulated laser signal can be directed to a polarization controller, which adjusts the polarization to the four Mueller states on the Poincaré sphere Three of these states, located on the equator, represent linear polarizations at 0º, 45º, and 90º, while the fourth state, at the pole, corresponds to circular polarization In cases where the device under test (DUT) shows polarization mode dispersion, averaging results from orthogonal polarization states helps determine the group delay (GD) average across all input polarizations By measuring GD at all four Mueller states, the differential group delay (DGD) can be calculated It is essential for the polarization controller to maintain adequate polarization stability throughout the measurement's wavelength range.
Reference jumper
The reference jumper is a single-mode fiber that can feature an optical connector, a fiber pigtail, or a bare fiber It is essential for the reference jumper to match the optical connection of the Device Under Test (DUT).
Swept wavelength interferometry method
General
The measurement setup for this method is illustrated in Figure 2, with a comprehensive description of the system's components and their functions provided in sections 5.2.2 to 5.2.7 This setup demonstrates the transmission measurement of a Device Under Test (DUT) featuring two optical ports.
The measurement of group delay (GD) is crucial for understanding its dependence on wavelength and polarization, as well as its sensitivity to external factors like temperature, pressure, mechanical stress, and noise in optical fiber networks To ensure accurate GD measurements, it is essential to have a stable setup that minimizes the impact of fiber movement and external changes This stability is especially important for the SWI method, which relies on tracing the optical phase, as it is highly sensitive to GD and its variations in the fiber.
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Figure 2 – SWI measurement method apparatus
Tunable laser source TLS
The SWI method relies on coherent interference, necessitating a tunable laser source that can emit variable wavelength signals across a specified range The tunable laser source must have a line-width of less than 1 MHz to meet typical coherence and wavelength resolution requirements With a device length of approximately 10m, including patch cords, the resulting interferogram period is around 20 MHz, which demands a significantly finer resolution for accurate characterization To achieve this, closely spaced measurements are essential, particularly based on the length and group delay (GD) range of the device under test (DUT) Therefore, it is crucial to conduct measurements during continuous wavelength scanning, ensuring the setup allows for precise control and monitoring of the wavelength throughout the sweeping process.
Wavelength monitor
To enhance wavelength accuracy, a wavelength monitor is utilized when the TLS falls short This monitor significantly improves both absolute and relative wavelength accuracy for each measurement point throughout the wavelength scanning process.
Reference branching devices RBD1, RBD2, RBD3
The RBD2 and RBD3 branching devices are essential for establishing the interferometer by dividing the optical path, allowing part of the light to pass through the Device Under Test (DUT) while the other part follows a reference path The light from both paths is recombined to create interference at the detectors, with these couplers typically featuring a 50:50 coupling ratio Additional branching devices may be employed for monitoring purposes, such as wavelength monitoring, and should be chosen to ensure sufficient signal strength The branching devices come in 1 × 2 or 2 × 2 configurations, and any unused ports of the RBD must be terminated to achieve less than -50 dB back-reflection.
Detectors D1, D2
Detectors are utilized to measure optical power across different wavelengths, producing two traces for light in orthogonal polarization states These traces typically exhibit rapid oscillations in power, necessitating a high density of wavelength measurements Consequently, a high-speed data acquisition system is essential The analysis assumes the output signal reflects optical power, and since only relative changes in power are assessed, it is crucial for the detectors to maintain good linearity while avoiding saturation.
Polarization controller
To achieve effective interference signals from the interferometer, it is crucial that light from both paths combines with the same polarization, as orthogonal polarization signals will not interfere Given that the polarization state of light at the DUT output is typically unknown, some level of polarization control is necessary The polarization controller and analyzer work together to fulfill this requirement.
Clause 5 Generally the polarization controller is used to establish the polarization at the DUT input and to “balance” the power at the two detectors from the reference path of the interferometer The polarization controller shall be able to provide satisfactory polarization stability over the wavelength range of the measurement, for example by using zero-order retarding plates The combination of polarization controller and analyzer also permits the calculation of DGD from a set of GD measurements at different polarization conditions.
Polarization analyzer
The polarization analyzer plays a crucial role in ensuring optimal interference conditions by utilizing polarization A practical implementation involves the use of a polarizing beam splitter (PBS) paired with two detectors, along with a polarization controller.
4.2.5 assures that similar power from the reference arm is present at both detectors, then the light from the DUT will also be split into two respective components with the same polarization at the detector as the reference light This assures a good interference signal.
Polarization phase shift method
General
Figure 3 shows a block diagram of the polarization phase shift method (PPS) A detailed explanation of the various components of this system and their functions is contained in 5.3.2 to 5.3.8
Detector (D1) Amplitude and phase comparator
Detector (D2) Amplitude and phase comparator
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Figure 3 – PPS measurement method apparatus
Tunable laser source TLS
A tunable laser source serves as the light source, with a wavelength tuning range that adequately covers the measurement spectrum To achieve optimal signal-to-noise ratio (SNR) and wavelength resolution, the laser must provide sufficient power and possess a narrow spectral line width Typically, a self-contained, temperature-controlled, and current-stabilized external cavity laser unit is utilized The output from the tunable laser is linked to an optical intensity modulator via a polarization-maintaining fiber.
The wavelength increment of the VWS shall be optimized for the period of the group delay ripple (GDR) of the DUT.
RF generator
The RF generator provides a modulated pattern for the optical intensity modulator Some of the modulated pattern is sent to the amplitude and phase comparator as a reference signal
A broadband RF signal source is essential for generating a sinusoidal modulated pattern with a frequency range of 50 MHz to 3 GHz When selecting the modulation frequency, it is important to consider the potential impacts of modulation sidebands and the resolution of CD measurements.
Sidebands are produced on either side of the optical signal, separated by a modulation frequency, \( f \), which indicates the spread of the optical spectrum The effective wavelength resolution, \( \Delta \lambda \) (in nm), is limited by these sidebands and is typically expressed as \( \frac{c}{f} \).
∆λ 2 λ 2 (1) where λ is wavelength (nm) f is the modulation frequency (GHz), and c is velocity of light in vacuum (m/s)
In addition, the GD measurement resolution, ΔGD(ps), is also restricted by the modulation frequency, f, and is typically given as: πf φ 2
∆φ is phase resolution of the phase comparator(radians) f is modulation frequency (GHz)
Amplitude modulator
The optical intensity modulator plays a crucial role in controlling the light intensity from a tunable laser source, synchronized with a modulated RF signal Key optical performance metrics, including insertion loss, on-off extinction ratio, and polarization extinction ratio, must meet specified values across the measurement wavelength range Typically, a LiNbO₃ (LN) modulator is employed to achieve these performance standards To connect with the tunable laser source, a polarization-maintaining fiber is utilized as the input fiber The driving voltage is determined based on the half-wavelength voltage (Vₗₙ) of the LN modulator, while the output power of the RF signal source is adjusted to ensure that the optical intensity modulation reaches approximately 20%.
Polarization controller
A polarization controller is essential for launching light with specific states of polarization (SOP) to the device under test (DUT) It comprises three key components: a polarizer, a 1/4-wave plate, and a 1/2-wave plate By adjusting the angles of the two retardation plates, any desired polarization state can be achieved The system must maintain an angle-adjustable resolution of less than ± 0.1 degrees and ensure a polarization extinction ratio exceeding 20 dB across the measured wavelength range.
Polarization splitter
The polarization splitter, positioned after the Device Under Test (DUT), effectively separates the output light into two orthogonally polarized signals: P- and S-polarized lights These signals are directed to optical detectors for analysis Constructed from a non-isotropic crystal like a calcite prism, the polarization splitter boasts a high polarization extinction ratio exceeding 20 dB, with an insertion loss of less than 1 dB It is essential that the optical performance metrics, including polarization extinction ratio and insertion loss, meet the specified requirements across the relevant wavelength range.
Detectors D1, D2
Optical receivers play a crucial role in converting modulated light from the Device Under Test (DUT) into electrical signals Typically, a PIN photodiode is employed due to its excellent linearity and low noise density of around 10 pA/(Hz)^{1/2} It is essential for the PIN photodiode to possess adequate response characteristics to effectively handle the modulation frequency of the RF signal source Furthermore, to achieve a high signal-to-noise ratio, a broadband low noise amplifier should be utilized following the optical detectors.
Amplitude and phase comparator
The amplitude and phase comparator evaluates the amplitude and phase of polarized waves by comparing them to a reference signal from the RF signal source The group delay, denoted as GD τ (ps), is determined from the phase using the equation: \$\tau = \frac{\phi}{2\pi f}\$.
= × (3) where φ is phase(radians) and f is the modulation frequency (GHz)
The reference signal, integral to the modulated pattern of the RF signal source, is supplied to the amplitude and phase comparator and must be synchronized with the modulated pattern To ensure adequate measurement precision, the total phase accuracy, including the frequency stability of the RF signal source, should be maintained within ± 0.3 degrees.
Modulation phase shift method
Measurement principle
GD, τ g , is defined as the derivative of the optical phase Φ opt with respect to its angular frequency ω opt =2πf opt according to
0 opt opt opt opt opt
In the MPS method, a wavelength tunable source is modulated in amplitude with a sinusoidal waveform at a radio (RF) /microwave frequency f RF , typically in a range of 100 MHz to 3 GHz
The modulated optical signal is sent to the device under test and detected by the receiver The phases of the RF signal, denoted as φ RF1, φ RF2, , φ RFn, are recorded at specific wavelengths λ 1, λ 2, , λ n, which correspond to optical frequencies f opt1, f opt2, , f optn These measurements facilitate the determination of relative group delay, indicating the change in group delay over a wavelength interval By analyzing the RF phases at two adjacent wavelengths, λ i and λ j, the change in group delay, ∆τ g (λ i, λ j), can be calculated.
RF modulation frequency
Selecting the RF modulation frequency requires careful consideration, as it involves a trade-off between GD noise on the measurement trace and the spectral resolution of the curve Table 1 presents the recommended maximum RF modulation frequencies based on the desired spectral resolution.
It is crucial to consider the relationship between wavelength sample spacing and modulation frequency, especially in devices with high dispersion The group delay (GD) difference across the wavelength sample spacing restricts the maximum modulation frequency to avoid phase shifts exceeding 180 degrees, which can result in ambiguous outcomes due to phase-wrap errors Therefore, the modulation frequency must be carefully selected to meet these criteria.
< ∆ f (6) where ∆τ max is the maximum GD difference over the sampling spacing
When the spectral resolution from modulation matches the wavelength sample, averaging measurements taken at successive wavelengths can effectively synthesize a higher value of f RF This occurs because the phase contributions from the upper side-band of one acquisition are canceled out by the equal and opposite phase contributions from the lower side-band of a neighboring acquisition.
Figure 4 presents a case with three acquisition points where the wavelength sample spacing matches the modulation frequency Each ellipse represents the optical spectrum at different wavelength snapshots By averaging these three successive snapshots, we obtain a single equivalent snapshot with an effective modulation frequency of 3f RF and an effective central wavelength of λ 2, which is the mean of λ 1, λ 2, and λ 3.
Table 1 – Modulation frequency versus wavelength resolution for C-band
3,0 48,1 f RF λ 1 f RF λ 2 f RF f RF λ 3 f RF f RF λ 2
Figure 4 – Sampling at the modulation frequency
Test sequence
Using the setup shown in Figure 1, follow these steps:
An RF generator produces a sinusoidal waveform with a frequency (\$f_{RF}\$) typically ranging from 100 MHz to 3 GHz This waveform is essential for driving the amplitude modulator and synchronizing phase detectors D1 and D2 Additionally, the frequency \$f_{RF}\$ can be chosen to correspond with the wavelength sample spacing, ensuring that consecutive samples overlap, as illustrated in figure 4.
The polarization controller can be optionally set to a 0º linear polarization, with its actual orientation being arbitrary Typically, this orientation corresponds to the state produced by the polarization controller, and subsequent states of polarization (SOP) are referenced to this initial setting in Step 7.
Connect a fiber patch-cord between TJ1 and TJ2 without attaching a DUT Scan the TLS wavelength, recording the wavelengths and phases from D1 and D2 at the chosen wavelength sample spacing The outcome will be an array of values represented as (\$λ_i, i\$).
Re f (D1) ϕ , ϕ Re f (D2) i ) This provides a “zero-loss” reference for normalizing the phase of the DUT signal
Attach the Device Under Test (DUT) at points TJ1 and TJ2 Scan the TLS wavelength while recording the wavelengths and phases from D1 and D2 at the chosen wavelength sample spacing The outcome is an array of values represented as (\$λ_i, ϕ_{DUT}(D1)_i, ϕ_{DUT}(D2)_i\$), which yields the phase of the DUT signal.
(5) Steps 3 and 4 can be repeated individually to reduce random noise in the phase measurements by “averaging” the multiple scans
If the modulation frequency \$f_{RF}\$ matches the wavelength sample spacing, boxcar smoothing can be applied to enhance measurements, simulating data acquisition at higher modulation frequencies.
To enhance the analysis, it is advisable to replicate steps 3 to 6 using the polarization controller set at 45º and 90º linear polarization states, along with a fourth state representing circular polarization on the Poincaré sphere This approach facilitates the calculation of the average group delay (GD) across all input polarization states.
Special notice for measurement of GDR
To optimize the period of group delay ripple (GDR) of the device under test (DUT), it is essential to select the wavelength resolution with care A broader wavelength resolution minimizes group delay noise; however, it compromises the ability to accurately resolve group delay ripple due to the smoothing effect.
Calculation of relative group delay
In 6.1.3, step 3 and step 4 provide a “zero-loss” reference and the phase measurements of the DUT signal The relative GD at the wavelength λ i can be calculated as shown
( f f π ϕ ϕ ϕ λ ϕ τ = − − − (7) where ϕ is the phase in radians,f RF is the modulation frequency in Hz and GD is in ps.
Swept wavelength interferometry method
Measurement principle
This method uses an optical interferometer and a tunable coherent light source to measure the dependence on wavelength of the optical phase of the light, ϕ, transferred by the DUT
The absolute GD is then calculated according to its definition as the derivative of phase with respect to optical frequency, ω ϕ d
The phase \( \phi \) denotes the phase of the optical wave, while \( \omega \) represents the optical frequency in radians per second For instance, the electric field strength of light traveling in a vacuum along the x-direction can be described as follows.
E 0 ω π λ (9) where the argument of the cosine function is the phase, ϕ, and the amplitude of the field E 0 is proportional to the square root of the optical power
Note that this method is different to Method D of IEC 60793-1-42, called “interferometry”, for measuring the CD of optical fibres, in which a low-coherence light source is used In that
Method D involves varying the length of the reference arm of the interferometer to align with the optical length of the arm that includes the Device Under Test (DUT) However, this method is unsuitable for measuring components such as filters that demand high wavelength resolution, as it requires a broadband light source to achieve an accurate resolution of Group Delay (GD).
The interferometer assesses the relative phase change of light from the Device Under Test (DUT) compared to the reference path across different wavelengths Constructive interference occurs when the phase alignment of the light results in increased power at the detector, while destructive interference leads to a decrease in power when only the reference path light is present.
As the wavelength is scanned, the power level typically oscillates due to the differing rates of phase advancement in two paths with varying optical lengths A larger path length difference results in more rapid changes in detected power with respect to wavelength The oscillation period, denoted as ∆λ, is defined by this relationship.
The optical path length difference (\( \Delta L \)) is given by the formula \( \Delta \lambda \lambda / (10) \) For a difference of 1 meter, the resulting period is merely 2.4 picometers (pm), and for a 10-meter difference, the period decreases to 0.24 pm This indicates that a flexible measurement setup capable of assessing various devices without reconfiguration must achieve a wavelength resolution finer than 0.1 pm.
After recording the trace of power vs wavelength, the interferogram, the dependence of phase on optical frequency can be extracted, which then allows calculating the absolute GD
The GD is then also a function of frequency or wavelength.
Test sequence
Using the setup shown in Figure 2, follow these steps:
To establish the initial input state of polarization, adjust the polarization controller to achieve equal power at detectors D1 and D2, ensuring that DUT is not connected and TJ1 and TJ2 remain unlinked It is advisable to perform this adjustment with the TLS positioned at the midpoint of the wavelength range being measured, while ensuring that the directivity of the branching device exceeds 50 dB.
To measure the reflectance spectrum of the Device Under Test (DUT), connect it at TJ1 and TJ2, utilizing a 2 x 2 coupler at RBD2 with TJ2 linked to the additional port on the left side For optimal accuracy in measurements, allow a few minutes for the temperature and position of the fiber pigtails to stabilize after attachment.
Scan the TLS wavelength, capturing the wavelengths and signals from D1 and D2 at intervals of 0.1 pm or smaller, depending on the DUT length This process yields an array of values represented as (λ i , P1 i , P2 i ).
(4) Optionally, a normalization measurement with a fibre patch-cord between TJ1 and TJ2 can also be made This provides a “zero-loss” reference for normalizing the amplitude of the
DUT signal, allowing accurate measurement of the attenuation This measurement also produces an array of values (λ i , N1 i , N2 i ), where N is the power trace from each detector
To minimize random noise in the spectra, steps 3 and 4 can be repeated through averaging multiple scans However, it is crucial to avoid smoothing out the interference oscillations during this process, so the averaging should be conducted using the raw data arrays obtained from the analyses in steps 3 and 4.
To enhance the analysis, it is advisable to replicate steps 2 to 5 for a second polarization state that is orthogonal to the first This can be achieved using a polarization controller, enabling the calculation of the group delay (GD) averaged across all input polarization states, as well as the differential group delay (DGD).
Special notice for measurement of GDR
Choosing the appropriate wavelength resolution is crucial for optimizing the group delay ripple (GDR) of the device under test (DUT) A broader wavelength resolution minimizes group delay noise but compromises the ability to accurately resolve group delay ripple due to the smoothing effect.
Calculation of group delay
The result of step 3 above actually yields two interferograms, given by the arrays (λ i , P1 i ) and
The analysis involves four interferograms, including the results from step 6, which are processed uniformly in subsequent calculations Each interferogram produces a GD spectrum, and variations may occur if the Device Under Test (DUT) exhibits non-zero Differential Group Delay (DGD).
The interferogram, which is here expressed in terms of ω=2πc / λ as P(ω), has values
The equation \( P = R + D + \phi \) describes the power at the detector, where \( R \) represents the power from the reference path, \( D \) denotes the power from the device under test (DUT), and \( \phi \) indicates the optical phase difference between the two paths, all of which are functions of frequency \( \omega \) To extract the phase information, the interferogram \( P(\omega) \) undergoes high-pass filtering, with the cut-off determined through a Fourier transform that identifies the interferogram frequencies associated with the group delay (GD) of the device Subsequently, the Hilbert transform is applied to derive the amplitude and phase values that depend on \( \omega \).
The data arrays can be averaged across multiple wavelength scans as outlined in step 5 of section 6.2.2 Additionally, the extensive data points can be condensed to achieve the desired wavelength resolution through boxcar averaging.
The GD is now obtained as:
The calculation for the interferograms of both detectors is averaged to create the polarization-averaged group delay (GD) spectrum for the specified input polarization state, which can be represented as a function of frequency (\(\omega\)) or wavelength (\(\lambda\)) The fully averaged GD spectrum is derived by additionally averaging the GD results from the analysis conducted in step 6 It is important to note that with a zero-length reference measurement, the GD values are absolute and reflect the length of the device.
The insertion loss of the Device Under Test (DUT) can be calculated by analyzing the normalization results from step 4, which yields the amplitude \(2 R(\omega) D N(\omega)\) derived from the Hilbert transform of the corresponding \(N(\omega)\) data Consequently, the polarization-averaged transfer \(T_{\text{ave}}\) of the DUT is defined.
T R (14) where the summation is over values from the two, or four if step 6 is used, polarization- resolved interferograms
The average insertion loss of the device is then given by the average of this from the interferograms of both detectors, expressed in dB
Polarization phase shift method
Modulation frequency
The modulation frequency shall be chosen based on the required wavelength resolution and
GD or CD noise For more information, refer to 6.3.2
Choosing the appropriate wavelength resolution is crucial for optimizing the group delay ripple (GDR) of the device under test (DUT) A wider wavelength resolution minimizes group delay noise but compromises the ability to accurately resolve group delay ripple due to the smoothing effect.
Wavelength increment
To calculate a CD value, two wavelengths are necessary, as the wavelength increment, ∆λ, is essential for this calculation The phase comparator can measure a phase difference of up to ± 180 degrees Consequently, the maximum group delay (GD) difference, Δτ max, that can be measured between adjacent wavelengths is determined by a specific expression.
This wavelength increment, ∆λ, will be called wavelength step size To measure up to a certain value, the wavelength step size is decided as follows max max
∆λ is wavelength step size (nm),
∆τ max is the maximum GD of the DUT in ps, f is the modulation frequency in GHz, and
CD max is the maximum CD to be measured in ps/nm
The minimum increment of wavelength of VWS shall be chosen to optimize for the period of the group delay ripple (GDR) of DUT.
Scanning wavelength and measuring CD
A tunable laser source conducts a wavelength sweep across a specified range, allowing for the calculation of the group delay (GD) value at each wavelength Furthermore, the chromatic dispersion (CD) value of the device under test (DUT) can be derived from the wavelength differentiation of the GD values obtained during each measurement.
This method uses a pair of orthogonal polarized waves (the 0-degree and 90-degree linearly polarized waves) The 0-degree and 90-degree linearly polarized waves are launched into the
The DUT separates the output into two polarized wave components using a polarization splitter Subsequently, the amplitudes and group delays (GDs) for the P- and S- polarized light at a specific measurement wavelength are assessed Specifically, the measured amplitudes are denoted as \(|T_{11}|^2_{\text{mea}}\) and \(|T_{21}|^2_{\text{mea}}\), while the GDs are represented as \(\frac{d\phi_{11}}{d\omega_{\text{mea}}}\) and \(\frac{d\phi_{21}}{d\omega_{\text{mea}}}\) for the 0-degree linearly polarized wave.
90-degree linearly polarized wave, the P- and S-polarized light amplitudes (|T 12 | 2 mea and
|T 22 | 2 mea ) and the GDs (dφ 12 /dω mea and dφ 22 /dω mea ) are measured.
Calibration
A calibration is performed on a single-mode fibre whose length is less than 1 m before the
To perform DUT measurement, first, adjust the 1/4- and 1/2-wave plates to create a 0-degree linearly polarized wave that aligns with the P-polarized wave of the polarization splitter Next, generate a 90-degree linearly polarized wave to match the S-polarized wave of the splitter At a designated measurement wavelength, measure the amplitude and group delay (GD) characteristics of the P- and S-polarized light, which are separated by the polarization splitter, while alternately launching the 0-degree and 90-degree linearly polarized waves This process involves calculating the amplitudes of the P- and S-polarized light, denoted as \(|T_{11}|^2\).
|T 21 | 2 cal , respectively) and the GDs (dΦ 11 /dω cal and dΦ 21 /dω cal , respectively) for the 0- degree linearly polarized wave are measured For the 90-degree linearly polarized wave, the
P- and S-polarized light amplitudes (|T 12 | 2 cal and |T 22 | 2 cal ) and GDs (dΦ 12 /dω cal and dΦ 22 /dω cal ) are measured The CD value is calculated from the measured values using the expression described in 6.3.5.
Calculation of relative group delay and CD
The P- and S-polarized light GDs are calculated using measured values from 6.3.3 and 6.3.4
Average GD in P-polarized light: d 2 d d d d d ave1 11 12
Average GD in S-polarized light: d 2 d d d d d ave2 21 22
Φ + Φ Φ = ω ω ω The GD and CD values on each wavelength are calculated by the next expressions
GD average that does not depend on polarization: d 2 d d d GD ave2 ave1
CD average that does not depend on polarization: ( ( ) ( ) ) Δλ Δλ λ Δλ λ ×
The error of measurement caused by PMD can be excluded from the measurement result by obtaining averaged GD and CD that doesn't depend on the polarization.
Measurement window (common for all test methods)
The spectral width of the measurement window is typically given in the specification of the
DUT Generally, the measurement window is defined in two different ways First, the measurement window is centred on an ITU wavelength with a defined width For example, the
The analysis of GD must be conducted within a 25 GHz optical bandwidth centered on the ITU frequency, as illustrated in Figure 5 for a multiple channel Device Under Test (DUT) Each channel is represented in relation to its corresponding ITU frequency.
In addition, it is essential to analyze the dispersion properties of the Device Under Test (DUT) within a measurement window defined by its loss characteristics For instance, if the DUT is a filter exhibiting wavelength-dependent loss, as illustrated in Figure 6, the dispersion measurement will be conducted within a range from \$\lambda_1\$ to \$\lambda_2\$ These wavelengths, \$\lambda_1\$ and \$\lambda_2\$, correspond to the minus \$x\$ dB points on the loss curve, with typical \$x\$ values ranging from 0.5 dB to 5 dB.
Frequency (GHz) Ins er tion lo ss ( dB ) –4,2
Figure 5 – Measurement window centred on an ITU wavelength with a defined width
A ver age i ns er tio n l os s (dB ) A ver age gr ou p d el ay ( ps )
Figure 6 – Measurement window determined by the insertion loss curve at 3dB
Noise reduction of group delay measurement
Averaging
Averaging multiple measurements of the phase difference between the reference signal and the detected optical signal can effectively reduce non-deterministic noise levels by the square root of the number of averages This process maintains wavelength resolution while introducing a time trade-off.
Spectral filtering
Filter methods are essential for minimizing measurement noise, with averaging over a defined spectral window being the most commonly used technique In the characterization of DWDM components, typical window widths range from 5 to 10 pm, while broadband components can accommodate widths of 1 nm or more It is important to note that the optical signal experiences spectral broadening due to RF modulation, resulting in a spectrally averaged measurement value Consequently, the measurement protocol must clearly specify the applied RF frequency and the width of the spectral filtering window.
In DWDM components, averaging multiple measurement points across a spectral window results in smoother measurement curves by lowering the spectral resolution However, it is crucial to ensure that important details of the measurement are not lost during this averaging process.
Linear phase variation
A linear phase system with a strictly linear phase response introduces a delay without causing distortion However, any deviation from linearity within the bandwidth of the signal can lead to signal distortion.
The linear phase system is expressed as
The optimal function \( f_{\text{opt}} \) is defined by the equation \( f_{\text{opt}} = \phi f_{\text{opt}0} + 2 \pi \tau_g (f_{\text{opt}} - f_{\text{opt}0}) \), where \( \tau_g \) is a constant A linear fit is applied to the phase for most components, and this linear curve is subsequently subtracted from the original phase The resulting phase value represents the deviation from the linear phase.
Chromatic dispersion
General
It is well known that CD is the derivative of the GD as a function of wavelength
However, in practice, this derivative must be performed numerically
The equation \$CD = -\lambda \cdot \lambda \cdot \tau \cdot \lambda \cdot \lambda \cdot \tau\$ (22), where \$i = 1, 2, \ldots, n\$, indicates that the wavelength sample spacing, defined as \$\Delta\lambda = \lambda_{i+1} - \lambda_i = \lambda_i - \lambda_{i-1}\$, plays a crucial role in the calculation When the wavelength sample spacing \$\Delta\lambda\$ is small, it can lead to an amplification of GD noise in the CD calculation To mitigate this calculated CD noise, several strategies can be employed, with two primary methods typically recommended.
Finite difference calculation
The spectral filtering method is utilized to minimize GD noise prior to CD calculations, particularly for narrow band devices The extent of measurement points filtered over a spectral window is determined by the desired improvement in CD noise, ensuring that significant measurement details are preserved and the processed GD curve remains undistorted.
Curve fit
A curve is fitted to the group delay (GD) data using the least mean squares procedure within a specified measurement window To minimize GD noise, the group delay dispersion (CD) is calculated by differentiating the fitted GD curve with respect to wavelength While this method is typically used for broadband devices, such as long spools of fiber, it can also be applied to narrow band devices if the GD variation is relatively smooth within the measurement window An example of a multiple channel device under test (DUT) is illustrated in Figure 7, and the CD is processed for each channel accordingly.
1) A 6 th order polynomial curve is fitted, by least mean squares procedure, to group delay data over a 25 GHz optical BW centred on the ITU frequency as shown in Figure 8
2) The offset frequency, in GHz, from the ITU grid frequency is used for the frequency axis to minimize decimal place requirements for good fit The fit is within ±0,5 ps of the raw data
3) CD is calculated from the differentiation of the fitted GD curve with respect to wavelength
The wavelength step used for calculation is 6 pm
Figure 7 – Calculated CD from fitted GD over a 25 GHz optical BW centred on the ITU frequency
Figure 8 – A 6th order polynomial curve is fitted to relative GD data over a 25 GHz optical BW centred on the ITU frequency
Phase ripple
General
The method of estimating the phase ripple from the measurement data of GD is shown below
This is only valid for DWDM dispersion compensators.
Slope fitting
To calculate the linear-fit value of group delay measurement results for the specified bandwidth in the DUT specifications, apply the least-square method to determine the deviation between the linear and group delay This analysis accounts for group delay ripples and focuses on the 3 dB bandwidth of the insertion loss characteristics unless stated otherwise.
GDR estimation
To determine the amplitude and period of the group delay ripple, analyze the results over two cycles The peak-to-peak group delay ripple should be identified as the maximum amplitude within the measurement range.
To accurately determine the period, it should be calculated as the average over multiple cycles that encompass the maximum amplitude The period can be established by analyzing the crossings of the mean value of group delay for each ripple As illustrated in Figure 9, this method for estimating group delay response (GDR) is effective only when the GDR is plotted against frequency.
GD dev ia tion from li near fi tti ng (ps ) A m pl itude
Figure 9 – Estimation of the amplitude of the GD ripple and the period
Phase ripple calculation
Calculate peak-to-peak phase ripple (∆θ) from group delay ripple using following equation
∆θ = f period *A rip (unit: radians) (23) where,
A rip peak-to-peak group delay ripple (unit: s) f period period of the group delay ripple (unit: Hz)
8.1 50GHz band-pass thin-film filter
Example results for the GD and IL spectra of a 50 GHz band- pass thin-film filter are shown in
Figure 10 – GD and loss spectra for a 50 GHz-channel-spacing DWDM filter
Planar waveguide filter component
Figures 11 and 12 show the examples of GD and CD measurement for a planar waveguide filter component
Figure 11 – Measured GD and loss spectra for planar waveguide filter
Figure 12 – Measured CD and loss spectra for planar waveguide filter
Tunable dispersion compensator (fiber bragg grating)
Figures 13 and 14 illustrate the GD deviation from linear fitting and the phase ripple measurement for a fiber Bragg grating, utilizing the Polarization Average MPS method, with a modulation frequency of 500 MHz.
GD dev ia tion from li near fi tti ng ( ps )
Figure 13 – Measured GD deviation of a fibre Bragg grating
Figure 14 – Measured phase ripple of a fibre Bragg grating
Random polarization mode coupling device
Figure 15 illustrates a GD measurement example for a device exhibiting random polarization mode coupling, highlighting the benefits of averaging GD across different polarization states In the absence of averaging, the GD curve can fluctuate by up to half of the DGD.
Figure 15 – Measured GD for a device with random polarization mode coupling
Figure 16 shows a CD measurement example for a device with random polarization mode coupling
Figure 16 – Measured CD for a device with random polarization mode coupling
The following details shall be specified
• Number of averages of phase measurement
Calculation of differential group delay
This standard employs polarized light sources for measuring components with polarization dependence To accurately determine the polarization-average group delay (GD) spectrum, it is essential to conduct measurements across a comprehensive range of input polarizations This approach also yields adequate data to establish the differential group delay (DGD) spectrum, DGD(λ), as outlined in this Annex.
This Annex aims to facilitate the simultaneous measurement of Group Delay (GD) and Differential Group Delay (DGD) using a single measurement apparatus Specific methods for measuring DGD and Polarization Mode Dispersion (PMD) are outlined in IEC 61300-3-32 and IEC 61282-9.
A.2 Calculation of DGD from measurements made with the MPS method at 4 states of input polarization
This method involves repeating steps 3 to 6 of section 6.1.3 for four distinct input states of polarization, which are selected from a Mueller set of input states of polarization (SOPs) The Mueller set can be effectively illustrated on the Poincaré sphere, as depicted in figure A.1.
Figure A.1 – Mueller states on Poincaré sphere
Orthogonal states of polarization (SOPs) are positioned 180° apart on the Poincaré sphere Within this sphere, three SOPs lie on a great circle, each separated by 90°, as demonstrated in figure A.1.
Using the right-hand rule relative to the north pole, starting from an arbitrary point A on the great circle, positions B and C are determined by adding 90° successively Position D is orthogonal to the other points and oriented upwards according to the right-hand rule The spherical coordinate system describes the normalized input Stokes vector, \( s_0 \), which is used to define an example of a Mueller set with the great circle located on the equator The parameter \( \theta \) represents the linear orientation of the associated normalized Jones vector, \( j_0 \), while the parameter \( \alpha \) indicates the phase difference between the x and y elements of that vector.
à θ à θ θ sin sin cos sin cos
Table A.1 shows the example of Mueller set
Table A.1 – Example of Mueller set
For each, position, A, B, C, and D, measure the phase shifts (radians), designated, φ A (λ), φ B (λ), φ C (λ), φ D (λ), respectively, as in 6.1.3
Calculate the average phase of the two PSPs, φ RF (λ), as:
Adjust the measured phase values by the average phase as:
Calculate the phase difference, δ RF (λ), as:
RFλ 2 φ λ φ λ φ λ δ = arctan tan + tan + tan (A.4)
The DGD (ps) is calculated using δ RF (λ) (radians) and the modulation frequency, f, (GHz) as:
A.3 Calculation of DGD from measurements made with the MPS method while scanning the states of input polarization, “all states method”
To measure the differential group delay (DGD), the input polarization state is scanned using a polarization controller, as shown in Figure 1, while the variable wavelength source (VWS) is set to fixed wavelength steps The relative group delay (GD) is then measured across a wide range of states of polarization (SOP) The DGD, reported in picoseconds (ps), is calculated as the difference between the maximum and minimum GD values at a specific wavelength.
To achieve the desired accuracy, it is essential to ensure that the set of Standard Operating Procedures (SOP) is adequately large, scanned at a rapid rate or for an extended duration, and sufficiently polarization-resolved by averaging individual samples over a short time relative to the polarization scanning rate.
Enhancing the accuracy of DGD determination can be achieved by analyzing the entire distribution of GD samples across the SOP, rather than relying solely on the maximum and minimum GD values in the dataset.
When input polarization is randomly scanned, a direct relationship exists between the standard deviation of the group delay (GD) values and the range between the minimum and maximum GD values The representation of the state of polarization (SOP) on the Poincaré sphere illustrates that the density of polarization states remains constant concerning the difference between the components of polarization along two orthogonal states By selecting these orthogonal states as the principal states of polarization (PSP), it follows that the density of polarization states is uniform across the measured GD range Consequently, the size of this range can be determined from the standard deviation of the GD samples.
DGD= max − min = (A.6) where σ is the standard deviation of the GD samples
A.4 Calculation of DGD from measurements made with the SWI method
The SWI method outlined in section 5.2, along with the measurement of two orthogonal polarization input states detailed in step 6 of section 6.2.2, enables the determination of the amplitude and phase of the transfer matrix elements for these polarization states This wavelength-dependent matrix can be utilized to compute the Differential Group Delay (DGD) through Jones Matrix Eigenanalysis (JME).
The transfer matrix, T(ω), is constructed by calculating the complex matrix elements T₁₁ and T₂₁ from the ω-dependent amplitude and phase values of the two output polarization states based on the initial input polarization state.
Similarly from the results for the second input state of polarization, the complex matrix elements T 12 and T 22 are computed according to:
In the setup illustrated in Fig 2, the phase of T 12 is inverted by an offset of π, as the phase relationship from the reference arm of the interferometer at the two detectors is reversed for the second input state compared to the first.
These elements are then combined to form the matrix T(ω):
The eigenvalues, denoted as \$\rho_1\$ and \$\rho_2\$, are determined for the expression \$T(\omega_{n+1})T^{-1}(\omega_n)\$, where \$\omega_n\$ and \$\omega_{n+1}\$ represent the optical frequencies at adjacent points in the measured spectra The average DGD values, \$\Delta\tau\$, for each interval from \$\omega_n\$ to \$\omega_{n+1}\$, are provided for every interval.
The argument function, denoted as Arg(), defines that Arg(ae^{i\phi}) = \phi This allows for the generation of the DGD spectrum across the measured range An illustrative example is provided in Figure A.2, which corresponds to the same device depicted in Figure 10.
Figure A.2 – DGD spectrum for a 50 GHz bandpass filter, measured with 30 pm resolution BW
A.5 Calculation of DGD from measurements made with the PPS method
The PPS method is described in 5.3 and 6.3 The following parameters are calculated using measured values in 6.3.3 and 6.3.4.
(A.11) where λ i , λ f are the initial and the final wavelength of δλ
The DGD value for each wavelength is calculated usingα 1 ,β 1 ,γ 1 andΘ0as:
The calculation technique can result in a series DGD values versus wavelength Figures A.3 and A.4 show examples of such characteristics
Figure A.3 – DGD versus wavelength for a random polarization mode coupling device (example)
Figure A.4 – DGD versus wavelength for a fibre Bragg grating filter (example)
The derivation of DGD concerning this method is described here, and is similar to the Jones
Matrix Eigenanalysis method The optical transfer function matrix can be expressed as:
( exp exp exp exp exp exp T exp T exp T exp
(A.14) where Θ the polarization angle φ the phase difference between T 11 and T 21 ψ the phase difference between T 11 and T 12 Φ the polarization-independent phase shift
The output of polarization vector, E out (ω), is expressed using T(ω) as:
E = × (A.15) where E in (ω) is the Fourier transform of an optical input signal
E out (ω) which is described by Taylor expansion around the optical carrier frequency ω 0 is expressed as:
The first order PMD operator D(ω) that should be called a transfer function differential operator is expressed as:
Therefore, the following expression is obtained by substituting A9 for A8
(A.18) where the high order term is negligible D(ω) is the first order PMD operator and dD(ω)/dω is the second order PMD operator They are not commutative with each other.
The following expression is obtained by diagonalising D(ω) with the unitary operator X.
Where -jΓ +/- are the eigenvalues of D(ω) and Γ + , Γ - are respectively the maximum and minimum group delay
That is, the difference between the imaginary parts of the eigenvalues of D(ω), Γ + -Γ - , is the first order PMD called differential group delay.
Four independent parameters Θ, φ, ψ and Φ described in expression A.14 make the following expression using Taylor expansion
Where δω=ω−ω c Θ 0 , φ 0 , ψ 0 , Φ 0 the values of Θ, φ, ψ,Φ at ω−ω c =0
α 1 ,β 1 ,γ 1 , β 1 the first order coefficients of Taylor expansion of Θ, φ, ψ, Φ
α 2 ,β 2 ,γ 2 , β 2 the second order coefficients of Taylor expansion of Θ, φ, ψ, Φ
The first order PMD operator D(ω) is expressed using expression A.20 as:
Therefore, the eigenvalues of D(ω) are expressed as: Θ +
Where β 1 is the polarisation-independent group delay.
The differential group delay, ∆τ, is given by the difference between the imaginary parts of the two eigenvalues as: Θ +
∆τ + − 2 α1 2 β 1 2 γ 1 2 2β 1 γ 1 cos2 (A.23) The PMD value within the wavelength range is given by the average value of DGD over the measured wavelength range
IEC 60793-1-42, Optical fibres – Part 1-42: Measurement methods and test procedures –
IEC 61282-9, Fibre optic communication system design guides – Part 9: Guidance on polarization mode dispersion measurements and theory
IEC 61300-1, Fibre optic interconnecting devices and passive components – Basic test and measurement procedures – Part 1: General and guidance
IEC 61300-3-1, Fibre optic interconnecting devices and passive components – Basic test and measurement procedures – Part 3-1: Examinations and measurements – Visual examination
IEC 61300-3-32, Fibre optic interconnecting devices and passive components – Basic test and measurement procedures – Part 3-32: Examinations and measurements – Polarization mode dispersion measurement for passive optical components
IEC/TR 62343-6-3, Dynamic Modules – Round robin measurement results for group delay ripple of tunable dispersion compensators
Frederick W King, Hilbert Transforms: Volume 1 (Encyclopedia of Mathematics and its
5.1 Méthode du déphasage par modulation 49
5.1.2 Source de longueur d'onde variable (VWS) 49
5.1.4 Dispositif de couplage de référence RBD1, RBD2 50
5.1.5 Dispositif de contrôle de la longueur d’onde (facultatif) 50
5.1.13 Câble de liaison de référence 52
5.2 Méthode de l'interférométrie de longueurs d'onde balayées 52
5.2.3 Dispositif de contrôle de la longueur d’onde 53
5.2.4 Dispositifs de couplage de référence RBD1, RBD2, RBD3 53
5.3 Méthode du déphasage par polarisation 54
5.3.8 Comparateur d’amplitude et de phase 57
6.1 Méthode du déphasage par modulation 57
6.1.4 Notification spéciale pour la mesure de la fluctuation du retard de groupe 60 6.1.5 Calcul du retard de groupe relatif 60
6.2 Méthode de l'interférométrie de longueurs d'onde balayées 60
6.2.3 Notification spéciale pour la mesure de la fluctuation du retard de groupe 62 6.2.4 Calcul du retard de groupe 62
6.3 Méthode du déphasage par polarisation 63
6.3.3 Balayage des longueurs d’onde et mesure de la dispersion chromatique 64 6.3.4 Étalonnage 64
6.3.5 Calcul du retard de groupe relatif et de la dispersion chromatique 64
6.4 Fenêtre de mesure (commune pour toutes les méthodes d'essai) 65
7.1 Réduction de bruit de la mesure du retard de groupe 67
7.4.3 Estimation des fluctuations du retard de groupe 70
7.4.4 Calcul de la fluctuation de phase 70
8.1 Filtre passe-bande à couche mince 50 GHz 71
8.2 Composants à filtres à guides d'ondes plans 71
8.3 Compensateur de dispersion accordable (réseau de Bragg de fibres) 72
8.4 Dispositif de couplage de mode de polarisation aléatoire 73
Annexe A (informative) Calcul du retard de groupe différentiel 75
Figure 1 – Appareil de la méthode de mesure du déphasage par modulation (MPS) 49
Figure 2 – Appareil de la méthode de mesure de l'interférométrie de longueurs d'onde balayées 53
Figure 3 – Appareil de la méthode de mesure du déphasage par polarisation (PPS) 55
Figure 4 – Échantillonnage à la fréquence de modulation 59
Figure 5 – Fenêtre de mesure centrée sur une longueur d'onde ITU avec une largeur définie 66
Figure 6 – Fenêtre de mesure déterminée par la courbe de perte d'insertion à 3 dB 66
Figure 7 – Dispersion chromatique calculée à partir d'un retard de groupe adapté sur une largeur de bande optique de 25 GHz centrée sur la fréquence ITU 69
Figure 8 – Courbe polynomiale du 6 ème ordre adaptée sur les données de retard de groupe relatif sur une largeur de bande optique de 25 GHz centrée sur la fréquence ITU 69
Figure 9 – Estimation de l'amplitude de la fluctuation du retard de groupe et la période 70
Figure 10 – Spectre de retard de groupe et de perte pour filtre à multiplexage par répartition en longueur d’onde à forte densité à espacement entre voies de 50 GHz 71
Figure 11 – Spectres de retard de groupe et de perte mesurés pour un filtre à guide d'ondes plan 71
Figure 12 – Spectres de dispersion chromatique et de perte mesurés pour un filtre à guide d'ondes plan 72
Figure 13 – Ecart de retard de groupe mesuré d'un réseau de Bragg de fibres 72
Figure 14 – Ecart d'ondulation de phase mesuré d'un réseau de Bragg de fibres 73
Figure 15 – Retard de groupe mesuré pour un dispositif avec couplage de mode de polarisation aléatoire 73
Figure 16 – Retard de dispersion chromatique pour un dispositif avec couplage de mode de polarisation aléatoire 74
Figure A.1 – États de Mueller sur la sphère de Poincaré 75
Figure A.2 – Spectre du retard de groupe différentiel pour un filtre passe-bande de 50
GHz, mesuré avec une largeur de bande de résolution de 30 pm 78
Figure A.3 – Retard de groupe différentiel (DGD) en fonction de la longueur d'onde pour un dispositif à couplage de mode de polarisation aléatoire (exemple) 80
Figure A.4 – Retard de groupe différentiel (DGD) en fonction de la longueur d'onde pour un filtre à réseau de Bragg de fibres (exemple) 80
Tableau 1 – Fréquence de modulation en fonction de la résolution de longueur d'onde pour la bande C 58
Tableau A.1 – Exemple d’ensemble de Mueller 76
DISPOSITIFS D’INTERCONNEXION ET COMPOSANTS PASSIFS À FIBRES OPTIQUES – PROCÉDURES FONDAMENTALES D'ESSAIS ET DE MESURES –
Partie 3-38: Examens et mesures – Retard de groupe, dispersion chromatique et fluctuation de phase