Polarization Measurement and Control in Optical Fiber Communication and Sensor Systems E-Book
X. Steve Yao
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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Wiley - IEEE
- Sprache: Englisch
Polarization Measurement and Control in Optical Fiber Communication and Sensor Systems A practical handbook covering polarization measurement and control in optical communication and sensor systems In Polarization Measurement and Control in Optical Fiber Communication and Sensor Systems, the authors deliver a comprehensive exploration of polarization related phenomena, as well as the methodologies, techniques, and devices used to eliminate, mitigate, or compensate for polarization related problems and impairments. The book also discusses polarization-related parameter measurement and characterization technologies in optical fibers and fiber optic devices and the utilization of polarization to solve problems or enable new capabilities in communications, sensing, and measurement systems. The authors provide a practical and hands-on treatment of the information that engineers, scientists, and graduate students must grasp to be successful in their everyday work. In addition to coverage of topics ranging from the use of polarization analysis to obtain instantaneous spectral information on light sources to the design of novel fiber optic gyroscopes for rotation sensing, Polarization Measurement and Control in Optical Fiber Communication and Sensor Systems offers: * A thorough introduction to polarization in optical fiber studies, including a history of polarization in optical fiber communication and sensor systems * Comprehensive discussions of the fundamentals of polarization, including the effects unique to optical fiber systems, as well as extensive coverage Jones and Mueller matrix calculus for polarization analysis * In-depth treatments of active polarization controlling devices for optical fiber systems, including polarization controllers, scramblers, emulators, switches, and binary polarization state generators * Fulsome explorations of passive polarization management devices, including polarizers, polarization beam splitters/displacers, wave-plates, Faraday rotators, and depolarizers * Extensive review of polarization measurement techniques and devices, including time-division, amplitude-division, and wave-front division Stokes polarimeters, as well as various Mueller matrix polarimeters for PMD, PDL, and birefringence measurements * Premiere of binary polarization state analyzers and binary Mueller matrix polarimeters pioneered by the authors, including their applications for highly sensitive PMD, PDL, and birefringence measurements * Comprehensive discussion on distributed polarization analysis techniques developed by the authors, including their applications in solving real world problems * Detailed descriptions of high accuracy polarimetric fiber optic electric current and magnetic field sensors Perfect for professional engineers, scientists, and graduate students studying fiber optics, Polarization Measurement and Control in Optical Fiber Communication and Sensor Systems enables one to quickly grasp extensive knowledge and latest development of polarization in optical fibers and will earn a place in the libraries of professors and teachers of photonics and related disciplines.
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Table of Contents
Cover
Title Page
Copyright
Dedication
Author Biographies
Preface
1 History of Light and Polarization
1.1 Early History of Light
1.2 History of Polarization
1.3 History of Polarization in Optical Fibers and Waveguides
References
Further Reading
2 Polarization Basics
2.1 Introduction to Polarization
2.2 The Degenerate Polarization States of Light
2.3 The Polarization Ellipse of Light
2.4 Poincaré Sphere Presentation of Polarization
2.5 Degree of Polarization (DOP)
2.6 Birefringence
2.7 Photoelasticity or Photoelastic Effect
2.8 Dichroism, Diattenuation, and Polarization Dependent Loss
2.9 Polarization Properties of Reflected and Refracted Light
2.A Appendix
References
Further Reading
3 Polarization Effects Unique to Optical Fiber Systems
3.1 Polarization Variation in Optical Fibers
3.2 Polarization Eigenmodes in a Single Mode Optical Fiber
3.3 Birefringence Contributions in Optical Fibers
3.4 Polarization Impairments in Optical Fiber Systems
3.5 Polarization Multiplexing
3.6 Polarization Issues Unique to Optic Fiber Sensing System
3.7 Polarization Issues Unique to Microwave Photonics Systems
References
4 Mathematics for Polarization Analysis
4.1 Jones Vector Representation of Monochromatic Light
4.2 Jones Matrix of Optical Devices
4.3 Jones Matrix of Multi‐element Optical Systems
4.4 Mueller Matrix Representation of Optical Devices
4.5 Polarization Evolution in Optical Fiber
4.6 Polarimetric Measurement of PMD
4.7 Polarization Properties of Quasi‐monochromatic Light
References
Further Reading
5 Polarization Properties of Common Anisotropic Media
5.1 Plane Waves in Anisotropic Media
5.2 Optical Properties of Anisotropic Crystals
5.3 Electro‐optic Effect
5.4 The Photoelastic Effect in Isotropic Media
Reference
Further Reading
6 Polarization Management Components and Devices
6.1 Polarization Management Fibers
6.2 Polarizers
6.3 Polarization Beam Splitters/Combiners
6.4 Linear Birefringence Based Polarization Management Components
6.5 Polarization Control with Linear Birefringence
6.6 Polarization Control with Circular Birefringence
6.7 PMD and PDL Artifacts
6.8 Depolarizer
References
Further Reading
7 Active Polarization Management Modules and Instruments
7.1 Polarization Stabilization and Tracking
7.2 Polarization Scrambling and Emulation
7.3 PDL Emulator
7.4 PMD Generation and Emulation
7.5 Polarization Related Tests in Coherent Systems
References
8 Polarization Related Measurements for Optical Fiber Systems
8.1 Stokes Polarimeters for SOP and DOP Measurements
8.2 Analog Mueller Matrix Polarimetry
8.3 Polarization Extinction Ratio Measurements
8.4 PDL, PDG, and PDR Measurements
8.5 Real‐Time Performance Monitoring of a Communication System with DOP Measurement
8.6 PMD Measurements of Optical Components and Optical Fibers
8.A Appendix
References
Further Reading
9 Binary Polarization Generation and Analysis
9.1 Highly Repeatable Magneto‐optic Binary PSG
9.2 Highly Accurate Binary Magneto‐optic Polarization State Analyzer (PSA)
9.3 Binary Mueller Matrix Polarimetry
9.4 Application Examples of Binary Mueller Matrix Polarization Analyzers
9.5 PDL Measurement of a Multi‐port Component Using a Binary PSG
9.6 Multi‐channel Binary PSA
9.7 WDM System Performance Monitoring Using a Multi‐channel Binary PSA
9.A Appendix
9.B Appendix
References
10 Distributed Polarization Analysis and Its Applications
10.1 Distributed Polarization Crosstalk Analysis and Its Applications
10.2 Distributed Mueller Matrix Polarimetry and Its Applications
10.3 Polarization Scrambled OFDR for Distributed Polarization Analysis
10.4 P‐OTDR Based Distributed Polarization Analysis Systems
10.A Appendix
References
11 Polarization for Optical Frequency Analysis and Optical Sensing Applications
11.1 Optical Frequency Analysis Techniques
11.2 Polarimetry Fiber Optic Gyroscope
11.3 Polarimetric Magnetic Field and Electrical Current Sensors
References
Index
End User License Agreement
List of Tables
Chapter 2
Table 2.1
Table 2.2
Table 2.3
Chapter 3
Table 3.1 Typical PDL values of common optical components.
Chapter 4
Table 4.1 Normalized Jones vectors of selected polarization states.
Table 4.2 Internal reflection sequence in a corner cube reflector.
Table 4.3 Summary of the Jones and Mueller matrices.
Table 4.4 Elementary rotation matrix and the corresponding unitary matrix.
Chapter 5
Table 5.1 Dielectric tensors of crystals with different crystal symmetries....
Chapter 6
Table 6.1 Important properties of commonly used birefringence crystals in op...
Table 6.2 Typical specifications of Polarcor glass polarizers.
Table 6.3 Properties of some commercial magneto‐optic rare‐earth iron garnet...
Table 6.4 Typical performance parameters of an in‐plane anisotropy thick MO ...
Table 6.5 Summary of sources of DGD uncertainty in a quartz DGD artifact.
a)
...
Table 6.6 Summary of sources of uncertainty in a YVO
4
SOPMD artifact.
a)
Table 6.7 Summary of uncertainty sources in a PDL artifact.
Chapter 9
Table 9.1 Logic table for a 4‐bit PSG.
Table 9.2 Logic table for a 6‐bit PSG of six distinctive SOPs.
Table 9.3 Stokes vectors for all possible logical states with component impe...
Table 9.4
α
,
β
, and logic states of a 6‐bit PSA.
Table 9.5 All possible PSA output currents under difference logical states (
Table 9.6 Comparison with a reference PSA (1500–1580 nm).
Table 9.7 Accuracy measurements with a polarizer (1460–1580 nm).
Table 9.8 Statistical results of 50 measurements (Yao et al. 2010).
Table 9.9 Comparison of effective Verdet constants of three different spun f...
Table 9.10 Relationship of
α
,
β
, and logic states of rotators.
Table 9.11 Least‐square‐fitting results of different wave plates.
Table 9.12 Uncertainty estimates for the wave‐plate analyzer.
Table 9.A.1 Logic table of all 64 polarization states of a 6‐bit PSG.
Table 9.B.1 Measured Mueller matrix and its decompositions of the 10.4 m spu...
Table 9.B.2 Measured Mueller matrix and its decompositions of the 10.4 m spu...
Chapter 10
Table 10.1 Comparison of PER measurements of a 13 m PM fiber jumper and a 25...
Table 10.2 Four parameters to fully characterize the quality of three differ...
Table 10.3 Repeated measurements of FUT's RB with non‐distributed polarizati...
Table 10.4 TF sensitivity and RB values obtained by varying force‐applying l...
Table 10.5 TF sensitivity and RB values obtained by varying TF on different ...
Table 10.6 Comparison of applied and measured TLF with the PA‐OFDR sensing s...
Table 10.7 Different SMF‐UT's TF sensitivity ζ measured with the PA‐OFDR sys...
Table 10.8 Custom‐made Type‐1 V‐grooves (Feng et al. 2022).
Table 10.9 Custom‐made Type‐2 V‐grooves (Feng et al. 2022).
Chapter 11
Table 11.1 Comparison of the performance data for the first proof‐of‐concept...
Table 11.2 Performance grade classification of gyroscopes (Lefèvre 1993).
List of Illustrations
Chapter 1
Figure 1.1 Historical milestones in understanding the polarization of light....
Chapter 2
Figure 2.1 Illustration of waves generated by wiggling a rope with different...
Figure 2.2 Illustration of two transverse waves propagating in the
z
directi...
Figure 2.3 Illustration of six degenerate polarization states. The optical b...
Figure 2.4 The polarization ellipse of a light wave showing a major axis of ...
Figure 2.5 Polarization ellipses with different orientation angles and sense...
Figure 2.6 (a) Illustration of a Poincaré sphere showing a point
P
on the sp...
Figure 2.7 (a) The SOP evolution trace on a Poincaré sphere with an elliptic...
Figure 2.8 Illustration of a calcite crystal to separate an incident beam of...
Figure 2.9 (a) Illustration of a sun ray is reflected by a glass plate to be...
Figure 2.10 Reflection and refraction of an optical beam at an interface of ...
Chapter 3
Figure 3.1 Illustration of SOP variations along a single mode fiber under di...
Figure 3.2 Typical SOP variations in a long haul optical fiber link: (a) Poi...
Figure 3.3 Electrical field distributions of the
x
‐polarized (a) and
y
‐polar...
Figure 3.4 Mechanisms for introducing birefringence inside a single mode fib...
Figure 3.5 (a) A fiber can be considered as a concatenation of many randomly...
Figure 3.6 Probability density function (PDF) of DGD for the case that the m...
Figure 3.7 A PMD compensation configuration in direct detection systems. DPC...
Figure 3.8 Illustration of different polarizations experience different tran...
Figure 3.9 Illustration of concatenation of PDL vectors in an optical fiber ...
Figure 3.10 Illustration of a simplified polarization division multiplexing ...
Figure 3.11 Illustration of polarization fading in an optical fiber interfer...
Figure 3.12 (a) An externally modulated microwave photonics link with a modu...
Chapter 4
Figure 4.1 Transverse electric field of a monochromatic plane wave in the ri...
Figure 4.2 A retarder or partial polarizer in principal coordinates.
Figure 4.3 Polarization rotator. (a) Polarization ellipse is rotated without...
Figure 4.4 Rotation between principal coordinates and laboratory Cartesian c...
Figure 4.5 Illustration of reflection and refraction.
θ
i
,
θ
r
, and
Figure 4.6 Electric‐field amplitude ratio of incident to emerging light as a...
Figure 4.7 Reflectivity as a function of the angle of incidence. (a) Externa...
Figure 4.8 Phase shift between
s
‐ and
p
‐polarizations as a function of the a...
Figure 4.9 Fresnel's rhomb retarder.
Figure 4.10 Two reflectors work as a 90‐degree rotator.
Figure 4.11 Polarization‐maintaining retroreflector consisting of two right‐...
Figure 4.12 (a) Geometry of the corner‐cube reflector, with AOB, BOC, and CO...
Figure 4.13 Illustration of the pair of linear polarization eigenvectors whe...
Figure 4.14 Construction of a rotator using three wave plates.
δ
is the...
Figure 4.15 A variable wave plate constructed by inserting a rotator between...
Figure 4.16 Eigen polarization states of optical devices. (a) Retardation pl...
Figure 4.17 The degradation of polarization orthogonality of lights after pa...
Figure 4.18 Experimentally obtaining Jones Matrix. Three input SOPs are requ...
Figure 4.19 Jones matrix in retracing optical path.
Figure 4.20 Jones matrix of a double pass optical system with a mirror.
Figure 4.21 Retroreflection by rotator + mirror.
Figure 4.22 Retroreflection by a Faraday rotator + mirror.
B
is the external...
Figure 4.23 Retroreflecting by quarter‐wave plate + mirror.
Figure 4.24 Retracing optical system with a reciprocal medium and a Faraday ...
Figure 4.25 Retracting optical system with quarter‐wave plate mirror.
Figure 4.26 The relationship between distributed Jones matrix
M
(
z
) and
N
‐mat...
Figure 4.27 The model of a spun highly birefringence fiber. The birefringenc...
Figure 4.28 The rotation axis and rotation angle of unitary optical devices ...
Figure 4.29 Finite rotation dependent on the order of the rotations. R1(π/2)...
Figure 4.30 Infinitesimal rotation
d
Φ
and rotation rate vector
Φ
ν
...
Figure 4.31 Evolution of polarization in media with different birefringences...
Figure 4.32 SOP evolution vs frequency on Poincaré sphere. The output polari...
Figure 4.33 PMD of two concatenated sections.
R
a
and
R
b
are the rotation mat...
Figure 4.34 PMD measurement by scanning optical frequency. (a) Measurement s...
Figure 4.35 Geometric relationships of PSP
, output polarizations hi(ωi)...
Figure 4.36 The electric fields of quasi‐monochromatic light while passing t...
Figure 4.37 A polychromatic light passes through a linear birefringence medi...
Figure 4.38 (a) Plot of the self‐correlation function |
γ
(Δ
τ
)|
Figure 4.39 (a) Plots of the self‐correlation function |γ(Δτ)|...
Chapter 5
Figure 5.1 The geometric relationships of directions of wave front normal
k
,
Figure 5.2 Index ellipsoid. The inner ellipse is the intersection between th...
Figure 5.3 Index ellipsoid and the normal surfaces of uniaxial crystals, whe...
Figure 5.4 Intersection of the normal surface (
n
) with the
x
–
z
plane for bi...
Figure 5.5 Double refraction at a boundary of a positive uniaxial crystal wh...
Figure 5.6 Spatial walk‐off between the
o
‐ray and the
e
‐ray in a negative (t...
Figure 5.7 The plane of linear polarization rotates in right‐handed opticall...
Figure 5.8 The index ellipses of LiNbO
3
when an electric field is applied al...
Figure 5.9 The index ellipses of LiNbO
3
when an electric field is applied al...
Figure 5.10 The index ellipses of LiNbO
3
when an electric field is applied a...
Chapter 6
Figure 6.1 Illustrations of Nicol prism polarizer (a) and Glan–Thompson pris...
Figure 6.2 Illustrations of four different prism PBS' made with birefringenc...
Figure 6.3 (a) The beam crossing angle Δ
β
of a Wollaston prism mad...
Figure 6.4 Illustrations of different polarization beam displacers (PBD). (a...
Figure 6.5 (a) 3D plot of Eq. (6.5a) showing the beam displacement
d
with
g
...
Figure 6.6 (a) Illustration of a polarization beam splitter cube made with a...
Figure 6.7 Illustration of pigtailing polarization devices. (a) The construc...
Figure 6.8 Illustration of an interferometer based PBS.
Figure 6.9 (a) Illustration of a wave plate having a slow and a fast axis; (...
Figure 6.10 (a) Rotation of a linear SOP by an angle of 2
ϕ
if the input...
Figure 6.11 Illustration of three different implementations of the tri‐plate...
Figure 6.12 (a) Illustration of a polarization controller based on Babinet–S...
Figure 6.13 Cross‐section of a fiber squeezer in which a fiber is sandwiched...
Figure 6.14 (a) Poincaré Sphere illustration of iteratively using the squeez...
Figure 6.15 Illustration of polarization controllers made with multiple wave...
Figure 6.16 (a) Illustration of a Babinet–Soleil polarization controller mad...
Figure 6.17 The structure of a YIG crystal showing the relative locations of...
Figure 6.18 (a) Absolute value of specific Faraday rotation of a Bi
1
Tb
2
Fe
4.5
Figure 6.19 (a) A top‐view photo of an MO thick film with perpendicular anis...
Figure 6.20 (a) Illustration of a light beam passing through a thick film of...
Figure 6.21 Magnetic properties of the Faraday rotation. (a) The measurement...
Figure 6.22 Overcoming the domain diffraction by applying a transversal magn...
Figure 6.23 Thick film planar Faraday rotator crystal. The top view photo of...
Figure 6.24 Faraday rotator and its application examples. (a) The constructi...
Figure 6.25 (a) A Faraday rotator made with a copper coil, a magnetic core, ...
Figure 6.26 (a) Construction of a polarization controller made with three Fa...
Figure 6.27 Illustration of the functionalities of an optical isolator (a), ...
Figure 6.28 Constructions of polarization sensitive or PM fiber pigtailed is...
Figure 6.29 (a) A polarization independent isolator made with polarization b...
Figure 6.30 (a) The construction of a polarization insensitive circulator. (...
Figure 6.31 Schematic design of DGD, SOPMD, and PDL artifacts. (a) Precision...
Figure 6.32 Illustrations of different spatial domain depolarizers made with...
Figure 6.33 Illustration of different time domain depolarizers. (a) Depolari...
Figure 6.34 The Lyot and Lyot equivalent depolarizers. (a) The fiber pigtail...
Figure 6.35 Different Yao‐depolarizer configurations. (a) A transmission con...
Chapter 7
Figure 7.1 (a) Illustration of using a polarization controller to stabilize ...
Figure 7.2 (a) A commercial polarization stabilizer made with fiber squeezer...
Figure 7.3 Different polarization monitoring schemes for active polarization...
Figure 7.4 (a) A commercial polarization synthesizer with a computer display...
Figure 7.5 (a) Diagram of a general purpose polarization tracker with an int...
Figure 7.6 PMD compensation using a polarization tracker. (a) Using a polari...
Figure 7.7 (a) A typical optical domain polarization division multiplexing s...
Figure 7.8 A polarization tracker with internal feedback can be used to stab...
Figure 7.9 Illustration of polarization scrambling. A stable input SOP is co...
Figure 7.10 Typical Poincaré sphere SOP traces of discrete scrambling (a) an...
Figure 7.11 Fiber squeezer arrangement and experiment setup for demonstratin...
Figure 7.12 (a) When SOP traces out a small circle on Poincaré sphere, the S...
Figure 7.13 (a) Random SOP variation of a Rayleigh scrambling scheme; (b) Th...
Figure 7.14 (a) A commercial polarization control instrument with Tornado SO...
Figure 7.15 Polarization scrambler application examples. (a) Determining the...
Figure 7.16 (a) The construction of a PDL emulator; (b) The photo of a comme...
Figure 7.17 Configurations of PMD emulators made with PBS and PBC. (a) A fir...
Figure 7.18 Description of a binary programmable DGD generator. (a) The stru...
Figure 7.19 Dynamic performance of the DGD generator. (a) Transient DGD betw...
Figure 7.20 (a) Generated DGD samples with an average
DGD
of 10 ps following...
Figure 7.21 All‐order PMD emulator with tunable statistics using variable DG...
Figure 7.22 Illustration of PMD effect on an optical signal. (a) The SOP of ...
Figure 7.23 Illustration of a ternary polarization rotation switch (a), a po...
Figure 7.24 (a) SOPMD generated by the ternary PMD source as a function of t...
Figure 7.25 The map of SOPMD vs. DGD showing all the PMD values can be gener...
Figure 7.26 (a) Illustration of the concept of PMD measurement by PMD compen...
Figure 7.27 A coherent receiver generally includes three polarization‐relate...
Figure 7.28 Polarization‐related performance tests where X represents SOP, P...
Figure 7.29 (a) Setup for testing the PMD tolerance of a pair of transceiver...
Chapter 8
Figure 8.1 The first Stokes polarimeter with a structure for sequentially in...
Figure 8.2 Different configurations of rotating element polarimeters. (a) An...
Figure 8.3 Stokes polarimeters with equivalent oscillating polarization elem...
Figure 8.4 Configurations for retardation modulation polarimetry. (a) Incomp...
Figure 8.5 Illustration of beam splitter based amplitude division polarimete...
Figure 8.6 Illustration of an in‐line polarimeter. (a) The internal structur...
Figure 8.7 Different configurations of wave‐front division polarimeters. (a)...
Figure 8.8 (a) Polarimeter calibration setup using a high DOP generator. (b)...
Figure 8.9 Illustration of a Mueller matrix polarimetry system.
Figure 8.10 Illustration of four different types of Mueller matrix polarimet...
Figure 8.11 (a) Illustration of a complete Mueller matrix polarimeter constr...
Figure 8.12 (a) Illustration of input SOP with respect to the slow and fast ...
Figure 8.13 (a) The configuration of a PER meter made with a rotating polari...
Figure 8.14 (a) Connecting two PM fibers with fusion machine capable of auto...
Figure 8.15 PER of two cascaded PM fibers.
Figure 8.16 (a) PER measurement setup using an in‐line polarizer to get a hi...
Figure 8.17 Attaching a PM fiber pigtail to a DFB laser requires aligning th...
Figure 8.18 (a) Illustration of a linearly polarized light misaligned by an ...
Figure 8.19 PER measurement results: (a) PER measurement result with low str...
Figure 8.20 Measurement methods for obtaining PDL, PDG, and PDR. (a) Polariz...
Figure 8.21 PDL measurement data and statistics for (a) an FC/APC–air interf...
Figure 8.22 (a) PDL repeatability measurement on the 10‐dB port of a 2 × 2 c...
Figure 8.23 Illustration of double reflection.
Figure 8.24 (a) Illustration of a PDL measurement setup involving PDLs of fo...
Figure 8.25 Illustration of using the polarization scrambling method (a), th...
Figure 8.26 Measuring DOP in an optical fiber system using the Stokes polari...
Figure 8.27 Comparison of DOP measured with the maximum–minimum search metho...
Figure 8.28 Illustration of the SNR degradation due to optical amplifiers' A...
Figure 8.29 SNR measurement using a spectrum analyzer by taking the ratio of...
Figure 8.30 Using DOP meter to measure the noise figures of optical amplifie...
Figure 8.31 (a) Configuration for monitoring SNR, PMD depolarization, and ch...
Figure 8.32 Illustration of time‐domain PMD measurement methods. (a) Pulse‐d...
Figure 8.33 (a) The fixed analyzer method with an optical spectrum analyzer....
Figure 8.34 (a) The SOP trace of a perfect circle after light from a tunable...
Chapter 9
Figure 9.1 (a) Illustration of an MO rotator cell, each is capable of ±22.5°...
Figure 9.2 Measurement setup for the characterization of the PSGs (Yao et al...
Figure 9.3 Poincaré sphere illustration of SOPs generated by the PSG measure...
Figure 9.4 Wavelength dependence of the polarization rotation angle of the 6...
Figure 9.5 Repeatability measurement of a 6‐state PSG (100 samples are taken...
Figure 9.6 Experimental results of measured Stokes parameters of different g...
Figure 9.7 Construction of a 6‐bit binary MO PSA. R
1
, R
2
, R
3
, R
4
, R
5
, R
6
are...
Figure 9.8 Schematic of a binary MO PSA and experiment setup. Light exits a ...
Figure 9.9 Experimental results of measured Stokes parameters
s
1
,
s
2
, and
s
3
Figure 9.10 The construction diagram (a) and a product photo (b) of a binary...
Figure 9.11 (a) SOP evolution as the pressure on the fiber is increased. (b)...
Figure 9.12 1st and 2nd order PMD of a 2‐cm quartz crystal DGD artifact (cal...
Figure 9.13 DGD and SOPMD measurement results for a PMD artifact made from t...
Figure 9.14 Measured PDL as a function of wavelength using the JME and MMM m...
Figure 9.15 (a) Total accumulated PMD and (b) total PDL of coils with differ...
Figure 9.16 Experimental setup. Light from a tunable laser first goes throug...
Figure 9.17 (a) Experimental results showing that the differential retardati...
Figure 9.18 (a) Measured Δ
n
C
of spun fiber at seven different temperatures. ...
Figure 9.19 (a) Measured Δ
n
L
of 10 m spun fiber at seven different temperatu...
Figure 9.20 (a) Polarization variations induced by ACs with amplitudes of 20...
Figure 9.21 (a) Polarization measurement setup for obtaining the Faraday rot...
Figure 9.22 (a) System noise floor for differential SOP angle ΔΦ m...
Figure 9.23 Measured differential SOP angles on the equator plane of the Poi...
Figure 9.24 (a) Three repeated measurements of the differential SOP ΔΦ...
Figure 9.25 Measured differential SOP rotation angles induced by different l...
Figure 9.26 The binary wave‐plate analyzer using four MO rotators (R
1
∼ R
4
):...
Figure 9.27 Typical measurement results with the normalized intensity for th...
Figure 9.28 Typical wavelength dependence curves of the retardation and orie...
Figure 9.29 Measuring the PDL of a multi‐port fiber optic device, such as a ...
Figure 9.30 A multi‐channel polarimeter made with a binary 4‐bit PSA and an ...
Figure 9.31 A multi‐channel PSA is used for monitoring the SNR a WDM communi...
Figure 9.32 (a) Performance monitoring of a WDM system using the multi‐chann...
Chapter 10
Figure 10.1 (a) Slow axis misalignment between two connecting PM fibers. (b)...
Figure 10.2 (a) Illustration of a ghost‐peak‐free distributed polarization c...
Figure 10.3 (a) Illustration of polarization coupling at locations
X
1
,
X
2
, a...
Figure 10.4 A typical polarization crosstalk curve measured with a distribut...
Figure 10.5 Illustration of different types of polarization cross talks. Lef...
Figure 10.6 (a) Crosstalk measurement result of a 340 m long PM fiber coil, ...
Figure 10.7 (a) Zoom‐in view on section B of the crosstalk measurement of Fi...
Figure 10.8 (a) The crosstalk curve of a low quality PM coil of 309 m. (b) T...
Figure 10.9 Left: illustration of the peak and non‐peak values of a discrete...
Figure 10.10 (a) Illustration of a length of PM fiber wound on a fiber spool...
Figure 10.11 (a) Polarization crosstalk curve of 280 m PM fiber wound on the...
Figure 10.12 (a) Measured group birefringence as a function of distance alon...
Figure 10.13 Envelope widths of crosstalk peaks induced by stress at various...
Figure 10.14 (a) Polarization crosstalk curves of a PM fiber as a function o...
Figure 10.15 (a) Polarization crosstalk curves of a 13 m jumper with two FC/...
Figure 10.16 Polarization crosstalk curves of three different PM fibers. (a)...
Figure 10.17 (a) Plot of Eq. (10.2b) showing
h
oscillates as
F
increases bey...
Figure 10.18 (a) Illustration of a sensing tape showing the birefringence ax...
Figure 10.19 (a) Illustration of the PM fiber based sensing tape on which th...
Figure 10.20 (a) Schematic of the equipment and process for fabricating PM f...
Figure 10.21 (a) The pressure plate design with a dowel pin to act on the se...
Figure 10.22 (a) Experimental and theoretical results of polarization crosst...
Figure 10.23 Post fabrication measurement of the birefringence orientation a...
Figure 10.24 (a) Sensing tape uniformity test with 14 identical pressure pla...
Figure 10.25 (a) Distributed force sensing with different weights applied to...
Figure 10.26 Experimental setup with eight preset stress points correspondin...
Figure 10.27 (a) Variations of delay difference Δ
z
23
between crosstalk ...
Figure 10.28 (a) Schematic of distributed polarization analysis (DPA) system...
Figure 10.29 Data acquisition and processing flow chart for obtaining the st...
Figure 10.30 (a) Experimental setup of bending‐induced birefringence measure...
Figure 10.31 (a) Birefringence curves of the SMF‐UT segment with 12 fiber lo...
Figure 10.32 (a) Bending‐induced birefringence as a function of fiber bendin...
Figure 10.33 Measurement setup of FUT's residual birefringence (RB) based on...
Figure 10.34 (a) Measurement setup of bending‐induced birefringence of SMF w...
Figure 10.35 Schematic of experimental setup for distributed TF fiber sensin...
Figure 10.36 (a) Measured birefringence curve along an SMF‐UT with a 400 g w...
Figure 10.37 (a) Measured birefringence curve along the SMF‐UT with 10 diffe...
Figure 10.38 Measured TLF curves from two separate experiments (Exp. I and E...
Figure 10.39 (a) TF‐induced birefringence as a function of applied TLFs gene...
Figure 10.40 (a) Experimental setup of single‐point TF loading and measureme...
Figure 10.41 (a) TF sensing with a 6.6 m SMF‐UT and a 103.5 m SMF‐UT. Peak‐1...
Figure 10.42 (a) Birefringence distributions as a function of fiber distance...
Figure 10.43 TF‐induced birefringence variations as a function of TLF using ...
Figure 10.44 Schematic diagrams of fiber showing (a) clamped in a V‐groove b...
Figure 10.45 Normalized birefringence induced in SM fiber clamped in a V‐gro...
Figure 10.46 Product photos of (a1) a standard 60° V‐groove made of ZrO
2
use...
Figure 10.47 Schematic diagrams of SM fiber (a1) clamped in a V‐groove by a ...
Figure 10.48 Birefringence distribution measured by DPA when an SM fiber is ...
Figure 10.49 Birefringence distribution measured by DPA when a fiber is (a) ...
Figure 10.50 (a) Distributed measurement I, with a clamping‐force of 245 N/m...
Figure 10.51 (a) Distributed measurement II, with a clamping‐force of 245 N/...
Figure 10.52 (a) Schematic diagram and (b) photo of fiber clamped in V‐groov...
Figure 10.53 Experimental setup of a PS‐OFDR based DPA for distributed trans...
Figure 10.54 A measured OFDR reflection trace with back‐reflections for an F...
Figure 10.55 PS‐OFDR signal from a length of fiber with six connectors and o...
Figure 10.56 Distributed stress measurement of a 250 m fiber coil connected ...
Figure 10.57 Different configurations of polarization OTDR (P‐OTDR). (a) The...
Chapter 11
Figure 11.1 (a) Illustration of laser frequency tuning nonlinearity (Solid l...
Figure 11.2 Concept of the polarimeter‐based optical frequency analyzer used...
Figure 11.3 P‐OFA experimental setup for analyzing two types of swept source...
Figure 11.4 (a) SOP (S1) of 1‐kHz tuning F–P filter (a). (b) The correspondi...
Figure 11.5 Polarimeter oscilloscope mode display. SOP evolutions are record...
Figure 11.6 Instantaneous wavelength and power as the input light source is ...
Figure 11.7 Concept and principle of the real‐time P‐OFA used for spectral s...
Figure 11.8 Experimental setup for spectrum analysis of fixed wavelength sou...
Figure 11.9 (a) Experimental results of DOP values when the DGD is changed f...
Figure 11.10 A 3D plot using the P‐OFA data. Swept wavelength is the added d...
Figure 11.11 (a) Basic configuration of a sine–cosine optical frequency dete...
Figure 11.12 Illustration of an OFD with absolute optical frequency (wavelen...
Figure 11.13 (a) Measured optical frequency of a tunable laser module (top) ...
Figure 11.14 Measurement results of swept‐wavelength laser made for OCT syst...
Figure 11.15 (a) Frequency up and down ramps of the OCT laser extracted from...
Figure 11.16 Measurement results of swept‐wavelength laser made for OCT syst...
Figure 11.17 Frequency scan nonlinearity analysis for the frequency ramp in ...
Figure 11.18 Sine–cosine OFD for sensing and laser frequency control applica...
Figure 11.19 Comparison between (a) I‐FOG; (b) P‐FOG configurations. NPBS: n...
Figure 11.20 Illustration of how the SOP is measured and its behavior. (a) T...
Figure 11.21 Photos of the proof‐of‐concept P‐FOG developed by the authors. ...
Figure 11.22 P‐FOG performance demonstration. (a) Real‐time P‐FOG output of ...
Figure 11.23 Detection sensitivity measurement of the P‐FOG. (a) The P‐FOG i...
Figure 11.24 Bias instability measurements of P‐FOG and I‐FOG. (a) Bias inst...
Figure 11.25 (a) Illustration of a transmissive magnetic field sensor relyin...
Figure 11.26 Experimental data of a transmissive current sensor using MO thi...
Figure 11.27 Experimental data of DC current measurement using the sensing h...
Figure 11.28 (a) Reflective magnetic and current sensor using a Faraday rota...
Figure 11.29 (a) A polarimetric electric current sensor using a length of op...
Figure 11.30 Experimental results of the fiber optic current sensor (FOCS) o...
Figure 11.31 Ratio error of the P‐FOCS at different current levels. (a) Shor...
Guide
Cover
Table of Contents
Title Page
Copyright
Dedication
Author Biographies
Preface
Begin Reading
Index
End User License Agreement
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Polarization Measurement and Control in Optical Fiber Communication and Sensor Systems
X. Steve YaoXiaojun (James) Chen
This edition first published 2023© 2023 John Wiley & Sons, Inc.
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The right of X. Steve Yao and Xiaojun (James) Chen to be identified as the authors of this work has been asserted in accordance with law.
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Cover design by WileyCover image: Courtesy of X. Steve Yao
To the memory of my father, Dunli Yao, whose lasting faith continues to inspire.
Author Biographies
X. Steve Yao is the founder of PolaLight Consulting LLC in Las Vegas, Nevada, and was the founder and Chief Technology Officer of General Photonics Corporation (now part of Luna Innovations) in Chino, California, dedicated to the design and engineering of polarization control and measurement products for over 25 years. He is also the founding director of the Photonics Information Innovation Center (PIIC) at Hebei University (his alma mater) in China. With over 100 journal publications and 80 US patents, Dr. Yao is a fellow of both IEEE and Optica, and holds a PhD degree in Electrical Engineering from the University of Southern California, USA.
Xiaojun (James) Chen is the founder and Chief Technology Officer of In‐line Photonics Inc. in San Gabriel, California, and was the Chief Scientist of General Photonics Corporation (now part of Luna Innovations) in Chino, California, dedicated to the design and engineering of polarization control and measurement products for over 20 years. Dr. Chen holds a PhD degree in Condense Matter Physics from Nankai University, China.
Preface
Polarization is one of the seven fundamental parameters that define the properties of light waves, along with intensity, wavelength, phase, direction, speed, and coherence. Unlike the other parameters, polarization is a multidimensional problem; it requires at least a three‐dimensional sphere, known as the Poincaré Sphere, to describe its behavior, which becomes more complicated when the light interacts with anisotropic materials.
Étienne‐Louis Malus is considered by many to be the father of polarization because he was the first to systematically study the polarization properties of reflected light, publishing his findings on the subject in 1809. He also published his theory of double refraction of light in crystals in 1810, although the phenomenon of double refraction was first observed by Vikings and by Thomas Bartholin. Throughout most of the 250‐year history of polarization research, studies have been limited to observations in free space or in short lengths of optical media that are stable over time.
The polarization behavior of light in an optical fiber is quite different from its behavior in free space or in a short span of a bulk optical medium, although the fundamental physics is the same. It is therefore not straightforward to apply the knowledge of polarization commonly covered in classical physics, which mostly focuses on light traveling in free space or in crystals, to fully understand the polarization characteristics of light in optical fibers for two main reasons. First, unlike in free space or in an optical crystal, the birefringence distribution over a long segment of single mode fiber is random and changes over time, which causes rapid polarization changes both along the fiber and over time. Second, most physics textbooks assume monochromatic light, whereas in optical fiber communication systems, the optical signals have finite bandwidths which increase with the data transmission rate, resulting in much more complicated polarization behavior when such broadband signals travel in a single mode fiber whose birefringence varies over distance and time.
The peculiar polarization behavior of light in optical fibers was first observed and studied in 1972 by researchers at Corning (F. Kapron, N. Borrelli, and D. Keck) and at Bell Labs (W. Schosser), when optical fibers with a loss less than 16 dB/km were first achieved. At that time, the adaptation of a coherent detection approach from radio communication to optical fiber communication was assumed, and therefore the studies of polarization behavior were actively pursued. Soon after, the simplest on–off key (OOK) modulation format was found to be adequate for optical fiber communications, especially after the adoption of Erbium doped fiber amplifiers (EDFA); the motivation for understanding polarization behavior in optical fibers in communication systems diminished because OOK at low data rates is essentially polarization independent. The topic remained largely neglected in optical fiber communication systems until around the year 2000, when data rates in new communications systems climbed beyond 10 Gbps, a rate at which the effects of polarization related issues such as polarization mode dispersion and polarization dependent loss could no longer be ignored. In contrast, polarization studies for optical fiber sensor systems have always remained active.
This book is based on the authors' experience over more than 20 years at General Photonics Corporation (now part of Luna Innovations) in designing and building devices and instruments for the control and measurement of polarization for optical fiber communication and sensing systems. It is intended to be a reference book to enable scientists, engineers, and graduate students to obtain a quick grasp of polarization issues in optical fiber systems, with detailed descriptions of practical devices or configurations for the control and measurement of polarization related parameters. The book includes a brief history of polarization (Chapter 1) with a drawing to show the historical milestones of human beings in understanding the polarization of light. Unlike many other books on polarization, which start with Maxwell equations and heavy mathematics for polarization analysis, this book starts the subject by introducing the basics of the polarization of light (Chapter 2) with minimal mathematics, followed by descriptions of polarization effects unique to optical fibers (Chapter 3), again without involving heavy mathematics. Instead, all mathematical methods for polarization analysis and related formulae are put into Chapter 4 for interested readers. Many of the formulae are directly used in subsequent chapters whenever applicable. In fact, Chapter 4 includes detailed derivations of almost all major polarization‐related formulae or conclusions, providing a “one‐stop shop” where interested readers can find not only the equations themselves, but also where they came from, without having to search for answers scattered over dozens of publications.
In Chapter 5, we review and summarize the properties of certain polarization phenomena in common anisotropic materials, such as the double refraction, optical activity, linear electro‐optic effect, and photo‐elastic effect, which are important for the discussion of polarization control in Chapter 6 that focuses on polarization management components and devices. Chapter 7 covers modules and instrument for active polarization management, focusing on the integration of components and devices introduced in Chapter 6 with electronics and algorithms for common polarization management applications.
Chapter 8 provides detailed coverage of the important topic of polarization measurement, including discussion of both Stokes polarimeters, which can measure the polarization properties of the light itself, such as its state of polarization, degree of polarization, and polarization extinction ratio; and Mueller matrix polarimeters, which can determine not only the polarization properties of the light, but also the polarization properties of optical media through which the light passes, including polarization mode dispersion and polarization dependent loss.
The polarization generators and analyzers described in Chapter 8 are traditional analog devices, relying on mechanical rotations and analog modulations with relatively poor repeatability and accuracy due to mechanical wear and tear and varied environmental conditions. To overcome these issues, we developed binary polarization generators and analyzers utilizing binary magneto‐optic rotators, with the specifics covered in Chapter 9. The binary polarization generation and analysis techniques pioneered by the authors of this book have never been discussed in any other books, which in our opinion represent a major advancement on the topic of polarization measurements.
The polarization analysis systems described in Chapters 8 and 9 can only measure the cumulative polarization effect of an optical medium (such as a fiber) on a light wave after transmission through the medium. Sometimes, it is important to know the position resolved polarization properties of the light wave in the medium. Chapter 10 focuses on such distributed polarization analysis techniques and their applications, mostly based on the authors' own research on this topic over the past 10 years.
Finally, in Chapter 11, we describe techniques for using polarization analysis to enable several new applications, including fast optical frequency detection, high accuracy rotation detection (polarimetric fiber optic gyroscope, P‐FOG), and high accuracy electrical current and magnetic field sensing, which summarize the authors' own research in these exciting directions over the past 15 years.
We have tried not to involve more advanced mathematics, such as spin‐vector calculus and group theory, in the polarization analysis in order to make it comprehensible to most readers with engineering backgrounds. Only the more well‐known Jones matrix calculus and Mueller matrix calculus are introduced in this book. We recognize that the spin‐vector calculus may be more elegant mathematically in treating certain polarization problems, and is easier to grasp for people with strong backgrounds in quantum mechanics. Interested readers are encouraged to read the book Polarization Optics in Telecommunications by Jay N. Damask (2005) on the spin‐vector calculus.
It is often difficult to visualize how a state of polarization (SOP) evolves on the Poincaré Sphere in response to the variations of linear or circular birefringence; we therefore include a SOP trace visualization software called PolaTrace™ written in Python to help readers to view SOP variation traces on the Poincaré Sphere when the magnitudes and/or the orientation angles of the birefringence in one or more locations in the optical path are changed. With the PolaTrace, one is able to see how the SOP can be manipulated with either a single polarization component, or multiple polarization components cascaded in series, such that polarization variations in an optical fiber discussed in Chapter 3 and various polarization controlling devices described in Chapters 4, 6, and 7 can be more easily understood. The owners of this book have the privilege to download the Python source codes at https://github.com/PolarizationInFiber/PolaTrace.
X. Steve Yao would like to dedicate this book to his parents, Dunli Yao and Xianrong Fu, for their constant love and unconditional support. He is grateful to Professors Jack Feinberg and Robert Hellworth at the University of Southern California (USC) for their excellent guidance in the graduate school, Professor Alan Willner of USC for his collaboration and support in the past 20 years (many of the joint research results are included in this book), and Mr. Eric Udd of Columbia Gorge Research for his encouragement for writing this book. His appreciation also goes to his students, Xiaosong Ma and Penghui Yao at Hebei University and Tianjin University, respectively, for their help in preparing some of the figures used in the book.
Xiaojun (James) Chen would like to dedicate this book to his lovely wife, Mengyan, for her understanding and care, and his amazing daughter, Jenny, for filling smiles in his life. He would also like to thank Steve for the opportunity to join General Photonics in 2004, and for his trust and support throughout the years while working at this highly innovative company.
Both of us are grateful to our formal colleagues at General Photonics for their help in turning many of our ideas on paper into real products (many of which are described in this book) and Susan Wey for editing most of the technical support documents of the company over the years (some of which are adapted in this book), including her help in editing this preface. Finally, we would like to express our sincere appreciations to Wiley editor Brett Kurzman, managing editor Sarah Lemore, cover editor Becky Cowan, and content refinement specialist Judit Anbu Hena, whose hard work and support make this book possible.
Las Vegas, NV 89109, USA
X. Steve Yao
San Gabriel, CA 91775, USA
Xiaojun (James) Chen
August 2022
1History of Light and Polarization
1.1 Early History of Light
Light is the most important element to the life on Earth, particularly to the existence of human beings. Light not only enables us to “see” for receiving visual information from our surroundings and communicating with others via gestures and expressions, but also provides the energy for living things to grow. The main source of light on Earth is the Sun, which provides the energy for the plants to grow via a process called photosynthesis (Morton 2009). While growing, the plants create sugars and carbohydrates (Stichler 2002), which release energy into the living things that digest them. Buried dead plants can also be turned into coal and fossil fuels by nature as a different form of energy. Another important source of light for humans has been fire, from ancient campfires using woods to last century's kerosene lamps using fossil fuels, which also originated from the Sun light. With the development of electric lights and power systems, electric lighting has effectively replaced firelight. Interestingly, the origin of the electrical energy is still the Sun light because it is produced by burning the coal or fossil oil, or by the direct conversion using solar panels via photovoltaic effect. Some species of animals generate their own light via a process called bioluminescence. For example, fireflies use light to locate mates, and vampire squids use it to hide themselves from prey.
The most recent form of man‐made light is laser beams, which are being widely utilized in human societies today, such as in optic fiber communication networks (the backbone of internet), printing (laser printers), navigation and guidance (optic gyroscopes and Lidar), medicine (laser diagnosis, surgical and treatment equipment), sensor (facial recognition in smart phones and temperature, pressure, and other sensors in industrial, medical, and defense equipment), and manufacturing (laser cutting and laser additive manufacturing), just to name a few. These laser applications have dramatically improved the quality of our lives behind scenes and many of us may not notice them. New laser based developments and applications are emerging almost every day to continue better our lives. That is why twenty‐first century is considered the century of optics by many, just as twentieth century was regarded as the century of electronics.
Humans have been trying to understand and utilize light since very early stage of our civilization. The early studies of light may likely be initialed from trying to understand vision because ancient men started to wonder why they could see, while the early man‐made optical devices may be for harvesting sun light. For example, the 3000‐year old Nimrud lens made with a quartz crystal unearthed in modern‐day Iraq was likely a sun‐light concentrator for starting fire. Bronze concave mirrors dating back around West Zhou period (c. 1046–771 BCE) unearthed in Shan'Xi, China, from 1972 to 1995 are also believed for concentrating sun light for fire‐starting. In fact, it was recorded in a book calledEtiquette of Zhou that the government had a dedicated official for using the concave mirror to start fire for religious rituals or ceremonies.
As early as sixth to fifth BCE, Ancient Indian developed some theories on light and believed that light rays were a stream of high velocity of tejas (fire) particles. In Ancient China, Mozi (c. 468–376 BCE), a renowned Chinese scientist and thinker during Warring States Period (c. 476–221 BCE) summarized 16 rules (eight each in two separate articles) regarding shadows, pin‐hole images, and mirror images in his book Mojing (Mo's Articles) around 388 BCE, describing the relationships between the shadows and the light source positions, the relationship between the images and pin‐hole positions, as well as the relationships between the image properties (size, location, and direction [inverted or upright]) and different types of mirrors (flat, concave, and convex).
Euclid of Alexandria (c. 325–265 BCE) is the first known author of a treatise on geometrical optics. His book, known as Euclid's Optics, influenced the work of later Greek, Islamic, and Western European Renaissance scientists and artists. In his book, Euclid observed that “things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal.” In the 36 propositions that follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. While Euclid had limited his analysis to simple direct vision, Hero of Alexandria (c. 10–70 CE) extended the principles of geometrical optics to consider problems of reflection (catoptrics) and demonstrated the equality of the angle of incidence and reflection on the grounds that this is the shortest path from the object to the observer. On this basis, he was able to define the fixed relation between an object and its image in a plane mirror. Specifically, the image appears to be as far behind the mirror as the object really is in front of the mirror. Claudius Ptolemy (c. 323–283 BCE), in his book Optics (known as Ptolemy's Optics), undertook studies of reflection and refraction of light on flat surfaces in the second century BCE. Both Euclid and Ptolemy believed that sight worked by the eyes emitting rays of light.
Ibn Sahl (c. 940–1000 CE), a Persian mathematician and scientist, is known to have compiled a commentary on Ptolemy's Optics and wrote an optical treaties around 984. He studied the optical properties of curved mirrors and lenses, and discovered the law of refraction which was mathematically equivalent to Snell's law. He used his law of refraction to compute the shapes of lenses and mirrors that focus light at a single point on the axis. Hasan Ibn al‐Haytham (c. 965–1040), an Arab mathematician, astronomer, and physicist, often referred to as “the father of modern optics,” studied the characteristics of light and the mechanism/process of vision, produced a comprehensive and systematic analysis of Greek optical theories, and wrote the influential Book of Optics. He was against Euclid and Ptolemy's opinion on eyes emitting light rays and insisted that vision occurs because rays enter the eyes and considered these rays as the forms of light and color. He then analyzed these rays according to the principles of geometrical optics and carried out various experiments with lenses, mirrors, reflections, and refractions to verify his analysis. He was an early proponent of the concept that a hypothesis must be supported by experiments based on confirmable procedures or mathematical evidence – an early pioneer in scientific method five centuries before Renaissance scientists. In the Far East, Shen Kuo (c. 960–1279), a Chinese polymathic scientist, was the first to have detailed description of camera obscura or pin‐hole imaging in his book Dreams Pool Essays in 1088. In the late thirteenth and early fourteenth centuries, Qutb‐al‐Din al‐Shirazi (1236–1311) and his student Kamal al‐Din al‐Farisi (1260–1320) continued the work of Ibn al‐Haytham, and they were among the first to give the correct explanations for the rainbow phenomenon. al‐Farisi published his findings in his book, The Revision of Optics (Kitab Tanqih al‐Manazir), for refining al‐Haytham's Book of Optics, which signified the beginning for humans to understand another important aspect of light: the color.
The English bishop, Robert Grosseteste (c. 1175–1253), may be the most influential figure in the understanding of light during the medieval Europe. He wrote on a wide range of scientific topics on the time of the origin and tended to apply mathematics and the Platonic metaphor of light in many of his writings. His works on light are more philosophical and have been credited with discussing light from four different perspectives: an epistemology of light, a metaphysics or cosmogony of light, an etiology of light, and a theology of light (Lindberg 1976). Grosseteste was the first of the Scholastics to fully understand Aristotle's vision of the dual path of scientific reasoning: generalizing from particular observations into a universal law, and then back again from universal laws to prediction of particulars. He had read several important works translated from Greek via Arabic and produced important work in optics of his own. In De Iride he wrote: “This part of optics, when well understood, shows us how we may make things a very long distance off appear as if placed very close, and large near things appear very small, and how we may make small things placed at a distance appear any size we want, so that it may be possible for us to read the smallest letters at incredible distances, or to count sand, or seed, or any sort of minute objects.” Grosseteste is now believed to have had a very modern understanding of color, as described in his treatise De Luce (On Light) written in about 1225. In De Luce, Grosseteste also explored the nature of matter and the cosmos, and described the birth of the Universe in an explosion, four centuries before Isaac Newton proposed gravity and seven centuries before the Big Bang theory. Other important figures in understanding of light during the medieval Europe include Roger Bacon (c. 1214–1294), John Pecham (died 1292), Witelo (born c. 1230, died between 1280 and 1314), and Theodoric Freiberg
