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Physics & Astronomy International Journal

Review Article Volume 3 Issue 1

Design optimization of non-zero dispersion shifted fiber for latency mitigation in optical fiber network

Faramarz E Seraji,1 Shima Safari,2 Marzieh Sadat Kiaee1

1Optical Communication Group, Communication Technol Dept, Iran telecom Research Center, Iran
2Electrical and Computer Eng. Dept. North Branch, Islamic Azad University, Iran

Correspondence: Faramarz E Seraji, Faculty member Optical Communication Group, Department of Communication Technology, Iran Telecom Research Center, Tehran, Iran, Tel 9821 8497 7723, Fax 9821 8863 0047

Received: December 19, 2018 | Published: January 29, 2019

Citation: Seraji FE, Safari S, Kiaee MS. Design optimization of non-zero dispersion shifted fiber for latency mitigation in optical fiber network. Phys Astron Int J. 2019;3(1):33-36. DOI: 10.15406/paij.2019.03.00153

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Abstract

Latency has an important role in new generation optical networks. There are a few ways to minimize latency in the optical networks. One way is to use silica in the core of optical fiber during the design of fabrication process. In this study, we have designed a non-zero dispersion shifted fibers (NZDSF) used as the transmission medium with minimal latency in an optical network. Using our optical fiber, the latency was improved by 0.016µs.

Keywords: design optimization, low-latency, NZDSF, optical fiber network

Introduction

Latency describes the time lapse between a transmitted and received signal. This parameter is crucial issue for high frequency traders associated with financial markets, In today’s marketing, high-frequency trading firms pay a premium for a latency advantage as just a few microseconds of delay in receiving trading information relative to a competitor can result in loss of deals with big financial impact.1,2

Latency in a link develops as a result of the delay caused by the following different factors:

  1. the signal processing in the electronics, the amplifiers, the dispersion compensating modules (if any) and
  2. the delay caused by optical propagations of the signal along the fiber length, the longer the fiber, the more latency.1,3

Besides the latency contributions from each of the above factors, it is apparent that the biggest contribution comes from the transmission fibers.4 As the transmission length exceeds 10km, the fiber becomes almost wholly responsible for the latency. The latency introduced by the fiber, is directly proportional to the group index of the fiber. So reducing the group index can lower the latency contribution from the transmission fiber.4

Latency is one of the important issues of new generation networks. To achieve lower latency, we need to use optical fiber with lower refractive index. So the core must be doped by using silica.

A typical pure silica core1 has a 0.4% lower group index relative to traditional fibers made of Ge-doped silica core [5]. This apparent insignificant latency would be noticeable in long haul propagation across the Atlantic Ocean. This time difference will be highly attractive to traders working between stock exchanges in two respective continents.

In order to optimize the latency of an optical network at higher distances, we should optimize the parameters of the optical fiber. During the light transmission, there are several parameters that affect on the quality of the received optical signals. One of these parameters is the nonlinear effects.6 To overcome nonlinearity, large effective area fibers (LEAF) have been employed.7 In the first generation, zero-dispersion shifted fibers (ZDSF) were used to achieve minimum loss and dispersion; but by increasing the number of signal wavelengths in DWDM networks, four-wave mixing (FWM) occurred which induces inter-channel crosstalk during the transmission of light.8,9

Besides ZDSFs, non-zero dispersion shifted fibers (NZDSF) have been designed which avoid the phase matching condition and reduce the effects of FWM in optical networks.1,4 By using NZDSF we may obtain a large effective area which minimizes the nonlinear effects;7 however, larger effective area makes fiber more sensitive to bending loss. So, choosing optimum parameters during the design of an optical fiber is very crucial for optical networks performances.

To start-up, we have studied the effects of other parameters while optimizing the optical fibers. During the design process, we have faced with many limitations. 1 Using optical fibers with very large effective area may cause a very high mode field diameter (MFD).10 In order to overcome this issue; the effective area must be limited. In a study, the upper limit of effective area in a single mode fiber was reported around 370 μ m 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaGI8o GaaOyBaKqbaoaaCaaaleqajeaibaqcLbmacaGIYaaaaaaa@3B98@ .11 In a study, an NZDSF with effective area of 95 μ m 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaGI8o GaaOyBaKqbaoaaCaaaleqajeaibaqcLbmacaGIYaaaaaaa@3B98@ , dispersion slop of 0.1ps/nm2km and bending loss of 0.005 dB has been designed. 12

An NZDSF with effective area of 102 μ m 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaGI8o GaaOyBaKqbaoaaCaaaleqajeaibaqcLbmacaGIYaaaaaaa@3B98@ , dispersion of 4ps/nm.km, dispersion slope of 0.06 ps/nm2km and bending loss of 0.0013dB/km at the wavelength 1550 nmwas designed and reported, where one dopant was employed in the core region of the optical fiber.13

In another study, these parameters were optimized by using three dopants to make different refractive index in the core; where the effective area was increased up to 120 μ m 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaGI8o GaaOyBaKqbaoaaCaaaleqajeaibaqcLbmacaGIYaaaaaaa@3B98@  and the bending loss was decreased down to 1.4× 10 14 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaaIXa GaaiOlaiaaisdacqGHxdaTcaaIXaGaaGimaKqbaoaaCaaajeaybeqc KfaG=haajugWaiabgkHiTiaaigdacaaI0aaaaaaa@42D5@ dB/km14. At wavelength 1550 nm, the dispersion, effective nonlinear refractive index and 1’st order PMD resulted in 5.78 ps/nm.km, 1.41× 10 16 c m 2 /W MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaaIXa GaaiOlaiaaisdacaaIXaGaey41aqRaaGymaiaaicdajuaGdaahaaWc beqcKfaG=haajugWaiabgkHiTiaaigdacaaI2aaaaKqzGeGaaO4yai aak2gajuaGdaahaaWcbeqcbasaaKqzadGaaOOmaaaajugibiaak+ca caGIxbaaaa@4AA7@ and 8.77× 10 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaaI4a GaaiOlaiaaiEdacaaI3aGaey41aqRaaGymaiaaicdajuaGdaahaaqc basabKazba4=baqcLbmacqGHsislcaaIYaaaaaaa@42A3@  ps, respectively.

Besides all above parameters’ optimizations, one important parameter in the next generation communication systems is the signal latency between transmitting and receiving ends. As it is reported before, the typical group delay in a conventional single mode fiber is about 5μs/km MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqadeGacaGaaiaabeqaamaabaabaaGcbaqcLbsacaGI1a GaaOiVdiaakohacaGIVaGaaO4Aaiaak2gaaaa@3C2A@ .15

Recently, we have designed an optical fiber network used in IoT in order to evaluate the quality of the received signals from 50 km of our designed NZDSF fiber. In this theoretical study, a non–zero dispersion shifted fiber (NZDSF) with a particular refractive index which had a minimum latency at 1352 nm was designed with an effective area of 102μ m 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaaigdacaaIWaGaaGOma8aacqaH8oqBcaGITbqcfa4aaWba aSqabKqaGeaajugWaiaaikdaaaaaaa@3E5F@ and macrobending loss of 7.31× 10 51 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0=wr0lb9qq=Ngj=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaaiEdacaGGUaGaaG 4maiaaigdacqGHxdaTcaaIXaGaaGimamaaCaaaleqabaGaeyOeI0Ia aGynaiaaigdaaaaaaa@403F@ 51dB/km. In comparison to a commercial NZDSF, the latency was improved by 0.002μs.16

To the best of our knowledge, considerable academic works have not been reported in the literatures on the present subject. In this paper, we have attempted to optimize design of an NZDSF fiber with minimal signal latency with an optimum effective area.

1Corning’s ultra-low-loss products (like SMF-28R ULL fiber and Vascade R EX2000 fiber).

Refractive index profile

As we know, the latency of light signal in a vacuum is 3.336μs MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0=wr0lb9qq=Ngj=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaabaaaaaaaaapeGaaG 4maiaac6cacaaIZaGaaG4maiaaiAdapaGaeqiVd0MaaO4Caaaa@3DC1@ , so we must find the ways to minimize the signal latency of propagating light in an optical fiber medium for most signal velocity. To achieve this aim, we should optimize the refractive index profile of the transmission fiber for minimal group index so as to mitigate the fiber group index, thus results in higher group velocity of propagating signal. We have designed an NZDSF with a core of exponential profile assumed with Germanium dopant.

Adding Germanium or Fluorine will increase or reduce the refractive index of pure silica, respectively. The refractive index n of m  mole-percentage doped material can be defined as follows:16

n= n 0 2 + m m 1 ( n 1 2 n 0 2 ) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gacqGH9aqpda Gcaaqaaiaad6gadaqhaaWcbaGaaGimaaqaaiaaikdaaaGccqGHRaWk daWcaaqaaiaad2gaaeaacaWGTbWaaSbaaSqaaiaaigdaaeqaaaaaki aacIcacaWGUbWaa0baaSqaaiaaigdaaeaacaaIYaaaaOGaeyOeI0Ia amOBamaaDaaaleaacaaIWaaabaGaaGOmaaaakiaacMcaaSqabaaaaa@46F2@               (1)

where n 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gadaqhaaWcba GaaGimaaqaaaaaaaa@38CA@  is the refractive index of the host material and n 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gadaqhaaWcba GaaGymaaqaaaaaaaa@38CB@  is the refractive index of doped material with m 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad2gadaWgaaWcba GaaGymaaqabaaaaa@38C9@  mole percentage. Then the exponential function of the core is as follows:16

n(x)=[n(0)n(w)]× e e1 ×exp x/w + e.n(w)n(0) e1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gacaGGOaGaam iEaiaacMcacqGH9aqpcaGGBbGaamOBaiaacIcacaaIWaGaaiykaiab gkHiTiaad6gacaGGOaGaam4DaiaacMcacaGGDbGaey41aq7aaSaaae aacaWGLbaabaGaamyzaiabgkHiTiaaigdaaaGaey41aqRaciyzaiaa cIhacaGGWbWaaeWaaeaacqGHsislcaWG4bGaai4laiaadEhaaiaawI cacaGLPaaacqGHRaWkdaWcaaqaaiaadwgacaGGUaGaamOBaiaacIca caWG3bGaaiykaiabgkHiTiaad6gacaGGOaGaaGimaiaacMcaaeaaca WGLbGaeyOeI0IaaGymaaaaaaa@604C@     (2)

where n(0) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gacaGGOaGaaG imaiaacMcaaaa@39F6@  and n(w) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gacaGGOaGaam 4DaiaacMcaaaa@3A38@  are the refractive indices at x=0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadIhacqGH9aqpca aIWaaaaa@39AD@  and x=w MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadIhacqGH9aqpca WG3baaaa@39EF@ , respectively, and e=1.6× 10 19 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadwgacqGH9aqpca aIXaGaaiOlaiaaiAdacqGHxdaTcaaIXaGaaGimamaaCaaaleqabaGa eyOeI0IaaGymaiaaiMdaaaaaaa@4131@ .

In order to calculate the latency of this fiber, we should find the group delay of light with refractive index of n MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gaaaa@37E3@  for a fiber length of L by the first frequency-derivation of the propagation constant given as:

G d =L dβ dω =z dλ dω d(n k 0 ) dλ = 2πcL ω 2 ( k 0 dn dλ +n dn dλ )= L c (nλ dn dλ ) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadEeadaWgaaWcba GaamizaaqabaGccqGH9aqpcaWGmbWaaSaaaeaacaWGKbGaeqOSdiga baGaamizaiabeM8a3baacqGH9aqpcaWG6bWaaSaaaeaacaWGKbGaeq 4UdWgabaGaamizaiabeM8a3baadaWcaaqaaiaadsgacaGGOaGaamOB aiaadUgadaWgaaWcbaGaaGimaaqabaGccaGGPaaabaGaamizaiabeU 7aSbaacqGH9aqpdaWcaaqaaiabgkHiTiaaikdacqaHapaCcaWGJbGa amitaaqaaiabeM8a3naaCaaaleqabaGaaGOmaaaaaaGccaGGOaGaam 4AamaaBaaaleaacaaIWaaabeaakmaalaaabaGaamizaiaad6gaaeaa caWGKbGaeq4UdWgaaiabgUcaRiaad6gadaWcaaqaaiaadsgacaWGUb aabaGaamizaiabeU7aSbaacaGGPaGaeyypa0ZaaSaaaeaacaWGmbaa baGaam4yaaaacaGGOaGaamOBaiabgkHiTiabeU7aSnaalaaabaGaam izaiaad6gaaeaacaWGKbGaeq4UdWgaaiaacMcaaaa@7286@    (3)

where N g =[nλ(dn/dλ)] MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6eadaWgaaqcba AaaiaadEgaaeqaaOGaeyypa0Jaai4waiaad6gacqGHsislcqaH7oaB caGGOaGaamizaiaad6gacaGGVaGaamizaiabeU7aSjaacMcacaGGDb aaaa@4663@ is the effective group index of the fiber and λ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabeU7aSbaa@38A4@  is the operating wavelength. The dispersion coefficient of the propagating light is computed by the following expression:

D total = L c λ d 2 N g d λ 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadseadaWgaaqcba AaaiaadshacaWGVbGaamiDaiaadggacaWGSbaabeaakiabg2da9iab gkHiTmaalaaabaGaamitaaqaaiaadogaaaGaeq4UdW2aaSaaaeaaca WGKbWaaWbaaSqabeaacaaIYaaaaOGaamOtamaaBaaajeaObaGaam4z aaWcbeaaaOqaaiaadsgacqaH7oaBdaahaaWcbeqaaiaaikdaaaaaaa aa@4ACC@             (4)

As we know, more effective area may decrease the none-linearity; so it is important to minimize the nonlinearity of fiber in our design. Assume that E(x,y) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadweacaGGOaGaam iEaiaacYcacaWG5bGaaiykaaaa@3BBE@  is the optical mode field distribution, then the effective area can be defined by using the following expression:16

Also, the nonlinear effective index in a fiber can be found as follows:

n eff = n(x,y)|F(x,y) | 4 dxdy |F(x,y) | 2 dxdy MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gadaWgaaWcba GaamyzaiaadAgacaWGMbaabeaakiabg2da9maalaaabaWaa8qaaeaa daWdbaqaaiaad6gacaGGOaGaamiEaiaacYcacaWG5bGaaiykaiaacY hacaWGgbGaaiikaiaadIhacaGGSaGaamyEaiaacMcacaGG8bWaaWba aSqabeaacaaI0aaaaOGaamizaiaadIhacaWGKbGaamyEaaWcbeqab0 Gaey4kIipaaSqabeqaniabgUIiYdaakeaadaWdbaqaamaapeaabaGa aiiFaiaadAeacaGGOaGaamiEaiaacYcacaWG5bGaaiykaiaacYhada ahaaWcbeqaaiaaikdaaaGccaWGKbGaamiEaiaadsgacaWG5baaleqa beqdcqGHRiI8aaWcbeqab0Gaey4kIipaaaaaaa@5FFC@           (6)

where n(x,y) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gacaGGOaGaam iEaiaacYcacaWG5bGaaiykaaaa@3BE7@  is the user-defined spatially dependent nonlinear refractive index of the various layers of the fiber and F(x,y) is the normalized mode field pattern.

Theory of signal latency

The total end to end network latency is the combination of all latencies incurred between the transmitting and receiving ends and all other elements, such as witches and routers etc. Therefore, the total latency l T MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabloriSnaaBaaale aacaqGubaabeaaaaa@3924@  is summarized as:

l T = l trans + l rec + allappliancesinlink ( l proc + l for + l que ) + links l f MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabloriSnaaBaaale aacaqGubaabeaakiaaykW7caqG9aGaaGPaVlabloriSnaaBaaajeaW baGaamiDaiaadkhacaWGHbGaamOBaiaadohaaSqabaGccaGIRaGaeS 4eHW2aaSbaaKqaahaacaWGYbGaamyzaiaadogaaSqabaGccqGHRaWk daaeqbqaaiaacIcacqWItecBdaWgaaqcbaAaaiaadchacaWGYbGaam 4BaiaadogaaSqabaGccaGIRaGaeS4eHW2aaSbaaKqaahaacaWGMbGa am4BaiaadkhaaSqabaGccaGIRaGaeS4eHW2aaSbaaKqaahaacaWGXb GaamyDaiaadwgaaSqabaGccaGGPaaaleaacaWGHbGaamiBaiaadYga caaMc8UaamyyaiaadchacaWGWbGaamiBaiaadMgacaWGHbGaamOBai aadogacaWGLbGaam4CaiaaykW7caWGPbGaamOBaiaaykW7caWGSbGa amyAaiaad6gacaWGRbaabeqdcqGHris5aOGaey4kaSYaaabuaeaacq WItecBdaWgaaqcbaCaaiaadAgaaSqabaaabaGaamiBaiaadMgacaWG UbGaam4AaiaadohaaeqaniabggHiLdaaaa@808C@          (7)

where l trans MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabloriSnaaBaaaje aWbaGaamiDaiaadkhacaWGHbGaamOBaiaadohaaSqabaaaaa@3DD8@ , l trans MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabloriSnaaBaaaje aWbaGaamiDaiaadkhacaWGHbGaamOBaiaadohaaSqabaaaaa@3DD8@ , l proc MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabloriSnaaBaaaje aObaGaamiCaiaadkhacaWGVbGaam4yaaWcbeaaaaa@3CBF@ , l for MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabloriSnaaBaaaje aWbaGaamOzaiaad+gacaWGYbaaleqaaaaa@3BED@ , l que MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabloriSnaaBaaaje aWbaGaamyCaiaadwhacaWGLbaaleqaaaaa@3BF1@ , and l f MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabloriSnaaBaaaje aWbaGaamOzaaWcbeaaaaa@3A02@  are latencies due to transmitter, receiver, processing, forwarding, queuing, and propagation of optical signals in the fiber, respectively

To focus our study, we consider the latency due to signal propagation in the transmission fiber which causes a major latency in an optical fiber network. The speed of an optical signal in a fiber is known as group velocity v g MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadAhadaWgaaqcba AaaiaadEgaaSqabaaaaa@39AD@  that can be determined by the effective group refractive index N g MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6eadaWgaaqcba AaaiaadEgaaeqaaaaa@397A@  by:

v g = c N g MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadAhadaWgaaqcba AaaiaadEgaaSqabaGccqGH9aqpdaWcaaqaaiaadogaaeaacaWGobWa aSbaaSqaaiaadEgaaeqaaaaaaaa@3DA0@            (8)

where c is the velocity of light in a vacuum. By knowing the length of the transmission fiber L and group velocity, the fiber latency can simply be calculated as:

l f = L v g = L N g c MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaGabbiab=nriSnaaBa aaleaacaWGMbaabeaakiabg2da9iaaykW7daWcaaqaaiaadYeaaeaa caWG2bWaaSbaaKqaGgaacaWGNbaaleqaaaaakiabg2da9maalaaaba Gaamitaiaad6eadaWgaaqcbaAaaiaadEgaaSqabaaakeaacaWGJbaa aaaa@44EA@             (9)

Design procedure

We have started our study by using the conventional NZDSF of Corning Inc. with dispersion of 4ps/nm.km, effective area of 72μ m 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaakEdacaGIYaGaaO iVdiaak2gadaahaaWcbeqaaiaakkdaaaaaaa@3BA0@  and effective group refractive index of 1.4693. Therefore, the latency l 1550 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaGabbiab=nriSnaaBa aaleaacaaIXaGaaGynaiaaiwdacaaIWaaabeaaaaa@3B41@ of this optical fiber at wavelength 1550 nm for the given values is calculated as follows:

V 1550nm =c/ N g = 299792.458 1.4693 =204037.608km/s MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKaaGjaadAfakmaaBa aaleaacaaIXaGaaGynaiaaiwdacaaIWaGaamOBaiaad2gaaeqaaKaa Gjabg2da9iaadogakiaac+cacaWGobWaaSbaaKqaahaacaWGNbaale qaaOGaeyypa0ZaaSaaaeaacaaIYaGaaGyoaiaaiMdacaaI3aGaaGyo aiaaikdacaGGUaGaaGinaiaaiwdacaaI4aaabaGaaGymaiaac6caca aI0aGaaGOnaiaaiMdacaaIZaaaaiabg2da9iaaikdacaaIWaGaaGin aiaaicdacaaIZaGaaG4naiaac6cacaaI2aGaaGimaiaaiIdacaaMc8 UaaGPaVlaaykW7caaMc8UaaO4Aaiaak2gacaGIVaGaaO4Caaaa@623F@            (10)

l 1550 = 1 km V 1550nm = 1 204037.608 =4.901μs MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaGabbiab=nriSnaaBa aaleaacaaIXaGaaGynaiaaiwdacaaIWaaabeaakiabg2da9maalaaa baGaaGymamaaBaaaleaacaWGRbGaamyBaaqabaaakeaacaWGwbWaaS baaSqaaiaaigdacaaI1aGaaGynaiaaicdacaWGUbGaamyBaaqabaaa aOGaeyypa0ZaaSaaaeaacaaIXaaabaGaaGOmaiaaicdacaaI0aGaaG imaiaaiodacaaI3aGaaiOlaiaaiAdacaaIWaGaaGioaaaacqGH9aqp caaI0aGaaiOlaiaaiMdacaaMc8UaaGimaiaaigdacaaMc8UaaGPaVl aaykW7caGI8oGaaO4Caaaa@5B6C@    (11)

where V is the velocity of light in fiber, c is the velocity of light in a vacuum, N g MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6eadaWgaaqcba CaaiaadEgaaSqabaaaaa@39A5@  is the effective group refractive index.

We have started our design procedure by employing the profile of an optical fiber which was used to achieve high negative dispersion in a dispersion compensating fiber (DCF).17 Since our first aim was to design an NZDSF with an appropriate dispersion, we have modified the sample core profile into an exponential function.

There are some literature reports that revealed the exponential profile would decrease the loss level.18,19 Accordingly, we have used two silica-based dopants with refractive index of 1.4–1.46 in the cladding region. By employing the proposed parameters’ values of the refractive profile given in Table 1, we have proposed a profile as illustrated in Figure 1, showing the refractive index and percentage of the refractive index difference.

Figure 1Exponential refractive index profile of the designed NZDSF.

Parameters

Regions

# 1 (Core)

#2

#3

#4

#5

Profile regions

Exponential

Gap

Ring

Gap

Clad

Width (μm)

2.2

0.5

0.8

1

58

Refractive Index

1.460 Max-1.446 Min

1.4448

1.45

1.4448

1.4462

Table 1 The proposed parameters’ values of the refractive index profile

The refractive index profile is divided into 5 Regions. The Region 1 forms the core of the fiber with a radius of 2.2 μ m MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaikdacaGGUaGaaG OmaiabeY7aTjaak2gaaaa@3BC9@ with an exponential variation of the refractive index changing from 1.446 to 1.460. The Region 2 is a gap of 0.5 μ m MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaicdacaGGUaGaaG ynaiabeY7aTjaak2gaaaa@3BCA@ with refractive index of 1.4448 between the core and the Region 3 with a width of 0.8 μ m MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaicdacaGGUaGaaG ioaiabeY7aTjaak2gaaaa@3BCD@ and refractive index of 1.45, considered as a refractive index ring at the vicinity of the core in the cladding.

Region 4 is yet another gap between the ring and the cladding with a width of 1μm MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaigdacqaH8oqBca GITbaaaa@3A5A@  and refractive index of 1.4448. The final Region 5 is forming the major part of the cladding with a span of 58 and refractive index of 1.4462, as shown in Figure 1.

Figure 2 shows the dispersion of the designed profile. As it is noted, total dispersion and dispersion slope are 3.089ps/nm.km MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaapeGaaG 4maiaac6cacaaIWaGaaGioaiaaiMdapaGaaOiCaiaakohacaGIVaGa aOOBaiaak2gacaGIUaGaaO4Aaiaak2gaaaa@4220@ and 0.0973ps/n m 2 .km MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaapeGaaG imaiaac6cacaaIWaGaaGyoaiaaiEdacaaIZaWdaiaakchacaGIZbGa aO4laiaak6gacaGITbWaaWbaaSqabeaacaaIYaaaaOGaaOOlaiaakU gacaGITbaaaa@43CC@ , respectively, at wavelength 1550 nm. The effective area of our profile is 130μ m 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaakgdacaGIZaGaaO imaiaakY7acaGITbWaaWbaaSqabeaacaGIYaaaaaaa@3C57@ . Because of this large effective area, there will be a limitation in bending, so also in the bending loss, as depicted in Figure 3. Above 1550 nm, the macro-bending loss increases with a higher slope.

Figure 2 Dispersion of the designed NZDSF profile versus wavelength. 1.5138 μm, Slope: 0.09730 ps/nm2.km.

Figure 3 Bending losses of the designed NZDSF profile versus wavelength.

The macro- and micro-bending losses in this profile are 0.79 and 1.28dB/km, respectively. Material loss is 0.19 dB/km and splices loss in the condition of splicing two matched optical fibers, is 4.77 dB.

We have found that the minimum latency is obtained at the wavelength of 1510 nm which is 1.4884μs MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaapeGaaG ymaiaac6cacaaI0aGaaGioaiaaiIdacaaI0aWdaiabeY7aTjaakoha aaa@3E41@ . Using Eq. 3 the group index of the above profile is 1.4644 at the wavelength 1550 nm. Replacing this amount in Eqs. 8 and 9 the estimated latency is obtained as 4.31μs. MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaapeGaaG inaiaac6cacaaIZaGaaGyma8aacqaH8oqBcaGIZbGaaOOlaaaa@3D76@  But the latency at the same wavelength is 4.884μs MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaapeGaaG inaiaac6cacaaI4aGaaGioaiaaisdapaGaeqiVd0MaaO4Caaaa@3D86@ ;so we have 0.574μs MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaapeGaaG imaiaac6cacaaI1aGaaG4naiaaisdapaGaeqiVd0MaaO4Caaaa@3D7E@  tolerance between the estimated and practical latency.

In Table 2, our obtained results are tabulated and are compared to the data of the large effective area fibers reported in Coning data sheet.

Parameters

Our model @

Corning’s NZDSF @

1550 nm

1310 nm

1550 nm

1310 nm

Group index

1.4644

1.4648

1.4693

-

Group delay (μs/km)

4.885

4.886

4.901

-

Group velocity (km/s)

204720.335

204664.431

204037.608

-

Latency (μs/km)

4.885

4.886

4.901

Dispersion (ps/nm.km)

3.23

-21.59

6-Apr

-

Effective area (μm2)

130

60

72

-

Material loss (dB/km)

0.19

0.36

0.19

<0.4

Macrobending loss (dB/km)

0.81

1.63

<0.5

-

PMD (ps)

18.06

-

9.5

-

Table 2 Designed values compared to the data of NZDSF reported by Coning Inc

For the next step, we have employed our designed NZDSF in an optical network to evaluate how far the light will be transmitted without using EDFA and DCF and can be detected with desirable quality. For this aim, we have designed an optical network based on an optical transmitter and a receiver with the bit rate of 10Gb/s. The received signal at the distance of 80kmwas monitored by using eye-diagram as shown in Figure 4. The quality factor and minimum bit-error rate of this signal were 10.91 and 5.03× 10 28 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaiwdacaGGUaGaaG imaiaaiodacqGHxdaTcaaIXaGaaGimamaaCaaaleqabaGaeyOeI0Ia aGOmaiaaiIdaaaaaaa@3FFC@ , respectively, which are desirable amounts for this distance of transmission.20,21

Figure 4 Eye-diagram of the received signals at the distance of 80 km.

Conclusion

In this study, we have designed an NZDSF with refractive index of 1.4644 at wavelength of 1550 nm which had minimum latency at 1352 nm. In comparison to Corning NZDSF, the latency for the designed NZDSF has improved about 0.016μs MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaapeGaaG imaiaac6cacaaIWaGaaGymaiaaiAdaiiaapaGae8hVd0MaaO4Caaaa @3D7A@ per kilometer The effective area is 130μ m 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wj0lH8qi=NMi=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaakgdacaGIZaGaaO imaiaakY7acaGITbWaaWbaaSqabeaacaGIYaaaaaaa@3C57@  and macro-bending loss is obtained as 0.79 dB/km. The dispersion of this fiber is 3.23ps/nm.km which is comparable to Corning NZDSF fiber.

We have employed our designed NZDSF in an optical fiber network in order to evaluate the quality of the received signals from 80 km of our fiber. The results have revealed that without using optical amplifier and DCF, the quality factor and minimum bit-error rate have been obtained as 10.91 and 5.03×10-28

respectively.

Acknowledgments

The authors acknowledge the allocated study mission project with the Permit No. 2210, in Communication Technology Dept., at Iran Telecom Research Center.

Conflict of interest

Authors declare there is no conflicts of interest.

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