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Acknowledgement

On 30 March 2001, I got an email from Brenny van Groesen, in which he wrote ``.....One type of spectacular new devices are microresonators, where constructive interference of light traveling in a circular disk, may lead to transfer of light from one waveguide to another. Mathematical challenge is to understand the qualitative behaviour (with new physical phenomena), and using numerical tools, approximate actual solutions. ..... My specific question to you: are you interested to accept this offer and to come to UTwente.....?'' What happened after that is in this thesis in your hands! Brenny, thank you very much for introducing me to fascinating vista of mathematical aspects of electromagnetics.

While Brenny gave me a canvas to paint my impressions, Manfred Hammer gave me brushes and colors. I explored the landscape under his supervision. At the start of Ph. D., Manfred explained me the project, and gave the relevant literature collection done by him. That helped me to orient myself quickly in the right direction. In middle of the course, he gave me his 2-D straight waveguides mode solver. On top of which, I developed 2-D bent waveguides mode solver, bent-straight waveguide couplers module, and resonators module.

I learned countless things from him. It took me quite some time to get embodied in his extremely organized and disciplined way of modus operandi. And now, it became a part of my modus vivendi! His style of comprehensive analysis of a topic, meticulous writing, spotless presentation, and single-minded hard working left the ever lasting impressions on me. During the formative phase of the Ph. D., his alacritous availability for discussions, his insistence on preciseness helped me a lot. In retrospect, working with Manfred was the venerable experience.

I also benefited by the experience and insight of Hugo Hoekstra, Remco Stoffer and Theo Valkering. The discussions with them during group meetings and review meetings helped me to develop an understanding of the present interdisciplinary work from the application point of view.

I will like to thank my colleagues from Applied Analysis and Mathematical Physics (AAMP) and Numerical Analysis and Computational Mechanics (NACM) groups. I have fond memories of my officemates Pearu Peterson (for enjoying all sorts of ``strange'' coffees), Fedderik van der Bos (voor Nederlands praten en vertalen), Arek Kuczaj (for software troubleshooting). It was a great fun to work with Linux enthusiastic guys like Vijaya Ambati (Ploting=Gnuplot), Christiaan Klaij (Viva Emacs!), Lars Pesch (The Jack of many GNU softwares), Joris van den Berg (Mr. Macintosh).....and of course Manfred (For C++ optimization ideas, Xfig).

Scientific discussions with Agus Suryanto, Ardhasena Sopaheluwakan, Jaqueline Nicolau, Henri Uranus, Didit Yudistira was very useful. I will like to thank Timco Visser, Hala Elrofai, Helena Margaretha, Hadi Susanto, Natanael Karjanto, Monica Polner, Janivita Sudirham, Mikhail Tchesnokov, and Davit Harutyunyan. Also thanks to Debby Lanser, Mike Botchev, Bernard Geurts, and Chris Stolk for sharing their valuable experiences with me.

I have the unique memories of two very special persons: Marielle Plekenpol and Diana Dalenoord. They act as binding forces, leaving no stone unturned (well.... that is a quite difficult task in The Netherlands!) to make all of us mingle, come together for informal gatherings like birthday celebrations, lunch-together, group outings. They have added many countries to my philatelic collection. I acknowledge Marielle's support for the administrative and practical matters.

Interaction with Mart Diemeer, Douwe Geuzebroek, Ronald Dekker, and many other colleagues from Integrated Optical MicroSystems (IOMS) group and MESA+ Research Institute, and also with NAIS project partners, especially with Ladislav Prkna, was very fruitful.

I thank Enno Oosterhuis and Ewout Bakker from computer helpdesk for their support for computational infrastructure. With the advent of the computers and wide spread use of digital format, a need to visit library is becoming less and less. Nevertheless, there is a team of dedicated librarians working quietly in the background. I thank the library support team for their efficient content provision. Thanks to Michel ten Bulte for his efficient co-ordination during moving from TWRC to Informatica, and from Informatica to Ravelijn. After a day's work, I used to leave my table in a bit of mess, but next day it used to be systematically cleaned and arranged. How can I forget those nameless, unknown hands? Very special thanks to them.

The presence of Indian friends at the University of Twente was very important for emotional composure; many thanks from heart to Makarand Pimplapure, Rahul Dahule, Salim Deshmukh, Sheela Sowariraj, Rajshekhar Kakumani, Ramkrishna Pasumarthy, Vijaya Ambati, Manish Arora, Amol Thakre, Chandrashekhar Murade, and Rajeev Roy; also to affectionate families Madhavi and Ravi Tupe, Shashi and Satyendra Tomar, Vishakha and Pramod Agarwal, Deepa and Viswanath Talasila, Kavitha and Kiran Thumma. I am recalling so many other names...... I will always cherish memories of all these gezellige people!

For the last four years, while I was working like a bee in my bonnet, far far away there are a few people who always used to encourage me without expressing their griefs. They gave me wings and power to fly. They supported my ideas to explore a new sky. I am indebted to my parents for giving me a free hand, and supporting me at the crucial moments. Thanks to my siblings Hemakka, Ashakka and Amit for taking care of the family, and leaving me free of any worries. I specially remember passing away of my grandmother, who was my the first mathematics teacher. Without the support of my siblings in ``those'' difficult situations, I don't know.....how I would have found my way. Thank you Netra for being with me, and synchronizing my heartbeats and brain-waves. Thanks to pals Balaji Kasal and Ganesh Bagler.

The experience of these four years will ``guide'' my journey ahead. Van harte bedankt allemaal, en tot straks.

K. R. (Kiran) Hiremath October 2005, Enschede


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Kirankumar Hiremath 2005-09-23