Rigorous simulations of emitting and non-emitting resonant periodic nano-optical structures (PhD thesis)

Overview

During little over 4 years I worked on a PhD research that gave me the opportunity to write my own rigorous computer model for calculating the propagation of light near nanoscale structures. To read the full research download my thesis. Below, some details are given, to see all the publications related to this research visit my academic profiles at ResearchGate or Academia.

Before the actual defense I gave a so-called layman's talk to introduce the layman audience to my research before the professors start drilling me with difficult questions. The visuals can be seen below (no audio/in Dutch).

Propositions

Next to defending my thesis I defended a set of propositions that should be about my research and about the world in general.

                            Propositions
                   accompanying the PhD thesis:

        Rigorous simulations of emitting and non-emitting
                    nano-optical structures

            to be defended on Tuesday, November 9, 2010 
                        at 3pm in Delft
                        by Olaf Janssen

1. For a given structure, both solar cell absorption and LED
emission can be determined from the same simulations.

2. The best active region in LEDs is in general nonplanar and
should be chosen based on both Fabry-Pérot and modal 
resonances.

3. Swapping source and detector in the reciprocity principle
becomes increasingly efficient for larger spatially
incoherent sources and smaller coherent detectors.

4. There is nothing perfect about the perfectly matched layer.

5. Since lattice surface waves occur in perfect metallic
gratings unlike surface plasmon polaritons, enhanced
transmission by metallic gratings is more determined by
lattice- than by plasmonic effects.

6. Programming a cutting-edge simulation tool and solving
cuttingedge problems at the same time poses unproductive
dilemmas.

7. Authors of scientific publications should grant their
readers a more honest insight into the disadvantages of the
methods they use.

8. The near-pathological compulsion to have an opinion about
everything leads to widely accepted misconceptions.

9. People do not like to be optimized.

10. A thorough study of a language is sufficient for
understanding a culture in its entirety.


These propositions are considered opposable and defendable
and as such have been approved by the supervisor, 
prof.dr. H.P. Urbach.

Refereed Journal Papers

J. Gómez Rivas, S. Kalaleh-Rahimzadeh Rodriguez, M.A. Schaafsma, G. Vecchi, A. Abass, B. Maes, O.T.A. Janssen Coupled Surface Lattice Resonances in Arrays of Nanoantennas (to be submitted)

S.L. Diedenhofen, G. Grzela, O.T.A. Janssen, J. Gómez Rivas Enhanced Optical Absorption in Ordered Arrays of Base-Tapered InP Nanowires (to be submitted)

O.T.A. Janssen, A.J. Wachters, H.P. Urbach Efficient Optimization Method for the Light Ex- traction from Periodically Modulated LEDs using Reciprocity Opt. Exp. 18, 21 (2010)

S. van Haver, J.J.M. Braat, A. Janssen, O.T.A. Janssen, S.F. Pereira Vectorial Aerial-Image Computations of Three-Dimensional Objects Based on the Extended Nijboer-Zernike Theory, J. Opt. Soc. Am. A 26, 5 (2009)

O.T.A. Janssen, H.P. Urbach, and G.W. ’t Hooft Giant Optical Transmission of a Subwavelength Slit Optimized using the Magnetic Field Phase, Phys. Rev. Lett. 99, 4 (2007)

M. Besbes, J.P. Hugonin, P. Lalanne, S. van Haver, O.T.A. Janssen, A.M. Nugrowati, M. Xu, S.F. Pereira, H.P. Urbach, A.S. van de Nes, and others Numerical Analysis of a Slit-Groove Diffraction Problem, J. Eur. Opt. Soc. 2, (2007)

O.T.A. Janssen, H.P. Urbach, and G.W. ’t Hooft On the Phase of Plasmons Excited by Slits in a Metal Film, Opt. Exp. 14, 24 (2006)

Conference Contributions

O.T.A. Janssen, H.P. Urbach Controlled Embedding of Nanoparticles in Light Emitting Diodes, EOS Anual Meeting, Paris 2010 (poster).

O.T.A. Janssen, H.P. Urbach, Photonic Crystal LED Surface Optimization Assisted by the Reci- procity Principle, Optics-Photonics Design & Fabrication, Yokohama 2010 (poster / could not attend, oral given instead)

O.T.A. Janssen, H.P. Urbach, LED Radiation Simulation and Optimization using Reciprocity, EOS Topical Meeting on Diffractive Optics, Koli 2010 (oral).

O.T.A. Janssen, H.P. Urbach, Simulation of LED Radiation Patterns, Fotonica Event, Nieuwegein 2009 (oral).

O.T.A. Janssen, H.P. Urbach, Smart LED Radiation Calculations using Reciprocity OSA Frontiers in Optics, Rochester 2008 (oral).

S. van Haver, O.T.A. Janssen, J.J.M. Braat, S.F. Pereira Characterization of a Novel Mask Imaging Algorithm Based on the Extended Nijboer-Zernike (ENZ) Formalism, NanoNed Symposium, Ede 2008 (poster).

O.T.A. Janssen, H.P. Urbach, Highly Efficient Photonic Crystal LED Simulations using Reci- procity, IEEE/LEOS Benelux, Enschede 2008 (poster).

O.T.A. Janssen, H.P. Urbach, and M. Megens, Smart Simulation of LED Radiation using Reci- procity, EOS Annual Meeting, Paris 2008 (oral).

S. van Haver, O.T.A. Janssen, A.J.E.M. Janssen, J.J.M. Braat, S.F. Pereira, Image Simulations of Extended Objects using an Algorithm based on the Extended Nijboer-Zernike (ENZ) Formal- ism, EOS Annual Meeting, Paris 2008.

S. van Haver, O.T.A. Janssen, J.J.M. Braat, S.F. Pereira, H.P. Urbach, An Alternative Method for Advanced Lithographic Imaging: the Extended Nijboer-Zernike Formalism, IISB Lithography Simulation Workshop, Athens 2008.

S. van Haver, O.T.A. Janssen, A.J.E.M. Janssen, J.J.M. Braat, S.F. Pereira, P. Evanschitzky, Characterization of a Novel Mask Imaging Algorithm Based on the Extended Nijboer-Zernike (ENZ) Formalism, Micro- and Nano-Engineering 34, Athens 2008 (poster).

S. van Haver, O.T.A. Janssen, A.J.E.M. Janssen, J.J.M. Braat, H.P. Urbach, and S.F. Pereira, General Imaging of Advanced 3D mask Objects Based on the Fully-Vectorial Extended Nijboer- Zernike (ENZ) Theory, Proceedings SPIE 6924, SPIE Optical Microlithography, San Jose 2008 (oral).

O.T.A. Janssen, S. van Haver, A.J.E.M. Janssen, J.J.M. Braat, H.P. Urbach, and S.F. Pereira, Extended Nijboer-Zernike (ENZ) Based Mask Imaging: Efficient Coupling of Electromagnetic Field Solvers and the ENZ Imaging Algorithm, Proceedings SPIE 6924, SPIE Optical Microlithography, San Jose 2008 (oral).

S. van Haver, O.T.A. Janssen, A.M. Nugrowati, J.J.M. Braat, S.F. Pereira, Novel Approach to Mask Imaging Based on the Extended Nijboer-Zernike (ENZ) Diffraction Theory Micro- and Nano-Engineering 33, Copenhagen 2007 (best poster award).

S. van Haver, O.T.A. Janssen, A.M. Nugrowati, J.J.M. Braat, S.F. Pereira, Combining Various Optical Simulation Tools to Enable Complex Optical System Simulations, NEMO meeting, Santiago de Compostela 2007 (poster).

O.T.A. Janssen, H.P. Urbach, G.W. ’t Hooft, Optical Transmission of a Subwavelength Slit Op- timized Using the Magnetic Field Phase, Frontiers in Nanophotonics and Plasmonics, Guaruja 2007 (oral).

A.M. Nugrowati, O.T.A. Janssen, S.F. Pereira, Spatial-Temporal Evolution of Femtosecond Pulses Through Resonant (Sub)Wavelength Structures, Surface Plasmon Photonics-3, Dijon 2007 (poster).

O.T.A. Janssen, H.P. Urbach, J. G´omez Rivas, On the Enhanced Scattering by Metallic Nanopar- ticles, OSA Nanophotonics, Hangzhou 2006 (oral).

O.T.A. Janssen, H.P. Urbach, On the Phase and Amplitude of Surface Plasmons Generated in a One and Two slit Experiment, EOS Topical Meeting on Molecular Plasmonic Devices, Engelberg 2006 (oral).

Patent Contributions

J. Gómez Rivas, R.W.I. de Boer, O.T.A. Janssen, A. Narayanaswamy, E.M.H.P. van Dijk, M.A. Verschuuren, Nanoantenna and Uses Thereof for Biosensing, Patent WO/2009/150598, 17 December 2009

Summary

In recent years, techniques to produce well-defined material structures smaller than the wavelength of light with a resolution of several nanometers have improved much. Such structures can be used to gain a degree of control over the flow of light that is not possible with larger structures. For this reason, they are crucial for making, for instance, light-emitting diodes (LEDs) and solar cells more efficient. Structures that show a repetitive pattern have the property that light can only exist in these structures in discrete states, or modes. At these so-called photonic crystal structures, incident light can be fully reflected although the individual materials the structure consists of are transparent. Conversely, surfaces that would otherwise reflect most of the light can be made to transmit more light by adding a photonic crystal structure to it.

To design these structures, a simulation tool that describes how light interacts on this small scale is very valuable. In this thesis, a rigorous and quite general electromagnetic field solver is described based on the finite-difference time-domain (FDTD) principle. In short, space is divided into small blocks representing the materials in the region of interest. Then by taking small steps in time, the propagation of the electromagnetic field is followed through space as it enters the region and interacts with the structure. While the principle is simple to understand, implementing it to work with metals and complex objects is not trivial. Periodic structures also pose problems and can cause pitfalls which we discuss in some detail. Highly resonant structures require long time-interval simulations, making the method rather inefficient. By using an extrapolation technique based on the Padé approximant accurate solutions can be obtained in shorter simulation times. In addition, the critical absorbing boundary layer surrounding the region of interest, the so-called perfectly matched layer (PML), works less than perfect. These computational problems can in most cases be overcome to the extend that this thesis contains simulations that compare well to experimental results.

The properties of photonic crystals are very important for enhancing the efficiency of LEDs. While light is efficiently generated in the semiconductor material, most of it is trapped inside the LED due to total internal reflection at the interface with air. By patterning this interface with a photonic crystal, light that is otherwise trapped can couple to the modes of the photonic crystal and subsequently to radiation in air. The radiation of an LED can be modeled by incoherent dipole sources located in the active region of the LED. An efficient method is discussed for computing the radiation of these dipoles that uses the reciprocity principle. It transforms the large radiation problem of an isolated dipole in a periodic structure into many similar scattering problems. For each angle of radiation, two small-scale scattering problems on the unit cell of the periodic structure have to be simulated (one for each polarization). The field intensity computed inside the structure is then directly proportional to the radiation of the incoherent dipoles located there in the direction of incidence. Although many angles of incidence have to be simulated, the simulations are much smaller and faster than the original radiation problem. Moreover, the radiation of all possible distributions of incoherent dipoles within the active region are directly known.

The method is used for several thin gallium nitride-based LEDs, but also for emitting indium phosphate nanowires. It is shown that the location of the active region is critical for the extraction of light from the structure and that this can be easily optimized using the reciprocity method. It is found that it is not always favorable to have a single planar active region. It is shown that the light-emitting nanowires can also act an as an efficient absorber for use in photovoltaic- or solar cells. Both effects can be studied using the same simulation data. It is shown that by means of tapering the nanowires, light can be absorbed for wavelengths in the visual range up to the near infrared. We show a structure that absorbs more than 90 % of the incident light, while less than 2 % is reflected.

Optimizing photonic crystals for light extraction in LEDs can be done using experience and physical insight. There is a trade-off between resonances that couple strongly to the photonic crystal modes but remain in the structure a long time before being radiated and weaker resonances that escape the structure almost immediately. In this thesis, an automated optimization algorithm is introduced which can be used to improve existing geometries in several optimization steps. To do this efficiently, an expression is derived for the derivative of the radiated intensity of the LED with respect to a change of the photonic crystal surface. Only one extra simulation is required to obtain the direction of steepest increase of the radiated intensity in the design space. At the basis of this technique is the so-called adjoint method, that relies again on the reciprocity principle. Although it is shown that the light extraction can be improved by using this optimization method, finding the most optimal structure without a good initial guess is in general not possible.

A property of small metallic structures is that light can be concentrated on very short length scales. This is useful for applications in biosensing where very weak signals from molecules need to be enhanced by strong electric fields. Periodic arrays of such metal structures show highly-resonant surface waves, which can further improve sensitivity.

In summary, in this thesis structures for enhanced emission, absorption and sensing are discussed. It also is an illustration of how electromagnetic simulations can be used to gain physical insight and to improve optical designs of today and tomorrow.