LinChBulk_v1 Class Reference

Linear channel model. More...

Inherits unit.

Public Member Functions
function	LinChBulk_v1 (in param)
	Class constructor. More...
function	traverse (in obj, in in)
	Traverse function. More...
function	cd_loading (in param, in Ein)
	Chromatic dispersion loading. More...
function	pmd_loading (in obj, in in)
	PMD loading. More...
Public Member Functions inherited from unit
function	traverseNode (in obj)
	Set unique ID when creating a unit. More...
function	connectOutput (in obj, in uobj, in unitOutput, in nextUnitInput)
	Specify where signal should go next. More...
function	connectOutputs (in obj, in units, in destInputs)
	Specify where signal should go next. More...
function	writeInputBuffer (in obj, in sig, in inputId)
	write input buffer
function	horzcat (in varargin)
	horizontal concatenation
function	vertcat (in varargin)
	vertical concatenation
function	setparams (in obj, in params, in REQUIRED_PARAMS, in QUIET_PARAMS)
	set parameters More...
function	view (in obj)
	Show interactive GUI through unit_view-class.

Static Public Member Functions
static function	random_unitary (in N)
	Generates a random unitary matrix. More...
static function	random_hermitian (in N)
	Generates a random hermitian matrix. More...
static function	stokes_from_U (in U)
	Converts unitary matrix to equivalent rotation matrix. More...
static function	D_lookup (in lambda)
	Dispersion lookup table. More...

Public Attributes
Property	nOutputs
	Number of outputs.
Property	nInputs
	Number of inputs.
Property	D
	dispersion coeff. (ps/nm km)
Property	S
	2nd order dispersion coeff. (ps/nm^2 km)
Property	L
	length (km)
Property	U
	Jones matrix.
Property	DGD
	modulus of DGD/PMD vector (s)
Property	tau
	vector of DGDs (s)
Property	P
	Matrix of principal modes.
Property	DGD_mode
	How to specify DGD {'set' | 'random'}.
Property	loss
	loss (dB/km)
Public Attributes inherited from unit
Property	inputBuffer
	Buffer for storing inputs as we traverse the graph.
Property	nextNodes
	Children nodes.
Property	destInputs
	Destination inputs in children.
Property	results
	For storing results.
Property	label
Property	draw
	enable/disable plotting
Property	nInputs
	Number of signals traverse expects.
Property	nOutputs
	Number of outputs traverse expects.

Detailed Description

Linear channel model.

Linear fiber optic channel model with polarization (mode) mixing, chromatic dispersion, PMD, and loss

Observations

1. Number of modes supported by fiber is set by the dimension of the input signal
2. Fiber parameters are taken from a look-up table for SMF28 unless otherwise specified.
3. Mode mixing is based on random matrix generation unless otherwise specified.
4. The general assumption is that the fiber supports "principal modes" and that these have a bandwidth that is larger than the signal bandwidth. This is fine for SMF, but potentially problematic for multimode fiber.

Examples

param = struct('D', 1e-6, 'S', .0092, 'L', 40, 'loss', .34);
channel = LinChBulk_v1(channel);

Will construct a 40km channel with .34 dB/km loss and negligible 1st order dispersion (typical parameters at 1310). These parameters will be fixed regardless of the wavelength of the input signal. The code

param = struct('L', 40);
channel = LinChBulk_v1(channel);
signal = signal_interface(field, struct('Fc', const.c/1310e-9, ...));
sigout = channel.traverse(signal);

Will also construct a 40km channel with .34 dB/km loss and negligible 1st order dispersion. If the input signal were at 1550 instead, the dispersion, loss, etc. would be different.

To remove the effect of polarization mixing, specify the Jones matrix of the fiber as an identity matrix:

param = struct('L', 40, 'U', eye(2));
channel = LinChBulk_v1(channel);

Author

Molly Piels

Version

2

Definition at line 58 of file LinChBulk_v1.m.

Constructor & Destructor Documentation

function LinChBulk_v1::LinChBulk_v1

(

in

param

)

Class constructor.

Constructs an object of type LinChBulk

Generally, if fiber parameters are not specified, the model will assume SMF-28 and use a lookup table based on the input signal's wavelength.

Parameters

param.D	Dispersion coefficient [ps/nm*km].
param.S	Dispersion slope [(ps/nm^2 km)] [Default 0].
param.L	Fiber length [km] [Default: 0].
param.U	Unitary matrix describing mode mixing [au] [Default: randomly generated]
param.DGD	Modulus of DGD/PMD vector [s] [Default: 0]
param.DGD_mode	How to interpret param.DGD: 'set' = the DGD is param.DGD (only makes sense for SMF); 'random' = the DGD is drawn randomly from an appropriate PDF with this mean. [Default: set]
param.loss	Fiber loss [dB/km]
param.tau	Vector of differential group delays to apply [s]
param.P	Matrix describing polarization alignment of DGD vector [au] [Default: randomly generated]

Return values

obj	An instance of the class ClassTemplate_v1

Member Function Documentation

function LinChBulk_v1::cd_loading	(	in	param,
		in	Ein
	)

Chromatic dispersion loading.

Chromatic dispersion loading - operates in frequency domain

Parameters

Ein	input signal (signal_interface)

Return values

Eout	output signal (signal_interface)
H	Transfer function of dispersion operator

static function LinChBulk_v1::D_lookup ( in  lambda )

static

Dispersion lookup table.

Dispersion lookup table based on Corning SMF 28

Parameters

lambda

wavelength in m

Return values

D_out

in ps/(nm km)

function LinChBulk_v1::pmd_loading	(	in	obj,
		in	in
	)

PMD loading.

PMD loading

Modes of operation: PMD can either be set ('set' mode) or drawn from an appropriate statistical distribution ('random' mode). In 'set' mode, for a 2-mode fiber, you specify the modulus of the DGD vector (DGD property), and the associated delays are +/- tau/2. For N-mode fiber, you can either set the modulus (DGD property) or specify the actual delays (tau property) In random mode, model draws from a chi distribution with <# of modes> degrees of freedom for actual modulus of PMD vector (Maxwell if N=2).

Main method: Delays are applied as shifts to randomly oriented principal modes. See J. P. Gordon and H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," Proc. Natl. Acad. Sci., vol. 97, no. 9, pp. 4541–4550, 2000. or K.-P. Ho and J. M. Kahn, "Statistics of Group Delays in Multimode Fiber with Strong Mode Coupling," J. Light. Technol., vol. 29, pp. 3119–3128, 2011.

Parameters

U	Jones matrix of fiber
in	input signal (signal_interface class)

Return values

Eout	output signal
mod_tau	modulus of DGD vector

static function LinChBulk_v1::random_hermitian ( in  N )

static

Generates a random hermitian matrix.

Generates a random Hermitian matrix with zero trace

Parameters

N	matrix dimension

Return values

H	NxN Hermitian matrix

static function LinChBulk_v1::random_unitary ( in  N )

static

Generates a random unitary matrix.

Generates a random unitary matrix. If called many times, the set of returned matrices will have appropriately statistically distributed eigenvalues. This is important for channel capacity calculations. The algorithm is from F. Mezzadri, "How to generate random matrices from the classical compact groups,” arXiv Prepr. math-ph/0609050, vol. 54, no. 5, pp. 592–604, 2006.

Parameters

N	matrix dimension

Return values

U	NxN unitary matrix

static function LinChBulk_v1::stokes_from_U ( in  U )

static

Converts unitary matrix to equivalent rotation matrix.

Maps U in C^2 to R in R^3 - returns rotation part of Mueller matrix of fiber given a fiber Jones matrix. Only applies to 2x2 Jones matrices.

Parameters

U	Jones matrix (must be 2x2)

Return values

R	rotation matrix

function LinChBulk_v1::traverse ( in  obj, in  in  )

virtual

Traverse function.

Applies polarization mixing, then chromatic dispersion, then PMD, then loss

Return values

out	signal after propagation through channel
results.Jones	Jones matrix of fiber
results.PMD	modulus of PMD vector
results.Stokes	Rotation matrix of fiber in Stokes space (SMF only)

Reimplemented from unit.

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The documentation for this class was generated from the following file:

• library/ch/LinChBulk_v1.m