Abstract

For optical communication links using wavelength-division multiplexing over a long-haul fiber optic backbone, four-wave mixing (FWM) may lead to significant transmission impairment. Lightwaves traversing through a wavelength-routed optical network (WRON) encounter progressive linear and nonlinear interactions and periodic loss/gain mechanisms through lossy fiber segments and noisy optical amplifiers. In this paper, the FWM power accumulated and received at the end of each lightpath in a WRON is estimated through analytical modeling of lightwaves. While estimating FWM interference for a given lightpath, various feasible lightpath topology scenarios, such as the possibility of any other lightpath joining the given lightpath or departing the given lightpath at any intermediate node, or co-propagating along with the given lightpath till the given lightpath end, are taken into account. The transmission impairments from the accumulated FWM crosstalk along with the amplified spontaneous emission (ASE) noise components from the inline optical amplifiers are considered for evaluating the overall optical signal-to-noise ratios (OSNRs) at the receiving ends of lightpaths. The values of FWM contributions and the OSNR for each lightpath, estimated by using the proposed analytical model, help in setting up lightpaths in a WRON, as one can predict whether the lightpath under consideration could offer a desirable physical-layer performance. From our earlier work [Opt. Switching Networking, vol. 6, pp. 10–19, 2009], though we observe that the count-based assessment of FWM interference (wherein the total number of generated FWM components is estimated from the co-propagating lightpaths) offers a simple method, the power-based evaluation of FWM, as developed in this paper, gives a more precise estimate of the FWM impact of the lightpath in a WRON setting. In view of this, we also carry out FWM-aware and FWM-unaware lightpath topology designs (LTDs) and compare the results of the two LTDs, based on the count-based and the power-based estimates of FWM.

© 2012 OSA

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  1. A. Adhya and D. Datta, “Design methodology for WDM backbone networks using FWM-aware heuristic algorithm,” Opt. Switching Networking, vol. 6, pp. 10–19, Jan.2009.
    [CrossRef]
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    [CrossRef]
  3. C. V. Saradhi and S. Subramaniam, “Physical layer impairment aware routing (PLIAR) in WDM optical networks: issues and challenges,” IEEE Commun. Surv. Tutorials, vol. 11, no. 4, pp. 109–130, 2009.
    [CrossRef]
  4. B. Ramamurthy, D. Datta, H. Feng, J. P. Heritage, and B. Mukherjee, “Impact of transmission impairments on the teletraffic performance of wavelength-routed optical networks,” J. Lightwave Technol., vol. 17, no. 10, pp. 1713–1723, Oct.1999.
    [CrossRef]
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    [CrossRef]
  6. N. Shibata, R. P. Braun, and R. G. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron., vol. QE-23, no. 7, pp. 1205–1210, July1987.
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    [CrossRef]
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    [CrossRef]
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  13. A. Ghatak and K. Thyagarajan, Optical Electronics. Cambridge University Press, 2004, Reprinted.
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  15. J. Santos, J. Pedro, P. Monteiro, and J. Pires, “Impact of collocated regeneration and differential delay compensation in optical transport networks,” in IEEE EUROCON—Int. Conf. on Computer as a Tool (EUROCON), 2011, pp. 1–4.
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    [CrossRef]
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  19. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed.Academic Press, 2007.

2010 (1)

K. Christodoulopoulos, K. Manousakis, and E. M. Varvarigos, “Offline routing and wavelength assignment in transparent WDM networks,” IEEE/ACM Trans. Netw., vol. 18, no. 5, pp. 1557–1570, Oct.2010.
[CrossRef]

2009 (3)

A. Adhya and D. Datta, “Design methodology for WDM backbone networks using FWM-aware heuristic algorithm,” Opt. Switching Networking, vol. 6, pp. 10–19, Jan.2009.
[CrossRef]

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. S. Pareta, and I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, pp. 926–944, 2009.
[CrossRef]

C. V. Saradhi and S. Subramaniam, “Physical layer impairment aware routing (PLIAR) in WDM optical networks: issues and challenges,” IEEE Commun. Surv. Tutorials, vol. 11, no. 4, pp. 109–130, 2009.
[CrossRef]

2004 (1)

1999 (2)

1996 (1)

R. Ramaswami and K. N. Sivarajan, “Design of logical topologies for wavelength-routed optical networks,” IEEE J. Sel. Areas Commun., vol. 14, no. 5, pp. 840–851, June1996.
[CrossRef]

1992 (1)

1987 (1)

N. Shibata, R. P. Braun, and R. G. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron., vol. QE-23, no. 7, pp. 1205–1210, July1987.
[CrossRef]

1978 (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys., vol. 49, pp. 5098–5106, 1978.
[CrossRef]

1965 (1)

Adhya, A.

A. Adhya and D. Datta, “Design methodology for WDM backbone networks using FWM-aware heuristic algorithm,” Opt. Switching Networking, vol. 6, pp. 10–19, Jan.2009.
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed.Academic Press, 2007.

Azodolmolky, S.

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. S. Pareta, and I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, pp. 926–944, 2009.
[CrossRef]

Braun, R. P.

N. Shibata, R. P. Braun, and R. G. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron., vol. QE-23, no. 7, pp. 1205–1210, July1987.
[CrossRef]

Careglio, D.

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. S. Pareta, and I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, pp. 926–944, 2009.
[CrossRef]

Christodoulopoulos, K.

K. Christodoulopoulos, K. Manousakis, and E. M. Varvarigos, “Offline routing and wavelength assignment in transparent WDM networks,” IEEE/ACM Trans. Netw., vol. 18, no. 5, pp. 1557–1570, Oct.2010.
[CrossRef]

Datta, D.

Eiselt, M.

Feng, H.

Ghatak, A.

A. Ghatak and K. Thyagarajan, Optical Electronics. Cambridge University Press, 2004, Reprinted.

Heritage, J. P.

Hill, K. O.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys., vol. 49, pp. 5098–5106, 1978.
[CrossRef]

Inoue, K.

Jeunhomme, L. B.

L. B. Jeunhomme, Single-Mode Fiber Optics, Principles and Applications. Marcel Dekker, Inc., 1983.

Johnson, D. C.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys., vol. 49, pp. 5098–5106, 1978.
[CrossRef]

Kawasaki, B. S.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys., vol. 49, pp. 5098–5106, 1978.
[CrossRef]

Keiser, G.

G. Keiser, Optical Fiber Communications, 3rd ed.McGraw-Hill International Editions, 2000.

Klinkowski, M.

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. S. Pareta, and I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, pp. 926–944, 2009.
[CrossRef]

MacDonald, R. I.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys., vol. 49, pp. 5098–5106, 1978.
[CrossRef]

Malitson, I. H.

Manousakis, K.

K. Christodoulopoulos, K. Manousakis, and E. M. Varvarigos, “Offline routing and wavelength assignment in transparent WDM networks,” IEEE/ACM Trans. Netw., vol. 18, no. 5, pp. 1557–1570, Oct.2010.
[CrossRef]

Marin, E.

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. S. Pareta, and I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, pp. 926–944, 2009.
[CrossRef]

Monteiro, P.

J. Santos, J. Pedro, P. Monteiro, and J. Pires, “Impact of collocated regeneration and differential delay compensation in optical transport networks,” in IEEE EUROCON—Int. Conf. on Computer as a Tool (EUROCON), 2011, pp. 1–4.

Mukherjee, B.

Murata, H.

H. Murata, Handbook of Optical Fibers and Cables. Marcel Dekker, Inc., 1988.

Pareta, J. S.

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. S. Pareta, and I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, pp. 926–944, 2009.
[CrossRef]

Pedro, J.

J. Santos, J. Pedro, P. Monteiro, and J. Pires, “Impact of collocated regeneration and differential delay compensation in optical transport networks,” in IEEE EUROCON—Int. Conf. on Computer as a Tool (EUROCON), 2011, pp. 1–4.

Pires, J.

J. Santos, J. Pedro, P. Monteiro, and J. Pires, “Impact of collocated regeneration and differential delay compensation in optical transport networks,” in IEEE EUROCON—Int. Conf. on Computer as a Tool (EUROCON), 2011, pp. 1–4.

Ramamurthy, B.

Ramaswami, R.

R. Ramaswami and K. N. Sivarajan, “Design of logical topologies for wavelength-routed optical networks,” IEEE J. Sel. Areas Commun., vol. 14, no. 5, pp. 840–851, June1996.
[CrossRef]

R. Ramaswami and K. N. Sivarajan, Optical Networks, a Practical Perspective, 2nd ed.Morgan Kaufmann Publishers, 2004.

Santos, J.

J. Santos, J. Pedro, P. Monteiro, and J. Pires, “Impact of collocated regeneration and differential delay compensation in optical transport networks,” in IEEE EUROCON—Int. Conf. on Computer as a Tool (EUROCON), 2011, pp. 1–4.

Saradhi, C. V.

C. V. Saradhi and S. Subramaniam, “Physical layer impairment aware routing (PLIAR) in WDM optical networks: issues and challenges,” IEEE Commun. Surv. Tutorials, vol. 11, no. 4, pp. 109–130, 2009.
[CrossRef]

Shibata, N.

N. Shibata, R. P. Braun, and R. G. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron., vol. QE-23, no. 7, pp. 1205–1210, July1987.
[CrossRef]

Sivarajan, K. N.

R. Ramaswami and K. N. Sivarajan, “Design of logical topologies for wavelength-routed optical networks,” IEEE J. Sel. Areas Commun., vol. 14, no. 5, pp. 840–851, June1996.
[CrossRef]

R. Ramaswami and K. N. Sivarajan, Optical Networks, a Practical Perspective, 2nd ed.Morgan Kaufmann Publishers, 2004.

Subramaniam, S.

C. V. Saradhi and S. Subramaniam, “Physical layer impairment aware routing (PLIAR) in WDM optical networks: issues and challenges,” IEEE Commun. Surv. Tutorials, vol. 11, no. 4, pp. 109–130, 2009.
[CrossRef]

Thyagarajan, K.

A. Ghatak and K. Thyagarajan, Optical Electronics. Cambridge University Press, 2004, Reprinted.

Tomkos, I.

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. S. Pareta, and I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, pp. 926–944, 2009.
[CrossRef]

Varvarigos, E. M.

K. Christodoulopoulos, K. Manousakis, and E. M. Varvarigos, “Offline routing and wavelength assignment in transparent WDM networks,” IEEE/ACM Trans. Netw., vol. 18, no. 5, pp. 1557–1570, Oct.2010.
[CrossRef]

Waarts, R. G.

N. Shibata, R. P. Braun, and R. G. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron., vol. QE-23, no. 7, pp. 1205–1210, July1987.
[CrossRef]

Way, W. I.

Wu, M.

Comput. Netw. (1)

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. S. Pareta, and I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, pp. 926–944, 2009.
[CrossRef]

IEEE Commun. Surv. Tutorials (1)

C. V. Saradhi and S. Subramaniam, “Physical layer impairment aware routing (PLIAR) in WDM optical networks: issues and challenges,” IEEE Commun. Surv. Tutorials, vol. 11, no. 4, pp. 109–130, 2009.
[CrossRef]

IEEE J. Quantum Electron. (1)

N. Shibata, R. P. Braun, and R. G. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron., vol. QE-23, no. 7, pp. 1205–1210, July1987.
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

R. Ramaswami and K. N. Sivarajan, “Design of logical topologies for wavelength-routed optical networks,” IEEE J. Sel. Areas Commun., vol. 14, no. 5, pp. 840–851, June1996.
[CrossRef]

IEEE/ACM Trans. Netw. (1)

K. Christodoulopoulos, K. Manousakis, and E. M. Varvarigos, “Offline routing and wavelength assignment in transparent WDM networks,” IEEE/ACM Trans. Netw., vol. 18, no. 5, pp. 1557–1570, Oct.2010.
[CrossRef]

J. Appl. Phys. (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys., vol. 49, pp. 5098–5106, 1978.
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Opt. Switching Networking (1)

A. Adhya and D. Datta, “Design methodology for WDM backbone networks using FWM-aware heuristic algorithm,” Opt. Switching Networking, vol. 6, pp. 10–19, Jan.2009.
[CrossRef]

Other (7)

R. Ramaswami and K. N. Sivarajan, Optical Networks, a Practical Perspective, 2nd ed.Morgan Kaufmann Publishers, 2004.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed.Academic Press, 2007.

L. B. Jeunhomme, Single-Mode Fiber Optics, Principles and Applications. Marcel Dekker, Inc., 1983.

G. Keiser, Optical Fiber Communications, 3rd ed.McGraw-Hill International Editions, 2000.

A. Ghatak and K. Thyagarajan, Optical Electronics. Cambridge University Press, 2004, Reprinted.

H. Murata, Handbook of Optical Fibers and Cables. Marcel Dekker, Inc., 1988.

J. Santos, J. Pedro, P. Monteiro, and J. Pires, “Impact of collocated regeneration and differential delay compensation in optical transport networks,” in IEEE EUROCON—Int. Conf. on Computer as a Tool (EUROCON), 2011, pp. 1–4.

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Figures (11)

Fig. 1
Fig. 1

Lightpaths (LP1, LP2, LP3, LP4) set up over the fiber topology in a given WRON.

Fig. 2
Fig. 2

Architecture of a wavelength-routing node using OXC [4] ( { w i } represents the operating wavelengths of the optical switches).

Fig. 3
Fig. 3

An example lightpath LP1 with FWM electric fields generated in different fiber sections. LP1 consists of two fiber links and several fiber sections.

Fig. 4
Fig. 4

LP1, LP2, and LP3 interfere to generate FWM in LP4.

Fig. 5
Fig. 5

Physical topology of the 14-node National Science Foundation Network (NSFNET) [15].

Fig. 6
Fig. 6

Dispersion profile for conventional single-mode fiber.

Fig. 7
Fig. 7

Dispersion profile for dispersion-shifted fiber.

Fig. 8
Fig. 8

Wavelength assignment for long and short lightpaths.

Fig. 9
Fig. 9

(Color online) Distribution of cumulative FWM count and OSNR (dB) for HLDA with a logical degree of 4.

Fig. 10
Fig. 10

(Color online) Distribution of inverse-cumulative FWM count and OSFR (dB) for HLDA with a logical degree of 4. Missing points in the plots and the corresponding missing lines connecting these points represent the cases wherein the OSFR approaches infinity due to the absence of FWM interference for the respective lightpaths.

Fig. 11
Fig. 11

(Color online) Distribution of OSNR (dB) for HLDA and FA-HLDA with a logical degree of 4.

Tables (5)

Tables Icon

Table I Parameters of Sellmeier Dispersion Equation [14]

Tables Icon

Table II Fiber Specifications

Tables Icon

Table III System Parameters and Their Respective Values

Tables Icon

Table IV Performance of HLDA

Tables Icon

Table V Distribution of Cumulative FWM Count, Inverse-Cumulative FWM Count, OSNR, and OSFR Using HLDA for Different Lightpath Indices With a Logical Degree of 4

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

G in L N L tap L dm = 1 .
G out L sw L mx L tap = 1 .
G k L k = 1 ; 1 k ( N 1 ) ,
E F ( k ) = i γ d E p ( 1 ) E q ( 1 ) E r ( 1 ) * exp α l k 2 exp [ i ( β p q r + Δ β ) d k + i β p q r l k ] 1 exp ( α l k + i Δ β l k ) α i Δ β ,
E i ( 1 ) = E i exp [ i β i d i ] ,
E F L E ( k ) = E F ( k ) exp [ i β p q r d r l ] G k L sw ,
E F L E ( k ) = i γ d E p ( 1 ) E q ( 1 ) E r ( 1 ) * exp [ i β p q r d t l ] exp [ i Δ β d k ] 1 exp ( α l k ) exp ( i Δ β l k ) α i Δ β L sw ,
V = 2 π λ a n 1 2 n 2 2 ,
b ( V ) = ( 1 . 1428 0 . 9960 V ) 2 ,
b ( V ) = β 2 k 0 2 n 2 2 k 0 2 n 1 2 k 0 2 n 2 2 ,
β ( ω i ) = β ( ω r ) + ( ω i ω r ) [ d β ( ω k ) / d ω ] + ( ω i ω r ) 2 [ λ r 2 D c ( λ r ) / 4 π c ] + ( ω i ω r ) 3 ( λ r 4 / 24 π 2 C 2 ) [ d D c ( λ r ) / d λ ] ,
D mat ( λ ) = λ c d 2 n 1 d λ 2 ,
D wg ( λ ) = n 1 Δ R I c λ V d 2 ( b ( V ) V ) d V 2 = n 1 Δ R I c λ V ( V b ) ,
V ( V b ) = 0 . 08 + 0 . 549 ( 2 . 834 V ) 2 .
d D c d λ = d D mat d λ + d D wg d λ .
Δ β = 2 π λ r 2 c Δ f p r Δ f q r ( D c ( λ r ) + ( Δ f p r + Δ f q r ) λ r 2 2 c d D c ( λ r ) d λ ) .
P F = | E F | 2 .
p ase ( W , λ i ) = 2 n sp ( G out 1 ) h υ i B o L tap ,
p ase ( W , λ i ) = p ase ( W 1 , λ i ) [ k = 1 N 1 G k ] G in [ k = 1 N 1 L k ] L N L dm L sw L mx G out L tap 2 + 2 n sp ( G 1 1 ) h ν i B 0 [ k = 2 N 1 G k ] G in [ k = 2 N 1 L k ] L N L dm L sw L mx G out L tap 2 + + 2 n sp ( G N 1 1 ) h ν i B 0 G in L N L dm L sw L mx G out L tap 2 + 2 n sp ( G in 1 ) h ν i B 0 L dm L sw L mx G out L tap + 2 n sp ( G out 1 ) h ν i B 0 L tap = p ase ( W 1 , λ i ) + 2 n sp ( G f 1 ) h ν i B 0 ( N 1 ) + 2 n sp ( G in 1 ) h ν i B 0 L dm + 2 n sp ( G out 1 ) h ν i B 0 L tap ,
p ase ( W , λ i ) = p ase ( W 1 , λ i ) L sw + 2 n sp ( G f 1 ) h υ i B o × ( N 1 ) L sw + 2 n sp ( G in 1 ) h υ i B o L dm L sw .
n 2 1 = a 1 λ 2 λ 2 b 1 + a 2 λ 2 λ 2 b 2 + a 3 λ 2 λ 2 b 3 ,
ρ FWM = i = 1 N FWM N section ( i ) ,