Use of a microwave photonic filter for demonstration of simultaneous bidirectional transmission

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por ser mi referente de vida. A mi familia, por su amor y apoyo constante. A la memoria de mi papi, porque desde el cielo me est´a cuidando.

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Agradecimientos

A Dios por darme la vida y por poner en mi camino ´angeles que con-tribuyeron en mi crecimiento personal y profesional.

A mis papas, porque me ofrecieron la dicha de crecer en un hogar basado en principios y valores.

A mis hermanos y cu˜nada, por sus palabras de aliento y apoyo emocional.

A mi hijo-sobrino Joaqu´ın, que a pesar de que no fui participe de su crecimiento, a la distancia estaba pendiente de ´el.

A la memoria de mi abu Laury, porque lo primero que quer´ıa hacer al regresar a Ecuador era escuchar sus amenas pl´aticas mientras disfrutabamos del tan infaltable caf´ecito.

A Jorgito porque desde ni˜na nunca me falto su apoyo. Gracias por ser mi segundo pap´a.

A Vic por ser parte de mi hermoso presente. Dios cuide y bendiga nues-tra relaci´on.

A mi asesor, el Dr. Ignacio Zald´ıvar, por ofrecerme la oportunidad de trabajar a su lado y brindarme sus ense˜nanzas. Gracias por ser mi mentor durante mi doctorado, por su paciencia, consideraci´on y amistad.

A mis sinodales, por sus sugerencias y comentarios.

Al Dr. Min Won Lee, por guiarme y permitirme explorar nuevos campos de la ´optica.

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A mis amigos de INAOE y de la Universit´e Paris 13, por su valioso apoyo.

A M´exico, mi segundo hogar, las experiencias y viviencias en este pa´ıs fueron, son y ser´an inolvidables.

A Consejo Nacional de Tecnolog´ıa (CONACYT) por el apoyo otorgado a trav´es de la beca No 335148.

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Abstract

The microwave photonic can be considered as the study of opto-electronic devices and systems processing signals at microwave frequencies. The key advantages of microwave photonic links over conventional electrical trans-mission systems, such as coaxial cables and waveguides, include reduced size, weight and cost, low and constant attenuation over the entire microwave modulation frequency range, immunity to electromagnetic interference, low dispersion and high-data transfer capacity. The weight and attenuation ben-efits of microwave photonic links over coaxial cables are particularly com-pelling: typically 1.7 kg/km and 0.5 dB/km for the fiber with 567 kg/km and 360 dB/km at 2 GHz for a coaxial cable.

Research activity in microwave photonic techniques has focused on the photonic distribution of microwave signals, the photonic processing of mi-crowave signals, the photonic generation of mimi-crowave signals and the pho-tonic analog-to-digital conversion. This research is developed taking into account the photonic distribution and processing of microwave signals using a microwave photonic filter.

A microwave photonic filter is a photonic subsystem designed with the aim of carrying equivalent tasks to those of an ordinary microwave filter within a Radio Frequency (RF) system, bringing supplementary advantages inherent to photonics, and also providing features which are very difficult or even impossible to achieve with traditional technologies, such as fast tunability and reconfigurability.

In literature, several architectures of microwave photonic filters have been proposed. However, we use a simple and easy implementation mi-crowave photonic filter architecture which consists of a multimode laser diode, a Mach-Zehnder intensity modulator, an optical fiber, and a photo-detector. The radio frequency to optical conversion is achieved by externally modulating the optical source. The RF signal is conveyed by an optical car-rier and the composite signal is injected to an optical fiber. At the fiber output, the resulting signal is optical to radio frequency converted by a

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photo-detector. The frequency response of this microwave photonic filter is constituted of a series of microwave band-pass windows and it depends on the parameters such as the electrical frequency of the signal injected to the Mach-Zehnder modulator, the fiber chromatic dispersion, the fiber length and the Fourier transform of spectral density of the optical source used.

Analyzing the characteristics of the filter frequency response, such as free spectral range (filter period) and full width half maximum (3-dB band-width), we realized that analog and digital signals could be coded on the filtered microwave band-pass windows. In this regard, it is experimentally demonstrated the bidirectional transmission of analog and digital signals using our microwave photonic filter architecture.

In the experimental results, the signal to noise ratio was the perfor-mance measure used in the transmission of analog TV and digital TV, while eye pattern and bit error rate were the two important metrics utilized to determine the transmission quality of a digital signal.

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Introduction

1.1 Motivation

Nowadays with the advance of the Internet and mobile technologies, we are seeing a growing number of the emerging multimedia applications, in particular in the entertainment domain. These include instant messag-ing, voice and video communication, social networkmessag-ing, online photo album, video-on-demand, high definition television (HDTV) and online gaming (Li et al., 2011). The development of these applications typically involves in an increase of bandwidth demands as well as the development of new technolo-gies that support such requirement.

In this regard, only optical fiber technologies provide the solution to the increasing user bandwidth demands. One of the major advantages of fibers over traditional copper and coax technologies is the virtually infinite bandwidth which translates into a higher data rate capacity and therefore more users (Avigdon, 2008). The wide bandwidth requirement creates new challenges and opportunities to the Service Providers, which are striving to develop emerging optical access technologies.

Fiber-To-The-Home (FTTH) defined as an access network architecture in which the final connection to the subscriber’s premises is the optical fiber, has become a promising solution for broadband access in the future (Bicsi, 2017). For example, according to the “FTTH Panorama LATAM” published by Idate, in Latin America (LATAM) the total number of subscribers will grow from about 14 million at the end of 2018 to about 36 million at the end of 2022. On the other hand, the households (homes passed) connected to fiber will grow from about 40 million at the end of 2018 to about 70 million at the end of 2022, as can be seen in Figure 1 (IDATE, 2018).

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The only disadvantage of having an FTTH system is its flat frequency response obtained due that the standard telecommunication fiber used ex-hibits a chromatic dispersion equal to zero. In this case, it is necessary to utilize a radio frequency filter to select a specific range of frequencies.

Figure 1: Subscribers and household reached by FTTH networks. Retrieved from (IDATE, 2018)

Additionally, the exploitation of the unique properties of the fiber (re-duced size-weight-cost, low and constant attenuation over the entire mi-crowave modulation frequency range, immunity to electromagnetic interfer-ence, low dispersion and high-data transfer capacity) has been a subject of constant research that has led to the development of other technologies. For instance, the microwave photonics that is an interdisciplinary area be-tween microwaves and optical waves. The major functions of microwave photonic systems include photonic distribution, processing and generation of microwave signals (Yao, 2009). This research has been developed taking into account the photonic distribution and processing of microwave signals using a microwave photonic filter.

A microwave photonic filter is a subsystem designed with the aim of car-rying out equivalent tasks to those of an ordinary microwave filter within a radio frequency system bringing supplementary advantages inherent to photonics and also providing features which are very difficult or even impos-sible to achieve with traditional technologies such as tunability and recon-figurability (Capmany et al., 2013). In general, the frequency response of a

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microwave photonic filter is constituted of a series of microwave band-pass windows, this filtering effect is due to the standard telecommunication fiber used exhibits a chromatic dispersion.

Analyzing FTTH systems and microwave photonic filter architectures we realized that a microwave photonic filter can be used in an FFTH system to avoid the radio frequency filters. This innovation could be a solution for broadband access technologies.

1.2 General and Specific Objectives

The main objective of this research is to use a microwave photonic filter architecture for demonstration of simultaneous bidirectional transmission with analog and digital signals.

In literature, several architectures of microwave photonic filter have been proposed and in general they consist of four basic components: an optical source (single continuous wave or a continuous wave source array), a mod-ulator (intensity or phase), a photonic component (delay line fiber or fiber Bragg grating) and a photo-detector. We utilize a Multimode Laser Diode (MLD), a Mach-Zehnder intensity modulator (MZ-IM), a Single Mode Stan-dard Fiber (SM-SF) and a photo-detector (PD), as shown in Figure 2. Com-pared to others architectures this microwave photonic filter architecture is cheaper, simple and easy to implement due to the use of an MLD.

Figure 2: Microwave photonic filter architecture

The frequency response of this filter is constituted of a series of mi-crowave band-pass windows and it depends on the parameters, such as elec-trical frequency of the signal injected to the Mach-Zehnder modulator, fiber chromatic dispersion, fiber length and Fourier transform of spectral density of the optical source used. Analyzing the characteristics of the filter fre-quency response, such as free spectral range (filter period) and full width half maximum (3-dB bandwidth), we realized that analog and digital signals could be coded on the filtered microwave band-pass windows. In this regard,

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it is experimentally demonstrated unidirectional transmission of analog and digital signals when we add radio frequency devices to the microwave pho-tonic filter architecture. These results were the base to propose a new filter architecture for bidirectional transmission of analog TV, digital TV and digital signals.

To fulfill the general goal, three specific objectives are proposed. The first objective is to investigate the bidirectional microwave photonic filtering ef-fect. For this purpose, a simultaneous frequency sweep using two microwave signal generators is performed for bidirectional transmission. In the left-to-right direction, a frequency sweep from 0.01 GHz to 10 GHz is applied. As a result, four filtered microwave band-pass windows in the frequency response of the filter are observed (Figure 48). Due to technical limitations in the maximum frequency of operation of the second microwave signal generator, in the right-to-left direction, only a frequency sweep from 9 kHz to 6 GHz is carried out. Therefore, the filter frequency response is just formed by two filtered microwave band-pass windows (Figure 49).

The second specific objective is to demonstrate bidirectional transmis-sion of analog TV, digital TV, and digital signals at the same time using our microwave photonic filter. These signals are coded on the filtered microwave band-pass windows located around 2 GHz. The selection of this band-pass windows is due to the lack of radio frequency devices operating at high fre-quencies, however, potentially the others filtered band-pass windows could be used. To carry out the bidirectional transmission of analog and digital signals some electronic devices are added such as two color bar generator, a pulse pattern generator, an electrical spectrum analyzer, an oscilloscope as well as radio frequency devices such as antennas and mixers.

The third objective is to analyze the obtained results taking into account figures of merit. The Signal to Noise Ratio (SNR) is the figure of merit used in transmission of analog TV and digital TV signals, while eye pattern and Bit Error Rate (BER) are the ones utilized in the transmission of a digital signal.

1.3 Contribution

The main contribution of this work is the fact that we can replace the traditional approach of signals filtering by a new approach of signals trans-mission using our microwave photonic filter architecture. Several experi-ments will be undertaken to demonstrate the bidirectional transmission of analog TV, digital TV and digital signals.

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To the best of our knowledge, this is the first demonstration of bidirec-tional transmission of analog and digital signals using a microwave photonic filter system. Thus, we found that adding electronic equipment and ra-dio frequency devices to the microwave photonic filter architecture to be a growth application and as yet to be exploited.

1.4 Organization

This thesis has been divided into six chapters. Chapter 1 contains the motivation, objectives, contribution and the organization of this work. Then, Chapter 2 provides the fundamental background used. Chapter 3 and Chapter 4 present the state-of-the-art and the mathematical model of the microwave photonic filter used, respectively. Afterward, Chapter 5 focuses on the experimental setups carry out to transmit bidirectionally analog TV, digital TV and digital signals. Finally, Chapter 6 summarizes the main conclusions and future directions of work are also considered.

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Basic Principles

In this chapter, the basic concepts used for the development of our re-search are defined. It is divided into seven sections. In the first section, the main microwave photonics techniques are explained. In the second section, the optical fiber impairments in optical communication systems are detailed. In the third section, the optical modulation techniques are provided. In the fourth section, the intensity modulation formats are reviewed. In the fifth section, the main characteristics of signals to be transmitted by using the microwave photonic architecture are included. In the sixth section, the fig-ures of merit used to evaluate the performance of our system are presented. Finally, in the seventh section a summary of the chapter is developed.

2.1 Microwave Photonics

The definition of microwave photonics can be considered as falling into two parts: firstly, the study of opto-electronic devices and systems processing signals at microwave frequencies and, secondly, the use of opto-electronic devices and systems for signal handling in microwave systems (Seeds and Williams, 2006; J¨ager and St¨ohr, 2005).

The key advantages of microwave photonic systems over conventional electrical transmission systems, include reduced size, weight and cost, low and constant attenuation over the entire microwave modulation frequency range, immunity to electromagnetic interference, low dispersion and high-data transfer capacity (Marpaung et al., 2013). The weight and attenuation benefits of fiber over coaxial cables are particularly compelling: typically 1.7 kg/km an 0.5 dB/km for fiber with 567 kg/km and 360 dB/km at 2 GHz for coaxial cable (Capmany and Novak, 2007).

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Research activity in microwave photonic techniques has focused on: 1) photonic distribution of microwave signals, 2) photonic processing of mi-crowave signals, 3) photonic generation of mimi-crowave signals and 4) photonic analog-to-digital conversion (Yao, 2012). This section focuses on the pho-tonic distribution and processing of microwave signals techniques, because this research is developed taking into account these issues.

2.1.1 Photonic Distribution of Microwave Signals

The main applications on the photonic distribution of microwave signals are: Radio-over-Fiber systems and Fiber-To-The-x systems. A brief review of these architectures are described below.

• Radio-over-Fiber Systems

The integration of fiber optic and wireless network form the Radio-over-Fiber (RoF) or Hybrid-Fiber-Radio (HFR) systems (Novak et al., 2016). The purpose of this system is the use of optical fiber links to distribute telecommunication standard such as: Wireless-Fidelity (Wi-Fi) (Lee and Choi, 2008) and Worldwide Interoperability for Mi-crowave Access (WiMAX) (Nuaymi, 2007). Table 1 compares the two standards in detail.

Table 1: Comparison of Wi-Fi and WiMAX Technologies. Retrieved from (IEEE, 2012)

Feature 802.11 802.11b 802.11a 802.11g 802.16 802.16a Frequency

(GHz) 2.46 2.4 5.8 2.4 10-66 2-11 Data Rate

(Mbps) 2 11 54 54 32-134 70

Propagation

Distance <100 m <100 m <100 m 200 m 1.5-5 km 5-8 km Channel

Bandwidth (MHz)

20 25 20 20 25 Adjustable

1.25-25

A typical RoF system is shown in Figure 3, where there is a Central Station (CS) or Central Office (CO) that contains data resources, op-tical transmitters (TX) and Receivers (RX) respectively with lasers and photo-detectors (PD).

In the down-link direction, the CS up-converts the electrical signal to optical signal and it uses the Optical Distribution Network (ODN) to communicate with the Base Station (BS), in some cases using Remote

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Nodes (RN) where the optical signal is amplified, splitted or multi-plexed towards the corresponding BS that converts it back to electrical domain and radiates it to the Mobile Terminal (MT) end-user.

In the up-link direction, the BS receives the signal from the MT, and depending on the configuration of the BS, this signal can be down-converted before modulating an electro-optical device to transmit the up-link information via the ODN back to the CS (Beas et al., 2013).

RoF has several advantages over conventional coaxial cables or wireless systems:

– Low attenuation by the use of optical fibers.

– Simplicity and cost-effectiveness since it centralizes resources at the CS where they can be shared; and remote simple BS consist-ing of only an optical-to-electrical converter, Radio Frequency (RF) amplifiers and antennas.

– High capacity because higher frequencies can be transported through RoF systems allowing accommodate hight data rates transmission for future service demands.

– Flexibility because it allows independent and multi-service op-eration, the same RoF network can be used to distribute traffic from many operators and services.

Figure 3: General RoF system architecture. Retrieved from (Beas et al., 2013)

• Fiber-To-The-x Systems

Fiber–To-The-x (FTTx) is a generic term to provide broadband con-nectivity to subscribers in the access network. The x letter indicates

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how close the fiber endpoint comes to the subscribers (Keiser, 2006). Figure 4 illustrates the most common FTTx architectures such as:

– Fiber-To-The-Home (FTTH)

It is an access network architecture, between the Optical Line Termination (OLT) and the Optical Network Unit (ONU) or Ter-minal (ONT), in which the final connection to the subscriber’s premises (home or place of business) is an optical fiber. The fiber optic communications path terminates on or inside the premises for the purpose of carrying communication services to a single subscriber (FTTH-Council, 2016).

– Fiber-To-The-Business/Curb/Cabinet (FTTB/C/Cab)

The FTTB/C and FTTCab network options are predominantly different only as a result of implementation, that means the fiber optic communications path end within a building, curb or cabinet. The final connection to the subscriber’s premises, between the ONU and the Network Termination (NT) is via copper cables (FTTH-Council, 2016).

Figure 4: FTTx architecture. Retrieved from (G.983.1, 2005)

• Passive Optical Network

The most popular solution deployed among operators for FTTH is the Passive Optical Network (PON). This Point-to-Multipoint (P2MP) architecture uses passive elements in the network transmission path,

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from source to destination, to divide up the bandwidth among the end users – typically 32 over a maximum distance of 10-20 km (Morant et al., 2011). The presence of only passive devices (optical fiber, splices and splitters) in the network makes it relatively more fault tolerant and decreases its operational and maintenance costs.

As illustrated in Figure 5, a typical PON consists of an OLT at the service provider’s CO, a number of terminals near end-user device called ONU or ONT, which deliver network traffic to the subscribers, and an ODN that provides the optical transmission medium for the physical connection of the ONUs to the OLTs (Lam, 2011).

Figure 5: PON Architecture. Retrieved from (G.983.1, 2005)

Table 2 shows the different PON technologies standardized by Interna-tional Telecommunication Union (ITU) and Institute of Electrical and Electronics Engineers (IEEE). The ITU is responsible for G.983 series Broadband PON (BPON) (G.983.1, 2005), and G.984 series Gigabit-capable PON (GPON) (G.984, 2012). The development of 802.3ah and 802.3av series are respectively in charge of IEEE for Ethernet PON (EPON) (Beck, 2005) and 10 GEPON (Tanaka et al., 2010).

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Table 2: PON Technologies. Retrieved from (Vukovic et al., 2007)

BPON EPON GPON 10 GEPON

Standar ITU G.983

IEEE 802.3ah (1 Gbps) IEEE 802.3av

(10 Gbps)

ITU G.984 IEEE P802.3av

Downstream Data Rate 155, 622 Mbps 1.25, 10.3 Gbps

155, 622 Mbps, 1.2, 2.5 Gbps

IP 2.4 Gbps Broadcast 5Gbps Upstream Data Rate 155, 622 Mbps 1.25, 10.3 Gbps

155, 622 Mbps,

1.2, 2.5 Gbps 2.5 Gbps Downstream

Wavelength

1490,

1550 nm 1550 nm

1490,

1550 nm 1550 nm Upstream

Wavelength 1310 nm 1310 nm 1310 nm 1310 nm Protocol ATM Ethernet ATM Ethernet,

TDM Ethernet

Voice ATM VoIP TDM VoIP

Video RF 1550 nm

IP 1490 nm IP 1550 nm

RF 1550 nm

IP 1490 nm IP 1490 nm Max

PON splits 32 32 64 128

Max

Distance 20 km 20 km 60 km 10 km

Avarage Bandwidth

per User

20 Mbps 60 Mbps 40 Mbps 20 Mbps

The bandwidth demand for PON subscribers is depicted in Table 3, where the bandwidth requirements for different applications in a typ-ical household is summarized.

Table 3: Bandwidth requirements for different IP services. Retrieved from (Lam, 2011)

Application Bandwidth QoS

Video (SDTV 3.5 Mbps Low loss, low jitter, constant bit rate Video (HDTV) 15 Mbps Low loss, low jitter, constant bit rate Telecommuting 10 Mbps Best effort, bursty

Video gaming 10 Mbps Low loss, low jitter, bursty

Voice 64 Kbps Low loss, low latency, constant bit rate Peer-to-peer

downloading

100 Kbps

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2.1.2 Photonic Processing of Microwave Signals

Microwave photonic techniques offer unique features for the processing of microwave signals. The application that has been extensively developed is the microwave photonic filtering (Capmany and Novak, 2007).

A Microwave Photonic Filter (MPF) is a photonic subsystem designed for carrying equivalent tasks to those of an ordinary microwave filter within an RF system, bringing supplementary advantages inherent to photonics such as low loss, high bandwidth, immunity to electromagnetic interference, and also providing features which are very difficult or even impossible to achieve with traditional technologies, such as fast tunability and reconfigurability (Capmany et al., 2013).

The main advantages and disadvantages of the MPF are listed below:

• Tunability: It refers to the possibility to dynamically change the po-sition of the filter resonances or notches, altering the sampling period

T. Solutions that include the use of switched fiber delay lines and high dispersion fibers have been proposed.

• Spectral Periodicity: It limits the bandwidth of the RF signals to be processed.

• Fiber Non-linearity: It can not be neglected if the optical carriers used in filter implementation deliver enough power in a fiber.

More information about the microwave photonic filters will be find in Chapter 3 and Chapter 4, where different MPFs architectures and the MPF mathematical model used will be respectively presented.

2.2 Optical Fibers

In this section the attenuation and dispersion as the most relevant optical fibers impairments that restrain the performance of the optical communica-tion systems are described. Attenuacommunica-tion is an intrinsic power loss that limits the magnitude of the optical power transmitted, whereas the dispersion lim-its the rate at which data may be transmitted by the fiber (Saleh and Teich, 1991). Their influence in the Single-Mode Standard Fiber (SM-SF) systems will be explained in detail in the following subsections.

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2.2.1 Attenuation

Light traveling through optical fiber exhibits a power that decreases ex-ponentially with the optical link length as a result of the material absorption and scattering. The attenuation coefficient α is usually expressed in units of [dB/km] as (Agrawal, 2012):

α=₋10

L log

Pout

(2.1)

wherePinis the power launched at the input of a fiber of lengthL, andPout is the transmitted power.

Figure 6 depicts the attenuation coefficient as a function of wavelength

λ, as well as the intrinsic (absorption by fused silica glass SiO2), and the

extrinsic (absorption by impurities within silica) losses that contribute to the light attenuation.

Figure 6: Attenuation versus wavelength. Retrieved from (Van Den Borne, 2008)

The sources of intrinsic absorption are ultraviolet absorption, infrared absorption and Rayleigh scattering (Van Den Borne, 2008). In the ultravio-let and infrared absorption, the dominant loss mechanisms are respectively electronic (λ < 400 nm) and vibrational (λ > 1700 nm) resonances of the

SiO2 molecules.

Rayleigh scattering arises from microscopic fluctuations in the material density. Silica molecules move randomly in the molten state and freeze in place during fiber fabrication. Resulting local fluctuations in the refractive index scatter light in all directions. It is proportional to the inverse fourth-power of wavelength (1/λ4

), and therefore attenuates shorter wavelength more than longer wavelength (Agrawal, 2007).

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The remaining contribution to the fiber attenuation is the extrinsic ab-sorption due to hydroxyl (OH−

) vibrations associated with the presence of residual water vapor in the silica. There are OH−

absorption peaks nearλ= 950 nm, 1240 nm and 1390 nm (Djordjevic et al., 2010) as shown in Figure 6.

Taking into account the precedent fiber impairments, the ITU defined wavelength bands of interest for optical communication systems (G.Sup39, 2016). Table 4 lists the spectral bands for SM-SF systems. The O band centered at λ0=1310 nm presents 0.5 dB/km of attenuation, and the C

band centered atλ0=1550 nm exhibits 0.275 dB/km of attenuation (G.652,

2016).

Table 4: Spectral bands for single-mode fiber systems. Retrieved from (G.Sup39, 2016)

Band Descriptor Range (nm) O Original 1260 to 1360 E Extended 1360 to 1460 S Short wavelenght 1460 to 1530 C Conventional 1530 to 1565 L Long wavelenght 1565 to 1625 U Ultra-long wavelenght 1625 to 1675

2.2.2 Chromatic Dispersion

When a short pulse of light travels through an optical fiber its power is dispersed in time because different frequency components that constitute the pulse travel at different velocities νg =c/n(λ), whereνg is the group veloc-ity, cis the speed of light in vacuum andn(λ) is the wavelength dependence of the fiber’s refractive index. The difference in velocities among different spectral components within the same mode is called chromatic dispersion.

In Figure 7, the pulse broadening in a dispersive fiber is shown. The low-frequency component (long wavelength) travels faster than the high fre-quency component (short wavelength) and arrives earlier (Saleh and Teich, 1991).

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Figure 7: Pulse broadening in a dispersive fiber. Retrieved from (Iga and Kokubun, 2005)

A specific spectral component, characterized by the angular optical fre-quencyω, will arrive at the output of the fiber after some time group delay as

τg =

L νg

(2.2)

whereνg is the group velocity at which the energy of an optical pulse travels and it is defined in function of the propagation constant β by (Djordjevic et al., 2010)

νg =

dβ dω

−1

(2.3)

As a result of the difference inτg, the optical pulse disperses after trav-eling a certain distance, and the pulse broadening ∆τg can be expressed in function of the frequency bandwidth of the source ∆ω as well as the wave-length bandwidth of the source ∆λ as follows

∆τg =

dτg

dω∆ω = dτg

dλ∆λ (2.4)

Replacing the equations 2.2 and 2.3 into the first term of Equation 2.4, we obtain

∆τg =

d

Ldβ dω

dω ∆ω =L d2

β

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If it is defined as ω= 2πc/λand ∆ω =−(2πc/λ2)∆λ, Equation 2.5 can be rewritten as

∆τg =L

d2

β dω2

−2_λπc2 ∆λ

=LD∆λ (2.6)

where D [ps/nm-km] represents the chromatic dispersion parameter deter-mined by (Agrawal, 2012)

D=₋2πc

λ2

d2

β dω2 =−

2πc

λ2 β2 (2.7)

The parameter β2 = d2β/dω2, known as the Group-Velocity Dispersion

GV D, determines how much an optical pulse would broaden on propagation inside the fiber. From Equation 2.7, it can be expressed as

β2=−D

λ2

2πc (2.8)

The chromatic dispersion has two contributions: material and waveguide dispersion. Therefore, Equation 2.7 can be extended using equations 2.2, 2.3 and ∆ω resulting in (Djordjevic et al., 2010)

D= 1

L dτg dλ = d − λ 2 2πc dβ dλ

dλ =−

1 2πc

2λdβ

dλ +λ

2d 2 β dλ2 (2.9)

where the material dispersionDM is determined by

DM =−

λ2

2πc d2

β

dλ2 (2.10)

and DW is the waveguide dispersion defined by

DW =−

λ πc

dβ

dλ (2.11)

In Figure 8, the material and waveguide dispersions are represented schemat-ically. The material dispersion is caused by the wavelength dependence on the fiber’s refractive index n(λ). The waveguide dispersion occurs because the propagation constant is a function of the fiber parameters and at the same time of wavelength. That means that the optical field is not totally confined to the core of the fiber, a part of it propagates in the cladding which has a different refractive index. This mismatch in refractive index causes waveguide dispersion (Van Den Borne, 2008).

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The dependency of wavelength on the propagation constant β(ω) can be expanded in a Taylor series about the frequency ω0 at which the pulse

spectrum is centered as (Agrawal, 2007)

β(ω) =β0+β1(ω−ω0) +

1

2β2(ω−ω0)

2

+...., (2.12) where βm is defined as the nth derivative of β with respect to the angular frequency

βm=

dm_β

dωm

ω=_ω0

(m= 0,1,2, ...) (2.13)

The term β0 in [1/km] represents a constant phase shift, β1= 1/vg in [ps/km] corresponds to the speed at which the envelope of the pulse propa-gates and the second order termβ2 in [ps2/km] is the GVD.

Figure 8: (a) Material and (b) waveguide dispersion. Retrieved from (Downing, 2004)

Figure 9 shows the chromatic dispersion for an SM-SF. Typical values of

Dare in the range 15–18 [ps/nm-km] near 1550 nm. High bit rates optical communications are possible at 1300 nm where D is zero, the drawback is that the attenuation is not minimum. Therefore, Dispersion Shifted Fibers (DSF) have been designed to have a zero-dispersion at 1550 nm, where the fiber attenuation is minimum. The ITU-T recommendation G.653 described in detail the characteristics of DSF (G.653, 2010).

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Figure 9: Chromatic dispersion for (a) SM-SF and (b) DSF fibers. Retrieved from (Massa, 2000)

2.3 Optical Modulation Techniques

This section presents the optical modulation techniques used to super-impose analog and digital signals, to be conveyed through the optical fiber, onto the optical carrier by altering one of the parameters of the carrier sig-nal with respect to a change in the sigsig-nals to be transmitted. The main techniques used to convert signals from the electrical to optical domain are direct modulation and external modulation.

In this work, the external modulation technique based on an intensity modulator Mach-Zehnder is used.

2.3.1 Direct Modulation

In Figure 10, the concept of direct modulation is illustrated. The output of the laser is modulated directly by varying the injection current of the laser diode. Direct modulation uses Return-to-Zero (RZ) modulation format, and the laser switches respectively between on and off for a logical ‘1’ and logical ‘0’, . Thus, the light is emitted only when a ‘1’ is transmitted and no light is emitted when a ‘0’ is transmitted.

The advantage and disadvantages of the direct modulation are (Alwayn, 2004):

• It is a cost-efficient technique and does not require any further optical component apart from the transmitter laser.

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• It cannot be used at bit rates greater than 2.5 Gbps due to the relax-ation oscillrelax-ation of commercial laser diodes.

• Directly modulated lasers are limited by distance.

Figure 10: Direct modulation. Retrieved from (Peucheret, 2009)

2.3.2 External Modulation

The scheme of an external modulation is depicted in Figure 11. A Con-tinuous Wave (CW) laser emits light which power is constant with time (injection current is held constant). A second component, known as a mod-ulator, is then used as a switch to let the light pass whenever the data corresponds to a high power level and to block it whenever the signal is a low power level.

The external modulation technique presents the following advantages and disadvantage (Fukuda, 1999; Numai, 2015):

• Due to the injection current into semiconductor lasers is constant, relaxation oscillation does not exist.

• Most external modulators use Non-Return-to-Zero (NRZ) and RZ modulation formats. The RZ format is preferred in long-haul and ultra-long-haul systems.

• Low optical couple efficiencies between optical modulators and lasers. To overcome this drawback integrated DFB (Distributed Feed-Back) lasers and modulators have been developed.

The external modulator in Figure 11 can be Electro-Absorption Mod-ulators (EAM) and Electro-Optic ModMod-ulators (EOM). The first type relies

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on the modification of the absorption of a semiconductor material when an external electrical field is applied, while the second type is based on the change of the refractive index observed for some crystal under an external electrical field.

The modulators commonly used in optical communication systems are the electro-optic modulators, therefore we exclusively focus on them.

Figure 11: External modulation. Retrieved from (Peucheret, 2009)

2.3.3 Electro-Optic Modulators

The electro-optic modulators are built with crystals such as lithium nio-bate (LiN bO3), lithium tantalate (LiT aO3), cadmium telluride (C_dT e), etc.

The refractive index n of these crystals changes when an electrical fieldE

is applied, this dependence n(E) is called electro-optic effect.

The functionn(E) varies only slightly with E, and can be expanded in Taylor’s series aboutE = 0 as (Saleh and Teich, 1991)

n(E) =n+a1 E+

1 2 a2 E

2

+... (2.14)

where the coefficients of expansion are n = n(0), a1 = (dn/dE)|E=0 and

a2 = (d2n/dE2)|E=0. The second and higher order terms are typically many

orders of magnitude smaller thann. Terms higher than the third can safely be neglected.

From Equation 2.14, if the second term is dominant the electro-optic effect is known as linear or Pockels effect, thus the Pockels medium is char-acterized by

n(E) =n₋1

2 rn

3

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wherer₌₋₂_a1/n3 is the Pockels coefficient.

The most commonly used electro-optic crystal to fabricate external mod-ulators is lithium niobate. LiN bO3 is a birefringent medium because its

refractive indexes depend on the polarization and propagation direction of light. Moreover, it is said to be negative uniaxial due to ne < n0, where

ne = 2.21 is the extraordinary andn0 = 2.3 is the ordinary refractive index

at 1550 nm.

Depending on the parameter of optical carrier to be controlled, the electro-optic modulators can be phase or intensity. The external modulators usingLiN bO3 are assumed by default as will be presented below:

Phase Modulator

A phase modulator is a device that manipulates the phase of optical carrier under the influence of an electric field created by an applied voltage (Binh, 2008). When a beam of light traverses a Pockels cell of lengthL to which an electric fieldE is applied, it undergoes a phase shift

ϕ=n(E)k0L (2.16)

wherek0 = 2π/λ0 is the wavenumber in free space.

Using Equation 2.16 and replacingk0 into Equation 2.16, we obtain

ϕ_≃ϕ0−π

r _n3

EL λ0

(2.17)

whereϕ0 = 2πnL/λ0. If E =V /d is obtained applying a voltageV across

two faces of the cell separated by a distanced, Equation 2.17 becomes

ϕ_≃ϕ0−π

V Vπ

(2.18)

Figure 12 illustrates the linear relation between the optical phase shift and the voltage. The phase of an optical wave can be modulated by varying the voltage that is applied to a material through which the light passes.

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Figure 12: Voltage vs optical phase shift. Retrieved from (Saleh and Teich, 1991)

From Equation 2.18, the parameterVπ (half-wave voltage) is the applied voltage at which the phase shift changes byπ, as

Vπ =

d L

λ0

r _n3 (2.19)

Since the crystal is an anisotropic medium, its electro-optic coefficientr

depends on the direction of light propagation, and the applied E. Taking this into account, the phase modulator can be respectively called longitu-dinal (see Figure 13(a)) or transverse (see Figure13(b)), if E is parallel or perpendicular to the direction of light propagation.

The speed at which a modulator operates is limited by electrical capacity effects, and by the transit timeT of the light through the material. If E(t) varies significantly within T, the traveling optical wave will be subject to different E as it transverses the crystal. One method to reduce T is to apply the voltage at one end of the crystal while the electrodes serve as a transmission line, as is showed in Figure 13(c). If the velocity of the traveling electrical wave matches that of the optical wave,T effects can be eliminated.

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Figure 13: Phase modulators configuration: (a) Longitudinal, (b) Transverse, and (c) Traveling-wave transverse. Retrieved from (Saleh and Teich, 1991)

Figure 14 shows an integrated phase modulator, the waveguide is often fabricated inLiN bO3 by diffusing titanium to increase the refractive

in-dex. The electrical field is applied to the waveguide using electrodes. Due to the transverse configuration of this modulator and the fact that the width of the waveguide is smaller than the length (d << L), the Vπ can be as small as a few volts.

Figure 14: Integrated phase modulator. Retrieved from (Saleh and Teich, 1991)

An anisotropic medium has two linearly polarized normal modes that propagate with different velocities (c0/n1 and c0/n2). In the presence of E

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the two refractive indices are modified in accordance to Equation 2.15, as

n1(E)≃n1−

1 2r1n

3 1E

n2(E)≃n2−

1 2r2n

3

2E (2.20)

wherer1andr2are Pockels coefficients. After the propagation of the distance

Lthe modes undergo a phase retardation (with respect to each other) given by

Ψ =k0[n1(E)−n2(E)]L

=k0(n1−n2)L−

1 2k0(r1n

3 1−r2n

3

2)EL (2.21)

If E is obtained by applying a voltage between two surfaces of the medium separated by a distance d, Equation 2.21 is reduced to

Ψ = Ψ0−π

V Vπ

(2.22)

where Ψ0 = k0(n1 −n2)L is the phase retardation in the absence of the

electrical field, and Vπ is the half-wave voltage necessary to obtain a phase retardation π, defined as

Vπ =

d L

λ0

r1n31−r2n32

(2.23)

Intensity Modulator

An intensity modulator can be formed by combining a phase modulator with an interferometer. In Figure 15(a) a phase modulator placed in one branch of a Mach-Zehnder interferometer to function as an intensity mod-ulator is illustrated. If the beam splitters divide the optical power equally, the transmitted intensity I0 is related to the incident intensity I_i by

I0 =

1 2Ii+

1

2Iicosϕ (2.24)

Using the trigonometric identity, cos2

(ϕ/2) = 1/2 + cosϕ/2, this equation can be rewritten as

I0 =I_icos 2 ϕ 2 (2.25)

where ϕ= ϕ1−ϕ2 is the difference between the phase shifts encountered

by light as it travels through the two branches. The transmittance of the interferometer is T ₌_I0/I_i= cos2(ϕ/2).

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Figure 15: Intensity modulator Mach-Zehnder: (a) Scheme and (b) Transmittance. Retrieved from (Saleh and Teich, 1991)

Due to the presence of the phase modulator in branch 1, according to Equation 2.18 we have ϕ1 = ϕ10−πV /Vπ, so that ϕ is controlled by the applied voltage in accordance with the linear relationϕ=ϕ1−ϕ2 =ϕ0−

πV /Vπ, where the constant ϕ0 = ϕ10 −ϕ2 depends on the optical path

difference. The transmittance of the device is, therefore, a function of the applied voltage

T₍_V_{) = cos}2

ϕ0

2 −

π

2

V Vπ

(2.26)

This function is plotted in Figure 15(b) for an arbitrary value of ϕ0. The

device can be operated as a linear intensity modulator by settingϕ0 =π/2

and operating in the nearly linear region around T _{= 0}_._{5. Alternatively,} the optical path difference may be adjusted so thatϕ0 is a multiple of 2π.

In this caseT_{(0) = 1 and}T₍_V_π_{) = 0, thus the modulator switches the light} on and off asV is switched between 0 andVπ.

Figure 16 shows the simple structure of an integrated Mach-Zehnder Intensity Modulator (MZ-IM). The input optical signal is splitted into two paths via a Y junction. One of the optical paths is phase-modulated and another path remains un-modulated. If theY junction splits the input signal into two equal electric fields, the induced phase difference isϕ0 = 0, and the

combined signal at another end of Y junction is (Ho, 2005)

I0 =

Ii 2

1 + cos

πv(t) Vπ

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where v(t) is the driven voltage which can be defined as

v(t) =Vbias+VRF (2.28)

whereVbias is a DC voltage called modulator bias, and VRF is the electrical drive signal applied to the IM electrodes. In order to operate the MZ-IM on its linear region, the voltage Vbias should vary about ±Vπ/2. If the electrical drive signal have the formVRF =Vmcos(ωmt), therefore, Equation 2.28 is rewritten as

v(t) = Vπ

2 +Vmcos(ωmt) (2.29)

where Vm is the electrical signal amplitude, ωm = 2πνm is the electrical angular frequency andνm is the modulation frequency.

Replacing Equation 2.29 into Equation 2.27, we get

I0 =

Ii 2

1 + cos

π

2 +π

Vm

Vπ

cos(ωmt)

(2.30)

and using the trigonometric identity cos(a+b) = cosacosb₋sinasinb, this equation is reduced to

I0=

Ii

2[1−sin(mcos(ωmt))] (2.31) wherem=π(Vm/Vπ) is the modulation index. If the MZ-IM operates on the linear region, the modulation index is small (m_≪0.1) and the second term of this equation becomes to sin(mcos(ωmt)) ≃ mcos(ωmt) (Al-Raweshidy and Komaki, 2002). Thus, Equation 2.31 can be written as

I0 =

Ii

2[1 +mcos(ωmt)] (2.32)

Finally, when the drive voltage of Equation 2.29 is applied to the modulator’s RF port, the transmittance of the MZ-IM is given by

T₍_t_{) =} 1

2x(t) (2.33)

where

x(t) = 1 +mcos(ωmt) = 1 +1

2mexp(jωmt) + 1

2mexp(−jωmt) (2.34) is the modulated optical signal at the output of the MZ-IM.

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Figure 16: Integrated intensity modulator Mach-Zehnder. Retrieved from (Saleh and Teich, 1991)

2.4 Intensity Modulation Formats

In this section the modulation format used to code an electrical signal onto the optical carrier is reviewed. The most popular modulation format is based on the binary intensity format for which the system design is simple and inexpensive.

The two common intensity modulation formats, in optical communi-cation systems, are Non-Return-to-Zero On-Off Keying (NRZ-OOK) and Return-to-Zero On-Of Keying (RZ-OOK). The NRZ is the modulation for-mat used in our experimental setup. The main features of the NRZ and RZ are described below.

2.4.1 Non-Return-to-Zero

In Figure 17 the features of the NRZ modulation format is presented. In the NRZ format, the pulse for a ‘1’ bit occupies the entire bit interval, and no pulse is used to ‘0’ bit. If there are two successive ‘1s’, the pulse occupies two successive bits intervals. In Figure 17(a) each bit is allocated at a time

T. NRZ pulses are twice as long as the RZ pulses.

The optical spectrum and the eye-diagram of an idealized NRZ signal are respectively illustrated in Figure 17(b) and Figure 17(c). The spectrum has a strong carrier component and there are deep nulls at the multiples of the bit rate (B = 1/T). The carrier frequency contains half the optical power but no information. The NRZ pulses possess a narrow optical spectrum to the lower on-off transitions. The reduced spectral width improves the chromatic dispersion tolerance, but on the other hand it affects the ISI between the

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pulses (Garc´ıa-P´erez et al., 2006).

The diagram of an NRZ transmitter, which is composed of a Continuous Wave laser (CW) and an external modulator MZ-IM, is shown in Figure 17(d). The diagram of a RZ receptor is the simplest, because it only needs a photo-detector to convert the optical signal to the electrical signal (see Figure 17(e)).

Figure 17: NRZ modulation format: (a) Intensity, (b) Optical spectrum (c) Eye-diagram, (d) Transmitter diagram and (e) Receptor diagram. Retrieved from (G.Sup39, 2016)

The operation of the MZ-IM for the NRZ modulation is depicted in Figure 18. The MZ-IM is voltage biased in the quadrature point and is driven from minimum to maximum transmittance. The NRZ electrical signal which is feed on the RF port of the modulator, requires a peak-to-peak amplitude of Vπ.

Another important parameter to be considered is the electrical spectrum. The electrical spectrum of the NRZ and RZ formats are depicted in Figure 19, theirs bandwidth are respectively BW = 1/T and BW = 2/T. In the NRZ format, the signal occupies a much smaller bandwidth about half that of the RZ format.

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Figure 18: Operation of a MZ-IM for NRZ modulation. Retrieved from (Van Den Borne, 2008)

Figure 19: Electrical Spectrum: (a) NRZ and (b) RZ. Retrieved from (Wartak, 2013)

The advantages and disadvantage of the NRZ format are listed below:

• It is not sensitive to laser phase noise compared to Phase Shift Keying (PSK).

• It requires a relatively low electrical bandwidth for transmitters and receivers compared with RZ.

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• It is not suitable for hight bit rate (>10 Gbps) and long-haul systems (1000 and 3000 km).

2.4.2 Return-to-Zero

The main characteristics of the RZ modulation format are provided in Figure 20. In the RZ format, the signal drops to ‘0’ after ‘1’ is transmitted, hence the pulses occupy half of the time slot reserved to each bit, as can be seen in Figure 20(a).

The optical spectrum and the eye-diagram of an idealized RZ signal, are respectively illustrated in Figure 20(b) and Figure 20(c). The RZ modulated signal has relatively broad optical spectrum, resulting in a reduced chromatic dispersion tolerance and a reduced spectral efficiency. The spectral efficiency is defined as the ratio of the bit rate to the bandwidth used by the signal (Wartak, 2013). The RZ pulse shape enables an increased robustness to fiber non-linearities (Garc´ıa-P´erez et al., 2006).

Figure 20(d) illustrates the block diagram of the RZ transmitter which is basically an NRZ transmitter with an extra external modulator (MZ-IM pulse carver) driven by an electrical clock that can be achieved by a sinusoidal signal at a half data rate (Djordjevic et al., 2010). The main drawback of RZ modulation is the more complex structure transmitter. The configuration of the RZ receptor is simpler, because it only needs a photo-detector (see Figure 20(e)).

Figure 20: RZ modulation format: (a) Intensity, (b) Optical spectrum (c) Eye-diagram, (d) Transmitter diagram and (e) Receptor diagram. Retrieved from (G.Sup39, 2016)

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2.5 Analog and Digital Signals

In this section, some characteristics of the signals transmitted by using the microwave photonic filter architecture are presented. Different analog and digital television broadcasting standards have been adopted in different parts of the world, only the standards used in M´exico are described below.

2.5.1 Analog TV

The National Television System Committee (NTSC) is the analog televi-sion system adopted in 1941 as the first standardized televitelevi-sion broadcasting and video format. NTSC is based on a 525-line, 60 fields/30 frames-per-second at 60 Hz system for transmission and display of video images. In 1953, a second NTSC standard was adopted to allow the color television broadcasting. The frame rate was altered to yield about 29.97 fps to avoid color dot-crawl effects and audio distortion (Cianci, 2012).

Figure 21 shows the main parameters of the NTSC channel. The bright-ness portion of the video signal, which contains all the information of the picture details, is commonly called luminance or visual carrier. It is 1.25 MHz above the lower bound of the channel and generates two sidebands, one above the carrier and one below (4.2 MHz each one). The entire upper sideband is transmitted, but only 1.25 MHz of the lower sideband, known as a vestigial sideband, is transmitted. The color portion of the video signal, which contains information about the picture hue (or tint) and color satu-ration, is called the chrominance or chroma subcarrier. It is located at 3.58 MHz above the video carrier. The sound audio carrier is called aural and it is 4.5 MHz above the video carrier, making it 250 kHz below the top of the channel. The total bandwidth of the NTSC channel is 6 MHz (Ovadia, 2001).

Assessment of picture quality in presence of noise interference is a matter of subjective judgment that may vary from viewer to viewer. In this regard, a number of studies have been done for the quality of television picture in terms of Signal-to-Noise-Ratio (SNR). One of the more extensive studies, the results of which are readily available an often quoted, was performed for the Television Allocation Study Organization (TASO) by Dean (Dean, 1960; Collins, 1969). The essential results of this study are indicated in Table 5 which gives the SNR of the TV signal corresponding to the rated quality and percentage of the viewers.

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Figure 21: TV channel spectrum. Retrieved from (Avigdon, 2008)

Table 5: Picture quality in terms of SNR by the 90% of the viewers. Retrieved from (Dhake, 1999)

Grade Quality

rating Description

SNR (dB)

1 Excellent Picture of extremely high quality as good as could be desired 50.6 2 Fine Picture of high quality providing

enjoyable viewing 39.4 3 Passable Picture of acceptable quality,

interference not objectionable 32.8 4 Marginal Picture poor in quality, interference

somewhat objectionable 28.6 5 Inferior Picture very poor but watchable,

interference definitively objectionable 22.6 6 Unusable Picture too bad to be watched <22

2.5.2 Digital TV

The analog shutdown is the process in which old analog television broad-casting is converted to and replaced by digital television. M´exico switched off its analog terrestrial services in 2015 and adopted the Advanced Televi-sion System Committee (ATSC) standard (IFT, 2015).

The ATSC is the Digital Television Terrestrial (DTT) standard designed to maximize the ability to transmit high quality video and audio and an-cillary data within a single 6 MHz terrestrial television broadcast channel. This system uses the MPEG-2 transport stream syntax for the packetization and multiplexing of video, audio, and data signals for digital broadcasting

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systems (BT.2140, 2018).

In the guide to the use of the ATSC digital TV standard, it is showed that the required SNR for digital TV reception is 14.9 dB (ATSC, 2006).

2.6 Figure of Merit

In this section, a review of three important and powerful measures to determine the transmission quality of analog and digital in an optical com-munication systems are discussed. These measurements are the Signal-to-Noise-Ratio (SNR), eye pattern and Bit-Error-Rate (BER) which are de-scribed below.

2.6.1 Signal to Noise Ratio

The SNR is a measure that compares the level of a desired signal to the level of background noise. The higher the value of SNR, the greater will be the quality of the received output. SNR is defined as the ratio of the signal powerPsignal to the noise power Pnoise as in (Dhake, 1999).

SN R= 10 log10

Psignal

Pnoise

(2.35)

2.6.2 Eye Pattern

The eye diagram is a useful tool for the qualitative analysis of digital signals. It is an oscilloscope display of a digital signal, repetitively sampled (superimposing the 1’s and 0’s) to get a good representation of its behavior. The majority of eye calculations are based on histograms plots. His-tograms are used to statically analyze time and amplitude data of eye di-agrams, offering important computational information when observing im-pairments in hight-speed digital signals. There are two types of histograms:

• Vertical histogram. For every time point, sum up the number of traces across vertical bins.

• Horizontal histogram. For every amplitude point, sum up the number of points across time axis.

Mean and standard deviation are two important aspects of the time and amplitude distortion in a high-speed data stream. The mean is the sum of data values divided by the number of values and the standard deviation is

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a measure of the spread of data. The _±1σ (_±34%) and _± 3σ (_±49.85%) are respectively the 68% and 99.7% of data points for a normal distribution (Agilent-Technologies, 2008).

Figures 22 and 23 illustrate the type of information that can be deter-mined from the eye diagram. The main parameters include amplitude and time definitions:

Amplitude definitions for eye patterns (vertical axis)

• One levelis the mean value of a logic one. The computed value of the one level comes from the histogram mean value of all the data samples captured inside the middle 20% (40 to 60 % region) of the eye period.

• Zero level is the mean value of the logic zero. It is also computed from the same 40 to 60 % region of the baseline area during the eye period as the one level.

• Eye amplitudeis the difference between the one and zero levels. The data receiver logic circuits will determine whether a received data bit is a ‘1’ or ‘0’ based on the eye amplitude. It is determined by

Eye amplitude=one level₋zero level (2.36) • Eye height is a measurement of the vertical opening of an eye dia-gram. The noise on the eye will cause the eye to close. The difference between the inner 3σ points on the inside of the histograms of the one and zero levels is defined as eye height as

Eye height= (one level₋3σ)₋(zero level+ 3σ) (2.37) • Eye crossing %is a measure of the amplitude of the crossing points relative to the one and zero level. It provides a clear indication of how well the system’s data pulse symmetry is performing. The Eye crossing % is obtained by

Eye crossing % = 100_×

crossing level₋zero level one level₋zero level

(2.38)

where the crossing level (eye crossing amplitude) is determined by taking the mean value of a thin vertical histogram window centered on the crossing point.

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• Q-factoris a figure of merit for an eye diagram indicating the vertical eye opening with respect to the noise at both the high and low voltage levels. The Q-factor or the Signal-to-Noise-Ratio (SNR) is calculated by

Q₋f actor= (one level−zero level) 1σ one level+ 1σ zero level

(2.39)

Higher Q-factor values are more desirable than lower Q-factor values.

Figure 22: Eye pattern parameters (amplitude). Retrieved from (Agilent-Technologies, 2008)

Time definitions for eye patterns (horizontal axes)

• Unit interval (UI) is the time between eye crossing (one data bit-width). This normalizing term is independent on the data rate, and therefore eye diagrams with different data rates can be easily com-pared. In a 10 Gbps data stream, for example, one UI is equivalent 100 ps.

• Eye width is a measure of the horizontal opening of an eye diagram. It is the distance between the inner 3σ points on the horizontal his-tograms.

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• Rise time is a measure of the mean transition time of the data on the upward slope of an eye diagram. To measure the rise time, two thin horizontal histogram slices are placed at the 20 % level (to the left of the eye crossing) and at the 80 % level (to the right of the eye crossing). This parameter is calculated using the following equation

Rise time=mean(80%time level)−mean(20%time level) (2.41)

• Fall time is measured on the downward transition time of a data bit and is determined by

F all time=mean(80%time level)−mean(20%time level) (2.42)

• Jitter is an instantaneous unintentional deviation in the ideal timing between symbols. Jitter occurs whenever the transition to the next symbol state occurs earlier or later than the end of the exact symbol time interval (Derickson and M¨uller, 2007).

Jitter is a measurement of the variance in time locations of the cross-ing points. To compute jitter, the time variances of the riscross-ing and falling edges of an eye diagram at the crossing point are determined. The peak-to-peak jitter is defined as the full width of the histogram, meaning all data points present. RMS jitter is the standard deviation of the histogram.

Figure 23: Eye pattern parameters (time). Retrieved from (Anritsu-Company, 2010)

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2.6.3 Eye Pattern Mask

Strict performance standards for the eye pattern diagnostic have been developed by the ITU-T. These guideline measurements represent the per-formance limit lines for the eye pattern and are known as “masks”.

Figure 24 shows the mask of the eye diagram for the transmission of signals at 155.52 Mbps, 622.08 Mbps and 1244.16 Mbps (BPON technology, see Table 2) (G.983.1, 2005).

Figure 24: Eye pattern mask. Retrieved from (G.983.1, 2005)

2.6.4 Bit Error Rate

Bit Error Rate (BER) measurements are the most important system performance characterization tools. It is defined as the ratio of the number of bits incorrectly received to the total number of transmitted bits during a specific time interval. Therefore, a lower BER indicates a better performance of the digital transmission systems. Most digital optical communication systems specified a BER of 10−9

as the operation requirement (Breed, 2005). BER is affected by the attenuation, dispersion, non-linear phenomena or jitter. Its performance may be improved by launching a strong signal into a transmission system or by choosing a robust modulation format.

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The mathematical relation between Q-factor and BER is given by (De-Cusatis and Kaminow, 2009; Freude et al., 2012)

BER= 1

Q√2π exp

−

Q2

2 (2.43)

From this equation, we can realized that BER decreases as the Q-factor increases. For a Q-factor ranging from 6 to 7, the BER is obtained as of 10−9

up to 10−12

(Agalliu and Lucki, 2014).

2.7 Summary

In this chapter was provided the fundamental background of the research and it was divided into six sections. In the first section, the definition, advantages, and techniques of the microwave photonic were reviewed. This work was focused on the photonic distribution and processing of microwave signals by using a microwave photonic filter. In the second section, the attenuation and chromatic dispersion in SF were presented. The SM-SF due to its optical structure gives the minimum pulse broadening and thus is capable of the greatest transmission bandwidth (100 GHz_×km).

In the third section, the advantages and disadvantages of the direct and external modulation were described. Furthermore, some characteristics of the phase and intensity modulator were given. Note that the external mod-ulation technique based on an intensity modulator was used in the exper-imental setup. In the fourth section, the advantages and disadvantages of the intensity modulation formats were reviewed. NRZ is the modulation format used.

In the fifth section, the main characteristics of analog and digital TV sig-nals to be transmitted by using the microwave photonic architecture were provided. Television’s main advantage is the transmission of visual images through electrical signals. NTSC is the standard for analog TV transmis-sion while ATSC is standard for digital TV transmistransmis-sion. Finally, in the sixth section, the figures of merit used to evaluate the performance of our system were presented. The Signal to Noise Ratio (SNR) is the performance measure in analog signals transmission, while that the eye pattern and BER are the performance measure in digital signals transmission.

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State of the Art

In this chapter, the architectures of the microwave photonic filters re-ported in the literature during the last years are reviewed. It is divided into two sections. In the first section, a general layout of a microwave pho-tonic filter is shown. According to this layout, the state of the art of the microwave photonic filter is performed taking into account the intensity modulator used. Finally, in the second section a summary of the chapter is presented.

3.1 Microwave Photonic Filter

In recent decades, extensive efforts have been directed to the design and successful implementation of different MPF architectures based on various photonic components. Figure 25 shows a general layout of an MPF and it consists of four components: an optical source (single source or array of sources), a modulator (intensity or phase), a photonic component and a photo-detector. The key device in the microwave photonic filter is the photonic component module, which can be implemented using an array of Fiber Bragg Gratings (FBG) or a dispersive fiber (Yao, 2015).

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Figure 25: General layout of a microwave photonic filter. Retrieved from (Gasulla and Capmany, 2012)

According to this layout, the state of the art of the microwave photonic filter is focused on those investigations that are based on an intensity mod-ulator, for being the closest to our research and they are described below.

3.1.1 Based on Intensity Modulator

In one of the first research works of Mora et al. (2002) report a tunable, reconfigurable and low cost microwave photonic filter based on a broadband optical source sliced by Uniform Fiber Bragg Grating (UFBG). High tun-ability can be performed by stretching the fiber with the gratings written in series. Figure 26(a) illustrates the experimental setup used. This filter is based on a Super-luminescent Diode (SLED), a UFBG, an optical cir-culator, a 90/10 optical coupler, an Electro-Optic Modulator (EOM), an Erbium Doped Fiber Amplifier (EDFA), an optical fiber, and a Light-wave Component Analyzer (LCA) which is not part of the microwave photonic filter.

The UFBGs are 5 cm-long and are written on photosensitive fiber in a series configuration, and they will be stretched to tune the reflection band-width, initially centered atλ0= 1544.69 nm,λ1= 1545.19 nm,λ2= 1545.69

nm andλ4= 1546.19 nm. A fiber length of 23 km is the dispersive element

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shows the experimental RF-transfer function of two filters with Free Spec-tral Ranges (FSRs) of 2.19 GHz (black: filter 1) and 4.05 GHz (blue: filter 2), respectively, together with the theoretical calculation (green: filter 1, red: filter 2). Moreover, the 3-dB bandwidths of the filter 1 and filter 2 is 510 MHz and 960 MHz, respectively.

(a) Experimental setup (b) Transfer function

Figure 26: Microwave photonic filter. Retrieved from (Mora et al., 2002)

In their next work Mora et al. (2003) present a microwave photonic filter configuration with a wide tuning range, good performance, low cost and easy implementation by using a broadband source with an UFBG. This configuration is formed by a Tunable Laser (TL), an UFBG, an EDFA, a 90/10 optical coupler, an EOM, an optical fiber, and an LCA as shown in Figure 27(a).

The authors implement three filters. In the first experiment, the broad-band optical source has a 3-dB broad-bandwidth of 5 nm near 1530 nm. The UFBG is 1 cm-long and is written on photosensitive fiber; its Bragg wavelength is 1530.96 nm, its 3-dB bandwidth is 0.15 nm, and it has a maximum reflectiv-ity of 8 dB. The fiber length is 23 km and exhibits a chromatic dispersion of 15.5 ps/nm.km at 1530 nm. To show the tunability of the system, authors plotted the experimental and theoretical transfer functions of two filters at FSR=1.09 GHz and FSR=5.15 GHz which are depicted in the figures 27(b) and 27(c), respectively.

In the second experiment, two UFBGs and three lasers with a wavelength separation of 1.16 nm are used. The FSR of the filter is 2.40 GHz and the 3-dB bandwidth is 0.437 GHz as can be seen in Figure 27(d). Finally, the

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third experiment includes an optical source with a large bandwidth of 28 nm, and a fiber length of 46 km (17 ps/nm.km at 1550 nm). The FSR is 0.815 GHz, and the 3-dB bandwidth of the filter is 0.176 GHz. Figure 27(e) shows the filter transfer function.

(a) Experimental setup

(b) Transfer function (FSR=1.09 GHz) (c) Transfer function (FSR=5.15 GHz)

(d) Transfer function (FSR= 2.40 GHz) (e) Transfer function (FSR= 0.815 GHz)

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Xue et al. (2009) in their research demonstrate a microwave photonic filter based on the use of slow and fast light effects in Semiconductor Optical Amplifiers (SOA) assisted by optical filtering.

Figure 28(a) describes the experimental scheme. The filter itself is a simple MZ interferometer composed of two arms by two 50/50 couplers, one of which incorporates the microwave phase shifter, shown in the dotted-line box, which is made up of an SOA followed by an FBG notch filter. The EDFA is used to adjust the SOA input optical power to 9 dBm, in order to ensure that the SOA operates in the saturation regime. After the microwave phase shifter, a tunable attenuator provides amplitude balance between the two arms to compensate _∼10 dB power change of the output signal after the SOA. Tuning of the frequency can be achieved by changing the injection current of the SOA. Through switching between the two operating stages (V1=4.5 V and V2=8.1 V) of the MZM. Figure 28(b) shows the measured

filter responses for currents from 90 mA to 230 mA, the FSR is 9.4 MHz.

(a) Experimental setup (b) Transfer function

Figure 28: Filter transfer function. Retrieved from (Xue et al., 2009)

On the other hand, the authors Shahoei and Yao (2013) proposed and demonstrated a tunable microwave photonic filter based on a Tilted Fiber Bragg Grating (TFBG) in an Erbium-Ytterbium (Er/Yb) co-doped fiber. Figure 29(a) shows the experimental setup which consists on: array of laser diodes, optical attenuator (Att), Mach-Zehnder Modulator (MZM), laser diode (LD), Wavelength Division Multiplexer coupler 980/1550 nm (WDM), Single Mode Fiber (SMF), Er/Yb co-doped fiber, EDFA and a

Use of a microwave photonic filter for demonstration of simultaneous bidirectional transmission

Agradecimientos

Abstract

Contents

Demonstration of Simultaneous

Bidirectional Transmission

Introduction

1.1

Motivation

1.2

General and Specific Objectives

1.3

Contribution

1.4

Organization

Basic Principles

2.1

Microwave Photonics

2.2

Optical Fibers

2.3

Optical Modulation Techniques

2.4

Intensity Modulation Formats

2.5

Analog and Digital Signals

2.6

Figure of Merit

2.7

Summary

State of the Art

3.1

Microwave Photonic Filter