Impact of Transmission Impairments on Demultiplexed Channels in WDMPONs Employing AWG-Based Remote Nodes

Jayashree Ratnam; Saswat Chakrabarti; Debasish Datta

doi:10.1364/JOCN.2.000848

Journal of Optical Communications and Networking
Vol. 2,
Issue 10,
pp. 848-858
(2010)
•https://doi.org/10.1364/JOCN.2.000848

Impact of Transmission Impairments on Demultiplexed Channels in WDMPONs Employing AWG-Based Remote Nodes

Jayashree Ratnam, Saswat Chakrabarti, and Debasish Datta

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Jayashree Ratnam, Saswat Chakrabarti, and Debasish Datta, "Impact of Transmission Impairments on Demultiplexed Channels in WDMPONs Employing AWG-Based Remote Nodes," J. Opt. Commun. Netw. 2, 848-858 (2010)

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About this Article
History
- Original Manuscript: February 22, 2010
- Revised Manuscript: July 6, 2010
- Manuscript Accepted: August 16, 2010
- Published: September 29, 2010

Abstract

This paper deals with the performance evaluation of a passive optical network (PON) using wavelength division multiplexing (WDM) by employing an arrayed-waveguide grating (AWG) in the remote node (RN). In such WDM-based PONs (WDMPONs) the RN demultiplexes the downstream WDM signal via distinct output ports through a static wavelength-routing mechanism. An analytical model is developed for evaluating the bit error rate (BER) performance of the demultiplexed channels as a function of the output port location in the AWG by incorporating a novel spectral-to-spatial domain transformation technique. The proposed model captures the impact of finite laser linewidth as well as the AWG characteristics in determining the received signal power at the individual optical network unit (ONU) attached to the output port (due to spectral-to-spatial mapping). Furthermore, the BER model accounts for several transmission impairments, including beat noise due to interchannel crosstalk in the AWG. Results indicate that the signal power captured by the output ports of AWGs and hence their BER values are not only determined by the Gaussian focal-field pattern of the AWG but also by the power spillover from adjacent ports for broader linewidths and higher data rates. A significant interplay is observed between data rate, source linewidth, and relevant device parameters while examining the loss and BER characteristics of a given AWG-based WDMPON.

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Parameter	Description
m	diffraction order in the AWG
FSR	free spectral range $(= f_{c} ∕ m)$
c	velocity of light in vacuum
$λ_{c}$	wavelength of the central channel (at port #0)
$R_{a}$	focal length of focusing slab waveguide
$N_{c}$	refractive index of channel waveguide
$β_{c}$	propagation constant in the channel waveguide
$N_{FPR}$	refractive index of free propagation region
$β_{FPR}$	propagation constant in the channel waveguide
$N_{g}$	refractive index of free propagation region
$β_{g}$	propagation constant in the free propagation region
$N_{g}$	group refractive index of waveguide $mode = N_{C} + f \frac{d N_{c}}{d f}$
$β_{g}$	propagation constant in the waveguide mode
$Δ L$	path difference between adjacent waveguides in the array
V	normalized V parameter of the waveguide material (fiber) $V = \frac{2 π a}{λ} \sqrt{(n_{1}^{2} - n_{2}^{2})}$ , where a, $n_{1}$ , and $n_{2}$ are fiber parameters
$w_{wg}$	width of the channel waveguide
$w_{e}$	effective mode width of the $waveguide = w_{wg} ⌊ 0.5 + \frac{1}{V - 0.6} ⌋ 1 < V < 10$
$w_{0}$	FWHM beam width of the far $field = w_{e} \sqrt{\frac{2}{π}}$
θ	dispersion angle due to path difference between adjacent waveguides
$θ_{in}$	diffraction angle in the input slab region
$θ_{op}$	diffraction angle in the output slab region

Parameter	Description
K	Boltzmann constant
$B_{e}$	noise equivalent bandwidth ( $= data$ rate/2)
$η_{th}$	noise power spectral density
T	absolute temperature in degrees Kelvin
$R_{L}$	load resistance
q	electronic charge
ϵ	laser extinction ratio $(= 0.1)$
$R_{λ}$	photodetector responsivity $(= 0.8)$
RIN	relative intensity noise coefficient $(= - 150 dB ∕ Hz)$
$n_{adj}$	number of adjacent ports contributing to crosstalk $(= 2)$
$ξ_{pol}$	polarization mismatch factor $(= 0.5)$
$p_{r - on}$	probability of data symbol being “1”
$P_{sig}^{i}$	optical signal power of the ith channel
$P_{adj \pm 1}^{i}$	optical signal power from adjacent channel
$P_{x t}^{i}$	optical crosstalk power of the ith channel
$σ_{th}^{2}$	thermal noise variance
$σ_{sh 0}^{2}$	shot noise variance for “0” bit
$σ_{sh 1}^{2}$	shot noise variance for “1” bit
$σ_{rin 0}^{2}$	laser relative intensity noise variance for “0” bit
$σ_{rin 1}^{2}$	laser relative intensity noise variance for “1” bit
$σ_{s g_x t}^{2}$	signal–crosstalk beat variance
$σ_{x t}^{2}$	crosstalk variance from adjacent channels
$σ_{x t_x t}^{2}$	crosstalk–crosstalk beat variance

Parameter	Description
m	diffraction order in the AWG
FSR	free spectral range $(= f_{c} ∕ m)$
c	velocity of light in vacuum
$λ_{c}$	wavelength of the central channel (at port #0)
$R_{a}$	focal length of focusing slab waveguide
$N_{c}$	refractive index of channel waveguide
$β_{c}$	propagation constant in the channel waveguide
$N_{FPR}$	refractive index of free propagation region
$β_{FPR}$	propagation constant in the channel waveguide
$N_{g}$	refractive index of free propagation region
$β_{g}$	propagation constant in the free propagation region
$N_{g}$	group refractive index of waveguide $mode = N_{C} + f \frac{d N_{c}}{d f}$
$β_{g}$	propagation constant in the waveguide mode
$Δ L$	path difference between adjacent waveguides in the array
V	normalized V parameter of the waveguide material (fiber) $V = \frac{2 π a}{λ} \sqrt{(n_{1}^{2} - n_{2}^{2})}$ , where a, $n_{1}$ , and $n_{2}$ are fiber parameters
$w_{wg}$	width of the channel waveguide
$w_{e}$	effective mode width of the $waveguide = w_{wg} ⌊ 0.5 + \frac{1}{V - 0.6} ⌋ 1 < V < 10$
$w_{0}$	FWHM beam width of the far $field = w_{e} \sqrt{\frac{2}{π}}$
θ	dispersion angle due to path difference between adjacent waveguides
$θ_{in}$	diffraction angle in the input slab region
$θ_{op}$	diffraction angle in the output slab region

Parameter	Description
K	Boltzmann constant
$B_{e}$	noise equivalent bandwidth ( $= data$ rate/2)
$η_{th}$	noise power spectral density
T	absolute temperature in degrees Kelvin
$R_{L}$	load resistance
q	electronic charge
ϵ	laser extinction ratio $(= 0.1)$
$R_{λ}$	photodetector responsivity $(= 0.8)$
RIN	relative intensity noise coefficient $(= - 150 dB ∕ Hz)$
$n_{adj}$	number of adjacent ports contributing to crosstalk $(= 2)$
$ξ_{pol}$	polarization mismatch factor $(= 0.5)$
$p_{r - on}$	probability of data symbol being “1”
$P_{sig}^{i}$	optical signal power of the ith channel
$P_{adj \pm 1}^{i}$	optical signal power from adjacent channel
$P_{x t}^{i}$	optical crosstalk power of the ith channel
$σ_{th}^{2}$	thermal noise variance
$σ_{sh 0}^{2}$	shot noise variance for “0” bit
$σ_{sh 1}^{2}$	shot noise variance for “1” bit
$σ_{rin 0}^{2}$	laser relative intensity noise variance for “0” bit
$σ_{rin 1}^{2}$	laser relative intensity noise variance for “1” bit
$σ_{s g_x t}^{2}$	signal–crosstalk beat variance
$σ_{x t}^{2}$	crosstalk variance from adjacent channels
$σ_{x t_x t}^{2}$	crosstalk–crosstalk beat variance

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Journal of Optical Communications and Networking