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eISSN: 2576-4543

Physics & Astronomy International Journal

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Received: January 01, 1970 | Published: ,

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Due to ever–increasing demands for optical fibers with low–latency used in IoT optical fiber networks, in this theoretical study, a non–zero dispersion shifted fiber (NZDSF) with a particular refractive index which had a minimum latency at 1352 nm is designed. In comparison to a commercial NZDSF, the latency has improved by 0.002 μs MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaGI8o GaaO4Caaaa@3AE3@  in the designed NZDSF with an effective area of 102 μ m 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH8o qBcaGITbqcfa4aaWbaaKqaGeqabaqcLbmacaGIYaaaaaaa@3E0E@ and macro bending loss of 7.31× 10 51  dB/km MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaaI3a GaaiOlaiaaiodacaaIXaGaey41aqRaaGymaiaaicdajuaGdaahaaqc basabeaajugWaiabgkHiTiaaiwdacaaIXaaaaKqzGeaeaaaaaaaaa8 qacaGGGcGaamizaiaadkeacaGGVaGaam4Aaiaad2gaaaa@4997@ . The dispersion of this fiber is found to be 1.10625ps/nm.km which is comparable to the commercial NZDSF fiber.

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. The results have shown that without using optical amplifier and DCF, the quality factor and minimum bit–error rate are obtained as 8.17 and 10 16 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaaIXa GaaGimaKqbaoaaCaaajeaibeqaaKqzadGaeyOeI0IaaGymaiaaiAda aaaaaa@3E7E@ , respectively.

Keywords: latency, NZDSF, optical networks, optimization

Introduction

In recent years, dense wavelength division multiplexing (DWDM) networks have been implemented as a result of increasing demands for a massive bandwidth in long–haul systems and internet of things (IoT) optical fiber networks.

During light transmission, there are many parameters which affect the quality of the received optical signals. One of these parameters is the nonlinear effects.1 To overcome nonlinearity effects, large effective area fibers (LEAF) have been employed.2 At 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, the effect of four–wave mixing (FWM) was observed which induces inter–channel crosstalk during the light transmission in optical links.3–4

Besides ZDSFs, non–zero dispersion shifted fibers (NZDSF) have been designed to avoid the phase matching condition and reduce the effects of FWM in optical networks.2,4 By using NZDSF, we may obtain a large effective area which minimizes the nonlinear effects;2 however, larger effective area makes fiber more sensitive to bending loss. So, the choice of optimum parameters during the design of an optical fiber are very important.

Using optical fibers with very large effective area may cause a very high mode field diameter (MFD).5 In order to avoid this outcome, effective area must be limited and optimized. 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@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaGI8o GaaOyBaOWaaWbaaSqabKqaGeaajugWaiaakkdaaaaaaa@3AF7@ .6 In a study, an NZDSF with effective area of 95 μ m 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH8o qBcaGITbWcdaahaaqcbasabeaajugWaiaakkdaaaaaaa@3B58@ , dispersion slope of 0.1 ps/n m 2 km MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaaicdacaGGUaGaaGymaiaacckapaGaaOiCaiaakohacaGI VaGaaOOBaiaak2galmaaCaaajeaibeqaaKqzadGaaOOmaaaajugibi aakUgacaGITbaaaa@434B@ and bending loss of 0.005 dB has been designed.7

An NZDSF with effective area of 102 μ m 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaaigdacaaIWaGaaGOmaiaacckapaGaaOiVdiaak2galmaa CaaajeaibeqaaKqzadGaaOOmaaaaaaa@3E71@ , dispersion of 4ps/nm.km, dispersion slope of 0.06 ps/n m 2 km MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaaicdacaGGUaGaaGimaiaaiAdacaGGGcWdaiaakchacaGI ZbGaaO4laiaak6gacaGITbWcdaahaaqcbasabeaajugWaiaakkdaaa qcLbsacaGIRbGaaOyBaaaa@440A@ and bending loss of 0.0013dB/km at the wavelength 1550nmwas designed in a report.8 One do pant has been employed in the core region of this optical fiber.

In another study, these amounts have been optimized by using three dopants regions with different refractive index in the core; then the effective area was increased up to 120 μ m 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaaigdacaaIYaGaaGimaiaacckapaGaaOiVdiaak2galmaa CaaajeaibeqaaKqzadGaaOOmaaaaaaa@3E71@ and the bending loss was decreased down to 1.4× 10 14  dB/km MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaaIXa GaaiOlaiaaisdacqGHxdaTcaaIXaGaaGimaSWaaWbaaKqaGeqabaqc LbmacqGHsislcaaIXaGaaGinaaaajugibabaaaaaaaaapeGaaiiOai aadsgacaWGcbGaai4laiaadUgacaWGTbaaaa@4620@ .9 At the wavelength of 1550nm, the dispersion, effective nonlinear refractive index and 1st order PMD were 5.78 ps/nm.km MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacPqFH0xe9v8qqaqFD0xXdHaVhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaaGynaiaac6cacaaI3aGaaGioaiaabcca caWGWbGaam4Caiaac+cacaWGUbGaamyBaiaac6cacaWGRbGaamyBaa aa@4661@ , 1.41× 10 16 c m 2 /W MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaaIXa GaaiOlaiaaisdacaaIXaGaey41aqRaaGymaiaaicdalmaaCaaajeai beqcKfaG=haajugWaiabgkHiTiaaigdacaaI2aaaaKqzGeGaaO4yai aak2galmaaCaaajeaibeqaaKqzadGaaOOmaaaajugibiaak+cacaGI xbaaaa@4999@ and 8.77× 10 2  ps MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaaI4a GaaiOlaiaaiEdacaaI3aGaey41aqRaaGymaiaaicdalmaaCaaajeai beqaaKqzadGaeyOeI0IaaGOmaaaajugibabaaaaaaaaapeGaaiiOai aadchacaWGZbaaaa@43D6@ , respectively.

Another important parameter in the next generation transmission communication systems is the latency. As it is reported before, the typical group delay in a conventional single mode fiber is about 5 μs/km MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeGabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaaI1aGaaiiOa8aacqaH8oqBcaGIZbGaaO4laiaakUgacaGI Tbaaaa@3EBA@ .10 Regarding optical network latency due to physical layer, much works have not been reported in the literatures. In our study, we have designed an NZDSF with positive dispersion with a minimal latency and an optimum effective area.

Design procedure

We have started our study by using the Corning conventional NZDSF with a dispersion of 4 ps/nm.km, effective area of 72 μ m 2 , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaGI3a GaaOOmaabaaaaaaaaapeGaaiiOa8aacaGI8oGaaOyBaSWaaWbaaKqa GeqabaqcLbmacaGIYaaaaKqzGeGaaiilaaaa@3F00@ and effective group refractive index of 1.4693. By assuming above values, we can calculate the latency MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeWabmGaaiaacaqabeaadaqaaqaaaOqaaGabbKqzGeGae8 3eHWgaaa@387C@ of the corresponding optical fiber by the following expressions at wavelength 1550 nm:

V 1550 =c/ n eff = 299792.458 1.4693 =204037.608km/s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGwb WcdaWgaaqcbasaaKqzadGaaGymaiaaiwdacaaI1aGaaGimaaqcbasa baqcLbsacqGH9aqpcaWGJbGaai4laiaad6galmaaBaaajeaibaqcLb macaWGLbGaamOzaiaadAgaaKqaGeqaaKqzGeGaeyypa0JcdaWcaaqa aKqzGeGaaGOmaiaaiMdacaaI5aGaaG4naiaaiMdacaaIYaGaaiOlai aaisdacaaI1aGaaGioaaGcbaqcLbsacaaIXaGaaiOlaiaaisdacaaI 2aGaaGyoaiaaiodaaaGaeyypa0JaaGOmaiaaicdacaaI0aGaaGimai aaiodacaaI3aGaaiOlaiaaiAdacaaIWaGaaGioaiaaykW7caGIRbGa aOyBaiaak+cacaGIZbaaaa@60BC@  (1)

1550 = 1 km V 1550 = 1 204037.608 =4.901μs MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaceeqcLbsacq WFtecBlmaaBaaajeaibaqcLbmacaaIXaGaaGynaiaaiwdacaaIWaaa jeaibeaajugibiabg2da9OWaaSaaaeaajugibiaaigdalmaaBaaaje aibaqcLbmacaWGRbGaamyBaaqcbasabaaakeaajugibiaadAfakmaa BaaajeaibaqcLbmacaaIXaGaaGynaiaaiwdacaaIWaaaleqaaaaaju gibiabg2da9OWaaSaaaeaajugibiaaigdaaOqaaKqzGeGaaGOmaiaa icdacaaI0aGaaGimaiaaiodacaaI3aGaaiOlaiaaiAdacaaIWaGaaG ioaaaacqGH9aqpcaaI0aGaaiOlaiaaiMdacaaMc8UaaGimaiaaigda caaMc8UaaOiVdiaakohaaaa@5DB1@  (2)

where V MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeWabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeGaamOvaa aa@3824@ is the phase velocity of light in a specific medium, c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeWabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeGaam4yaa aa@3831@ is the velocity of light in a vacuum, n eff MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGUb WcdaWgaaqcbasaaKqzadGaamyzaiaadAgacaWGMbaajeaibeaaaaa@3BC7@ is the effective group refractive index, and MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeWabmGaaiaacaqabeaadaqaaqaaaOqaaGabbKqzGeGae8 3eHWgaaa@387C@ is the latency of optical signals at wavelength of 1550 nm.

As we know, the latency of light in vacuum is 3.336 μs/km MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeWabmGaaiaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaaIZaGaaiOlaiaaiodacaaIZaGaaGOnaiaacckapaGaeqiV d0MaaO4Caiaak+cacaGIRbGaaOyBaaaa@41B6@ ; so we should find a way to minimize the latency of light in optical fiber used as a transmission medium in an optical fiber network. For this purpose, we have designed an NZDSF with a core of exponentially changing refractive index profile.

As we know, adding Germanium or Fluorine atoms would increase or reduce the refractive index of pure silica, respectively. The refractive index n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeWabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeGaamOBaa aa@383C@ of m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeWabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeGaamyBaa aa@383B@ mole–percentage doped material can be defined as follows:11

n= n 0 2 + m m 1 ( n 1 2 n 0 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGUb Gaeyypa0JcdaGcaaqaaKqzGeGaamOBaSWaa0baaKqaGeaajugWaiaa icdaaKqaGeaajugWaiaaikdaaaqcLbsacqGHRaWkkmaalaaabaqcLb sacaWGTbaakeaajugibiaad2galmaaBaaajeaibaqcLbmacaaIXaaa jeaibeaaaaqcLbsacaGGOaGaamOBaSWaa0baaKqaGeaajugWaiaaig daaKqaGeaajugWaiaaikdaaaqcLbsacqGHsislcaWGUbWcdaqhaaqc basaaKqzadGaaGimaaqcbasaaKqzadGaaGOmaaaajugibiaacMcaaS qabaaaaa@53D9@  (3)

where n 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGUb GcdaWgaaqcbasaaKqzadGaaGimaaWcbeaaaaa@39A1@ is the refractive index of the host material and n 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGUb WcdaWgaaqcbasaaKqzadGaaGymaaqcbasabaaaaa@39C2@ is the refractive index of doped material. Thus, the exponential profile function of the core can be shown as follows:11

n(x)=[ e/(e1) ][n(0)n(w)]exp( x/w )+[ en(w)n(0) ]/(e1) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGUb GaaiikaiaadIhacaGGPaGaeyypa0JcdaWadaqaaKqzGeGaamyzaiaa c+cacaGGOaGaamyzaiabgkHiTiaaigdacaGGPaaakiaawUfacaGLDb aajugibiaacUfacaWGUbGaaiikaiaaicdacaGGPaGaeyOeI0IaamOB aiaacIcacaWG3bGaaiykaiaac2facaaMc8UaciyzaiaacIhacaGGWb GcdaqadaqaaKqzGeGaeyOeI0IaamiEaiaac+cacaWG3baakiaawIca caGLPaaajugibiabgUcaROWaamWaaeaajugibiaadwgacaaMc8Uaam OBaiaacIcacaWG3bGaaiykaiabgkHiTiaad6gacaGGOaGaaGimaiaa cMcaaOGaay5waiaaw2faaKqzGeGaai4laiaacIcacaWGLbGaeyOeI0 IaaGymaiaacMcaaaa@696A@  (4)

where n(0) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGUb GaaiikaiaaicdacaGGPaaaaa@396C@ and n(w) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGUb GaaiikaiaadEhacaGGPaaaaa@39AE@ are the refractive indices at x=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeWabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeGaamiEai abg2da9iaaicdaaaa@3A06@ and x=w MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeWabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeGaamiEai abg2da9iaadEhaaaa@3A48@ , respectively, and e=1.6× 10 19 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGLb Gaeyypa0JaaGymaiaac6cacaaI2aGaey41aqRaaGymaiaaicdalmaa CaaajeaibeqaaKqzadGaeyOeI0IaaGymaiaaiMdaaaaaaa@41FF@ . 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@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeWabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeGaamOBaa aa@383C@ for the distance of L MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeWabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeGaamitaa aa@381A@ by the first frequency–derivation of the propagation constant as follows:12

l=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@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGSb Gaeyypa0JaamitaOWaaSaaaeaajugibiaadsgacqaHYoGyaOqaaKqz GeGaamizaiabeM8a3baacqGH9aqpcaWG6bGcdaWcaaqaaKqzGeGaam izaiabeU7aSbGcbaqcLbsacaWGKbGaeqyYdChaaOWaaSaaaeaajugi biaadsgacaGGOaGaamOBaiaadUgakmaaBaaajeaibaqcLbmacaaIWa aaleqaaKqzGeGaaiykaaGcbaqcLbsacaWGKbGaeq4UdWgaaiaaykW7 cqGH9aqpkmaalaaabaqcLbsacqGHsislcaaIYaGaeqiWdaNaam4yai aadYeaaOqaaKqzGeGaeqyYdCNcdaahaaWcbeqcbasaaKqzadGaaGOm aaaaaaqcLbsacaGGOaGaam4AaOWaaSbaaKqaGeaajugWaiaaicdaaS qabaGcdaWcaaqaaKqzGeGaamizaiaad6gaaOqaaKqzGeGaamizaiab eU7aSbaacqGHRaWkcaWGUbGcdaWcaaqaaKqzGeGaamizaiaad6gaaO qaaKqzGeGaamizaiabeU7aSbaacaGGPaGaeyypa0JcdaWcaaqaaKqz GeGaamitaaGcbaqcLbsacaWGJbaaaiaacIcacaWGUbGaeyOeI0Iaeq 4UdWMcdaWcaaqaaKqzGeGaamizaiaad6gaaOqaaKqzGeGaamizaiab eU7aSbaacaGGPaaaaa@8143@      (5)

The total dispersion of light is calculated by the following expression:

D total = L c λ d 2 N eff d λ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGeb WcdaWgaaqcbasaaKqzadGaamiDaiaad+gacaWG0bGaamyyaiaadYga aKqaGeqaaKqzGeGaeyypa0JaeyOeI0IcdaWcaaqaaKqzGeGaamitaa GcbaqcLbsacaWGJbaaaiabeU7aSPWaaSaaaeaajugibiaadsgalmaa CaaajeaibeqaaKqzadGaaGOmaaaajugibiaad6ealmaaBaaajeaiba qcLbmacaWGLbGaamOzaiaadAgaaKqaGeqaaaGcbaqcLbsacaWGKbGa eq4UdWMcdaahaaWcbeqcbasaaKqzadGaaGOmaaaaaaaaaa@53EF@                                                                   (6)

As we know, more effective area would decrease the none–linearity effects; so it is important to minimize the none–linearity of fiber in our design. Assume that E(x,y) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGfb GaaiikaiaadIhacaGGSaGaamyEaiaacMcaaaa@3B34@ is the optical mode field distribution, then the effective area can be defined by using the following expressing:13

A eff = [ |E(x,y) | 2 dxdy ] 2 |E(x,y) | 4 dxdy MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGbb WcdaWgaaqcbasaaKqzadGaamyzaiaadAgacaWGMbaajeaibeaajugi biabg2da9OWaaSaaaeaajugibiaacUfakmaapeaabaWaa8qaaeaaju gibiaacYhacaWGfbGaaiikaiaadIhacaGGSaGaamyEaiaacMcacaGG 8bWcdaahaaqcbasabeaajugWaiaaikdaaaqcLbsacaWGKbGaamiEai aadsgacaWG5bGaaiyxaSWaaWbaaKqaGeqabaqcLbmacaaIYaaaaaWc beqabKqzGeGaey4kIipaaSqabeqajugibiabgUIiYdaakeaadaWdba qaamaapeaabaqcLbsacaGG8bGaamyraiaacIcacaWG4bGaaiilaiaa dMhacaGGPaGaaiiFaOWaaWbaaSqabKqaGeaajugWaiaaisdaaaqcLb sacaWGKbGaamiEaiaadsgacaWG5baaleqabeqcLbsacqGHRiI8aaWc beqabKqzGeGaey4kIipaaaaaaa@67E1@                                                        (7)

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

n eff = n 2 (x,y)|F(x,y) | 4 dxdy |F(x,y) | 2 dxdy MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGUb WcdaWgaaqcbasaaKqzadGaamyzaiaadAgacaWGMbaajeaibeaajugi biabg2da9OWaaSaaaeaadaWdbaqaamaapeaabaqcLbsacaWGUbWcda WgaaqcbasaaKqzadGaaGOmaaqcbasabaqcLbsacaGGOaGaamiEaiaa cYcacaWG5bGaaiykaiaacYhacaWGgbGaaiikaiaadIhacaGGSaGaam yEaiaacMcacaGG8bWcdaahaaqcbasabeaajugWaiaaisdaaaqcLbsa caWGKbGaamiEaiaadsgacaWG5baaleqabeqcLbsacqGHRiI8aaWcbe qabKqzGeGaey4kIipaaOqaamaapeaabaWaa8qaaeaajugibiaacYha caWGgbGaaiikaiaadIhacaGGSaGaamyEaiaacMcacaGG8bWcdaahaa qcbasabeaajugWaiaaikdaaaqcLbsacaWGKbGaamiEaiaadsgacaWG 5baaleqabeqcLbsacqGHRiI8aaWcbeqabKqzGeGaey4kIipaaaaaaa@6B5C@                                               (8)

where n(x,y) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGUb GaaiikaiaadIhacaGGSaGaamyEaiaacMcaaaa@3B5D@ is the user–defined spatially dependent nonlinear refractive index of the various layers of the fiber and F(x,y) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGgb GaaiikaiaadIhacaGGSaGaamyEaiaacMcaaaa@3B35@ is the normalized mode field pattern. We have started our study by employing the profile of an optical fiber which was used to achieve a high negative dispersion in a DCF.14 Since our first purpose was to design a positive dispersion NZDSF, we have changed the core profile into an exponential function. There are some literatures that showed the exponential profile would decrease the loss level.15,16 Further, we have used two silica–based dopants with refractive index of 1.44–1.45 in the cladding region. To increase the density of the silica glass, Germanium dioxide (GeO2) is added to the substrate glass, while for decreasing the density, Fluorine (F) is used. Our designed profile is shown in Figure 1.

Figure 1 Exponential refractive index profile.

The core with a radius of 3 μm MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeGabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaaIZaGaaiiOa8aacqaH8oqBcaGITbaaaa@3C17@ has a refractive index changing linearly from 1.4615 to 1.44692, marked as region 1. Regions 3, 5, and 7 have refractive indices of 1.455, 1.45, and 1.449 with the radius of 2, 3.7, and 52.58 μm MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeGabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaaI1aGaaGOmaiaac6cacaaI1aGaaGioaiaacckapaGaeqiV d0MaaOyBaaaa@3F08@ , respectively. The refractive index of Regions 4 and 6 are 1.45 with radii of 1.0 and 0.2 μm MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeGabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaaIWaGaaiOlaiaaikdacaGGGcWdaiabeY7aTjaak2gaaaa@3D82@ , respectively. Also, Region 2 is formed with refractive index of 1.4448 and radius of 0.02 0.02 μm MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeGabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaaIWaGaaiOlaiaaicdacaaIYaGaaiiOa8aacqaH8oqBcaGI Tbaaaa@3E3C@ .

We have found that the minimum latency of 1.487 μs MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeGabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaaIXaGaaiOlaiaaisdacaaI4aGaaG4naiaacckapaGaeqiV d0MaaO4Caaaa@3F0E@ is obtained at the wavelength of 1352 nm. Using Equation 3, the group index of the above profile is found as 1.46888. Replacing this amount in Equations 1 and 2, the estimated latency is obtained as 4.899 μs MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeGabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaaI0aGaaiOlaiaaiIdacaaI5aGaaGyoaiaacckapaGaeqiV d0MaaO4Caaaa@3F18@ . So, we have 0.002 μs MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFeYlLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeGabiGaaiaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaaIWaGaaiOlaiaaicdacaaIWaGaaGOmaiaacckapaGaeqiV d0MaaO4Caaaa@3EFC@ tolerance between the estimated and practical latencies. Figure 2 shows the dispersion of the designed profile. As it’s noted, total dispersion and dispersion slope are 1.10625 ps/nm.km and 0.09112 ps/n m 2 .km MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaaicdacaGGUaGaaGimaiaaiMdacaaIXaGaaGymaiaaikda caGGGcWdaiaakchacaGIZbGaaO4laiaak6gacaGITbWcdaahaaqcba sabeaajugWaiaakkdaaaqcLbsacaGIUaGaaO4Aaiaak2gaaaa@46F9@ , respectively, at the wavelength of 1352 nm.

Figure 2 Dispersion at the wavelength of 1352nm.

The effective area of the profile is calculated as 102 μ m 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaaigdacaaIWaGaaGOmaiaacckapaGaaOiVdiaak2galmaa CaaajeaibeqaaKqzadGaaGOmaaaaaaa@3E6F@ . Because of the large effective area, there will be a limitation in bending condition. The corresponding macro–and micro–bending losses are depicted in Figure 3. The macro–and micro–bending losses in this profile are obtained as 7.31× 10 51 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaaI3a GaaiOlaiaaiodacaaIXaGaey41aqRaaGymaiaaicdalmaaCaaajeai beqaaKqzadGaeyOeI0IaaGynaiaaigdaaaaaaa@40C9@ and 0.031 dB/km, respectively, at the wavelength of 1352 nm.

Figure 3 Bending loss at the wavelength of 1352nm.

For the next step, we have employed our designed NZDSF in an optical network to evaluate how far the light will be transmitted and can be detected with desirable quality without using EDFA and DCF. For this aim, we have designed an optical network based on an optical transmitter and a receiver with the bit rate of 10 Gb/s. The received signal at a distance of 50 kmwas monitored by using the eye–diagram, as shown in Figure 4. The quality factor and minimum bit–error rate of the received signal are 8.17 and , respectively, which are desirable amounts for this transmission distance.17–19

Figure 4 Eye–diagram of the received signals at a distance of 50km.

Conclusion

In this study, we have designed an NZDSF with core refractive index of 1.46888 which had a minimum latency at 1352 nm. In comparison to Corning NZDSF, the latency has improved by 0.002 μs MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaOiVdiaako haaaa@3821@ . The effective area is found to be 102 μ m 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaaigdacaaIWaGaaGOmaiaacckapaGaaOiVdiaak2gajuaG daahaaqcbauabeaajug4aiaakkdaaaaaaa@3F34@ and macro bending loss is 7.31× 10 51  dB/km MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaaI3a GaaiOlaiaaiodacaaIXaGaey41aqRaaGymaiaaicdajuaGdaahaaqc basabeaajugWaiabgkHiTiaaiwdacaaIXaaaaKqzGeaeaaaaaaaaa8 qacaGGGcGaamizaiaadkeacaGGVaGaam4Aaiaad2gaaaa@4997@ . The dispersion of this fiber is 1.10625 ps/nm.km which is comparable to Corning NZDSF fiber.

In addition, we have presented an optical fiber network in order to evaluate the quality of the received signals from 50 km of our designed fiber. The results have shown that without using optical amplifier and DCF, the quality factor and minimum bit–error rate are obtained as 8.17 and 10 16 , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaaIXa GaaGimaSWaaWbaaKqaGeqabaqcLbmacqGHsislcaaIXaGaaGOnaaaa jugibiaacYcaaaa@3D07@ respectively.

Acknowledgements

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 conflict of interest.

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