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.
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-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) = ncoq1 − 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:
∆ = n2co− n2cl
2n2co ≈ nco− ncl
nco (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
n2co− n2cl (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
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, 2πaλ and an optical factor.
The optical factor is called the numerical aperture (NA) and is according to Equation (2.3) given by:
NA = q
n2co− n2cl (2.5)
The N A of a fiber is related to the capture of the meridional rays by:
φair,max = arcsin NA (2.6)
where φair,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]: The local acceptance angle is given by
φair,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 com-pared 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 nco= 1.350 (Perfluorinated (PF) doped material which yields lower loss), a cladding index of ncl= 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
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 investi-gated 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.