Eindhoven University of Technology MASTER Receiver design for a radio over polymer optical fiber system Giesberts, A.

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MASTER

Receiver design for a radio over polymer optical fiber system

Giesberts, A.

Award date:

2003

Link to publication

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Receiver Design for a

Radio over Polymer Optical Fiber System

Almar Giesberts

MSc graduation thesis September 2002 - June 2003 almar.giesberts@praeclara.nl

Supervisors

Anthony Ng’oma, MSc, MTD dr. ir. Idelfonso Tafur Monroy

dr. ir. Peter Smulders Graduation Professor

prof. ir. Ton Koonen

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Preface

This thesis describes my graduation project done at the end of my Master of Science studies in Electrical Engineering at the Eindhoven University of Technology in the Netherlands at the department of Electro-Optical Communications.

I wish to thank my supervisor Anthony Ng’oma for the many discussions and encourage- ments that gave direction to this work. Secondly, I wish to thank my graduation professor prof. ir. Ton Koonen for staying so close to, and having great interest in this work.

Because of the many practical issues involved in this work I wish to thank Frans Huijskens, Peter van Bennekom, Jaap Swijghuisen Reigers and the people at the mechanical workshop for their technical support. Secondly, I wish to thank Jesus Paul Tomillo for writing the measuring-automation software for me.

I wish to thank Piet van Heijningen for lending me the 17.2 GHz microwave filter from his private collection.

I would like to acknowledge the Dutch Ministry of Economic Affairs, Royal Philips Elec- tronics, KPN and Agere Systems for partly funding this project within the BraBant Breed- Band (B4) framework.

Last but not least, I wish to thank my parents and sister, family, friends and especially my girlfriend Karin for giving me the support, encouragement and moments to relax to finish this work.

Almar Giesberts, Eindhoven, June 17, 2003

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Abbreviations

DFB Distributed FeedBack FBG Fiber Bragg Grating FP Fabry-Perot

FP-FBG Fabry-Perot Fiber Bragg Grating FSR Free Spectral Range

GI Graded-Index

GIPOF Graded-Index Polymer Optical Fiber GRIN GRaded-INdex

GaAs Gallium-Arsenide

IM-DD Intensity Modulation Direct Detection

IR InfraRed

InP Indium-Phosphide

MGDM Mode Group Diversity Multiplexing MMF Multi Mode Fiber

NA Numerical Aperture NEP Noise Equivalent Power OSA Optical Spectrum Analyzer PC Polarization Controller PD PhotoDetector

PF PerFluorinated

PMMA PolyMethylMethAcrylate POF Polymer Optical Fiber RF Radio Frequency

RFSA Radio Frequency Spectrum Analyzer RHD Remote Heterodyning Detection RLAN Radio Local Area Network

RMS Root-Mean-Square

RoPOF Radio over Polymer Optical Fiber SMF Single Mode Fiber

SNR Signal to Noise Ratio

SOA Semiconductor Optical Amplifier TLD Tunable Laser Diode

VIS Visible

WDM Wavelength Division Multiplexing

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Abstract

Wireless Local Area Networks are being used at an increasing number of places, in office buildings, hospitals, airport lounges, etc. With the raise in demand for high speed data delivery, these WLANs need to provide higher data transfer capacities, which requires higher microwave frequencies. Thus, the reach of the radio antenna stations gets smaller, and ever more antenna stations are needed to cover a certain area. To keep the system’s costs under control, the antenna stations should be as simple as possible, and as much as possible signal processing functions should be centralized at the headend station. The modulated microwave signals need then to be carried transparently between the antenna station and the headend station. Single-mode optical fibre, as extensively used in long- distance and metropolitan networks, offers adequate bandwidth for this, but is expensive for in-door deployment. Multimode optical fiber, and in particular Polymer Optical Fiber (POF), is much easier to install, but has a limited bandwidth. A novel technique has been devised in the Electro-Optical Communications group to carry microwave signals over POF networks, surmounting the bandwidth bottleneck. The technique relies on optical frequency multiplying, resulting from wavelength-sweeping an optical signal from the headend site over a number of transmission peaks of a periodic optical bandpass filter located at the receiver site.

The task of this M.Sc. graduation project was to design, build and evaluate a receiver performing the optical frequency multiplying. This receiver consists of an optical signal processing part, and an optical-to-electrical high-speed signal processing part.

A careful study has been made of the optical signal processing part. Two main functions can be discerned:

• coupling light from the large core POF to the small active area high-bandwidth photodetector, and

• optical periodic bandpass filtering.

An optical coupling and imaging system using various lenses has been designed and analyzed, which besides POF-to-photodetector coupling should also allow the insertion of a Fabry-Perot etalon acting as the periodic optical bandpass filter. In general, lenses with a short focal length improve the light coupling, but reduce the finesse of the FP etalon.

Achromatic or aspherical lenses should be preferred, as these minimize the spherical aberration, an important limiting factor in lens coupling and FP performance.

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A flexible and comprehensive laboratory setup has been built to test a number of the lens system configurations, and to characterize the FP etalon. Various solid-state FP etalons have been tested, made out of InP substrates by the Opto-Electronic Devices group. Also, in cooperation with the University of Valencia, a Fabry-Perot Fiber Bragg Grating (FP-FBG) has been specified and realized, which has been tested in the laboratory setup. Finally, the system setup has been completed with a high-bandwidth multimode photodetector and a waveguide microwave bandpass filter in order to select and analyze a 17.2 GHz carrier generated by the system.

It has been shown experimentally that very pure microwave carriers can indeed be generated following this optical frequency multiplying method (e.g., a linewidth of less than 100 Hz for a carrier of 17.2 GHz). The POF link does not affect the linewidth of the signal. The measurement results have been compared to the theoretical predictions, and found to be in accordance. The limiting factor in the power stability of the generated microwave carrier is the presence of modal noise due to spatial filtering in the optical signal processing part. The limiting factor in the FP etalon approach has been found to be the pinhole finesse, which is low due to the large core of the launching POF in relation to the small focal length of the lenses because of the limited size of the FP mirrors. The FP-FBG approach looks quite promising due to its low loss and ease of handling, but needs improvement in order to increase the wavelength operation range and equalization of the transmission peaks and their spacings.

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Introduction

Telecommunication technologies have established an important role in our lives. We are working from the information economy to an experience economy in which the experience takes in a more central place than gaining static information only. In the information economy, we cannot interact with the statically provided information that leads to bore- dom. People look for possibilities to interact with information to be part of an adventure.

This adventure or experience is preferably shared with friends. In a business environment flexibility and mobility play an important role. People have to do their work and must communicate with colleagues, at any place, any time in any way.

The consumer and business trends can be seen as the upcoming of an E-culture. In the E-culture, experience takes in a central place for people, and storage and distribution of information takes in a central place for technology. This E-culture changes our lives in the way we communicate.

Our task is to provide the technology needed to drive the upcoming experience economy.

To be specific, broadband wireless networks must be realized to let all multimedia applications and devices communicate smoothly and with high capacity, thus enabling user access anywhere, any time.

1.1 Radio over Fiber

The goal for researchers and engineers is to realize wireless broadband networks that can offer data rates of more than 100 Mbit/s. Wireless systems offering more than 100 Mbit/s will require carrier frequencies beyond 10 GHz [1]. At increasing carrier frequencies, the coverage per radio access point shrinks because the propagation losses become higher and communication becomes a line of sight transmission. The limited covering area per access point will require therefore many access points.

A question can be raised if some functionality of each of the large number of access points can be combined and shared between the access points to reduce the costs of the access points. The answer of this fundamental question is affirmative, and has resulted into a novel research area in which many researchers are working.

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1.1.1 Sharing functionality

To realize a central site, in which functionality of the many remote sites is combined and shared, we have to define that functionality and evaluate if it can be combined and shared. We always have to think about the combination ’broadband’ and ’wireless’ to say something about the architecture of the total system. Let’s start with looking for possibilities to share functionality in the straightforward system architecture where every access point generates a microwave signal and modulates it with data and vice versa.

There must be an antenna at every remote station, which obviously cannot be shared.

Every remote station must have a mechanism to generate the microwave carrier. The generation of stable high-quality microwave carriers is expensive so, if this functional element can be shared among the many access point, we can greatly reduce on costs. The mechanism for generating the microwave carriers is not a function of geometrical space, so there are possibilities for investigating how the generation of microwave carriers can be shared. Down-converting the microwave signal to a baseband signal and the processing of the baseband signal to the actual data signal can also be done at a place away from the antenna. The generation of microwaves, down-converting to baseband and baseband processing can be seen separately at first.

1.1.2 Transporting a microwave signal

If we want to share system function for generating microwaves, we have to put this element in the central site. If we do so, there must be a way to transport this microwave signal, in any form, to the remote stations. If we generate the actual microwave signal at the central site, we have to transport the microwave signal by means of e.g. coaxial cable.

A transmission length of about 500 meters must be achievable for in-building use. For carrier frequencies beyond 10 GHz, coaxial cable is very lossy. The use of coaxial cable for transporting 10 GHz signals over 500 meters, is is therefore not possible.

1.1.3 Using Optical Fiber

Fiber-optic cable has a low loss, a large bandwidth and is cheap compared to coaxial cable, so transportation of microwaves by using fiber-optic cables is very attractive. Transporting microwaves over optical fiber is called in general Radio over Fiber. A way to transport a microwave signal is by modulating it onto an optic carrier by using a laser, and transport it over fiber-optic cable and convert it back to a microwave electrical signal by intensity detection in a photodiode. This is called intensity modulation - direct detection (IM- DD) [2]. A drawback of this configuration is that a microwave source is needed at the frequency of the generated microwave signal and that a laser must be used that is capable of modulating the light by the microwave signal. A different way to (virtually) transport a microwave signal is to generate two optical carriers separated by a frequency equal to the microwave signal to be generated. In the photodetector at the receiving end, the two optical carriers are mixed and the relevant part of mixing products at the output of the photodetector consists of a signal with a frequency equal to the frequency separation of the optical carriers. This is called remote heterodyning detection (RHD) [2]. Some other procedures to use fiber optic cable to transport microwaves are investigated by researchers around the world [3]. Since the RHD method is a coherence method, the

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1.2. RADIO OVER POLYMER OPTICAL FIBER SYSTEM 3

lasers used must be highly coherent and the link must retain this coherency. Singlemode silica fibers can retain the coherency since only one transverse mode is travelling in the fiber. Singlemode silica fibers have a small core, are very delicate and special equipment is needed to handle such fibers. They are extensively used in high-performance long-reach core and metropolitan networks. The use of polymer optical fiber, that is a multimode fiber, is preferred because of its large core, flexibility and its ease to handle. Guiding light in multiple modes, as done in multimode (silica or polymer) optical fibres, destructs the phase coherence needed for RHD, and the pertaining modal dispersion strongly limits the fiber’s bandwidth and thus the microwave IM-DD potential. The use of a multimode fiber requires therefore a system where the retainment of the coherency in the link is not important. This report will focus on the use of polymer optical fiber as transport or distribution medium for microwave signals.

1.2 Radio over Polymer Optical Fiber System

Now, we know that radio over fiber is a promising technique to offer low cost broadband wireless access points. But, as explained in the previous section, costs can even more be reduced if multimode fiber in general and in particular polymer optical fiber (POF) can be used. In Figure 1.1 we can see the radio over POF system which overcomes the requirement of a coherency retaining link. At the base station the light with a wavelength

Figure 1.1: Schematic diagram of the Radio over POF system.

λ₀ of a fast tunable laser is swept periodically at a low frequency rate f_sw. The data is intensity-modulated on the swept signal by means of an external modulator. The light is launched into and transported through a graded index polymer optical fiber (GIPOF) network. At each radio access point the light passes a periodic optical filter. The periodic optical filter (such as a Fabry-Perot etalon) has transmission peaks separated by the free spectral range (FSR) of the filter. The FSR must be smaller than the wavelength range over which the optical frequency is swept in order to have multiple transmission peaks in that wavelength range. If the number of transmission peaks is N , the intensity of the light at the output of the optical periodic filter fluctuates with a fundamental frequency 2N fsw

(and also contains higher-order harmonics). The intensity fluctuations are converted to the electrical domain by using a high-bandwidth photodetector. The electrical signal will therefore have a frequency fmm = 2N fsw as well. Because the data is intensity modulated onto the wavelength swept light (and thus is the envelope of the optical signal), the data is detected but not up-converted in frequency. The electrical signal coming from the

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Figure 1.2: Generated microwave signals for sinusoidal sweeping of the laser wavelength.

Figure 1.3: Generated microwave signals for triangular sweeping of the laser wavelength.

photodetector is filtered, amplified and analyzed. Thus, the net result is that a microwave signal can be generated at the radio access point using a multimode fiber as the transport medium.

1.2.1 Microwave signal

If the wavelength of laser is swept with a sinusoidal signal, the generated microwave signal is frequency modulated as can be seen in Figure 1.2. A better microwave signal can be obtained by sweeping the wavelength of the laser with a triangular sweeping signal as showed in Figure 1.3. In case the periodic optical bandpass filter is a Fabry-Perot etalon, the periodic microwave signal can be expanded in a Fourier series according to [1]

i(t) = i₀

1 + F sin²(2πN f_swt) (1.1)

= i0·1 − R

1 + R·ⁿ1 + 2

∞

X

n=1

Rⁿcos (4πnN fswt)^o (1.2)

Where F = 4R/(1 − R)² and R is the power reflection coefficient of the Fabry-Perot mirrors. The power of the fundamental microwave component 2N fsw is maximized when R = √

2 − 1 ≈ 41%. The maximized fundamental component can be filtered out from the higher-order harmonics by using a microwave bandpass filter. The electrical bandpass filter can select one of the harmonics to become the microwave carrier of the system by choosing the central frequency of the bandpass filter equal to the desired harmonic to be obtained. If a higher-order harmonic is desired, a higher Fabry-Perot mirror reflectivity R equal to R = (^p(1 + n²) − 1)/n must also be achieved to maximize the power of the n-th order-harmonic. A plot of the relative powers of the harmonic components of the generated microwave signal is shown in Figure 1.4.

1.2.2 Bi-directional system

The system can be extended to a bi-directional system as shown in Figure 1.5 The downlink and uplink are realized in general by using two wavelengths λ₀ and λ₁ respectively. A wavelength division multiplexing (WDM) device (e.q. using an interfernce filter) is used

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1.3. GRADUATION ASSIGNMENT: ROPOF RECEIVER 5

Figure 1.4: Relative powers of the harmonic components as function of the mirror reflectivity R of a Fabry- Perot optical filter for a triangular sweep signal.

to separate the wavelength-channels. To realize the uplink, the transmitter must not be sending any data but must only generate the unmodulated microwave carriers. The unmodulated microwave signal is used again to downconvert the microwave signal from the mobile station by using a mixer. At the output of the mixer, the IF data signal can be found. After amplification and filtering a cheap laser or LED on λ1 is modulated with the data and the light is fed to the GIPOF link in upstream direction through the WDM device. At the base station, λ₁ is spatially separated and fed to the photodetector. At the output of the photodetector the data is available for further processing after filtering and amplification. The upstream data speed is limited by the bandwidth of the GIPOF link, which can be as high as 2 Gbit/s for 500m fiber length [4].

Figure 1.5: Schematic diagram of the radio over POF bi-directional system.

1.3 Graduation assignment: RoPOF Receiver

This graduation project focussed on the design of the RoPOF receiver. The concept of the receiver, its aspects to be investigated and some design considerations can be seen in Figure 1.6. In general, the most important demand for the optical part, is that the receiver can process nearly all of the optical modes delivered by a large core POF (core diameter 120µm). Light from the large core POF should be able to couple into the periodic optical

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Figure 1.6: Schematic diagram of the radio over POF receiver and its issues.

filter. The type of coupling depends of the type of periodic optical filter. At the exit of the periodic optical filter most of the light should be coupled into a high bandwidth photodetector. Again, the type of coupling depends of the type of periodic optical filter and the type of photodetector. The electrical signal at the output of the photodetector is fed to an electrical band-pass filter. After that the electrical signal should eventually be amplified.

The graduation project tasks as provided in the beginning of the project are summa- rized below:

• Analyze the theoretical problem of the POF-to-SMF/photodetector.

• Design and build an imaging and coupling system for POF fiber itself.

• Design the periodic filter. One of the possibilities is to use a semiconductor-based Fabry-Perot cavity as the periodic filter. However, other options must be explored as well. Problems related to beam collimation will have to be addressed.

• Design the opto-electrical conversion system. The output of this task should be the specifications of the photodetector and the other required RF components.

• Using the analysis, and components above, the actual receiver will be constructed.

This receiver should incorporate the POF-to-whatever coupling, the periodic filter using the appropriate imaging system, the photodetector, and the RF amplifier.

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1.4. REPORT OUTLINE 7

1.4 Report Outline

The report is divided into chapters devoted to the several sub systems of the receiver.

In Chapter 2 some parameters important for the guiding and coupling of light in multimode fibers are given. Measurements are done on the POF loss and modal noise to obtain information about optical power fluctuations introduced by the POF itself and its (possible imperfect) splices to other system parts which may reduce the power stability of the generated microwave carrier.

In Chapter 3 some theory is given to understand the problems relating to the coupling of light from the large core POF to an optical (periodic) filter and from the optical filter to the photodetector. A design has been made and realized, and some performance measurements have been done in terms of loss and modal noise introduced by the coupling system.

Two optical filters, namely a Fabry-Perot filter and a Fiber-Bragg-Grating (FBG) are explored and discussed in Chapter 4.

The optical and microwave issues related to the photodetector and electrical bandpass filter are discussed in Chapter 5. Practical issues and measurements are discussed as well in this chapter.

Some system experimental results are given in Chapter 6 to review the performance of the receiver in terms of e.g. optical to electrical power conversion, microwave carrier stability for a back-to-back system and for a system with the POF link.

Finally, conclusions and recommendations for further improvements about the constructed receiver and its performance in the system are provided in Chapter 7.

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Chapter 2

Polymer Optical Fiber

Optical fibers can be classified in two categories: singlemode fibers (SMF) and multimode fibers (MMF). In general, singlemode fibers have a small core (typically 5 or 9 µm in diameter), and silica multimode fibers have a larger core (typically 50 or 62.5 µm in diameter). The large core of multimode fibers makes it possible to use relatively cheap high tolerance connectors since lateral misalignments are not critical. The bandwidth- length product of singlemode fibers is much larger than the bandwidth-length product of multimode fibers. However, because of the easiness to use multimode fiber, multimode fiber is ideal for short-reach links.

Traditionally, multimode fibers are made out of glass. The main disadvantage of using glass, is that the fiber breaks easily when stretched, especially if the core size is increased.

A second disadvantage is that special equipment is needed to prepare the fiber for fixing connectors to it. Glass fiber is due to its small size and sharpness, not safe to work with in e.g. in-house environments. Therefore, an alternative for silica multimode fibers was introduced by DuPont in the late sixties [5], namely using plastic (polymer) in stead of glass. The polymer optical fiber (POF) was born. The core diameter of POF ranges from 120 µm to 1000 µm. Compared to silica multimode fiber, POF is very flexible and ductile and no special equipment is needed to prepare for connection. Secondly, because of the large core, lateral misalignments are less harmful which make using even cheaper high tolerance connectors possible. The large core diameter implies many guided modes which reduces also modal noise that could be introduced by lateral misalignments when connecting.

In this chapter, some theory is given to understand the guiding and coupling of light in multimode fibers. Also a comparison is made between different POF types in terms of bandwidth and loss. Finally, some measurements are done on a POF sample to measure the near field intensity pattern, loss and modal noise.

2.1 Guiding light through multimode fiber

Light travelling through multimode step refractive-index fiber is guided by the principle of total internal reflection. A step-index fiber consists of a core made up of high refractive material surrounded by a cladding consisting of a low refractive material. A light-ray entering the fiber, reflects on the core-cladding interface and after multiple reflections,

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the light-ray leaves the fiber at the fiber endface. If the incident angle is too high, there is no internal reflection and the light-ray escapes out of the fiber core. In graded-index (GI) fibers, there is no real core and cladding boundary. The refractive index gradually decreases when moving from the center of the core. A light ray entering the fiber will be gradually bend in zigzag and spiral shaped course through the fiber.

The next paragraphs will describe important theoretical aspects of the light guiding in multimode fibers such as the refractive-index profile, number of guided modes and numerical aperture. A qualitative description of the near field patterns and modal noise is given as well.

2.1.1 Refractive index

Standard singlemode glass fibers have a step refractive-index profile. It is common to use a graded index profile for multimode fibers to increase the bandwidth (subsection 2.2.2).

The core refractive index of a graded index multimode fiber varies with the distance r to the symmetry axis, following the expression [6]:

n(r) = n_co^q1 − 2∆(r/R)^g, r ≤ R (2.1) where R, is the radius of the core and the value of ∆ is the relative difference between indices:

∆ = n²_co− n²_cl

2n²_co ≈ n_co− n_cl

n_co (2.2)

The exponent factor g is equal to 2 for a parabolic-index profile and g → ∞ for a step-index profile. The highest fiber bandwidth can be realized with an approximately parabolic-index profile [6].

2.1.2 Generalized frequency and number of guided modes

Singlemode fibers have a small core (5 − 9µm diameter) and must be analyzed with the wave model of light using Maxwell’s electromagnetic field equations because the size of the structure is comparable with the wavelength of the propagating light. Multimode fibers have a much larger core and could be analyzed with a ray-tracing model. In a ray-tracing model, the propagating light through an optical system can be seen as the propagation of individual light rays. All the individual light rays follow a slightly different path. The paths can be calculated using standard geometrical optics. The calculated paths can be analyzed to draw conclusions about the performance of the system. Important is the so-called V-number or generalized frequency which is given by

V = 2πa λ

q

n²_co− n²_cl (2.3)

where a is the radius of the core. For a certain wavelength, the fiber is single-mode if V ≤ 2.405. The fiber is multi-mode (and thus the geometric ray-tracing model can be used) if V 2.405. The number N of guided modes, for V 2.405 or N > 20, is approximately described by

N ≈ 1 2

g

g + 2V² (2.4)

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2.1. GUIDING LIGHT THROUGH MULTIMODE FIBER 11

Thus for a fiber with a parabolic-index profile the number of guided modes is N ≈ ¹₄V². For a step-index profile this will be N ≈ ¹₂V² In general we can say that the higher the V-number is, the more modes are supported and the more reliable the ray-tracing model is.

2.1.3 Numerical aperture and acceptance angle

The V-number (Equation 2.3) is a product of a geometric factor, ^2πa_λ and an optical factor.

The optical factor is called the numerical aperture (NA) and is according to Equation (2.3) given by:

NA = q

n²_co− n²_cl (2.5)

The N A of a fiber is related to the capture of the meridional rays by:

φ_air,max = arcsin NA (2.6)

where φ_air,max is the maximum incident angle in air for which the fiber guides the incident light ray. This maximum angle is called the acceptance angle. Twice the acceptance angle is referred to the aperture angle. In graded-index POF (GIPOF) the radial refractive index is not constant across the core. The numerical aperture is a function of the refractive index and is therefore also not constant over the core. The local numerical aperture NA(r) is given by [7]:

NA(r) = q

n²(r) − n²_cl= q

n²_co(0)(1 − 2∆(r/R)^g) − n²_cl= NA(0) q

1 − (r/R)^g (2.7) The local acceptance angle is given by

φ_air,max(r) = arcsin NA(r) (2.8)

From this we can conclude that, for a parabolic index fiber, the acceptance angle decreases quadratically over the fiber core. POF has a large numerical aperture of about 0.2 compared to the numerical aperture of a singlemode fiber which is about 0.1. Fibers with a large NA can capture light very easily. Because of the large NA in POF, coupling is done very efficiently. But some attention must be paid to the varying NA. The largest numerical apertures exist only around the center of the fiber core because of the high local numerical aperture as explained in subsection 2.1.3. This means that for light with a certain incident angle only a specific area of the fiber core can be used. First the area acceptance angles over the fiber core must be calculated. Together with the maximum angle of the incident light, the radius of the core area which accept light, can be determined (Figure 2.1). The GIPOF of Figure 2.1 has a core refractive index of n_co= 1.350 (Perfluorinated (PF) doped material which yields lower loss), a cladding index of n_cl= 1.336 (PF not doped material) and a parabolic index profile with g = 2. The core diameter is 2R = 120µm. For this fiber, a core area with a diameter of about 84 µm around the core can be used for incident light with a maximum incident angle of 8^◦.

2.1.4 Near field pattern and modal noise

For coupling light from the GIPOF to the optical periodic filter, it is important to know whether the core is overfilled because it gives requirements for the imaging and coupling

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Figure 2.1: Determination of the core area which can be lighted

system. Secondly, the existence of a speckle pattern at the fiber endface must be investigated to have an indication of how many modes are excited. The number of modes excited as seen at the output strongly depends on the launching conditions and length of the fiber.

Daum et. al [5] mention an equilibrium mode distribution, due to mode coupling, after a certain fiber length. The details like the fiber length where mode equilibrium is reached and the launch conditions are unfortunately not stated. By doing experiments we shall see if mode equilibrium is reached after the 300m of PF GIPOF that is available in our lab.

A speckle pattern is caused by the interference of the propagating modes. If the relative phases of these field are changed somehow (e.g. by mechanical vibrations, temperature effects, source wavelength changes), the speckle pattern will change [8]. If some spatial filtering occurs, this phenomenon will result in intensity fluctuations which is called modal noise. A fine-grain speckle pattern indicates that a large number of modes is excited and a coarse-grain indicates that a low number of modes is excited [9].

There is another contributing factor to modal noise as well. Higher-order fiber-modes have a higher loss than the lower order fiber-modes. The number of modes travelling in the fiber depends strongly on the launching conditions. If a fundamental mode from a laser is injected into the POF, the fundamental mode instantly excites higher modes and due to mode coupling while travelling through the POF, more modes will be excited. The fiber is sensitive to mechanical forces introduced by e.g. bending, vibrations and temperature changes. Because of these environmental changes, the path of the light guided through the fiber is changed, which corresponds to a change in the distribution of excited fiber- modes. This we will call path dependent loss. The fiber-modes have a different loss, if the distribution changes, the loss changes and the output power will fluctuate, even if no spatial filtering occurs.

2.2 Transmission properties of GIPOF

For the transmission of communication signals, attenuation and bandwidth are important parameters. In this section two types of widely used polymer optical fibers are discussed.

Secondly, the benefits of using a graded-index core profile (subsection 2.1.1) is explained.

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2.2. TRANSMISSION PROPERTIES OF GIPOF 13

2.2.1 Loss

Polymethylmethacrylate (PMMA) (better known as Plexiglass) has been widely used as core material for graded-index fiber [5]. However, the use of PMMA is not attractive due to its high attenuation of about 100 dB/km at 570nm (Figure 2.2). Today, Perfluorinated (PF) GIPOF is widely used because of its high bandwidth and low attenuation (Figure 2.2) from the visible to the near IR wavelengths compared to PMMA GIPOF [10]. In 1998, the PF GIPOF has a attenuation of around 30 dB/km at 1310nm. Lower and lower values of attenuation are being achieved. The theoretical limit of PF POF is 0.7 dB/km at 1250-1390nm (Figure 2.2). In our lab, 300m of PF GIPOF was available.

Figure 2.2: Loss as function of the wavelength for PMMA and PF based POF.

2.2.2 Bandwidth

Because multimode fibers can guide many modes, intermodal dispersion is the limiting bandwidth factor [6]. Intermodal dispersion is caused by the fact that the lower order modes propagate mainly along the waveguide axis, while the higher-order modes follow a more zigzag path, which is longer. If a short light pulse is excited at the input of the fiber, the lowest order modes arrive first at the end of the fiber and the higher order modes arrive later. The output pulse will thus be built up of all modes, with different arrival times, so the pulse is broadened.

Graded refractive-index fibers have a refractive index profile as described in subsection 2.1.1. Light travelling in a low refractive-index structure, has a higher speed than light travelling in a high index structure (c = c₀/n). The higher order modes bend gradually towards the fiber axis in a shorter period of time because the refractive index is lower at regions away from the fiber-core. The time difference between the lower order modes and the higher order modes is smaller, and so the broadening of the pulse leaving the fiber is reduced.

Dispersion could also be introduced by the effect that the speed of propagation of light of different wavelengths differs. This is called chromatic dispersion. In PF POF the

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chromatic dispersion is much smaller than in silica MMF for wavelengths up to 1100nm.

For wavelengths above 1100nm, the dispersion of the POF retains and the dispersion of silica MMF increases. In general we can conclude that the chromatic dispersion of GIPOF is much smaller than that of silica MMF.

If a light is launched with a very low numerical aperture in the center of the core, few fiber modes will be excited. Accordingly, the arrival time differences between fiber-modes will be smaller, which result in a smaller broadening of a pulse travelling over the fiber.

Thus bandwidth can be increased by launching light into the POF with a low numerical aperture [5]. A bandwidth for PF GIPOF of about 10 Gb/s·km in the 1300nm window can theoretically be achieved [4]. In this project no measurements on POF bandwidth are done because it is not one of the objectives of this project.

2.3 Measurement Results

Measurements are done on the 300m of PF-POF that was available in our lab. Because we want to couple light from the POF to a device or a fiber with a different core size, we want to know the loss, the modal noise and the modal distribution over the core-endface when a single longitudinal and transverse mode laser is used as a source, and when a single transverse mode broadband source is used as a source.

2.3.1 Near field pattern

As stated in subsection 2.1.4, we want to measure the near-field pattern of the POF endface (by using 2 different sources) since it gives an indication if we can expect modal noise.

Secondly, we want to know if the core is overfilled to obtain the actual spotsize that is used for designing the coupling and imaging system.

The image of the near-field pattern is captured by an infrared (IR) camera, and the image of the POF endface and connector is captured by a visible (VIS) camera. The camera is mounted on a microscope and the fiber is placed in the focal point of the microscopic objective lens. A software tool was used to process the camera-images by a computer [11].

The image of the POF and connector endface is shown at the left-hand side of Figure 2.3. The core cannot be distinguished from the cladding, because the materials of both the core and cladding are the same. The center of the POF is determined by visible inspection.

After that, the VIS-camera is removed and replaced by an IR-camera. Care is taken of using the same magnification to obtain images with the same scale. Light from a single longitudinal and transverse mode laser (in our case a 20 mW distributed feedback laser (DFB)) at 1310nm is launched at the input of the POF. The picture at the right-hand side of Figure 2.3 shows the IR snapshot. At the core-cladding interface, a clear speckle pattern can be observed. Also a slow variation of this the speckle pattern is observed.

This is an important observation since the varying speckle-pattern will introduce modal noise when spatial filtering is done. In the center region, no speckle pattern could be observed due to the high sensitivity of the IR camera and the large light intensity in the center core region or the insufficient resolution of the IR camera. In Figure 2.4 the near field intensity profile is shown. We can clearly see that the core is overfilled because the width of the intensity curve is 120 µm which is the core size of the fiber. This gives an

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2.3. MEASUREMENT RESULTS 15

important requirement to the imaging and coupling system since we know now that the light entering the imaging and coupling system has a spotsize of 120µm if the DFB laser is used as a source.

Figure 2.3: Photograph of POF endface, and IR photograph of 1310nm light in core.

Figure 2.4: Near field intensity profile at the output of 300m of POF with 1300nm singlemode launch

2.3.2 Modal noise and loss

The power stability at the output of the POF provides information about the path dependent loss of the modes travelling in the fiber. Two sources are used to see the effects of mode path dependent losses. First, a high power DFB laser operating at 1310nm is used as a source. After that the laser is replaced by a semiconductor optical amplifier (SOA) with no input connected, so as to generate a broad spectrum ASE signal. The laser and SOA power were stable during at least the measuring time of 30 minutes as can be seen in Appendix A. Figure 2.5 shows the measurement setup for measuring the power output stability of the POF with the laser. Light from the laser is launched into

Figure 2.5: Setup for measuring the modal noise in 300m of POF

the POF by means of butt-coupling from a single mode fiber patch cable. At the output, light is measured every 10 seconds over 30 minutes by a power meter. A SOA is used as a broadband source as well. The input of the SOA is left unconnected, the output of the SOA will produce light due to spontaneous emission over a very broad spectrum because of the large gain bandwidth of the SOA. The time-power plots are shown in Figure 2.6

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and Figure 2.7. All the light at the output of the POF is measured by the power meter as Path dependent loss in POF

Figure 2.6: High power laser as a source (Pin

= 10 dBm): Pmean= -0.12 dB; Pmin= -0.27 dB;

Pmax= -0.02 dB; Pfluct= 0.25 dB

Figure 2.7: SOA as a source (Pin= 5.5 dBm):

Pmean= -5.52 dBm; Pmin= -5.54 dBm; Pmax= -5.52 dBm; Pfluct= 0.02 dB

shown in Appendix B. Thus, at this point no mode filtering can take place. If the POF is excited with a single transversal and longitudinal laser as a source, small modal noise of about 0.2 dB is measured due to path dependent losses as explained in subsection 2.1.4.

If the POF is excited with the SOA as a source, the modal noise vanishes. The SOA pro- duces a single transverse mode, but hundreds or thousands of longitudinal modes. Each longitudinal mode follows a slightly different path through the fiber. All these longitudinal modes contribute to the power output at the fiber endface. If the paths are changed due to environmental changes, the chance is very high that other modes will take a similar path because of the large number of modes. No path dependent loss will therefore occur.

2.4 Conclusions

POF is used particularly for short-reach applications (e.g. in in-building data networks) because of its limited bandwidth-length product of typically 1 GHz·km, its flexible char- acter and its large core which make coupling easy. The mean loss of the 300m of POF is measured to be 10 dB at 1310nm. The power fluctuates at the output of the POF with a magnitude of only 0.2 dB due to path dependent losses, if a DFB laser is used as a source. If the POF is excited with a ASE noise from a SOA (a ’broad source’), modal noise vanishes almost completely. If the 300m of POF is excited with a single transverse and longitudinal mode laser, the core is overfilled at the POF endface. The speckle pattern changes in time due to environmental changes. If spatial filtering occurs, modal noise will be the result.

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Chapter 3

Imaging and Coupling

The imaging and coupling system in the RoPOF receiver must realize a parallel beam of a specific width to drive the optical periodic filter, and must couple the light after passing the optical periodic filter to a multimode silica fiber which feeds the photodiode (Figure 1.6). Besides that, the imaging and coupling system must facilitate the mounting for the optical periodic filter.

In this chapter the requirements, design and construction of the optical coupling system are discussed. Finally, measurements are done to evaluate the performance of the system in terms of coupling loss and modal noise.

3.1 Lens coupling

To create a parallel beam for the optical periodical filter, lenses are used. In this section formulas are derived to calculate the behavior of a coupling system using lenses. The differences between an ideal and a real lens system are analyzed and discussed as well as the solutions to approximate an ideal coupling system.

3.1.1 Snell’s law and paraxial approximation

The direction of a light ray after refraction at the interface between two media with refracting indices n1 and n2 is given by Snell’s law:

n₁sin θ₁ = n₂sin θ₂ (3.1)

where θ₁ is the angle of incidence and θ₂ is the angle of refraction with respect to the surface normal. By using Snell’s law, all light rays refracted by lenses in an optical system can be calculated precisely. Usually, the behavior of the optical system is first determined by drawing light rays by hand. To make the drawing by hand possible, a first order approximation is done on Snell’s law of refraction. The first order approximation is given by sin θ ≈ θ for small angles. Formulas based on this approximation are called paraxial formulas. In the next sections lens system properties will be derived using the paraxial approximations.

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3.1.2 Ideal lens coupling

For maximum fiber-to-fiber coupling, a one-to-one image should be made of the emitting fiber core upon the receiving fiber core, and the launching angle from the fiber endface plane has to be the same as the receiving angle of the other fiber endface plane. All these conditions are satisfied if the fiber endfaces are positioned in the focal planes of the lenses, while the foci of the lenses coincide [12]. In Figure 3.1 a graphical representation of these conditions is shown. Even if the above conditions are obeyed, coupling may not be perfect

Figure 3.1: Universal arrangement for optimal lens coupling

due to non-ideal lenses.

3.1.3 Non con-focal lens coupling

In this graduation project, not only maximum coupling between fibers is required. In between the lenses, a parallel beam (a so called collimated beam) with a certain width is required as well. Secondly, the distance between the lenses must be large enough to insert the mounting for the optical periodic filter. Because of the small focal lengths for the lenses (as we will see in the next sections), the condition to coincide the focal points of the collimating and focussing lens cannot be satisfied. In Figure 3.2, the emitting fiber is placed in the focal point of the collimating lens. The lenses are separated by a lens separation L that is much larger than the sum of the two focal lengths of the lenses. The receiving fiber is placed in the focal point of the focussing lens. What immediately can be seen in Figure 3.2, is an increase in numerical aperture of the light entering the receiving fiber. The light beam is not collimated due to the simple fact that the object has a finite size. The width of the optical field w(z) = 2h(z) can be found by applying goniometric algebra.

NA_in = sin θ (3.2)

δ = f₁tan θ = f₁tan arcsin NA_in (3.3) ϕ = arctanD₁/2

f1

(3.4) w(z) = 2h(z) = 2δ + 2 |(z − f₁)|D₁/2

f₁ (3.5)

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3.1. LENS COUPLING 19

Figure 3.2: Fiber coupling with lenses in non-confocal condition

Equation (3.5) can be simplified by using approximations for the goniometric functions because the angles in radians are small. The beam width equation 3.5) will then evolve in:

w(z) ≈ 2f₁NA + |(z − f₁)|D₁ f1

(3.6) The angle ϕ of the nearly collimated beam, the output numerical aperture NA_out and the image size 2∆ is given by:

ϕ ≈ D₁

2f₁[rad] (3.7)

∆ = f₂tan ϕ ≈ D₁ f2

2f₁ (3.8)

(3.9) NA_out,max = sin arctanh(z = L) − ∆

f₂ (3.10)

= sin arctanⁿf1

f₂NAin+|(L − f₁)| D1/2 f₁f₂ − D1

2f₁

o (3.11)

≈ f₁ f2

NAin+|(L − f₁)| D₁ 2f1f2

− D₁ 2f1

(3.12) We can see that the output numerical aperture increases if the length L between the lenses is increased, the focal length f1 of the collimating lens decreases, the object size D1

increases or the focal length f₂ of the focussing lens decreases. The divergence ϕ of the nearly collimated beam increases if the object size D₁ increases or if the focal length f₁ of the collimating lens decreases. The receiving fiber can collect all power if the output numerical aperture NA_out of the imaging system is smaller than the NA of the fiber and if the image size 2∆ is smaller than the core diameter D₂ of the fiber. The collimating

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lens must have a diameter larger than D₁+ 2f₁NA_in and the focussing lens must have a diameter larger than w(L) to process all the light. We can clearly see that in the non- confocal situation, light coming from the center of the emitting fiber, is perfectly collimated (i.e. parallel to the system’s optical axis). Light coming off axis from the emitting fiber, diverges (i.e. makes an angle with the system’s optical axis) after passing the lens. If we place the emitting fiber not in the focal point of the collimating lens, but little further away from the lens, we can reduce the diversion of the marginal rays. In Figure 3.3 a situation is illustrated when the emitting fiber is placed in the focal point of the lens. For legibility, to show clearly the reduction in beam divergence, the object size is increased and thus does not represent the actual emitting fiber. A clear light beam divergence between the lenses is shown. The lens is a achromatic lens (see subsection 3.1.5) with a focal length of 6 mm. The object distance is 4.6802 mm to realize a 1:1 imaging system. In Figure 3.4

Figure 3.3: A large beam divergence occurs when placing the emitting object in the focal plane of the lens.

the object distance is increased to 8 mm. Clearly is shown that the light beam divergence has reduced. A consequence is that the imaging system is not a one-to-one imaging system anymore, but the image size is reduced. The tradeoff when placing the emitting fiber not

Figure 3.4: The beam divergence is reduced by placing the emitting object further away from the lens its focal plane.

in the focal point of the lens but slightly further away, is that we introduce converging of the rays coming from the center of the emitting fiber. This can clearly be seen in Figure 3.4. The converging of the light rays in this figure is large due to the large displacement of the object from the focal point for legibility reasons. Overall, placing the fiber a little bit further away from the lens (i.e. out of its focal point), will give a more collimated beam and thus a better coupling performance when the lens separation is large.

3.1.4 Spherical and Chromatic aberration

In the previous sections we have assumed ideal lenses. The aberrations between an ideal situation and the real situation come from the fact that we use paraxial formulas to characterize the optical system. In reality, rays through the system obey Snell’s law

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(Equation (3.1)). The difference between Snell’s law and the paraxial approximation that sin θ ≈ θ are called lens aberrations.

The first aberration is caused by the fact that the focal length is a function over the lens aperture. This is called spherical aberration. For a positive lens, light rays impinging on the lens surface away from the optical axis experience a shorter focal length than light rays impinging on the lens surface close to the optical axis (Figure 3.5). The result will be that a light beam is not focussed in only one point, but in an certain area. The spherical aberration is approximately proportional to the square of the radius (h(z) in Figure 3.2) of the zone on the lens surface where the light ray impinges [13]. For a negative lens, exactly the opposite occurs. In our non-confocal imaging system for example, the focussing lens cannot image the object (the emitting fiber) onto the receiving fiber endface very well.

In stead, a blur circle due to the spherical aberration, is created around the image. A consequence is that no abrupt focal point can be found while moving the receiving fiber along the optical axis. The point where there is a best focus is called the ’point of least confusion’. This is the point where the spot size (image) is the smallest.

The second aberration is caused by the fact that for each wavelength the lens has a different focal length. This is called chromatic aberration. For a positive lens, the shorter (blue) wavelengths focus closer to the lens than the longer (red) wavelengths (Figure 3.6).

A consequence is that not all the colors in the beam are focussed in only one point. In this project, chromatic aberrations are not very important because we only operate in a small wavelength region. Chromatic aberrations become important in WDM systems where a large wavelength range is used and coupling performance must be equal for all wavelengths.

Figure 3.5: Spherical aberrations in a lens.

Figure 3.6: Chromatic aberration in a lens.

3.1.5 Achromatic lens

The spherical and chromatic aberrations can be reduced by combining positive and negative singlet lenses of different materials (Figure 3.7)[13]. The most common combined lens is the achromatic doublet, or simply called the achromat. The achromat is thus used for reducing the spherical aberrations as well, while the name incorrectly suggests that only the chromatic aberration is compensated for.

An achromat with a positive net focal power is formed by cementing together a large power positive lens made of glass with a low refractive index (crown glass), and a small power negative lens made of glass with a high refractive index (flint glass). The material dispersion of the lenses are chosen to be equal. The combined power is positive, while the

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dispersion is compensated. The spherical aberration is reduced due to the fact that the positive lens focusses rays off-axis closer to the lens, and the negative lens focusses rays off- axis further away from the lens. The combination will thus compensate for the spherical aberration as well. A second reduction of spherical aberration is achieved because the radius of the convex surface of the positive lens is larger than the radius of the convex shape of the negative lens, if the lens is positioned as showed in Figure 3.7. If the lens is turned around, the spherical aberrations will increase severely.

Figure 3.7: Achromatic lens: Compensated for spherical and chromatic aberrations

3.1.6 Aspheric Lens

To overcome spherical aberrations completely, a lens surface with a varying radius of curvature could be used. Such lenses are called aspherical lenses. The lens is designed in such a way that it exactly compensates for the fact that sin (θ) is not equal to θ at larger angles. This means that the lens surface is designed such, that parallel rays entering the lens over the full lens aperture, will all focus in the focal point. An aspherical lens is shown in Figure 3.8. Aspherical lenses are very expensive, since polishing techniques, that

Figure 3.8: Aspheric lens: Compensates for spherical aberrations

naturally produce spherical surfaces, cannot be used. In stead, the surface must be ground using diamond cutters. The grinding must be controlled by a computer in such a way that the resulting lens surface has polishing quality immediately. In non critical applications, aspheric molded lenses could be used, which give a better performance already. These lenses are e.g. made for compact disc player systems.

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3.1.7 Anti-reflection coating

Even if the lenses are ideal, light impinging on the lens is partly reflected from the lens surface due to the refraction-index difference. A consequence is loss of light. Secondly, the light reflection is highly unacceptable since light reflecting between e.g. two lens surfaces can form a cavity. The cavity can make the transmission of light through the imaging system unintendedly wavelength dependent. Therefore an antireflection coating can be applied to the lens surfaces (and its composition e.g. multi-layer coating). The wavelength range can be controlled by the thickness, the refractive index and the type of antireflection coating. In Figure 3.9 the operating principle of an anti-reflection coating (that basically is a thin-film) is shown.

Figure 3.9: Operating principle of an anti-reflection coating

Most of the light impinging on the coating (ray 1), is refracted (ray 2) and a part of the incident light is backwards reflected (ray 3). After passing the air-coating interface, most of the refracted light is refracted again when passing the coating-lens interface (ray 3).

A part of the incident light is backwards reflected (ray 4) and refracts at the coating-air interface before leaving the coating (ray 5). If the two backwards reflected light rays (ray 3 and 5) interfere destructively, no light will be reflected (in which we neglect multiple reflections).

When light reflects on a surface, it experiences a phase change of π if the ray strikes the boundary between the two media from the side where light travels with higher velocity [13]. This means that if a light ray travels in air and is reflected on a boundary with a refractive-index n > nair, it experiences a phase shift π. If the light travels in a medium with refractive-index n, and reflects on the boundary with air, it experiences no phase shift.

The light rays 3 and 5 in Figure 3.9 interfere destructively if the thickness d of the coating is λ/2 and if the refractive index of the coating nc lies between n0 and nlto realize a zero phase shift when reflection occurs as mentioned above. Then, ray number 5 is delayed by λ/4 + λ/4 = λ/2 and will cancel out with ray number 3 which is not delayed.

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The reflected rays will only cancel out completely if the two reflected rays 3 and 5 have the same intensity. The intensity of a reflected beam from a single surface, at normal incidence is given by [14]:

I_{ref lected}= I_incident·1 − p 1 + p

2

(3.13) with p the ratio of the refractive indices of the two materials at the boundary. To have the intensities of the reflective beams the same for both reflected rays, it is necessary that the refractive-index ratio p are the same for both the boundaries air-coating and coating-lens respectively:

n_air nc

= n_c nl

(3.14) Since the refractive index for air is 1.0, the coating should have a refractive-index of√

n_l. Finally, the performance of the antireflection coating depends on the incident angle.

The coating performs well up to incident angles of about 40^◦[14]. In this project incident angles will not be more than 40^◦at all, so no angle-dependent deterioration of the reflection behavior is expected.

3.2 Design and Construction

To realize a non-confocal imaging system with the requirement to create a nearly parallel beam of a specific width and minimum coupling loss, attention has to be paid to some aspects as given below:

• Maximal mechanical stability

• Maintain optical axis accurately

• Minimal lens separation distance

• Minimal divergence of nearly parallel beam

• Minimal optical reflections

• Flexibility in using different lenses

• Flexibility in alignment

Minimization of optical reflections can be realized by using lenses with an antireflection coating. Minimum divergence of the nearly parallel beam, correct output numerical aperture and output spotsize, can be realized by using achromatic or aspherical lenses. The output numerical aperture and the blur around the output spot can also be minimized by minimization of the lens separation distance. The mechanical stability can be maximized and the optical axis can be maintained by mounting the opto-mechanical components on a single Aluminium mounting plate by using accurate mounting holes. The emitting and receiving fibers must be able to be aligned because different fibers should be used in experiments. The emitting fiber of the non-confocal imaging system in the final RoPOF

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3.2. DESIGN AND CONSTRUCTION 25

receiver is a POF with 120 µm core diameter, and the receiving fiber is a 50µm core silica fiber (Chapter 5). Sufficient space must be left between the lenses for placing the periodic optical filter. The periodic optical filter should be able to be translated in the three directions, rotated and tilted. This is to position the filter in the parallel beam and to perform experiments on the effect of rotating the optical periodic filter as described in Chapter 4.

3.2.1 Optics Design

The image size of the non-confocal system is equal to the POF core of 120 µm, since we know from subsection 2.3.1 that the core is overfilled at the output if we launch with a DFB laser. However, this is a worst-case situation since most of the optical power is delivered by the lower-order fiber-modes which are in the center region of the core. The input numerical aperture is equal to 0.2 which is the numerical aperture of the POF.

However, this is a worst case situation as well because the numerical aperture of 0.2 of the fiber is only 0.2 in the center of the fiber and decreases when moving from the center of the core (Equation (2.7)). The size of the nearly parallel beam must be 3mm to meet with the thickness of the Fabry-Perot filter (Chapter 4). We want to see the effects on coupling the light from the POF to a 50 µm MMF and to a 9 µm SMF. Coupling to the SMF will lead to huge losses and huge modal noise. However, we want to know exactly how much the loss and modal noise is, because usually we have no other option than coupling POF to SMF since nearly all the measuring equipment have a singlemode input. Coupling to a 50 µm MMF is important because the photodetector has a 50 µm MMF pigtail (Chapter 5).

The imaging and coupling system is illustrated in Figure 3.10. Different lens types are used to compare their performances with respect to coupling loss and modal noise. The imaging system is characterized in terms of coupling light from the POF to a multimode fiber and a singlemode fiber respectively. The focal length needed for generating the 3mm

Figure 3.10: Model of the imaging system for generating a parallel beam and for coupling power from the POF to fiber patch cables by using different lens-types.

beam with a 120 µm image and a numerical aperture of 0.2 is equal to 7.2mm according to Equation (3.6), if the coupling and imaging system is assumed to be ideal. Lenses with a focal length near 7.2mm are found in the market. The lenses were selected on the basis of focal length, diameter, coating and design wavelength. If the lens is used as the focussing lens, the diameter must be as large as possible to collect most of the light of the slightly diverging beam. Since lenses in general are mainly used in the visible wavelengths, some compromises had to be made on design wavelength and coating. The lenses selected are shown in Table 3.1. A molded aspherical lens with a very low focal length and large diameter has been selected to make smaller parallel beams than 3mm. The