Bragg gratings have found widespread application for wavelength dependent filtering in optical fibers and integrated waveguides. In this project you will learn how to fabricate gratings in waveguides. You will participate in the fabrication process where waveguides first are written on a chip with a UV laser beam and then imprinted with Bragg gratings in a second UV exposure through a holographic optical element. By writing waveguides that curve in special ways you will experience how advanced grating properties can be realized in a simple way. The project involves both numerical grating design, component fabrication and characterization. The chips with waveguides and gratings is even for keeps!

Supervisor/Contact: Mikael Svalgaard, svlgrd@com.dtu.dk Location: building 344, room 915

Motivation: Phase-Locked Loops (PLLs) find application in a wide range of different fields spanning from telecommunication, space communication, instrumentation, optics, optoelectronics etc. In the proposed project work, PLLs are used for synchronization of a locally generated clock signal (clock extraction) to an incoming high-speed data signal. The set-up of the PLL based clock recovery and a phase-plane plot illustrating the stability of the loop are shown in Figure 1. The performance of the PLL with a Proportional Integrator Differentiator (PID) loop filter is to be investigated in this project.

Fig. 1. (a) Schematic set-up of the PLL. (b)  Phase-plane plot illustrating the stability of the PLL.

Objectives: The objective of this course is to gain knowledge about phase-locked loops used for clock extraction in high-speed optical transmission systems. After completing the course the students will be able to perform numerical analysis of a phase-locked loop on an elementary level.  

Description: A brief introduction to Phase-Locked Loop techniques is given at the start of the project. A differential equation describing the considered system is derived and solved numerically using MATLAB. The numerical simulations are used to investigate the stability of this type of loop and the time needed to obtain synchronization. After completing this step, the model equations are modified in order to include a time delay which has an impact on the stability of the loop. If time allows the numerical simulations are supported by a small signal analysis, which leads to approximate analytical expressions for evaluating the stability and the locking time of the loop. Although approximate, the analytical results provide insight to the influence of the main design parameters of the loop.  

Prerequisites: Interest in numerical analysis

Number of students: 1-2

Supervisor/contact: Darko Zibar, e-mail: dz@com.dtu.dk COM, building 343 room 212

Project description:

The action of modulation, i.e. transferring the data to be transmitted from the electrical to the optical domain, is an essential functionality of optical communication systems. While at low bit-rates (e.g. up to 2.5 Gbit/s), this can be easily performed by directly modulating the current of a semiconductor laser, external modulators are required for high-speed modulation (e.g. at 10 and 40 Gbit/s). Those modulators act as some kind of fast switch that turn an incoming continuous-wave light off or let it go through, depending on the electrical data to be transmitted, as illustrated in Figure 1. Typical requirements for such modulators is that they allow high speed operation, present low loss, and do not induce non-desired effects such as frequency chirping (time dependent phase equivalent to variation of the instantaneous frequency) when pure intensity modulation is sought. Practical considerations such as drift-free operation, compact size and low power consumption also need to be taken into account.

Figure - Illustration of the operation of modulation of an electrical data stream onto a continuous lightwave by the use of an external modulator. By adjusting the operation mode of such a modulator, or by combining a number of external modulators driven by different signals, variuous modulation formats such as return-to-zero (RZ), carrier-suppressed return-to-zero (CS-RZ) or RZ differential phase-shift keying (RZ-DPSK) can be obtained.

The electro-optic Mach-Zehnder modulator has become an ubiquitous device for high speed optical communication systems. It is customarily used as an intensity modulator for typical systems making use of the non return-to-zero (NRZ) or return-to-zero (RZ) modulation formats, and has recently demonstrated its potential for phase modulation in future systems making use of the differential phase-shift keying (DPSK) format. Such modulators are made from an electro-optic crystal (typically lithium-niobate, LiNbO₃), whose refractive index depends on the electric field, hence voltage, that is applied to it. The electrical data can thus modulate the refractive index of the crystal, hence the phase of the incoming lightwave. Incorporating the crystal into an interferometric structure (Mach-Zehnder interferometer) in turn converts the phase modulation into intensity modulation.

Although the principle of such a modulator is fairly simple, its operation can present many degrees of freedom and resulting trade-offs. The purpose of this project is therefore to explore the operation modes of electro-optic Mach-Zehnder modulators and their consequences on the quality of the modulated optical signal. One particular task will be to establish relations between the extinction ratio (defined as the ratio of the power transmitted into a binary `1´ and `0´) of the modulated optical signal and its frequency chirping, depending on the chirp generation mechanism (optical or electrical imbalance of the Mach-Zehnder modulator).

The different steps of the project are:

• Understand the operation of electro-optic modulators based on the Mach-Zehnder structure
• Develop a simple analytical model of such a modulator, taking a number of non-ideal behaviours into account
• Based on the developed model, explore the consequences of the introduced non-ideal behaviours on the quality of the generated optical signal. For this purpose, systematic variations of selected parameters will be performed, for instance using Matlab.
• Once the functioning of the non-ideal modulator is well understood, the implications on transmission over optical fibre will be evaluated using a commercial state-of-the-art optical system simulator (VPItransmissionMaker WDM).
• Write a report summarising the different findings.

Requirements and expected ben efits:
Through this project the students will learn how to build a system-oriented model of an apparently simple component offering a large number of degrees of freedom in its operation. Starting from ideal operation, a number of imperfections will be introduced and their effect studied. Comparison with models made available in a commercial simulation package will be performed, enabling the students to discuss their suitability for various problems (which is often taken for granted by the users of such commercial packages). The students will also have to identify which parameters are relevant for their investigation and how do those parameters interact and influence the quality of the generated optical signal. The project is also expected to give them insights into the field of advanced high-speed optical communication systems.

Contact information:
Christophe Peucheret, cp@com.dtu.dk; COM, building 343, room 222.

Motivation:
In various applications computer simulations of Maxwell’s equations are used to understand the behaviour of the electromagnetic field. In photonics, optical components are constructed from basic building blocks such as wave-guides, splitters, amplifiers, multiplexers etc.  In most cases these cannot be studied analytically so instead computer software is used not only to model the properties of existing components but also to test new design ideas before they are actually implemented.  The development of efficient computer models is thus an important part of photonic engineering.

Description:
This project is an exercise in applied theoretical physics.  The student will start at Maxwell’s equations and will be guided through the mathematical steps necessary to develop a modelling tool describing the electromagnetic field as function of refractive index geometry.  The student will write the program from scratch and the tool will then be used to analyse a simple optical component.

Prerequisites:   
The student should be familiar with Maxwell’s equations and with linear algebra (inner product spaces, matrix operations and eigenproblems) to understand the mathematical procedures.  Basic Matlab programming skill is also recommended.

Number of students: 1-2

Supervisor/Contact: 
Niels Gregersen, 345v / 178, phone 4525 3789, email: ngr@com.dtu.dk
Jørn Hedegaard Povlsen, 345v / 271, phone 4525 3776, email: jhp@com.dtu.dk                  

Background: The development of lasers at shorter (blue) wavelengths around 500nm is of considerable interest to all major telecommunications and electronics companies. By halving the wavelength the storage capacity of, e.g., a CD is quadrupled. However, such blue lasers are difficult and expensive to develop. Second-harmonic generation (SHG) in quadratic nonlinear optical materials provides a relatively easy and cheap way of generating light at half the wavelength, and is therefore attractive not just commercially, but also from a fundamental scientific point of view. Blue lasers using a standard cheap red laser to pump a quadratic nonlinear crystal, are already being manufactured, also in Denmark .

Aim: The project aims at developing a mathematical model of quadratic nonlinear optical materials, which describes the propagation of and interaction between the input red light and the generated blue light at half the wavelength. The model should be implemented numerically in Matlab and a graphical interface should be developed that allows the user to easily experiment with the input field and the material parameters. The model should finally be used to identify the values of the material parameters that are optimal for efficient SHG.  

Keywords: Ordinary differential equations, initial value problems, second-harmonic generation.

Prerequisites: Knowledge of complex numbers and either Matlab.

Supervisor/Contact: Ole Bang, COM, building 345v, room 270, phone 4525 6373, bang@com.dtu.dk

Liquid crystals are fluids which possess some kind of orientational order. Usually they are long molecules which tend to align themselves in parallel, so that one spatial direction (the length axis of the molecules) becomes distinct from the other in terms of, for instance, the refractive index. Liquid crystals can undergo several phase transformations as a function of temperature, and their orientation and alignment can also be influenced by static electric fields, or by electromagnetic radiation. These properties make liquid crystals interesting as building blocks for tunable optical components.

At COM we are currently working to infiltrate liquid crystals into microstructured optical fibers (MOFs). These are glass fibers which ordinarily guide light in a solid core of pure glass surrounded by a micrometer-sized array of airholes, which depress the average refractive index in the region surrounding the core (usually denoted the cladding).

Thus, these fibers are analogous to the standard optical fibers where the refractive index of the light-guiding core is raised by Germanium doping. When liquid crystals are infiltrated into the airholes the average index of the cladding is raised above that of pure glass, but light guidance can still occur in certain wavelength regions by a photonic bandgap effect. This effect is strongly dependent on the orientation of the liquid crystal molecules in the holes, which can be controlled in various ways. In the left figure below, a wavelength filter based on a liquid-crystal filled MOF is shown.

It can be seen that the colour of the transmitted light is strongly dependent on the temperature of the device.

Motivation:
Liquid crystals are fluids which possess some kind of orientational order. Usually they are long molecules which tend to align themselves in parallel, so that one spatial direction (the length axis of the molecules) becomes distinct from the other in terms of, for instance, the refractive index. Liquid crystals can undergo several phase transformations as a function of temperature, and their orientation and alignment can also be influenced by static electric fields, or by electromagnetic radiation. These properties make liquid crystals interesting as building blocks for tunable optical components. At COM we are currently working to infiltrate liquid crystals into microstructured optical fibers (MOFs). These are glass fibers which ordinarily guide light in a solid core of pure glass surrounded by a micrometer-sized array of airholes, which depress the average refractive index in the region surrounding the core (usually denoted the cladding). Thus, these fibers are analogous to the standard optical fibers where the refractive index of the light-guiding core is raised by Germanium doping. When liquid crystals are infiltrated into the airholes the average index of the cladding is raised above that of pure glass, but light guidance can still occur in certain wavelength regions by a photonic bandgap effect. This effect is strongly dependent on the orientation of the liquid crystal molecules in the holes, which can be controlled in various ways. In the left figure below, a wavelength filter based on a liquid-crystal filled MOF is shown. It can be seen that the colour of the transmitted light is strongly dependent on the temperature of the device.

Left: Transmission through a liquid-crystal filled MOF at different temperatures. Right: Light scattered from a single liquid-crystal filled microchannel

Description:
The aim of this project is to gain a basic understanding of how liquid-crystal orientation influences the properties of optical waveguides. For simplicity, we will restrict ourselves to modeling of light guidance in a single liquidcrystal filled microchannel, as shown in the right panel of Fig. 1. We study a simple free energy functional for a liquid crystal in a cylindrical channel, and find the equilibrium configuration for two different boundary conditions, which gives the refractive index distribution. Hereafter, we study how the orientation of the liquid crystal influences the waveguiding properties of a microchannel, using a standard electromagnetic modeling tool. The dispersion curves and field patterns obtained are compared with the results for a standard step-index fiber to elucidate the importance and effects of anisotropy in the refractive index.

Prerequisites:  
It is a prerequisite to have completed first course in photonics and basic courses in mathematics and physics.

Number of students: No limitations

Supervisor/Contact: Jesper Lægsgaard, jl@com.dtu.dk; phone 4525 6350, building 345v/ room 175.