Multilevel modulation formats for robust long-haul high capacity transmission

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Multilevel modulation formats for robust long-haul high

capacity transmission

Citation for published version (APA):

Al Fiad, M. S. A. S. (2011). Multilevel modulation formats for robust long-haul high capacity transmission. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR712656

DOI:

10.6100/IR712656

Document status and date: Published: 01/01/2011 Document Version:

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Multilevel Modulation Formats for Robust

Long-Haul High Capacity Transmission

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de rector magnificus, prof.dr.ir. C.J. van Duijn, voor een

commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op donderdag 23 juni 2011 om 16.00 uur

door

Mohammad Saeed Alfiad

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prof.ir. A.M.J. Koonen

Copromotoren: dr.ir. H. de Waardt en

Dr. T. Wuth

A catalogue record is available from the Eindhoven University of Technology Library

Alfiad, Mohammad Saeed

Multilevel Modulation Formats for Robust Long-Haul High Capacity Transmis-sion/ by Mohammad Saeed Alfiad.

Eindhoven: Technische Universiteit Eindhoven, 2011. ISBN : 978-90-386-2500-3

NUR : 959

Trefw.: optische telecommunicatie/ modulatie / signaalverwerking / optische po-larisatie.

Subject headings: optical fibre communication / electro-optical modulation / si-gnal processing/ optical fibre polarisation.

Copyright c⃝2011 by Mohammad Saeed Alfiad

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prof.dr.ir. A.C.P.M. Backx, Technische Universiteit Eindhoven prof.ir. A.M.J. Koonen, Technische Universiteit Eindhoven dr.ir. H. de Waardt, Technische Universiteit Eindhoven Dr. T. Wuth, Nokia Siemens Networks

Prof.dr.ing W. Rosenkranz, Christian-Albrechts-Universit¨at zu Kiel dr. P. Poggiolini, Politecnico di Torino

prof.dr.ir. M.K. Smit, Technische Universiteit Eindhoven Dr.Ing. P. Winzer, Bell Labs, Alcatel-Lucent

The work leading to this thesis was part of a cooperation between Nokia Siemens Networks, Munich, Germany and the Electro-Optical communications (ECO) group, department of Electrical Engineering of the Eindhoven University of Tech-nology , Eindhoven, The Netherlands

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Summary

In the past couple of years, we have witnessed a rapid growth in the required bandwidth due to a variation of Internet applications. This has trigged a signifi-cant interest in the development of optical transponders with fast data rates and high spectral eﬃciencies. The recent developments in DSP speeds brought optical coherent detection back into the picture, which has opened a whole new world of robust multilevel optical modulation formats capable of matching the increase in required transmission capacity.

Recently, the polarization multiplexed (POLMUX) diﬀerential phase shift key-ing (DPSK) modulation format with coherent detection has been proposed for realizing the ultra long-haul transmission with a data rate of 43 Gb/s. In the first part of this theses we compare the 43 Gb/s POLMUX-RZ-DPSK and POLMUX-RZ diﬀerential quadrature phase shift keying (DQPSK) modulation formats in terms of their suitability for ultra long-haul optical transmission. We experimentally demonstrate that the higher robustness of the 43 Gb/s POLMUX-RZ-DPSK signal against nonlinear impairments allows for av 40% increase in feasible transmis-sion distance in comparison to POLMUX-RZ-DQPSK. The extra robustness of the 43 Gb/s POLMUX-RZ-DPSK signal has enabled the transmission over more than 7000 km of field deployed fiber.

After the data rate of 40 Gb/s, 100 Gb/s seemed to be the next logical step in data rate for the optical communication community. The transmission of 100 Gb/s channels was successfully demonstrated using several modulation formats such as the Vestigial sideband modulation (VSB) or DQPSK with direct detection. Ho-wever, the most cumbersome issues with such solutions are the high susceptibility of the 100 Gb/s signal to linear optical impairments and its low spectral eﬃciency (SE). In 2007, the long-haul transmission of the 111 Gb/s POLMUX-RZ-DQPSK signal with a SE ofv 2 b/s/Hz together with coherent detection has been demons-trated for the first time. This solution has been considered very favorably due to the excellent immunity of the whole system to the diﬀerent optical impairments and its high SE.

In the second part of this theses we investigate on the tolerance of the 111 Gb/s POLMUX-RZ-DQPSK signal to the diﬀerent transmission impairments. The com-patibility of the 111 Gb/s channels with existing networks has been investigated both using lab experiments and a field trial. We have demonstrated the transmis-sion of the 111 Gb/s signal over field deployed fiber with co-propagating 10.7 Gb/s on oﬀ keying (OOK) and 43 Gb/s DPSK channels. We showed that by carefully choosing the launch power levels of the neighbouring channels and their

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confi-guration (e.g. the arrangement of the different channels types) a 111 Gb/s channel can fit in existing transmission links. Furthermore, we studied the tolerance of the 111 Gb/s signal to the different nonlinear transmission impairments in different link structures. We have analyzed the transmission performance of the 111 Gb/s si-gnal in case of having different dispersion maps. We demonstrated that increasing the per span under compensation in the dispersion map can significantly reduce the performance difference between dispersion manged (DM) and non-dispersion manged (NDM) transmission links.

Despite of the high OSNR requirements of the POLMUX- 16 level quadrature amplitude modulation (16QAM) and its low tolerance to nonlinear transmission eﬀects it can practically achieve a SE as high as 4 b/s/Hz. Consequently, the POLMUX-16QAM modulation format can be utilized to enable the transmission of 200 Gb/s channels on the standard 50 GHz channel grid. In the last part of this theses we demonstrate the generation and detection of a 224 Gb/s POLMUX-RZ-16QAM signal with around 4 dB of penalty in comparison to the theoretical limits. In addition, we show that by employing the hybrid Raman/EDFA am-plification scheme together with a NDM transmission link the transmission of eleven 224 Gb/s POLMUX-RZ-16QAM channels over 670 km of SSMF with a SE of 4.2 b/s/Hz can be achieved. This transmission distance has been extended up to 1500 km through implementing advanced fiber types in order to both suppress nonlinear transmission impairments and increase Raman gain.

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Introduction

This thesis is intended to study the use of multilevel optical modulation formats for robust long-haul high capacity transmission. In this introductory chapter, we will list the targets of this research and the main open questions that will be answered in the subsequent chapters.

1.1 Motivation

Nowadays, telecommunication networks all over the world are witnessing a gi-gantic growth in the capacity demands. The annual growth rate in bandwidth demands is estimated now to bev 40% [1, 2]. In order to match this growth rate before running into a capacity crunch, the current dense wavelength division mul-tiplexed (DWDM) 10 Gb/s channels running in today’s optical networks should be updated with higher data rates.

Since deploying new transmission systems and transmission links to support the new high bit rate channels is expected to be very costly, the new high data rate channels are required to be compatible with currently deployed systems and transmission links. This compatibility implies that the new channels should be able to tolerate both linear and nonlinear optical transmission impairments taking place in the transmission links. Furthermore, they should be able to fit with the conditions of today’s transmission systems such as the channel spacing and the transmission reach.

In order to satisfy all of these needs, new multi-level optical modulation for-mats should be exploited together with advanced detection and equalization tech-niques. Naturally, when choosing a certain modulation format and a signal shape, several trade-offs should be taken into account. These trade-offs include spectral efficiency (SE), optical signal to noise ratio (OSNR) requirements, tolerance to nonlinear transmission impairment and the complexity of the transceiver. For instance, in order to achieve a data rate of 100 Gb/s, the polarization multiplexed

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(POLMUX) return to zero (RZ) diﬀerential quadrature phase shift keying (DQPSK) modulation format is proposed together with coherent detection [3]. Despite that this modulation format is vulnerable to cross phase modulation (XPM) and to cross polarization modulation (XPolM), it can still provide the necessary SE to fit in the legacy 50 GHz channel grid. Furthermore, the moderate OSNR requirements of this signal enables it from being used in long-haul transmission.

In this thesis we will asses the possibility of upgrading currently existing trans-mission links with data rates of 40 Gb/s, 100 Gb/s and 200 Gb/s, taking advantage from optical coherent detection and advanced multilevel optical modulation for-mats. We will study the possibility of enhancing the tolerance of these high data rate signals to linear optical impairments through using linear digital equalizers in the coherent receiver. Furthermore, we will examine the tolerance of these si-gnals to nonlinear transmission impairments. Finally, we will investigate on the design rules for the optimum signal shape and transmission link configuration to guarantee lowering these nonlinear impairments.

1.2 Structure of this thesis

This thesis is divided into eight chapters. The next chapter will give an introduc-tion to the most important theoretical concepts in optical telecommunicaintroduc-tions, in order to facilitate understanding the work presented in the subsequent chapters. The third chapter is dedicated for introducing the concepts of optical coherent de-tection, since this detection technique is used in all of the experiments discussed in this thesis. In the same chapter, the digital signal processing (DSP) algorithms used in the coherent receiver for detecting and equalizing the received optical signals are discussed in details.

The fourth chapter studies the polarization multiplexed (POLMUX) return to zero (RZ) diﬀerential phase shift keying (DPSK) modulation format as a candidate for achieving ultra long-haul transmission with a data rate of 43 Gb/s. The main properties of this modulation format are characterized in this chapter. Further-more, the ultra long-haul transmission of 43 Gb/s POLMUX-RZ-DPSK channels over more than 7000 km of field deployed fiber is demonstrated.

Chapter five is devoted to throughly study the properties and transmission performance of 111 Gb/s POLMUX-RZ diﬀerential quadrature phase shift keying (DQPSK) modulated signals. Mainly, the chapter will concentrate on the tolerance of the 111 Gb/s POLMUX-RZ-DQPSK signal to nonlinear transmission eﬀects, and on its compatibility with existing transmission links in the field.

In chapter six, the generation, transmission and detection of 224 Gb/s POLMUX-RZ 16-level quadrature amplitude modulated (16QAM) signals are studied. First, the chapter starts with an introduction to the main challenges associated with the generation of such a high level optical modulation format. Afterwards, the transmission results of eleven wavelength division multiplexed (WDM) 224 Gb/s POLMUX-RZ-16QAM channels over distances of up to 1500 km will be given.

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1.3. CONTRIBUTIONS 3

Finally, chapter seven draws some conclusions from the results presented in this thesis, while the last chapter will give our outlook on how the technology will evolve in the field of long-haul optical transmission systems.

1.3 Contributions

The author is solely responsible for assembling and carrying out all the descri-bed experiments in this thesis except for those reported in Sec. 4.3, Sec. 4.4 and Sec. 5.4.3. The measurements of Sec. 4.3 have been carried out by ir. Vincent Sleiﬀer as a part of his master thesis, under the direct supervision of the author. Further-more, a team from Nokia Siemens networks was responsible for preparing the transmission link in the field trials reported in Sec. 4.4 and Sec. 5.4.3, while the author was responsible for carrying out the measurements.

All of the digital signal processing algorithms that have been used oﬀ-line in the digital coherent receiver were programmed by Dr. Maxim Kuschnerov. This PhD project has been carried out under the direct supervision of dr.ir. Huug de Waardt from Eindhoven University of Technology and Dr. Torsten Wuth with the help of dr.ir. Dirk van den Borne from Nokia Siemens networks.

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Chapter 2

Fiber Optic Transmission

Systems

Since the beginning of the last decade, the world has started witnessing a com-plete change in the style of people’s lives, forced by the introduction of Internet. Nowadays, Internet is taking part in people’s daily aspects, including telecommu-nications, health, entertainment and business [4–7]. This new social behavior led to an enormous growth in the amount of traﬃc running on telecommunication networks [1, 2]. As a result of this growth, optical telecommunication networks has started replacing satellite telecommunication links, since they are considered to be much faster, more reliable and to have a better quality.

This chapter is devoted to study the physical layer of optical telecommuni-cation networks. The chapter is divided into five sections. The first section will give a short overview on the structure of today’s optical networks. In the second section, the properties of the optical fiber channel and the diﬀerent impairments associated with it will be introduced. The third section will discuss the diﬀerent modulation formats currently in use or proposed for being used in optical com-munications. In the fourth section, a short introduction to forward error correction techniques will be presented. Finally, the fifth section will give a summary for this chapter.

2.1 Structure of Todays Optical Networks

Fig. 2.1 gives a general overview on the structure of the telecommunication net-work in the world as of today [8,9]. It is obvious in this figure that optical commu-nication links represent the backbone of the whole network [10]. The fiber type used in the optical part of the network is single mode fiber (SMF), which will be discussed in detail in the following section. In each fiber section in this network,

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several wavelength division multiplexed (WDM) channels are running simulta-neously. These WDM channels are multiplexed with a channel spacing of either 100 GHz or 50 GHz according to the standards of the international telecommu-nications union (ITU). Nowadays, the most common data rates for these WDM channels are 2.5 Gb/s, 10 Gb/s and 40 Gb/s per channel.

Figure 2.1: Structure of today’s optical transmission networks

As shown in Fig. 2.1, the telecommunication network is divided into several sections which are summarized in Table 2.1. These sections differ from each other both in their transmission reach and in the amount of traffic they are carrying. For instance, long-haul and ultra long-haul links connect different countries or different continents with each other. Since these links are carrying the aggregated transmitted data from all of the other network sections, they usually have total transmission rates in the order of several hundreds Gb/s. Increasing the data rates in these links represents the main target of this thesis.

Regional links connect major cities with each other, and metro links connect small cities and possibly small countries together. The access links, or what is referred to usually as the last mile, run inside the cities and deliver the diﬀerent services to end customers. Although access links are mainly dominated by ra-dio transmission and copper cables, optical fiber communications have started recently penetrating that part of the network as well [11].

In order to increase the flexibility of the optical links, reconfigurable optical add-drop multiplexers (ROADM) are employed. In ROADMs the optical signals

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2.2. FIBER OPTIC TRANSMISSION CHANNEL 7

Table 2.1: Transmission ranges of the diﬀerent telecommunication network sec-tions

Band Wavelength Range Access (or last mile) <100 km Metro <300 km Regional 300-1000 km Long-haul 1000-3000 km Ultra long-haul >3000 km

are routed in the optical domain, i.e. without the need to transfer them first to the electrical domain [12], thus reducing the cost of these routing nodes and the overall delay of the network.

2.2 Fiber Optic Transmission Channel

Fig. 2.2 depicts the structure of a SMF, which is considered nowadays to be the most important transmission medium. The outer shell of the SMF is referred to as the jacket and its main task is the mechanical protection for the fiber. Inside the jacket lies the core and the cladding of the fiber which are mainly made out of Silica glass. The transmitted light propagates in the core of the fiber, and its confinement there is guaranteed by the total internal reflection law. In order to achieve the total internal reflection condition, the refractive index of the core has to be higher than that of the cladding. The diﬀerence in refractive index between the core and the cladding of the optical fiber is achieved either through doping the core with Germanium-Oxide (GeO2) or doping the cladding with Fluoride (F).

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The nonlinear Schr ödinger equation describes the propagation of optical si-gnals inside the fiber [13], as well as the different impairments taking place on the propagating optical signals. The Schr ödinger equation for SMF can be written as (for a single polarization):

dE(z, t) dz + i 2β2(z) d2_E(z_{, t)} dt2 − 1 6β3(z) d3_E(z_{, t)} dt3 + α(z)

2 E(z, t) = iγ | E(z, t) |

2_E(z_{, t) (2.1)}

where E(z, t) is the optical field, β2(z) andβ3(z) are the second and third order

chromatic dispersion parameters respectively,α(z) is the fiber attenuation and γ is the Kerr nonlinear coeﬃcient. Each of these parameters will be explained in the following subsection and its eﬀect on the optical transmission will be discussed.

2.2.1 Fiber Loss

Theα(z) parameter mentioned in Equ. 2.1 represents the attenuation in the power of the optical signal propagating through the fiber. Theα(z) parameter is usually constant over the fiber length, and therefore can be written as α. The power decay due toα is exponential with the transmission distance and therefore can be expressed as:

P(z)= P0e−αz (2.2)

where P(z) is the power after a transmission distance z and P0is the initial power

at the input of the fiber. As can be understood from Fig. 2.3, α is a function of wavelength. The figure shows the attenuation parameter for three different generations of standard SMF (SSMF). Fiber attenuation is caused mainly by a combination of two effects, which are material absorption and Rayleigh scattering. Rayleigh scattering (named after the British physicist Lord Rayleigh) refers to the scattering of light in all directions by particles much smaller than the wave-length of the light. This scattering results from the density fluctuations of silica and its efficiency reduces with the increase of wavelength. Rayleigh scattering is a fundamental source of attenuation in the fiber, and therefore it sets the limit of fiber loss.

Material absorption represents the second source of power attenuation in op-tical fibers. Fig. 2.3 shows that the absorption of Silica molecules is dominant at very high wavelengths. In addition, the figure depicts that some impurities of OH- ion in the fiber material can cause a large attenuation peak in the wave-lengths range between 1360 nm to 1460 nm. With the recent advancements in fiber manufacturing process, the amount of OH- contaminations in the fiber material is significantly reduced [14, 15]. Consequently, the OH- absorption peak has almost completely disappeared in new fiber generations as evident from Fig. 2.3.

According to Fig. 2.3 and table 2.2, the wavelengths range of the fiber channel is divided into six bands. Given that the C- and L-bands have the minimum loss

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Figure 2.3: Typical attenuation values for standard single mode fibers (SSMF). (α ≈ 0.2 dB/km) they were chosen for long-haul transmission [8, 16]. Nowadays, research is concentrating on producing new fiber types with an attenuation pa-rameter that is below 0.2 dB/km [17, 18]. Reducing the attenuation papa-rameter of the SMF is very beneficial for improving the power budget of long-haul transmis-sion links, since that can translates into a longer reach for high data rate optical channels.

Table 2.2: The diﬀerent wavelength bands in optical telecommunications Band Wavelength Range

O-band 1260 to 1360 nm E-band 1360 to 1460 nm S-band 1460 to 1530 nm C-band 1530 to 1565 nm L-band 1565 to 1625 nm U-band 1625 to 1675 nm

2.2.2 Fiber Loss Compensation

As mentioned in the previous subsection, the C- and L-bands have been chosen for WDM optical transmission due to their low loss. Nevertheless, the low loss coeﬃcient of around 0.2 dB/km at these bands means that a fiber span of 100 km will have a total loss of 20 dB. A power loss of 20 dB implies that only 1% of the transmitted power will be detected at the receiver side. Consequently, some loss compensation techniques should be employed in order to enable the transmission of the signal over longer distances.

Until the beginning of the 1990’s, the only method known for overcoming the fiber loss problem was the optoelectronic generation. An optoelectronic re-generator is a receiver and transmitter pair that works first on detecting the optical

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signal after a fiber span and transforming it to the electrical domain. Afterwards, it re-generates the optical signal with high power in order to transmit it again over the next fiber span. This technique is very costly, besides of being ineﬃcient in case of having a WDM transmission with many channels as depicted in Fig. 2.4a. Therefore, there has been a need for a loss compensation technique, that can amplify the power of all WDM channels simultaneously in the optical domain. Fig. 2.4b explains the principle of optical amplification (or optical re-generation). According to the figure, the optical amplifiers are placed periodically along the transmission fiber to compensate for the fiber loss. This subsection introduces the two most famous optical amplifier types in use today. These amplifiers are erbium doped fiber amplifiers (EDFA) and Raman amplifiers.

Figure 2.4: (a) Optoelectronic and (b) optical re-generation of optical signals.

EDFA Amplification

An erbium doped fiber amplifier (EDFA) is a lumped element that is composed from a piece of fiber, as short as a couple of meters, doped with the rare earth erbium (Er3+) element [19,20]. The working principle of this amplifier is illustrated in Fig. 2.5 [21]. As can be seen in the figure, a laser with a wavelength in the vicinity of either 980 nm or 1480 nm should be pumped into the erbium doped fiber (EDF) in order to excite the electrons of the erbium element and move them to higher power levels. This process is usually referred to as population inversion. In order to guarantee the highest possible population inversion, Er is usually concentrated in the center of the fiber core, since the light intensity is the highest in that area (as illustrated in Fig. 2.6). Considering that the electrons in the higher power states are usually not in a stable condition, these power states are referred to as the

metastable energy band. In the metastable energy band the electrons are willing to lose

their energy in the form of photons and return back to their initial energy state, where they are more stable. In case of erbium, the emitted photons can have any wavelength in the C or L bands. This emission of photons can either be stimulated or spontaneous.

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In case of stimulated emission, a photon propagating through the EDF with a wavelength in the C or L bands stimulates the energy drop of an electron and subsequently generates another photon. The stimulated photon will have exactly the same wavelength, phase and propagation direction as the stimulating photon. The photons duplicate themselves in each stimulated emission and as so the amplification of the propagating light can be achieved. On the other hand, in case of spontaneous emission the electrons drop their energy spontaneously without any external influence. These spontaneously emitted photons will have a random frequency, phase and propagation direction. During their propagation through the EDFA, spontaneously emitted photons get amplified by stimulating the generation of other photons. In optical communication systems, this amplified

spontaneous emission (ASE) is considered as the main source of noise to the optical

signals.

Figure 2.5: Working principle of er-bium doped fiber amplification.

Figure 2.6: Structure of an erbium do-ped fiber.

Fig. 2.7 depicts the typical structure of an EDFA. The figure shows the erbium doped fiber and two laser pumps. In practice, the laser pumps are used to pumped the fiber in the same (co-propagating) or in the opposite (counter-propagating) direction of the signal, or in both directions (bi-directional) as in the example given in Fig. 2.7.

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The performance of optical amplifiers is usually described in terms of their noise figure (NF), which can be defined as:

NF= 10log(OSNRin

OSNRout) (2.3)

where OSNR stands for: optical signal to noise ratio. This parameter is very similar to the signal to noise ratio (SNR) parameter defined for electrical signals, however it deals with optical powers. Consequently, the NF parameter of a certain amplifier describes the level of deterioration caused by this amplifier to the OSNR of its input optical signals. The OSNR parameter can be defined as:

OSNR= Pout PASE

(2.4) = Pout

2No∆ fo (2.5)

where Poutis the output optical power from the amplifier, PASEis the power of the

ASE noise and No is the noise power spectral density per polarization. Usually

the OSNR is normalized to a bandwidth (∆ fo) of 0.1 nm. The noise power spectral

density Nois defined as:

No= nsph fo(G− 1) (2.6)

where nsp is the spontaneous emission coeﬃcient (usually ≥ 1), h is Planck’s

constant, fois the reference frequency and G is the gain of the amplifier.

Using a laser pump for the EDFA in the wavelength range around 980 nm guarantees having a maximum population inversion which subsequently lowers the NF of the amplifier. On the other hand, using a pump with a wavelength around 1480 nm guarantees having a higher output power from the amplifier, but does not provide a NF that is as low as what can be achieved using a 980 nm pump. As a result, the choice of the pump type depends completely on the application of the amplifier [22].

Raman Amplification

Raman amplification is based on the Raman scattering phenomena discovered by Sir C.V. Raman in 1928 [23, 24]. The Raman scattering process is explained in Fig. 2.8 and Fig. 2.9. In this scattering process, the incident photon with a frequency v on the molecules of a certain material loses some of its energy to these molecules which appears in the form of vibrational energy or what is called a phonon (Fig. 2.8). The energy of the phonon equals to hvR, where h is Planck’s

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some of its energy, its frequency decreases as well. The new frequency (vstokes) can

be expressed as:

hvstokes= hv − hvR (2.7)

In a similar way, the incident photon might absorb some of the molecule’s vibrational energy, which increases its energy. In this case, the photon’s new frequency is called the anti-stokes frequency vanti−stokesand it is expressed as:

hvanti−stokes= hv + hvR (2.8)

Figure 2.8: Raman scattering pheno-mena.

Figure 2.9: Working principle of Ra-man amplification.

Fig. 2.9 models the Raman scattering process using an energy levels diagram. Compared to the case of EDFA, Fig. 2.9 shows that the energy levels used to explain the Raman scattering process are virtual. Raman scattering can either be stimulated or spontaneous. In case of stimulated Raman scattering, the presence of a photon with the frequency vstokes can stimulate the scattering of another photon that has the same frequency, phase and polarization state. Stimulated Raman scattering represents the working principle of Raman amplifiers.

In Raman amplifiers, the transmission fiber itself is considered as the amplifi-cation medium. Raman amplifiers have the advantage of being able to amplify any wavelength. In order to amplify a certain wavelength, with the maximum Raman amplification eﬃciency, a pump source with a wavelength that is downshifted by 100 nm should be provided. This 100 nm represents the stokes wavelength shift in Silica due to the Raman scattering. In optical communication systems, Raman amplifiers employ usually more than one pump, as explained in Fig. 2.10. This is necessary to amplify a certain range of wavelengths with a good flatness in the gain spectrum.

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Figure 2.10: Most common structures of Raman amplifiers.

Fig. 2.10 depicts the two most commonly used Raman amplification schemes in today’s deployed optical networks. The first scheme employs back-ward Raman pumping, together with EDFA amplification. This scheme is usually used in long-haul transmission links to improve the transmission performance in comparison to EDFA only amplification. Fig. 2.11 explains the advantage of this amplification scheme by showing the power evolution in the transmission fiber both in case of EDFA-only and hybrid Raman/EDFA amplification. In case of EDFA-only am-plification, the lumped amplifiers will have to deliver large power levels at the input of each fiber span in order to make sure that enough power will arrive to the input of the following amplifier. Such large input powers to the fiber can excite nonlinear Kerr transmission eﬀects as will be explained later on in this section.

In addition, due to fiber attenuation the input power to the following EDFA will be relatively low, which consequently degrades the OSNR of the signal. On the other hand, in case of hybrid Raman/EDFA amplification the output power from the EDFA to the fiber span can be significantly reduced since the Raman amplifier at the end of the span works on boosting the power before getting into the next EDFA stage. As a result, the excitation of nonlinear Kerr transmission eﬀects will be dramatically reduced at the beginning of the link. Furthermore, the input power to the next EDFA stage will be boosted to a decent power level which prevents any severe degradation to the OSNR of the signal. As a result, this amplification scheme can considerably increase the transmission distance of the signal compared to the EDFA-only scheme [26].

The second Raman amplification scheme shown in Fig. 2.10 uses bi-directional pumping into the transmission fiber, i.e. pumping at the beginning and at the end of the fiber span. This amplification scheme is specially interesting for under-sea transmission links since it can enable the transmission over longer fiber spans.

It is not straight forward to calculate the gain of a Raman amplifier. To simplify this issue, the ON/OFF gain (GON/OFF) term has been introduced for Raman

am-plifiers. To measure GON/OFF, the output power at the end of the span is measured

with the Raman pumps are turned ON and OFF. The diﬀerence between the two powers represents the ON/OFF gain of the Raman amplifier. In order to analyti-cally derive the GON/OFFwe should first write down the equations governing the

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Figure 2.11: Power evolution in transmission fiber in case of EDFA only and hybrid EDFA+ back-ward pumping Raman amplification.

dPs dz = gR Ae f f PpPs− αsPs (2.9) ±dPp dz = − wp ws gR Ae f f PpPs− αpPp (2.10)

where Ps(p) and ws(p) are the power and the wavelength of the signal (pump)

respectively, gR is the Raman gain eﬃciency for the fiber material, Ae f f is the

eﬀective area of the fiber and αs(p) is the attenuation coeﬃcient of the signal

(pump) wavelength. The first term on the right-hand side of Equ. 2.9 represents the signal gain from stimulated Raman scattering, while the second term represents its propagation loss. In Equ. 2.10 the + and − signs stand for co- and counter-pumping directions respectively. The first term on the right hand side of the equation represents the depletion of the pump power due to Raman scattering and the second term is the propagation loss of pump power due to fiber attenuation. Since the pump power is considerably large, the pump depletion term in Equ. 2.10 can be neglected. In this case, Equ. 2.10 can be solved for the case of back-ward pumping into:

Pp(z)= P0e−αp(L−z) (2.11)

where P0 is the input pump power and L is length of the fiber. Substituting

Equ. 2.11 into Equ. 2.9 and numerically solving the diﬀerential equation gives [23]:

Ps(L)= Ps(0)e

gR

Ae f fP0Le f f−αsL

(2.12) where

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Le f f =

[1− e−αpL_]

αp

(2.13) Therefore, GON/OFFcan be written down as:

GON/OFF= e

gR Ae f fP0Le f f

(2.14) One of the main conclusions that can be made from Equ. 2.14 is that GON/OFFis

inversely related to the effective area of the transmission fiber employed (which is the amplification medium as well). In Fig. 2.12, this point is illustrated by showing the Raman gain coefficient in different fiber types with different effective areas [23].

Figure 2.12: Raman gain spectrum in diﬀerent fiber types. Eﬀective areas of these fiber types are: DCFv 20 µm2_{, DSF}_{v 50 µm}2_{and SSMF}_{v 80 µm}2_.

In general, Raman amplifiers are considered as distributed amplification ele-ments (i.e. the amplification is distributed over the transmission fiber). However, Raman amplifiers can be realized as lumped elements as well. In this case, a piece of highly nonlinear fiber, that is highly doped with germanium (Ge), in oder to improve its Raman gain coeﬃcient, is used as the lumped amplification me-dium. Similar to EDFA amplifiers, these lumped Raman amplifiers can be placed anywhere in the transmission link [27–29].

2.2.3 Chromatic Dispersion

The refractive index of optical fibers is a function of wavelength, which conse-quently means that the group velocity for the waves traveling through the fiber is a function of wavelength as well. In optical telecommunications, this pheno-mena is usually referred to as group velocity dispersion (GVD). Due to GVD the

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diﬀerent wavelength components of a certain optical pulse will travel through the optical fiber with diﬀerent speeds, or in other words the optical pulse will be chromatically dispersed. As illustrated in Fig. 2.13, this chromatic dispersion (CD) broadens optical pulses in time, which can lead to a cross-talk between adjacent optical pulses, or what is usually referred to as inter-symbol-interference (ISI).

Figure 2.13: Pulse broadening due to chromatic dispersion.

There are two factors responsible for the dependency of the refractive index in optical fibers on wavelength, which are material and waveguide dispersion. The material dispersion refers to the dependence of the refractive index in fiber’s bulk material on wavelength. This implies that material dispersion is merely a physical property that can only be controlled through changing the fiber material, or its dopant.

On the other hand, waveguide dispersion is independent of the fiber material and merely a function of fiber’s shape. Waveguide dispersion can be explained by solving Maxwell’s equations for cylindrical waveguides. In the solution of these equations, even with no material dispersion, the resulting eﬀective refractive index will be a function of wavelength. This solution has been interpreted with what so called Heuristic explanation. This explanation states that the distribution of the optical field in the fibers radial direction changes with optical frequency. As a result, shorter wavelengths will be more confined to the core of the fiber, and their refractive indices will be closer to the refractive index of the core material. On the other hand, longer wavelengths will be distributed near to the cladding material, which means that their refractive indices will be closer to the refractive index of the cladding material.

In the Schr ¨odinger equation given in Equ. 2.1,β2represents GVD or the change

in group velocity with the angular frequency w. It is therefore defined as:

β2 = d2_β(w) dw2 _w_=w 0 (2.15)

whereβ(w) is the propagation constant, and w0is the reference frequency at which

GVD will be calculated. Theβ3parameter is Equ. 2.1 represents the change in GVD

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β3= dβ2 dw _w_=w 0 (2.16) β3 is sometimes referred to as the third order CD. Since the maximum

band-width of optical channels in todays networks is limited to around 100 GHz, GVD is considered to be constant within one channel. Consequentlyβ3is often neglected

and it is only taken into account for the diﬀerence in GVD between neighbouring WDM channels. In optical fiber communications, it is very common to use the dispersion parameter D rather thanβ2to represent CD. The dispersion parameter

D has the units of (ps/[nm.km]) and it is defined as:

D= −2πc

λ2 β2 (2.17)

Fig. 2.14 depicts an example for the contributions from material and waveguide dispersion to the total dispersion D in an SSMF. By controlling the refractive index profile of the fiber, both the material and waveguide dispersion can be modified. Consequently, the total D value of the fiber can be tailored [30–32].

Figure 2.14: The dispersion parameter in an SSMF.

Chromatic Dispersion Compensation

The dispersion parameter of SSMF, which represents the majority of deployed fiber in the field, is in the range between 15.5 and 17.8 ps/nm/km (Fig. 2.14). The ISI caused by such a considerable amount of dispersion can be a limiting factor for transmitted data rates or maximum link reach. As a result, CD compensation has been one of the most active research fields in optical telecommunications for a long time.

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Compensation of CD in the optical domain is considered to be the first, and most popular technique. This technique is mainly based on the linear nature of CD accumulation. This technique works on sending the chromatically dispersed signal through another medium that has the opposite amount of CD compared to the transmission fiber. As a result, the spectral components of the optical signal will be dispersed in time again but in an opposite order compared to the dispersion that took place in the transmission fiber. Eﬀectively, this leads to a full compensation of CD. Compensation of CD in the optical domain is very widely used in todays networks. Fig. 2.15 illustrates the typical implementation of this technique in optical transmission links. According to the figure, after each fiber span (typically 80 to 100 km), the signal is amplified and afterwards CD compensated using an optical dispersion compensation module (DCM). In order to overcome the power losses in the DCM, the signal is amplified again and then sent to the subsequent fiber span. The most famous DCM types are based on either dispersion compensation fibers (DCF) [33–35] or fiber Bragg gratings (FBG) [36–39].

Figure 2.15: Implementation of optical CD compensation in a transmission link.

The main reason for the popularity of optical CD compensation techniques is their simplicity. Nevertheless, DCMs are usually expensive, they add an extra de-lay to the total propagation time of the signal and they often introduce nonlinear Kerr eﬀects on the transmitted signal. As a result of having all of these downsides for DCMs, we are witnessing currently an increased interest in alternative CD compensation techniques that are based in the electronic domain. Electronic CD compensation techniques are benefiting from the mature ISI compensation tech-niques developed for radio telecommunications and from the progress in signal processing speeds that can be achieved nowadays. Maximum likelihood sequence estimation (MLSE) [40–43], linear finite impulse response (FIR) filters [3] and fre-quency domain equalizers [44] represent the most widely considered electrical CD compensation techniques. FIR and frequency domain equalizers will be treated in more details in Ch. 3.

Throughout this thesis, the dispersion managed (DM) link term will refer to any transmission link employing in-line optical DCMs. Similarly, the non-dispersion

managed (NDM) link term will be used to refer to transmission links without

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2.2.4 Polarization Mode Dispersion

Even in SMF there exists two orthogonal HE11 modes that are referred to as

the vertical and horizontal polarizations. In a perfectly circular fiber, composed from an isotropic material, both polarizations are supposed to propagate in an identical way (i.e. both propagating with identical group velocities). However, in reality fibers are not perfectly circular, due to some imperfections in their manufacturing process, and furthermore the fiber material is slightly anisotropic. Consequently, the two polarizations of the propagating light through the fiber will have a diﬀerence in their group velocities (∆β), which is defined as [9,16]:

∆β = βx− βy (2.18) = wnv c − wnh c = w∆n c

where w is the angular optical frequency, nv and nh are the eﬀective refractive

indices for the vertical and horizontal polarizations respectively. ∆n is usually referred to as the birefringence of the fiber. As illustrated in the example of Fig. 2.16, the birefringence causes a propagation delay between the waves traveling in the two polarizations. Such an eﬀect is referred to as the diﬀerential group delay (DGD).

Figure 2.16: The diﬀerential group delay (DGD) eﬀect introduced to an optical pulse by a birefringence element [9]

In optical fiber telecommunications, DGD leads to optical pulse broadening and eventually to ISI. The DGD (∆τ) introduced by a certain birefringence element is defined as:

∆τ = L · ∆β (2.19)

where L is the length of the birefringence element. As can be noticed in Equ. 2.19 the DGD is a linear eﬀect that increases linearly with the length of the birefringence

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element. It should be noted that the birefringence∆n of a certain fiber section and the orientation of its fast/slow axis are not constant and they vary with time, temperature and with the change in the mechanical disturbance on the fiber (such as twisting or bending the fiber section).

Since the birefringence elements have different orientations along the optical fiber, Equ. 2.19 can be only applied for short pieces of fiber. The variation of bire-fringence along the fiber is caused by the manufacturing process which imposes different amounts of stress and twists on different locations in the fiber. Further-more, the process of laying down the fiber in the ground can as well induce local twists on the fiber at different locations. Therefore, a fiber can be thought of as a concatenation of many small fiber sections, each with its own birefringence pro-perties and with its own slow and fast axes, as depicted in Fig. 2.17. Since each of these sections has its own orientation, it can either add to or subtract from the total accumulated birefringence. It has been shown that the DGD of these small sections accumulates as a three-dimensional random-walk and this results in a Maxwellian distribution for the DGD as a function of frequency (for a fixed time instance) or alternatively as a function of time for a fixed frequency. The polarization mode dispersion (PMD) value is the mean value of this distribution (E{∆τ}) and strictly correlates also to its width. So, once the PMD value is known, the whole distribution is determined. PMD increases with the square root of the distance [9, 16], and consequently has the unit of ps/√km.

Figure 2.17: The concatenation of many small fiber sections with diﬀerent bire-fringence values and orientations [9]

Although we have nowadays fiber types with a PMD coeﬃcient of less than 0.1 ps/√km [45–48] there still exist some old deployed fiber with a PMD coeﬃcient

of around 0.8 ps/√km [49, 50]. Furthermore, the process of laying down new fiber

with a low PMD coeﬃcient in the ground induces local twists on the fiber at diﬀerent locations and hence changes its PMD characteristics. Therefore, PMD is considered nowadays as one of the major obstacles towards increasing the data rates on existing links up to 40 Gb/s and beyond.

2.2.5 Nonlinear Transmission Impairments

The SMF has an eﬀective area that is as small as 20 − 130 µm2_{, in order to prevent}

the excitation of higher order modes. With such a small area, pumping an optical power as small as a couple of milli-Watts into the fiber translates eﬀectively into a power density of several MW/cm2_{. Such large powers can temporarily change}

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the physical properties of the fiber material, specially its refractive index. The refractive index of a fiber can be actually expressed as [16]:

˜n(w, |E|2)= n0(w)+n2|E| 2

Ae f f

(2.20) where n0(w) is the linear refractive index, which is only a function of wavelength,

n2is the nonlinear refractive index parameter, E is the optical field inside the fiber

and Ae f f is the eﬀective area of the fiber. As can be noticed, the dependence of

the refractive index on the intensity of the optical field is inversely related to the eﬀective area Ae f f. According to Equ. 2.20, the phase of the transmitted signal will

continuously change with the change in the power of the transmitted pattern. This leads to some distortions in the shape of the optical signal, that are function of the input optical power. These eﬀects are called the Kerr eﬀects.

In the Schr ödinger equation given in Equ. 2.1, the Kerr effects are presented in the iγ |E|2E term. The nonlinear coefficient γ is defined as:

γ = n2w0

cAe f f

(2.21) where c is the speed of light and w0is the central optical frequency. The unit ofγ

is 1/(W ·km). Note that the Kerr effects depend on the total power presented in the fiber at a certain point in time, regardless if this power comes from one channel or several WDM channel presented at the same time in the fiber channel. To explain the interactions taking place between the different powers in the fiber and their effect on fiber nonlinearities, Equ. 2.1 should be rewritten using the separate field propagation. For simplicity, we will consider in this case that only three WDM channels, or three optical pulses from the same channel are interacting with each other in the fiber. The three channels/pulses will be referred to as E1, E2 and E3,

where E1 is the channel/pulse of interest. In this case the Schr¨odinger equation

should be written in the form of three coupled equations. The equation describing

E1can be expressed as [13, 51]: dE1 dz + i 2β2(z) d2_E 1 dt2 − 1 6β3(z) d3_E 1 dt3 + α(z) 2 E1 = (2.22) iγ |E1|2E1+ 2iγ(|E2|2+ |E3|2)E1+ iγE2₂E∗3

In Equ. 2.22, the fiber nonlinear eﬀects are contained in the three terms on the right hand side. These terms will be explained in details below for two diﬀerent cases. The first case assumes that E2and E3are neighbouring WDM channels to the

E1channel. The nonlinear eﬀects generated in this case are called the interchannel

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optical pulses in the same optical channel. The nonlinear eﬀects introduced from neighbouring pulses E2and E3 to E1are called the intrachannel nonlinear eﬀects.

Below, both interchannel and intrachannel nonlinear eﬀects will be discussed in detail.

Interchannel Nonlinear E

ﬀects

As has been emphasized before, interchannel nonlinear eﬀects refer to the nonli-near interactions between the WDM neighbouring channels transmitted into the same fiber. In this case, the terms E1, E2and E3in Equ. 2.22 refer to three diﬀerent

WDM channels.

The first, and most important, interchannel nonlinear eﬀect taking place in this case is cross-phase modulation (XPM). In Equ. 2.22, XPM is presented in the 2iγ(|E2|2+ |E3|2)E1term. As can be understood from this term, both the powers of

E2and E3channels will change the optical phase of the E1channel. As a result, the

shape of the channel E1will be distorted as a function of the patterns transmitted

in channels E2and E3. In general, the eﬃciency of XPM decreases with increasing

the wavelength spacing between the interacting WDM channels, increasing the dispersion parameter of the transmission fiber, or increasing the data rate of the interacting channels.

The second interchannel nonlinear eﬀect in fiber communications is four-wave

mixing (FWM). As can be understood from its name, FWM describes the nonlinear

interaction between four diﬀerent waves propagating in the transmission fiber. According to the theory of FWM, if three photons with frequencies w1, w2and w3

have the same phase they mix together and annihilate to generate a fourth photon at frequency w4[13], where w4 = w1+ w2+ w3. Nevertheless, the probability of

having three phase matched photons at three diﬀerent frequencies in the same time is quite low. As a result this sort of FWM is not of a great interest for optical communications.

A more probable type of FWM deals with the mixing and annihilation of two phase matched photons at frequencies w1and w2to generate two photons at

frequencies w3and w4. In order for the energy to be conserved, the four frequencies

in this case should satisfy the equation w1+ w2 = w3+ w4. The eﬃciency of this

FWM type can be significantly increased in case of having w1 = w2. This implies

that two photons at the wavelength w1will generate two photons at wavelengths

of w3and w4according to the relation w1− w3= w4− w1.

FWM is represented by the iγE2

2E∗3term in Equ. 2.22. In this case, photons from

channels E2 and E3 annihilate and generate photons with the same frequency

of channel E1, such that the total energy and momentum are conserved. These

annihilated photons will act as noise to the already existing E1 channel, which

will affect its transmission performance. Fig. 2.18 depicts an example for the effect of FWM in a WDM transmission system. Similar to XPM, the efficiency of FWM decreases with the increase of the dispersion parameter in the transmission fiber.

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This can be understood by knowing that a high dispersion parameter leads to a faster change in the phase of the optical signal. Consequently, the phase matching condition between two diﬀerent photons will happen only for a very short time which significantly decreases the eﬃciency of FWM.

Figure 2.18: An example for the FWM between two WDM channels that generates unwanted components to an existing WDM channel.

Intrachannel Nonlinear E

ﬀects

In contrary to interchannel nonlinear effects, intrachannel effects refer to the non-linear transmission impairments induced on the optical channel by the channel itself [16, 51]. To understand intrachannel nonlinear effects, Equ. 2.22 should be reconsidered but this time with E1, E2 and E3 as adjacent optical pulses in the

same channel. Accordingly, the three terms on the right hand side of Equ. 2.22 should be re-interpreted as three diﬀerent intrachannel nonlinear eﬀects.

The first term in the right hand side of Equ. 2.22 (iγ |E1|2E1) refers to the

nonlinear eﬀect introduced on the E1 pulse by itself. This eﬀect is called the

isolated pulse self phase modulation (SPM). In this case, the power variations in the E1optical pulse will induce some phase variation on the pulse itself.

The second nonlinear term in Equ. 2.22 (2iγ(|E2|2+ |E3|2)E1) describes the

non-linear eﬀect taking place on the E1pulse from the E2and E3neighbouring pulses.

Due to its similarity to the XPM eﬀect, this nonlinear eﬀect is referred to as

intra-channel XPM (IXPM). The mechanism of IXPM is explained in the example given

in Fig.2.19. For simplicity, this example is showing only the IXPM eﬀect from one neighbouring pulse (E2) on E1. In the presence of CD, optical pulses spread out

in time which usually causes some ISI. By definition, ISI means that two opti-cal pulses will be overlapping in the same time slot. The nonlinear interaction between these overlapping pulses is what we call IXPM. IXPM leads to some phase shifts in the optical pulses, which shows up eventually as a timing jitter, as explained in the example shown in Fig.2.19.

The third nonlinear eﬀect in Equ. 2.22 is iγE2

2E∗3, which represents intrachannel

FWM (IFWM). The IFWM name came from the similarity between this eﬀect

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Figure 2.19: The mechanism of intrachannel cross-phase modulation (IXPM). example the power and frequency components of three optical pulses are shown versus time before and after the accumulation of CD in the signal. The figure shows that in the presence of a CD level that is high enough to overlap three pulses over each other, they will mix up together and annihilate to generate a new optical pulse. In the right hand side of Fig.2.20 it is shown that after CD compensation optical pulses will have a variation in their powers and some new optical pulses will be generated in time slots where no optical pulses were located originally.

Figure 2.20: The mechanism of intrachannel four-wave mixing (IFWM).

Cross-Polarization Modulation

So far, we have assumed that the optical signal propagating through the fiber has only one polarization. In case both polarizations X and Y are considered, the Schr ¨odinger equation given in Equ.2.1 should be written in the form of two couple-mode equations: dEx dz + i 2β2 d2_E x dt2 − 1 6β3 d3_E x dt3 + α 2Ex = (2.23) iγ(|Ex|2+ 2 3 Ey 2 )Ex+ iγ 3E ∗ xE2ye−2i∆βz dEy dz + i 2β2 d2Ey dt2 − 1 6β3 d3Ey dt3 + α 2Ey = (2.24) iγ(Ey 2 +2 3|Ex| 2_)E y+ iγ 3E ∗ yE2xe−2i∆βz

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where Ex and Ey are the X and Y polarization components of the optical field

and∆β is the diﬀerence in the group velocities of the two polarizations defined in Equ. 2.18. Equ.2.23 and Equ.2.24 report that there is always a 2/3 factor for the strength of nonlinear interaction between the two orthogonal polarizations.

Lets assume for now that we have a signal with the frequency w1, which has

power in both polarizations and another signal with the frequency w2 that has

power only in polarization X. In this case, the power in polarization X of the w2

signal will aﬀect both polarizations of the w1 signals through XPM. The XPM

eﬀect on the Y polarization of w1 will be less than the XPM on polarization X

by a factor of 3. This means that the relative phase diﬀerence between the two polarizations of signal w1will change. This phase diﬀerence will keep changing

with the alteration of the pattern on w2 which implies that the polarization state

of the w1signal will continuously change with a speed that is equal to the symbol

rate of w2. The depolarization of signals through XPM is what we refer to as

cross-polarization modulation (XPolM) [52–55].

Nonlinear Phase noise

The nonlinear phase noise effect is often referred to as the Gordon-Mollenauer effect after J.P. Gordon and L.F. Mollenauer who reported on this effect for the first time [56]. This nonlinear distortion originates from the amplitude variations of the signal caused by the additive ASE noise which induce nonlinear phase shifts to the signal.

In this thesis, the signals and data rates that are under consideration have high OSNR requirements. Consequently, the ASE noise level will never be high enough in such signals for exciting the Gordon-Mollenauer eﬀect. Therefore this eﬀect will be neglected in the studies presented in this thesis.

2.3 Optical Modulation Techniques

Recently, a great deal of research has been carried out in the subject of optical modulation formats [16, 51, 57, 58]. The main target of this research is to inves-tigate candidate optical modulation formats capable of achieving higher spec-tral eﬃciencies (SE) and eventually higher transmission capacities over optical transmission links. This research is mainly supported by the rich field of modula-tion formats developed for radio and cable communicamodula-tions [59], and the recent developments in optical integration techniques that allowed the realization of advanced optical modulators, such as those described in [60–66].

The research on optical modulation formats concentrates mainly on finding candidate modulation formats capable of achieving a compromise between spec-tral eﬃciency and the tolerance to the diﬀerent optical impairments. In this section, several optical modulation formats will be introduced and their properties will

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2.3. OPTICAL MODULATION TECHNIQUES 27

be discussed. Some techniques related to modulation such as pulse carving and polarization multiplexing will be discussed as well by the end of the section.

2.3.1 On-O

ﬀ Keying

On-oﬀ keying (OOK) represents the oldest, simplest and most widely used optical modulation format. In this modulation format, the binary data to be transmitted is encoded into the amplitude of the optical signal. The name of this modulation formats refers to two light amplitude states that are used to carry this binary data (i.e. On and Oﬀ). In the field of radio and cable telecommunications, this modulation format is usually referred to as binary amplitude shift keying (2-ASK). The OOK signal can be generated using either a directly modulated laser [67–69], an electro-absorption modulator [70, 71] or a Mach-Zehnder modulator (MZM) [16]. Directly modulated lasers and electro-absorption modulators represent the cheapest solutions and they require a smaller amplitude for the electrical driving signals to the optical modulator (in comparison to the commercially available MZMs nowadays). Nevertheless, the fact that they usually introduce some chirp into the signal make them less suitable for long-haul/ultra long-haul transmission systems in comparison to MZMs.

Figure 2.21: Structure of a MZM-based OOK modulator

Fig. 2.21 depicts the structure of MZM-based OOK transmitter [57]. As shown in the figure, the MZM modulates the output light of a laser source with the binary electrical data driving it. The MZM should be biased in its quadrature biasing point and its driving signal should have a peak-to-peak amplitude of around Vπ(Vπ

is the voltage required to change the phase of the output optical signal byπ), as illustrated in Fig. 2.22. The eye and constellation diagrams of the OOK signal are shown in Fig. 2.23 and Fig. 2.24 respectively.

As a binary modulation format, OOK has a poor SE in comparison to the multilevel optical modulation formats discussed in the following subsections. In order to slightly enhance its SE, the versatile side band (VSB) OOK modulation has been proposed. VSB-OOK has a practical SE of around 1 b/s/Hz [72]. Nevertheless, OOK has a low tolerance to nonlinear transmission eﬀects due to its strong carrier, which makes it unappealing for data rates≥ 40 Gb/s. Nowadays, OOK with direct-detection is very widely deployed for data rates in the order of 10 Gb/s. The choice

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Figure 2.22: Driving a MZM to generate an OOK signal.

of the OOK modulation in this case is mainly due to its low complexity transmitter structure, and the possibility of detecting it merely using a single photo-detector (PD).

Figure 2.23: Simulated OOK eye dia-gram.

Figure 2.24: OOK constellation dia-gram.

OOK channels tend to introduce a strong XPM eﬀect on their neighbouring channels, due to the fact that they have a strong carrier. Today, the XPM eﬀect from the heritage 10.7 Gb/s OOK channels represents the biggest challenge for the upgrading scenarios of deployed links with≥ 40 Gb/s channels [73–76]. This topic is discussed in further details in Ch. 4 and Ch. 5.

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2.3. OPTICAL MODULATION TECHNIQUES 29

2.3.2 Duobinary

Duobinary is a binary modulation format that was introduced back in the 1960s for electrical cable communications [77]. As a matter of fact, duobinary is usually thought of as a line coding technique that is used to shape up the spectrum of the signal rather than a modulation format [57]. The constellation diagram of Duobinary is shown in Fig. 2.25. This constellation diagram has three symbols at +1, 0, and -1 that are used to represent a binary signal, which already gives an impression on why Duobinary is considered to be a line coding technique.

The working principle of the duobinary transmitter is explained in Fig. 2.26 and Fig. 2.27. In Fig. 2.26, a delay and add block is employed to change the binary driving signal into a three level electrical signal. Typically, the delay and add opera-tion is performed using a narrow band low-pass electrical filter through the ISI it introduces between the adjacent symbols. The typical bandwidth for this filter is around B/4, where B = 1

T and T is the symbol duration. The correlation between

the adjacent bits that is introduced by the delay and add block leads to a reduction in the bandwidth of the optical signal.

Figure 2.25: Duobinary constellation diagram.

Figure 2.26: Duobinary modulator structure.

To generate a duobinary signal, the MZM should be biased in its trough point and the driving three-level electrical signal should have a peak-to-peak amplitude of 2Vπ as explain in Fig. 2.27. Information in duobinary is coded both in the

amplitude and the phase of the optical signal (the symbols are 1· ej.0_{, 0 and 1· e}j.π_).

Consequently, this modulation is also sometimes referred to as phase-shaped binary transmission (PSBT) modulation [78].

The eye diagram of the optical duobinary signal is depicted in Fig. 2.28. The smooth transitions between the two amplitude levels in the eye diagram can give an indication about the reduction in the bandwidth of the signal. Due to the changes introduced to the transmitted binary data by the delay and add block, a pre-coding stage is required in duobinary [79]. The pre-coding stage implements the inverse transfer function of the delay and add block, modulation and receiver combined. Consequently, no further actions are required at the receiver side to decode the detected signal.

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trans-Figure 2.27: Driving a MZM with a three-level electrical driving signal to generate a Duobinary signal.

ponders [80, 81]. Nevertheless, since it has a penalty of around 2− 3 dB in terms of OSNR requirements in comparison to OOK (which results from the triangular shape of the duobinary eye diagram with residual energy in the 0s) it is considered as an unfavorable solution for long-haul transmission.

Figure 2.28: Duobinary eye diagram.

2.3.3 Di

ﬀerential Binary Phase Shift Keying

Diﬀerential binary phase shift keying, or what is referred to for short as diﬀerential phase shift keying (DPSK), is a binary modulation format that encodes informa-tion in the optical phase of the optical symbols. The DPSK signal has two phase states (0 orπ) which can be generated either using an optical phase modulator or a MZM [58]. Due to the chirp and phase inaccuracy problems of optical phase

Multilevel modulation formats for robust long-haul high capacity transmission

Multilevel modulation formats for robust long-haul high

capacity transmission

Multilevel Modulation Formats for Robust

Long-Haul High Capacity Transmission

PROEFSCHRIFT

Summary

Contents

Chapter 1

Introduction

1.1

Motivation

1.2

Structure of this thesis

1.3

Contributions

Chapter 2

Fiber Optic Transmission

Systems

2.1

Structure of Todays Optical Networks

2.2

Fiber Optic Transmission Channel

2.2.1

Fiber Loss

2.2.2

Fiber Loss Compensation

EDFA Amplification

Raman Amplification

2.2.3

Chromatic Dispersion

Chromatic Dispersion Compensation

2.2.4

Polarization Mode Dispersion

2.2.5

Nonlinear Transmission Impairments

Interchannel Nonlinear E

ﬀects

Intrachannel Nonlinear E

ﬀects

Cross-Polarization Modulation

Nonlinear Phase noise

2.3

Optical Modulation Techniques

2.3.1

On-O

ﬀ Keying

2.3.2

Duobinary

2.3.3

Di

ﬀerential Binary Phase Shift Keying