
Solmaz Naghizadeh, Adeel Afridi, Ongun Arısev, Aziz Karaşahin, Şükrü Ekin Kocabaş, "Experimental Investigation of Stub Resonators Built in Plasmonic Slot Waveguides," IEEE Photonics Technology Letters, vol. 29, no. 8, pp. 663666, April 15, 2017. abstract pdf url
In this work, we focus on stub resonators embedded in plasmonic slot waveguides. The resonators have potential applications in optical interconnects and sensors. We fabricate the samples by electron beam lithography and liftoff. We use a scattering matrix based model to quantify the optical power output from the samples. We measure the properties of the resonators by coupling light in and out of the slot waveguides by optical antennas, making use of a crosspolarization based setup utilizing a supercontinuum source and a high numerical aperture objective lens operating in the telecomwavelength range. Our model agrees well with the measured data. Further development on the stub resonators can be made by using the methods in this paper.

Solmaz Naghizadeh, Şükrü Ekin Kocabaş, "Guidelines for designing 2D and 3D plasmonic stub resonators," J. Opt. Soc. Am. B 34, 207217 (2017). abstract pdf url
In this work, we compare the performance of plasmonic waveguide integrated stub resonators based on 2D metaldielectricmetal and 3D slot waveguide (SWG) geometries. We show that scattering matrix theory can be extended to 3D devices, and by employing scattering matrix theory, we provide the guidelines for designing plasmonic 2D and 3D singlestub and doublestub resonators with a desired spectral response at the design wavelength. We provide transmission maps of 2D and 3D doublestub resonators versus stub lengths, and we specify the different regions on these maps that result in a minimum, a maximum, or a plasmonically induced transparency shape in the transmission spectrum. Radiation loss from waveguide terminations leads to a degradation of the 3D SWGbased resonators. We illustrate improved waveguide terminations that boost resonator properties. We verify our results with 3D finitedifference timedomain (FDTD) simulations.

Adeel Afridi, Şükrü Ekin Kocabaş, "Beam steering and impedance matching of plasmonic horn nanoantennas," Opt. Express 24, 25647–25652 (2016). abstract pdf url
In this paper, we study a plasmonic horn nanoantenna on a metalbacked substrate. The horn nanoantenna structure consists of a twowire transmission line (TWTL) flared at the end. We analyze the effect of the substrate thickness on the nanoantenna's radiation pattern, and demonstrate beam steering in a broad range of elevation angles. Furthermore, we analyze the effect of the ground plane on the impedance matching between the antenna and the TWTL, and observe that the ground plane increases the back reflection into the waveguide. To reduce the reflection, we develop a transmission line model to design an impedance matching section which leads to 99.75% power transmission to the nanoantenna.

Şükrü Ekin Kocabaş, "Fewphoton scattering in dispersive waveguides with multiple qubits," Opt. Lett., 41, 25332536 (2016). abstract pdf url
We extend the Krylovsubspacebased timedependent numerical simulation technique for a qubit interacting with photons in a waveguide to the multiple qubit case. We analyze photon scattering from two qubits and derive expressions for the bound states in the continuum (BICs). We show how the BIC can be excited. We use the BIC in a recent PauliZ gate proposal involving decoherence free subspaces and obtain the gate fidelity as a function of the gate parameters. The techniques presented in this Letter are useful for investigating the time evolution of quantum gates and other manybody systems with multiple quenches in the Hamiltonian.

Şükrü Ekin Kocabaş, "Effects of modal dispersion on fewphoton–qubit scattering in onedimensional waveguides," Physical Review A, vol. 93, no. 3, p. 033829, Mar 2016.
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We study one and twophoton scattering from a qubit embedded in a onedimensional waveguide in the presence of modal dispersion. We use a resolvent based analysis and utilize techniques borrowed from the Lee model studies. Modal dispersion leads to atomphoton bound states which necessitate the use of multichannel scattering theory. We present multichannel scattering matrix elements in terms of the solution of a Fredholm integral equation of the second kind. Through the use of the LippmannSchwinger equation, we derive an infinite series of Feynman diagrams that represent the solution to the integral equation. We use the Feynman diagrams as vertex correction terms to come up with closed form formulas that successfully predict the trapping rate of a photon in the atomphoton bound state. We verify our formalism through Krylovsubspace based numerical studies. Our results provide the tools to calculate the complex correlations between scattered photons in a dispersive environment.

Şükrü Ekin Kocabaş, Eden Rephaeli, Shanhui Fan, "Resonance fluorescence in a waveguide geometry," Physical Review A, vol. 85, no. 2, p. 023817, Feb 2012. abstract pdf url
We show how to calculate the first and secondorder statistics of the scattered fields for an arbitrary intensity coherentstate light field interacting with a twolevel system in a waveguide geometry. Specifically, we calculate the resonance fluorescence from the qubit, using inputoutput formalism. We derive the transmission and reflection coefficients, and illustrate the bunching and antibunching of light that is scattered in the forward and backward directions, respectively. Our results agree with previous calculations on one and twophoton scattering as well as those that are based on the master equation approach.

Eden Rephaeli, Şükrü Ekin Kocabaş, Shanhui Fan, "Few photon transport in a waveguide coupled to a pair of colocated twolevel atoms," Physical Review A, vol. 84, no. 6, p. 063832, Dec 2011. abstract pdf url
We calculate the one and twophoton scattering matrices of a pair of collocated nonidentical twolevel atoms coupled to a waveguide. We show that by proper choice of a twophoton input, the background fluorescence by the atoms may be completely quenched, as a result of quantum interference, and that when the atoms’ detuning is smaller than their linewidths, extremely narrow fluorescence features emerge. Furthermore, the system emits a twophoton bound state which can display spatial oscillations or quantum beats, and can be tuned from bunched to antibunched statistics as the total photon energy is varied.

Shanhui Fan, Şükrü Ekin Kocabaş, JungTsung Shen, "InputOutput Formalism For FewPhoton Transport in OneDimensional Nanophotonic Waveguides Coupled to a Qubit," Physical Review A, vol. 82, no. 6, p. 063821, Dec 2010. abstract pdf url
We extend the inputoutput formalism of quantum optics to analyze fewphoton transport in waveguides with an embedded qubit. We provide explicit analytical derivations for one and twophoton scattering matrix elements based on operator equations in the Heisenberg picture.

Salman Latif, Şükrü Ekin Kocabaş, Liang Tang, Christof Debaes, and David A. B. Miller, "Low capacitance CMOS Silicon photodetectors for optical clock injection," Applied Physics A: Material Science & Processing, vol. 95, no. 4, pp. 1129–1135, 2009. abstract pdf url
We have studied the response of CMOS compatible detectors fabricated in a silicononsapphire (SOS) process, operated under short pulse excitation in the blue.These high speed, low capacitance detectors would be suitable for very precise, surfacenormal clock injection with silicon CMOS. We characterize the capacitance of the detector structure through a combination of experimental techniques and circuitlevel and electromagnetic simulations.The transittimelimited response of the detectors is validated through pump–probe experiments. Detector response times of ∼35 ps have been measured, and devices have capacitance as low as ∼4 fF.

Georgios Veronis, Şükrü Ekin Kocabaş, David A.B. Miller, Shanhui Fan, "Modeling of plasmonic waveguide components and networks," Journal of Computational and Theoretical Nanoscience, vol. 6, no. 8, pp. 1808–1826, August 2009. abstract pdf url
We review some of the recent advances in the simulation of plasmonic devices, drawing examples from our own work in metalinsulatormetal (MIM) plasmonic waveguide components and networks.We introduce the modematching technique for modeling of MIM waveguide devices. We derive the complete set of orthogonal modes that the MIM waveguide supports and use it to apply the modematching technique to the analysis of plasmonic waveguide networks. We also introduce several different equivalent models for plasmonic waveguide components, such as the characteristic impedance model for deep subwavelength MIM waveguides, the scattering matrix description of MIM waveguide junctions, and equivalent circuit models. The model abstraction provided by these equivalent models is important for the analysis and synthesis of device functions, as illustrated with the design of a waveguide mode converter.

Georgios Veronis, Zongfu Yu, Şükrü Ekin Kocabaş, David A. B. Miller, Mark L. Brongersma, Shanhui Fan, "Metaldielectricmetal plasmonic waveguide devices for manipulating light at the nanoscale," Chinese Optics Letters, vol. 7, no. 4, pp. 302–308, 2009. abstract pdf url
We review some of the recent advances in the development of subwavelength plasmonic devices for manipulating light at the nanoscale, drawing examples from our own work in metaldielectricmetal (MDM) plasmonic waveguide devices. We introduce bends, splitters, and mode converters for MDM waveguides with no additional loss. We also demonstrate that optical gain provides a mechanism for on/off switching in MDM plasmonic waveguides. Highly efficient compact couplers between dielectric waveguides and MDM waveguides are also introduced.

Şükrü Ekin Kocabaş, Georgios Veronis, David A. B. Miller, Shanhui Fan, "Modal Analysis and Coupling in MetalInsulatorMetal Waveguides," Physical Review B, vol. 79, p. 035120, 2009. abstract pdf url
This paper shows how to analyze plasmonic metalinsulatormetal waveguides using the full modal structure of these guides. The analysis applies to all frequencies, particularly including the near infrared and visible spectrum, and to a wide range of sizes, including nanometallic structures. We use the approach here specifically to analyze waveguide junctions. We show that the full modal structure of the metalinsulatormetal (MIM) waveguides—which consists of real and complex discrete eigenvalue spectra, as well as the continuous spectrum—forms a complete basis set. We provide the derivation of these modes using the techniques developed for SturmLiouville and generalized eigenvalue equations. We demonstrate the need to include all parts of the spectrum to have a complete set of basis vectors to describe scattering within MIM waveguides with the modematching technique. We numerically compare the modematching formulation with finitedifference frequencydomain analysis and find very good agreement between the two for modal scattering at symmetric MIM waveguide junctions. We touch upon the similarities between the underlying mathematical structure of the MIM waveguide and the PT symmetric quantummechanical pseudoHermitian Hamiltonians. The rich set of modes that the MIM waveguide supports forms a canonical example against which other more complicated geometries can be compared. Our work here encompasses the microwave results but extends also to waveguides with real metals even at infrared and optical frequencies.
 Here is the code that implements the argument principle method. It was written under Mathematica 6. Might need to be modified to work under newer versions.

I also have the Mathematica sheets for the implementation of mode matching. I did not have the time to add more comments to them, if you'd like to take a look at those please let me know, I'll be much more motivated to put them online then.

Şükrü Ekin Kocabaş, Georgios Veronis, David A. B. Miller, Shanhui Fan, "Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components," IEEE Journal of Selected Topics in Quantum Electronics, vol. 14, no. 6, pp. 1462–1472, 2008. abstract pdf url
Modeling of waveguide junctions using transmission lines and lumped circuit elements is common practice in microwave networks. By the help of the scattering matrix formalism, it is possible to describe junction effects in a very concise way. Such a representation is crucial for the design of complex systems containing many interacting parts. Using scattering matrices, we characterize symmetric junctions between 2D metalinsulatormetal (MIM) waveguides with optical signals at infrared frequencies (1550 nm) propagating in them. We verify our characterization by perfectly matching a wavelengthsized MIM waveguide to a subwavelengthsized one using a Smith chart. We then map the scattering matrix description to an equivalent lumped circuit representation and discuss the physical significance of its elements. We show that the simplified characteristic impedance model is appropriate for the deep subwavelength regime. The scattering matrix model for the MIM junctions leads to simplified analysis that can be integrated into circuit modeling software packages, such as SPICE.

DanySebastien LyGagnon, Şükrü Ekin Kocabaş, David A. B. Miller, "Characteristic Impedance Model for Plasmonic Metal Slot Waveguides," IEEE Journal of Selected Topics in Quantum Electronics, vol. 14, no. 6, pp. 1473–1478, 2008. abstract pdf url
We investigate the transmission properties of a subwavelength plasmonic slot waveguide. We show that the transmission can be accurately calculated using the characteristic impedance of the propagating mode. Using such a model, we show that it is possible to design devices without extensive 3D finitedifference timedomain (FDTD) computer simulations. We illustrate the approach with calculations of an asymmetric FabryPerot germanium photodetector based on the slot waveguide geometry, showing predicted detector efficiencies as high as 69% despite metallic losses.

Liang Tang, Şükrü Ekin Kocabaş, Salman Latif, Ali K. Okyay, DanySebastien LyGagnon, Krishna C. Saraswat, David A. B. Miller, "Nanometrescale germanium photodetector enhanced by a nearinfrared dipole antenna," Nature Photonics, vol. 2, pp. 226–229, 2008. abstract pdf url
A critical challenge for the convergence of optics and electronics is that the micrometre scale of optics is significantly larger than the nanometre scale of modern electronic devices. In the conversion from photons to electrons by photodetectors, this size incompatibility often leads to substantial penalties in power dissipation, area, latency and noise. A photodetector can be made smaller by using a subwavelength active region; however, this can result in very low responsivity because of the diffraction limit of the light. Here we exploit the idea of a halfwave Hertz dipole antenna (length approx 380 nm) from radio waves, but at nearinfrared wavelengths (length approx 1.3 µm), to concentrate radiation into a nanometrescale germanium photodetector. This gives a polarization contrast of a factor of 20 in the resulting photocurrent in the subwavelength germanium element, which has an active volume of 0.00072 µm^{3}, a size that is two orders of magnitude smaller than previously demonstrated detectors at such wavelengths.
 Here is the finite difference frequency domain code used in the simulations of the paper. There are a fair number of lines of comments in the code, but I did not have the time to go over and describe in detail how different sections (C++ for number crunching, Matlab for data analysis, Mathematica for fitting multipole Drude parameters) talk to each other. Email me if you would like to learn more about the code.

Şükrü Ekin Kocabaş, Abdullah Atalar, "Binary sequences with low aperiodic autocorrelation for synchronization purposes," IEEE Communications Letters, vol. 7, no. 1, pp 36–38, Jan 2003. abstract pdf url
An evolutionary algorithm is used to find three sets of binary sequences of length 49100 suitable for the synchronization of digital communication systems. Optimization of the sets are done by taking into consideration the type of preamble used in data frames and the phaselock mechanism of the communication system. The preamble is assumed to be either a pseudonoise (PN) sequence or a sequence of 1s. There may or may not be phase ambiguity in detection. With this categorization, the first set of binary sequences is optimized with respect to aperiodic autocorrelation which corresponds to the random (PN) preamble without phase ambiguity case. The second and third sets are optimized with respect to a modified aperiodic autocorrelation for different figures of merit corresponding to the predetermined preamble (sequence of 1s) with and without phase ambiguity cases.