# Publications

You can also find a list of my published works on my Google Scholar page.

**Journal articles**

[60] M.-A. Miri and V. Menon, “Neural Computing with Coherent Laser Networks,” *arXiv preprint*, arXiv:2204.02224 (2022).

**We show that a coherent network of lasers exhibits emergent neural computing capabilities. The proposed scheme is built on harnessing the collective behavior of laser networks for storing a number of phase patterns as stable fixed points of the governing dynamical equations and retrieving such patterns through proper excitation conditions, thus exhibiting an associative memory property. The associative memory functionality is first discussed in the strong pumping regime of a network of passive dissipatively coupled lasers which simulate the classical XY model. It is discussed that despite the large storage capacity of the network, the large overlap between fixed-point patterns effectively limits pattern retrieval to only two images. Next, we show that this restriction can be uplifted by using nonreciprocal coupling between lasers and this allows for utilizing a large storage capacity. This work opens new possibilities for neural computation with coherent laser networks as novel analog processors. In addition, the underlying dynamical model discussed here suggests a novel energy-based recurrent neural network that handles continuous data as opposed to Hopfield networks and Boltzmann machines which are intrinsically binary systems.**

[59] J. Shin, Y. Ryu, M.-A. Miri, S.-B. Shim, H. Choi, A. Alù, J. Suh, and J. Cha, “On-Chip Microwave Frequency Combs in a Superconducting Nanoelectromechanical Device,” Nano Letters, vol. XX, pp. XX-XX (2022).

[58] M. Honari-Latifpour, M. S. Mills, and M.-A. Miri, “Combinatorial Optimization with Photonics-Inspired Clock Models,” Communications Physics, vol. 5, pp. 1-8 (2022).

**NP-hard combinatorial optimization problems are in general hard problems that their computational complexity grows faster than polynomial scaling with the size of the problem. Thus, over the years there has been a great interest in developing unconventional methods and algorithms for solving such problems. Here, inspired by the nonlinear optical process of q-photon downconversion, we introduce a single-variable nonlinear dynamical model that allows for efficiently approximating the ground state of the classical q-state planar Potts Hamiltonian. This reduces the exhaustive search in the large discrete solution space of a large class of combinatorial problems that are represented by the Potts Hamiltonian to solving a system of coupled dynamical equations. We introduce two different annealing mechanisms, adiabatic deformation and chaotic annealing, and show that numerical simulations of the proposed dynamical model can efficiently approximate the solution of hard combinatorial problems. The proposed algorithm is applied to graph-q-partitioning as an example.**

[57] M. Honari-Latifpour, J. Ding, M. Barbuto, S. Takei, and M.-A. Miri, “Self-organized vortex and antivortex patterns in laser arrays,” Phys. Rev. Applied, vol. 16, pp. 054010 (2021).

**Recently, it was shown that dissipatively coupled laser arrays simulate the classical XY model. We show that phase-locking of laser arrays can give rise to the spontaneous formation of vortex and antivortex phase patterns that are analogous to topological defects of the XY model. These patterns are stable although their formation is less likely in comparison to the ground state lasing mode. In addition, we show that small ratios of photon to gain lifetime destabilize vortex and antivortex phase patterns. These findings are important for studying topological effects in optics as well as for designing laser array devices.**

[56] M.-A. Miri, “Integrated random projection and dimensionality reduction by propagating light in photonic lattices,” Optics Letters, vol. 46, pp. 4936-4939 (2021). [web]

**It is proposed that the propagation of light in disordered photonic lattices can be harnessed as a random projection that preserves distances between a set of projected vectors. This mapping is enabled by the complex evolution matrix of a photonic lattice with diagonal disorder, which turns out to be a random complex Gaussian matrix. Thus, by collecting the output light from a random subset of the waveguide channels, one can perform an embedding from a higher- to a lower-dimensional space that respects the Johnson–Lindenstrauss lemma and nearly preserves the Euclidean distances. The distance-preserving random projection through photonic lattices requires intermediate disorder levels that allow diffusive propagation of light. The proposed scheme can be utilized as a simple and powerful integrated dimension reduction stage that can greatly reduce the burden of a subsequent neural computation stage.**

[55] F. Shafiei, T. Orzali, A. Vert, M.-A. Miri, P.Y. Hung, M.H. Wong, A. Alu, G. Bersuker, M.C. Downer, "Detection of subsurface, nanometer-scale crystallographic defects by nonlinear light scattering and localization,'' Advanced Optical Materials, vol. 9, pp. 2002252 (2021). [web]

[54] A. Roy, S. Jahani, Q. Guo, A. Dutt, S. Fan, M.-A. Miri, A. Marandi, "Non-dissipative non-Hermitian dynamics and exceptional points in coupled optical parametric oscillators,'' Optica, vol. 8, pp. 415-421 (2021). [web]

[53] M. Honari-Latifpour, and M.-A. Miri, “Mapping the XY Hamiltonian onto a network of coupled lasers,” Physical Review Research, vol. 2, pp. 043335 (2020). [web]

**In recent years there has been a growing interest in the physical implementation of classical spin models through networks of optical oscillators. However, a key missing step in this mapping is to formally prove that the dynamics of such a nonlinear dynamical system is toward minimizing a global cost function which is equivalent with the spin model Hamiltonian. Here we introduce a minimal dynamical model for a network of dissipatively coupled optical oscillators and prove that the dynamics of such a system is governed by a Lyapunov function that serves as a cost function for the system. This cost function is in general a function of both phases and intensities of the oscillators and depends strongly on the pump parameter. In the case of bipartite network topologies, the amplitudes of the oscillators become identical in the steady state and the cost function reduces to the XY Hamiltonian. In the general case for nontrivial network topologies, however, the cost function approaches the XY Hamiltonian only in the strong pump limit. We show that by adiabatically tuning the pump parameter, the network can largely avoid trapping into the local minima of the governing cost function and stabilize into the ground state of the associated XY Hamiltonian. These results show the great potential of laser networks for unconventional computing.**

[52] M.-A. Miri, "Phase tristability in parametric three-photon down-conversion,'' Optics Letters, vol. 45, pp. 5546-5549 (2020). [web]

**This Letter shows that the parametric processes of spontaneous three-photon down-conversion is accompanied by phase tristability of the sub-harmonic signal. The oscillations of the signal in a resonant cavity are modeled through an analytically solvable second-order nonlinear oscillator. Self-sustained oscillations of the signal at a finite amplitude are found to be equally probable in three states with uniform phase contrasts. The onset of oscillations is a case of bifurcation from infinity. The stability of the ternary states is proven through an energy landscape function that identifies the attractor basins of the three states. An analogy is drawn between the oscillation threshold of a three-photon down-conversion oscillator and a first-order phase transition. The investigated phase-tristable oscillator can serve as a classical ternary bit for unconventional computing applications.**

[51] M. Honari-Latifpour, and M.-A. Miri, “Optical Potts machine through networks of three-photon down-conversion oscillators,” Nanophotonics, vol. 9, pp. 4199-4205 (2020). [web]

**In recent years, there has been a growing interest in optical simulation of lattice spin models for applications in unconventional computing. Here, we propose optical implementation of a three-state Potts spin model by using networks of coupled parametric oscillators with phase tristability. We first show that the cubic nonlinear process of spontaneous three-photon down-conversion is accompanied by a tristability in the phase of the subharmonic signal between three states with 2π/3 phase contrast. The phase of such a parametric oscillator behaves like a three-state spin system. Next, we show that a network of dissipatively coupled three-photon down-conversion oscillators emulates the three-state planar Potts model. We discuss potential applications of the proposed system for all-optical optimization of combinatorial problems such as graph 3-COL and MAX 3-CUT.**

[50] H. Li, Y. Cao, B. Shi, T. Zhu, Y. Geng, R. Feng, L. Wang, F. Sun, Y. Shi, M.-A. Miri, M. Nieto-Vesperinas, C.-W. Qiu, and W. Ding, "Momentum-topology-induced optical pulling force," Physical Review Letters, vol. 124, pp. 143901 (2020). [web]

[49] M. Barbuto, M.-A. Miri, A. Alu, F. Bilotti, and A. Toscano, "A topological design tool for the synthesis of antenna radiation patterns," IEEE Transactions on Antennas and Propagation, vol. 68, pp. 1851 (2020). [web]

[48] A. Krasnok, D. Baranov, H. Li, M.-A. Miri, F. Monticone, and A. Alu, "Anomalies in light scattering," Advances in Optics and Photonics, vol. 11, pp. 892-951 (2019). [web]

[47] J. Ding, I. Belykh, A. Marandi, and M.-A. Miri, "Dispersive versus dissipative coupling for frequency synchronization in lasers," Physical Review Applied, vol. 12, pp. 054039 (2019). [web]

**Coupling-enabled frequency synchronization is essential for an array of light sources operating in a photonic system. Using a two-dimensional nonlinear oscillator model of a laser, we analyze the role of two distinct types of coupling, dispersive and dissipative, in promoting frequency locking between two nonidentical lasers. In both scenarios the two oscillators synchronize into a frequency-locked state when the coupling level exceeds a critical value. We show that the onset of dispersive and dissipative synchronization processes is associated with hard and soft frequency transitions, respectively. Through analysis and numerics, we demonstrate that the dispersive coupling yields bistable synchronization modes, accompanied by asymmetric intensities, and the frequency controlled by the coupling strength. In contrast, dissipative coupling induces monostable synchronization with symmetric intensities and a coupling-independent frequency. Our results are expected to provide a basis for understanding the coupling mechanisms of frequency locking toward controlling synchronization in laser arrays.**

[46] J. Ding, and M.-A. Miri, “Mode discrimination in dissipatively coupled laser arrays,” Optics Letters, vol. 44, pp. 5021-5024 (2019). [web]

**We show that dissipative coupling between an array of passive optical resonators creates a ladder of decay rates in the complex eigenfrequencies. This effect promotes mode discrimination in laser arrays, while the lowest-order and highest-order modes exhibit the highest and lowest lasing thresholds, respectively. The array supermodes and their corresponding eigenfrequencies are calculated analytically through a tight-binding model, and the single-mode operation range is derived. The results are exemplified through the finite element simulation of an array of transversely coupled semiconductor laser cavities.**

[45] M.-A. Miri, M. Cotrufo, and A. Alu, "Anomalous optical forces in PT-Symmetric waveguides," Optics Letters, vol. 44, pp. 3558-3561 (2019). [web]

[44] Y. J. Zhang, H. Kwon, M.-A. Miri, M. S. Tong, and A. Alu, "Noninvasive glucose sensor based on parity-time symmetry," Physical Review Applied, vol. 11, pp. 044049 (2019). [web]

[43] Y. Li, Y.-G. Peng, L. Han, M.-A. Miri, W. Li, M. Xiao, X.-F. Zhu, J. Zhao, A. Alu, S. Fan, C.-W. Qiu, "Anti-parity-time symmetry in diffusive systems," Science, vol. 364, pp. 170-173 (2019). [web]

[42] M.-A. Miri, and A. Alu, "Exceptional points in optics and photonics," Science, vol. 363, pp. eaar7709 (2019). [web]

[41] M.-A. Miri, M. Cotrufo, A. Alù, "Optical gradient forces between evanescently coupled waveguides," Optics Letters, vol. 43, pp. 4104-4107 (2018). [web]

**Evanescently coupled dielectric waveguides exert optical forces on each other, which may be attractive or repulsive as a function of the excited optical mode. Through energy conservation considerations, it is possible to show that the optical force between two waveguides is proportional to the derivative of the effective propagation index with respect to the separation between waveguides. Here, we prove analytically that the lateral force calculated from the spatial derivative of the propagation index is equivalent to the one obtained from a formal calculation based on the Maxwell’s stress tensor. Interestingly, this latter approach reveals that the sign and magnitude of the force depends only on the field intensity at the channel interfaces. In addition, our derivation provides insights into the design of the waveguide profile in order to increase or decrease the optical forces between coupled channels.**

[40] M. Barbuto, M.-A. Miri, A. Alù, F. Bilotti, and A. Toscano, "Exploiting the topological robustness of composite vortices in radiation systems," Progress in Electromagnetics Research, vol. 172, pp. 39-50 (2018).

**Recent years have witnessed an increasing interest in topological states of condensed matter systems, whose concepts have been also extended to wave phenomena. Especially at optical frequencies, several studies have reported applications of structured light exploiting topological transitions and exceptional points or lines, over which a field property of choice is undefined. Interesting properties of light beams with phase singularities (such as the creation, annihilation or motion of these topological points) have been observed in composite vortices consisting of superimposed light beams with different topological charges. Here, we discuss how these concepts may have a relevant impact on antenna technology at microwave frequencies. We obtain the superposition of vortex fields with different topological charges by simultaneously exciting different modes of a patch antenna. This can be useful to give a physical interpretation for the behavior of some structures, already proposed at microwave frequencies, which use superposition of different radiating modes to manipulate the radiation pattern of patch antennas. Moreover, this approach may open new strategies to design at will the directivity properties of a patch antenna with inherently robust responses, and it may find applications in the design of smart antenna systems, requiring pattern reconfigurability.**

[39] F. Ruesink, J. P. Mathew, M.-A. Miri, A. Alu, and E. Verhagen, "Optical circulation in a multimode optomechanical resonator,'' Nature Communications, vol. 9, pp.1798 (2018).

**Optical circulators are important components of modern day communication technology. With their ability to route photons directionally, these nonreciprocal elements provide useful functionality in photonic circuits and offer prospects for fundamental research on information processing. Developing highly efficient optical circulators thus presents an important challenge, in particular to realize compact reconfigurable implementations that do not rely on a magnetic field bias to break reciprocity. We demonstrate optical circulation based on radiation pressure interactions in an on-chip multimode optomechanical system. We show that mechanically-mediated optical mode conversion in a silica microtoroid provides a synthetic gauge bias for light, which enables a 4-port circulator by exploiting tailored interference between appropriate light paths. We identify two sideband conditions under which ideal circulation is approached. This allows to experimentally demonstrate ~ 10 dB isolation and < 3 dB insertion loss in all relevant channels. We show the possibility of actively controlling the bandwidth, isolation ratio, noise performance and circulation direction, enabling ideal opportunities for reconfigurable integrated nanophotonic circuits.**

[38] M.-A. Miri, Giuseppe D'Aguanno, and A. Alu, "Optomechanical frequency combs,'' New Journal of Physics, vol. 20, pp. 043013 (2017).

**We study the formation of frequency combs in a single-mode optomechanical cavity. The comb is composed of equidistant spectral lines centered at the pump laser frequency and located at different harmonics of the mechanical resonator. We investigate the classical nonlinear dynamics of such system and find analytically the onset of parametric instability resulting in the breakdown of a stationary continuous wave intracavity field into a periodic train of pulses, which in the Fourier domain gives rise to a broadband frequency comb. Different dynamical regimes, including a stationary state, frequency comb generation and chaos, and their dependence on the system parameters, are studied both analytically and numerically. Interestingly, the comb generation is found to be more robust in the poor cavity limit, where optical loss is equal or larger than the mechanical resonance frequency. Our results show that optomechanical resonators open exciting opportunities for microwave photonics as compact and robust sources of frequency combs with megahertz line spacing.**

[37] M.-A. Miri, F. Ruesink, E. Verhagen, and A. Alu, "Optical non-reciprocity based on optomechanical coupling," Physical Review Applied, vol. 7, pp. 064014 (2017).

**Optical isolation, nonreciprocal phase transmission, and topological phases for light based on synthetic gauge fields have been raising significant interest in the recent literature. Cavity-optomechanical systems that involve two optical modes coupled to a common mechanical mode form an ideal platform to realize these effects, providing the basis for various recent demonstrations of optomechanically induced nonreciprocal light transmission. Here, we establish a unifying theoretical framework to analyze optical nonreciprocity and the breaking of time-reversal symmetry in multimode optomechanical systems. We highlight two general scenarios to achieve isolation, relying on either optical or mechanical losses. Depending on the loss mechanism, our theory defines the ultimate requirements for optimal isolation and the available operational bandwidth in these systems. We also analyze the effect of sideband resolution on the performance of optomechanical isolators, highlighting the fact that nonreciprocity can be preserved even in the unresolved sideband regime. Our results provide general insights into a broad class of parametrically modulated nonreciprocal devices, paving the way towards optimal nonreciprocal systems for low-noise integrated nanophotonics.**

[36] M.-A. Miri, and A. Alu, "Coupled cavity optomechanical meta-waveguides,'' Journal of the Optical Society of America B, vol. 34, pp. D68-D76 (2017).

**We explore waveguiding in a one-dimensional array of coupled optomechanical cavities, each supporting a pair of optical and mechanical modes. The dispersion relation of such waveguides is derived for different scenarios as a function of the level of optical, mechanical, and optomechanical coupling rates. The mechanical coupling with light is found to have a profound effect on the dispersion properties, leading to intriguing optical phenomena. In addition, the emergence of an exceptional point in the dispersion diagram is shown to induce a singularity associated with reduced attenuation. The drive power and frequency can largely control the band diagram of such periodic structures, offering a great tool for engineering and reconfiguring the coupled cavity optomechanical meta-waveguide. The peculiar band structure of the system is probed, investigating the linear propagation of short pulses and revealing interesting dynamics such as deceleration and acceleration, secondary pulse emission, and mechanically mediated enhanced light transmission. These concepts pave the way towards a new generation of meta-waveguides and multi-dimensional metamaterials in which strong optomechanical interactions overcome some of the limitations of passive, linear optical metamaterials based exclusively on optical resonances.**

[35] M.-A. Miri, E. Verhagen, and A. Alu, "Optomechanically-induced spontaneous symmetry breaking,'' Physical Review A, vol. 95, pp. 053822 (2017).

**We explore the dynamics of spontaneous breakdown of mirror symmetry in a pair of identical optomechanical cavities symmetrically coupled to a waveguide. Large optical intensities enable optomechanically induced nonlinear detuning of the optical resonators, resulting in a pitchfork bifurcation. We investigate the stability of this regime and explore the possibility of inducing multistability. By injecting proper trigger pulses, the proposed structure can toggle between two asymmetric stable states, thus serving as a low-noise nanophotonic all-optical switch or memory element.**

[34] F. Ruesink, M.-A. Miri, A. Alu, E. Verhagen, "Nonreciprocity and magnetic-free isolation based on optomechanical interactions," Nature Communications, vol. 7, pp. 13662 (2016).

**Nonreciprocal components, such as isolators and circulators, provide highly desirable functionalities for optical circuitry. This motivates the active investigation of mechanisms that break reciprocity, and pose alternatives to magneto-optic effects in on-chip systems. In this work, we use optomechanical interactions to strongly break reciprocity in a compact system. We derive minimal requirements to create nonreciprocity in a wide class of systems that couple two optical modes to a mechanical mode, highlighting the importance of optically biasing the modes at a controlled phase difference. We realize these principles in a silica microtoroid optomechanical resonator and use quantitative heterodyne spectroscopy to demonstrate up to 10 dB optical isolation at telecom wavelengths. We show that nonreciprocal transmission is preserved for nondegenerate modes, and demonstrate nonreciprocal parametric amplification. These results open a route to exploiting various nonreciprocal effects in optomechanical systems in different electromagnetic and mechanical frequency regimes, including optomechanical metamaterials with topologically non-trivial properties.**

[33] Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett., vol. 117, pp. 123601 (2016).

**We experimentally demonstrate PT-symmetric optical lattices with periodical gain and loss profiles in a coherently prepared four-level N-type atomic system. By appropriately tuning the pertinent atomic parameters, the onset of PT-symmetry breaking is observed through measuring an abrupt phase-shift jump between adjacent gain and loss waveguides. The experimental realization of such a readily reconfigurable and effectively controllable PT-symmetric waveguide array structure sets a new stage for further exploiting and better understanding the peculiar physical properties of these non-Hermitian systems in atomic settings.**

[32] H. Hodaei, A. Hassan, W. Hayenga, M.-A. Miri, and D. N. Christodoulides, M. Khajavikhan, “Dark-state lasers: Mode management using exceptional points,” Opt. Lett., vol. 41, pp. 3049-3052 (2016).

**By exploiting the inherent characteristics of dark-state resonators, we experimentally realize a single-frequency integrated microring laser system. This semiconductor laser can remain single-mode, even at high pump power levels, while allowing tunability over a wide spectral range. Our results demonstrate the potential of exceptional points as a versatile tool for mode selection in micro-cavity laser configurations.**

[31] M.-A. Miri, A. Alu, “Nonlinearity-induced PT-symmetry without material gain,” New. J. Phys., vol. 18, pp. 065001 (2016). (Invited Paper)

**Parity-time symmetry has raised a great deal of attention in optics in recent years, yet its application has been so far hindered by the stringent requirements on coherent gain balanced with loss. In this paper, we show that the conditions to enable parity and time symmetry can be simultaneously satisfied for a pair of modes with mixed frequencies interacting in a nonlinear medium, without requiring the presence of material gain. First, we consider a guided wave structure with second order nonlinearity and we derive the PT-symmetric Hamiltonian that governs the interaction of two waves of mixed frequencies when accompanied by a high intensity pump beam at the sum frequency. We also extend the results to an array of coupled nonlinear waveguide channels. It is shown that the evolution dynamics of the low-frequency waves is associated with a periodic PT-symmetric lattice while the phase of the pump beams can be utilized as a control parameter to modify the gain and loss distribution, thus realizing different PT lattices by design. Our results suggest that nonlinear wave mixing processes can form a rich platform to realize PT-symmetric Hamiltonians of arbitrary dimensions in optical systems, without requiring material gain.**

[30] A. U. Hassan, H. Hodaei, M.-A. Miri, M. Khajavikhan, and D. N. Christodoulides, “Integrable nonlinear parity-time-symmetric optical oscillator,” Phys. Rev. E, vol. 93, pp. 042219 (2016).

**The nonlinear dynamics of a balanced parity-time-symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain, thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time-symmetric systems. Unlike other saturable parity-time-symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.**

[29] M.-A. Miri, M. A. Eftekhar, M. Facao, A. F. Abouraddy, A. Bakry, M. A. N. Razvi, A. Alshahrie, A. Alu, and D. N. Christodoulides, “Scattering properties of PT-symmetric objects,” J. Opt., vol. 18, pp. 075104 (2016).

**We investigate the scattering response of parity-time (PT) symmetric structures. We show that, due to the local flow of energy between gain and loss regions, such systems can deflect light in unusual ways, as a function of the gain/loss contrast. Such structures are highly anisotropic and their scattering patterns can drastically change as a function of the angle of incidence. In addition, we derive a modified optical theorem for PT-symmetric scattering systems, and discuss its ramifications.**

[28] H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, M. Khajavikhan, “Single mode lasing in transversely multi-moded PT-symmetric microring resonators,” Laser Photon. Rev., vol. 10, pp. 494–499 (2016).

**Conventional techniques for transverse mode discrimination rely on introducing differential external losses to the different competing mode sets, enforcing single-mode operation at the expense of additional losses to the desirable mode. We show how a parity-time (PT) symmetric design approach can be employed to achieve single mode lasing in transversely multi-moded microring resonators. In this type of system, mode selectivity is attained by judiciously utilizing the exceptional point dynamics arising from a complex interplay of gain and loss. The proposed scheme is versatile, robust to deviations from PT symmetry such as caused by fabrication inaccuracies or pump inhomogeneities, and enables a stable operation considerably above threshold while maintaining spatial and spectral purity. The experimental results presented here were obtained in InP-based semiconductor microring arrangements and pave the way towards an entirely new class of chip-scale semiconductor lasers that harness gain/loss contrast as a primary mechanism of mode selectivity.**

[27] M. Parto, M. A. Eftekhar, M.-A. Miri, R. Amezcua-Correa, G. Li, and D. N. Christodoulides, “Systematic approach for designing zero-DGD coupled multi-core optical fibers,” Opt. Lett., vol. 41, pp. 1917-1920 (2016).

**An analytical method is presented for designing N-coupled multi-core fibers with zero differential group delay. This approach effectively reduces the problem to a system of N-1 algebraic equations involving the associated coupling coefficients and propagation constants, as obtained from coupled mode theory. Once the parameters of one of the cores are specified, the roots of the resulting N-1 equations can be used to determine the characteristics of the remaining waveguide elements. Using this technique, a number of pertinent geometrical configurations are investigated to minimize intermodal dispersion.**

[26] H. Hodaei, A. U. Hassan, J. Ren, W. E. Hayenga, M.-A. Miri, D. N. Christodoulides, and M. Khajavikhan, “Design considerations for single mode microring lasers using parity-time-symmetry,” IEEE J. Sel. Topics Quantum Electron., vol. 22, pp. 1500307 (2016). (Invited Paper)

**Coupled microring arrangements with balanced gain and loss, also known as parity-time symmetric systems, are investigated both analytically and experimentally. In these configurations, stable single-mode lasing can be achieved at pump powers well above threshold. This self-adaptive mode management technique is broadband and robust to small fabrication imperfections. The results presented in this paper provide a new avenue in designing mode selective chip-scale in-plane semiconductor lasers by utilizing the complex dynamics of coupled gain/loss cavities.**

[25] M. Wimmer, M.-A. Miri, D. N. Christodoulides, U. Peschel, “Observation of Bloch oscillations in complex PT-symmetric photonic lattices,” Sci. Rep., vol. 5, pp. 17760 (2015).

**Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals exhibit unusual properties like secondary emissions and resonant restoration of PT symmetry. In addition, we present a versatile method for reconstructing the real and imaginary components of the band structure by directly monitoring the light evolution during a cycle of these oscillations.**

[24] A. U. Hassan, H. Hodaei, M.-A. Miri, D. N. Christodoulides, M. Khajavikhan, “Nonlinear reversal of the PT-symmetric phase transition in a system of coupled semiconductor microring resonators,” Phys. Rev. A, vol. 92, pp. 063807 (2015).

**A system of two coupled semiconductor-based resonators is studied when lasing around an exceptional point. We show that the presence of nonlinear saturation effects can have important ramifications on the transition behavior of this system. In sharp contrast with linear PT-symmetric configurations, nonlinear processes are capable of reversing the order in which the symmetry breaking occurs. Yet, even in the nonlinear regime, the resulting non-Hermitian states still retain the structural form of the corresponding linear eigenvectors expected above and below the phase-transition point. The conclusions of our analysis are in agreement with experimental data.**

[23] H. Hodaei, M.-A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric coupled microring lasers operating around an exceptional point,” Opt. Lett., vol. 40, pp. 4955-4958 (2015).

**The behavior of a parity-time-symmetric coupled microring system is studied when operating in the vicinity of an exceptional point. Using the abrupt phase transition around this point, stable single-mode lasing is demonstrated in spectrally multimoded microring arrangements.**

[22] M. Wimmer, A. Regensburger, M.-A. Miri, C. Bersch, D. N. Christodoulides, and U. Peschel, “Observation of optical solitons in PT-symmetric lattices,” Nature Commun., vol. 6, pp. 7782 (2015).

**Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated.**

[21] J. Wang, J. Sheng, M.-A. Miri, D. N. Christodoulides, and M. Xiao, “Observation of discrete diffraction patterns in an optically induced lattice,” Opt. Exp., vol. 23, no. 15, pp. 19777-19782 (2015).

**We have experimentally observed the discrete diffraction of light in a coherently prepared multi-level atomic medium. This is achieved by launching a probe beam into an optical lattice induced from the interference of two coupling beams. The diffraction pattern can be controlled through the atomic parameters such as two-photon detuning and temperature, as well as orientations of the coupling and probe beams. Clear diffraction patterns occur only near the two-photon resonance.**

[20] M. Heinrich, M.-A. Miri, D. N. Christodoulides, S. Stutzer, S. Nolte, and A. Szameit, "Supersymmetric mode converters and transformation optics," Optics and Photonics News, Year in Optics 2014, vol. 25, pp. 40, (2014).

**The idea of supersymmetry (SUSY) was conceived within the framework of quantum field theory as a means to treat bosons and fermions on equal footing. While SUSY verification remains an ongoing task, some of its fundamental notions have been adapted to other fields. Optics can provide a versatile platform where SUSY transformations can be studied and directly observed.**

[19] H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, M. Khajavikhan, “Parity-time-symmetric micro-ring lasers,” Science, vol. 346, no. 6212, pp. 975-978 (2014).

**The ability to control the modes oscillating within a laser resonator is of fundamental importance. In general, the presence of competing modes can be detrimental to beam quality and spectral purity, thus leading to spatial as well as temporal fluctuations in the emitted radiation. We show that by harnessing notions from parity-time (PT) symmetry, stable single–longitudinal mode operation can be readily achieved in a system of coupled microring lasers. The selective breaking of PT symmetry can be used to systematically enhance the maximum attainable output power in the desired mode. This versatile concept is inherently self-adapting and facilitates mode selectivity over a broad bandwidth without the need for other additional intricate components. Our experimental findings provide the possibility to develop synthetic optical devices and structures with enhanced functionality.**

[18] M. Heinrich, M.-A. Miri, S. Stützer, S. Nolte, D. N. Christodoulides, and A. Szameit, “Observation of supersymmetric scattering in photonic lattices,” Opt. Lett., vol. 39, no. 21, pp. 6130-6133 (2014).

**Supersymmetric (SUSY) optical structures display a number of intriguing properties that can lead to a variety of potential applications, ranging from perfect global phase matching to highly efficient mode conversion and novel multiplexing schemes. Here, we experimentally investigate the scattering characteristics of SUSY photonic lattices. We directly observe the light dynamics in such systems and compare the reflection/transmission properties of SUSY partner structures. In doing so, we demonstrate that discrete settings constitute a promising testbed for studying the different facets of optical supersymmetry.**

[17] M.-A. Miri, M. Heinrich, D. N. Christodoulides, “SUSY-inspired one-dimensional transformation optics,” Optica, vol. 1, pp. 89-95 (2014).

**Transformation optics aims to identify artificial materials and structures with desired electromagnetic properties by means of pertinent coordinate transformations. In general, such schemes are meant to appropriately tailor the constitutive parameters of metamaterials in order to control the trajectory of light in two and three dimensions. Here, we introduce a new class of one-dimensional optical transformations that exploits the mathematical framework of supersymmetry (SUSY). This systematic approach can be utilized to synthesize photonic configurations with identical reflection and transmission characteristics, down to the phase, for all incident angles, thus rendering them perfectly indistinguishable to an external observer. Along these lines, low-contrast dielectric arrangements can be designed to fully mimic the behavior of a given high-contrast structure that would have been otherwise beyond the reach of available materials and existing fabrication techniques. Similar strategies can also be adopted to replace negative-permittivity domains, thus averting unwanted optical losses.**

[16] A. K. Sarma, M.-A. Miri, Z. H. Musslimani, and D. N. Christodoulides, “Continuous and discrete Schrödinger systems with parity-time-symmetric nonlinearities,” Phys. Rev. E, vol. 89, 052918 (2014).

**We investigate the dynamical behavior of continuous and discrete Schrödinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear Schrödinger counterparts. In particular, the PT-symmetric nonlinear Schrödinger equation can simultaneously support both bright and dark soliton solutions. In addition, we study a discretized version of this PT-nonlinear Schrödinger equation on a lattice. When only two elements are involved, by obtaining the underlying invariants, we show that this system is fully integrable and we identify the PT-symmetry-breaking conditions. This arrangement is unique in the sense that the exceptional points are fully dictated by the nonlinearity itself.**

[15] M. Heinrich†, M.-A. Miri†, S. Stützer†, R. El-Ganainy, S. Nolte, A. Szameit, D. N. Christodoulides, “Supersymmetric mode converters,” Nature Commun., vol. 5, 3698 (2014).

**Originally developed in the context of quantum field theory, the concept of supersymmetry can be used to systematically design a new class of optical structures. In this work, we demonstrate how key features arising from optical supersymmetry can be exploited to control the flow of light for mode-division multiplexing applications. Superpartner configurations are experimentally realized in coupled optical networks, and the corresponding light dynamics in such systems are directly observed. We show that supersymmetry can be judiciously used to remove the fundamental mode of a multimode optical structure while establishing global phase-matching conditions for the remaining set of modes. Along these lines, supersymmetry may serve as a promising platform for versatile optical components with desirable properties and functionalities.**

[14] M. Scheller, M. Mills, M.-A. Miri, W. Cheng, J. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nature Photon., vol. 8, pp. 297-301 (2014).

**Plasma channels produced in air through femtosecond laser filamentation hold great promise for a number of applications, including remote sensing, attosecond physics and spectroscopy, channelling microwaves and lightning protection. In such settings, extended filaments are desirable, yet their longitudinal span is limited by dissipative processes. Although various techniques aiming to prolong this process have been explored, the substantial extension of optical filaments remains a challenge. Here, we experimentally demonstrate that the natural range of a plasma column can be enhanced by at least an order of magnitude when the filament is prudently accompanied by an auxiliary beam. In this arrangement, the secondary low-intensity ‘dressing’ beam propagates linearly and acts as a distributed energy reservoir, continuously refuelling the optical filament. Our approach offers an efficient and viable route towards the generation of extended light strings in air without inducing premature wave collapse or an undesirable beam break-up into multiple filaments.**

[13] M. Wimmer, A. Regensburger, C. Bersch, M.-A. Miri, S. Batz, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Optical diametric drive acceleration through action-reaction symmetry breaking,” Nature Phys., vol. 9, pp 780-784 (2013).

**Newton’s third law of motion is one of the pillars of classical physics. This fundamental principle states that the forces two bodies exert on each other are equal and opposite. Had the resulting accelerations been oriented in the same direction, this would have instead led to a counterintuitive phenomenon, that of diametric drive. In such a hypothetical arrangement, two interacting particles constantly accelerate each other in the same direction through a violation of the action–reaction symmetry. Although in classical mechanics any realization of this process requires one of the two particles to have a negative mass and hence is strictly forbidden, it could nevertheless be feasible in periodic structures where the effective mass can also attain a negative sign. Here we report the first experimental observation of such diametric drive acceleration for pulses propagating in a nonlinear optical mesh lattice. The demonstrated reversal of action–reaction symmetry could enable altogether new possibilities for frequency conversion and pulse-steering applications.**

[12] J. Sheng, M.-A. Miri, D. N. Christodoulides, and M. Xiao, “PT-symmetric optical potentials in a coherent atomic medium,” Phys. Rev. A, vol. 88, 041803(R) (2013).

**We propose that a coherently prepared four-level atomic medium can provide a versatile platform for realizing parity-time (PT) symmetric optical potentials. Different types of PT-symmetric potentials are proposed by appropriately tuning the exciting optical fields and the pertinent atomic parameters. Such reconfigurable and controllable systems may open up new avenues in observing PT-related phenomena with appreciable gain-loss contrast in coherent atomic media.**

[11] M.-A. Miri, M. Heinrich, R. El-Ganainy, D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett., vol. 110, 233902 (2013).

**We show that supersymmetry can provide a versatile platform in synthesizing a new class of optical structures with desired properties and functionalities. By exploiting the intimate relationship between superpatners, one can systematically construct index potentials capable of exhibiting the same scattering and guided wave characteristics. In particular, in the Helmholtz regime, we demonstrate that one-dimensional supersymmetric pairs display identical reflectivities and transmittivities for any angle of incidence. Optical supersymmetry is then extended to two-dimensional systems where a link between specific azimuthal mode subsets is established. Finally, we explore supersymmetric photonic lattices where discreteness can be utilized to design lossless integrated mode filtering arrangements.**

[10] A. Regensburger†, M.-A. Miri†, C. Bersch, J. Näger, G. Onishchukov, D. N. Christodoulides, U. Peschel “Observation of defect states in PT-symmetric optical lattices,” Phys. Rev. Lett., vol. 110, 223902 (2013).

**We provide the first experimental demonstration of defect states in parity-time (PT ) symmetric mesh-periodic potentials. Our results indicate that these localized modes can undergo an abrupt phase transition in spite of the fact that they remain localized in a PT -symmetric periodic environment. Even more intriguing is the possibility of observing a linearly growing radiation emission from such defects provided their eigenvalue is associated with an exceptional point that resides within the continuum part of the spectrum. Localized complex modes existing outside the band-gap regions are also reported along with their evolution dynamics.**

[9] M.-A. Miri, M. Heinrich, D. N. Christodoulides, “Supersymmetry-generated complex optical potentials with real spectra,” Phys. Rev. A, vol. 87, 043819 (2013).

**We show that the formalism of supersymmetry (SUSY), when applied to parity-time (PT) symmetric optical potentials, can give rise to refractive index landscapes with altogether nontrivial properties. In particular, we find that the presence of gain and loss allows for arbitrarily removing bound states from the spectrum of a structure. This is in stark contrast to the Hermitian case, where the SUSY formalism can only address the fundamental mode of a potential. Subsequently we investigate isospectral families of complex potentials that exhibit entirely real spectra, despite the fact that their shapes violate PT symmetry. Finally, the role of SUSY transformations in the regime of spontaneously broken PTsymmetry is investigated.**

[8] P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett., vol. 109, 203902 (2012).

**We show that new families of diffraction-free nonparaxial accelerating optical beams can be generated by considering the symmetries of the underlying vectorial Helmholtz equation. Both two-dimensional transverse electric and magnetic accelerating wave fronts are possible, capable of moving along elliptic trajectories. Experimental results corroborate these predictions when these waves are launched from either the major or minor axis of the ellipse. In addition, three-dimensional spherical nondiffracting field configurations are presented along with their evolution dynamics. Finally, fully vectorial self-similar accelerating optical wave solutions are obtained via oblate-prolate spheroidal wave functions. In all occasions, these effects are illustrated via pertinent examples.**

[7] R. El-ganainy, M.-A. Miri, and D. N. Christodoulides, “Enhanced optical Anderson localization effects in modulated Bloch lattices,” Europhys. Lett., vol. 99, 64004 (2012).

[6] M.-A. Miri, A. B. Aceves, T. Kottos, V. Kovanis, D. N. Christodoulides, “Bragg solitons in nonlinear PT-symmetric periodic potentials,” Phys. Rev. A, vol. 86, 033801 (2012).

**It is shown that slow Bragg soliton solutions are possible in nonlinear complex parity-time (PT) symmetric periodic structures. Analysis indicates that the PT-symmetric component of the periodic optical refractive index can modify the grating band structure and hence the effective coupling between the forward and backward waves. Starting from a classical modified massive Thirring model, solitary wave solutions are obtained in closed form. The basic properties of these slow solitary waves and their dependence on their respective PT-symmetric gain-loss profile are then explored via numerical simulations.**

[5] A. Regensburger, C. Bersch, M.‐A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature (London), vol. 488, pp. 167-171 (2012).

**The development of new artificial structures and materials is today one of the major research challenges in optics. In most studies so far, the design of such structures has been based on the judicious manipulation of their refractive index properties. Recently, the prospect of simultaneously using gain and loss was suggested as a new way of achieving optical behaviour that is at present unattainable with standard arrangements. What facilitated these quests is the recently developed notion of ‘parity–time symmetry’ in optical systems, which allows a controlled interplay between gain and loss. Here we report the experimental observation of light transport in large-scale temporal lattices.**

[4] M.-A. Miri, A. Regensburger, U. Peschel, D. N. Christodoulides, "Optical mesh lattices with PT-symmetry," Phys. Rev. A, vol. 86, 023807 (2012).

**We investigate a class of optical mesh periodic structures that are discretized in both the transverse and longitudinal directions. These networks are composed of waveguide arrays that are discretely coupled, while phase elements are also inserted to discretely control their effective potentials and can be realized both in the temporal and the spatial domain. Their band structure and impulse response are studied in both the passive and parity-time (PT)-symmetric regime. The possibility of band merging and the emergence of exceptional points, along with the associated optical dynamics, are considered in detail both above and below the PT-symmetry breaking point. Finally, unidirectional invisibility in PT-synthetic mesh lattices is also examined, along with possible superluminal light transport dynamics.**

[3] M.-A. Miri, P. LiKamWa, and D. N. Christodoulides, “Large area single-mode parity-time-symmetric laser amplifiers,” Opt. Lett., vol. 37, no. 5, pp. 764-766 (2012).

**By exploiting recent developments associated with parity–time (PT) symmetry in optics, we here propose a new avenue in realizing single-mode large area laser amplifiers. This can be accomplished by utilizing the abrupt symmetry breaking transition that allows the fundamental mode to experience gain while keeping all the higher order modes neutral. Such PT-symmetric structures can be realized by judiciously coupling two multimode waveguides, one exhibiting gain while the other exhibits an equal amount of loss. Pertinent examples are provided for both semiconductor and fiber laser amplifiers.**

[2] R. El-Ganainy, K. G. Makris, M.-A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A, vol. 84, 023842 (2011).

**Within the framework of the tight-binding model we demonstrate that Wannier-Stark states can freely accelerate in uniform optical lattices. As opposed to accelerating Airy wave packets in free space, our analysis reveals that in this case the beam main intensity features self-bend along two opposite hyperbolic trajectories. Two-dimensional geometries are also considered and an asymptotic connection between these Wannier-Stark ladders and Airy profiles is presented.**

[1] M.-A. Miri, A. Khavasi, M. Miri, and K. Mehrany, “A transmission line resonator model for fast extraction of electromagnetic properties of cavities in two-dimensional photonic crystals,” IEEE Photon. J., vol. 2, pp. 677-685 (2010).

**In this paper, photonic cavities made of point defects in 2-D photonic crystals are modeled by finite-size transmission lines terminated at both ends by appropriate scalar impedances. The proposed model forms a simple transmission line resonator and is demonstrated to be quite beneficial in fast extraction of resonant frequency, quality factor, and mode profile of such photonic cavities. In this manner, an approximate yet quite accurate approach is introduced to characterize the electromagnetic properties of photonic crystal cavities. This method is successfully applied to different structures for both major polarizations and is shown to be as accurate as rigorous numerical methods, viz. the finite element method.**