Abstract
In this chapter, we introduce the inverse design of disordered photonic structures with the target modal response. Starting from the concept of metadisorder , which is defined by order -random interactions in the multivariable parameter space, we discuss the realization of anomalous wave transport and localization in photonic structures as an example of the independent control of wave quantities. As a generalization of this approach, we introduce the concept of Bohmian photonics inspired by the alternative interpretation of quantum mechanics, which enables independent control of the amplitude and phase information of light. Various practical applications of Bohmian photonics , including optical phase trapping, phase-conserved energy confinement and annihilation, and constant-intensity wave transport, are discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Amaral, L.A.N., Scala, A., Barthelemy, M., Stanley, H.E.: Classes of small-world networks. Proc. Natl. Acad. Sci. 97, 11149–11152 (2000)
Anderson, P.W.: Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492 (1958)
Aspuru-Guzik, A., Walther, P.: Photonic quantum simulators. Nat. Phys. 8, 285–291 (2012)
Assawaworrarit, S., Yu, X., Fan, S.: Robust wireless power transfer using a nonlinear parity-time-symmetric circuit. Nature 546, 387–390 (2017)
Bender, C.M.: Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 70, 947–1018 (2007). https://doi.org/10.1088/0034-4885/70/6/r03
Bender, C.M., Boettcher, S.: Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243 (1998)
Bender, C.M., Boettcher, S., Meisinger, P.N.: PT-symmetric quantum mechanics. J. Math. Phys. 40, 2201–2229 (1999)
Bender, C.M., Brody, D.C., Jones, H.F.: Complex extension of quantum mechanics. Phys. Rev. Lett. 89, 270401 (2002)
Bender, C.M., Brody, D.C., Jones, H.F., Meister, B.K.: Faster than Hermitian quantum mechanics. Phys. Rev. Lett. 98, 040403 (2007)
Bohm, D.: A suggested interpretation of the quantum theory in terms of “hidden” variables. I. Phys. Rev. 85, 166 (1952)
Bullmore, E.T., Bassett, D.S.: Brain graphs: graphical models of the human brain connectome. Annu. Rev. Clin. Psychol. 7, 113–140 (2011)
Cai, W., Chettiar, U.K., Kildishev, A.V., Shalaev, V.M.: Optical cloaking with metamaterials. Nat. Photonics 1, 224–227 (2007)
Chang, L., Jiang, X., Hua, S., Yang, C., Wen, J., Jiang, L., Li, G., Wang, G., Xiao, M.: Parity-time symmetry and variable optical isolation in active–passive-coupled microresonators. Nat. Photonics 8, 524–529 (2014)
Chen, H., Chan, C., Sheng, P.: Transformation optics and metamaterials. Nat. Mater. 9, 387–396 (2010)
Chertkov, E., DiStasio Jr., R.A., Zhang, G., Car, R., Torquato, S.: Inverse design of disordered stealthy hyperuniform spin chains. Phys. Rev. B 93, 064201 (2016)
Choi, M., Lee, S.H., Kim, Y., Kang, S.B., Shin, J., Kwak, M.H., Kang, K.-Y., Lee, Y.-H., Park, N., Min, B.: A terahertz metamaterial with unnaturally high refractive index. Nature 470, 369–373 (2011)
Christodoulides, D.N., Lederer, F., Silberberg, Y.: Discretizing light behaviour in linear and nonlinear waveguide lattices. Nature 424, 817–823 (2003)
Dürr, D., Fusseder, Goldstein, S., Zanghi, N.: Comment on “Surrealistic Bohm trajectories”. Z. Naturforsch. A 48, 1261 (1993). https://doi.org/10.1515/zna-1993-1219
El-Ganainy, R., Makris, K.G., Khajavikhan, M., Musslimani, Z.H., Rotter, S., Christodoulides, D.N.: Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018)
Englert, B.-G., Scully, M.O., Süssmann, G., Walther, H.: Surrealistic Bohm trajectories. Z. Naturforsch. A 47, 1175–1186 (1992)
Englert, B.-G., Scully, M., Süssmann, G., Walther, H.: Reply to comment on “Surrealistic Bohm trajectories”. Z. Naturforsch. A 48, 1263–1264 (1993)
Feng, L., Xu, Y.L., Fegadolli, W.S., Lu, M.H., Oliveira, J.E., Almeida, V.R., Chen, Y.F., Scherer, A.: Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies. Nat. Mater. 12, 108–113 (2013). https://doi.org/10.1038/nmat3495
Feng, L., Wong, Z.J., Ma, R.-M., Wang, Y., Zhang, X.: Single-mode laser by parity-time symmetry breaking. Science 346, 972–975 (2014)
Feng, L., El-Ganainy, R., Ge, L.: Non-Hermitian photonics based on parity-time symmetry. Nat. Photonics 11, 752–762 (2017)
Florescu, M., Torquato, S., Steinhardt, P.J.: Designer disordered materials with large, complete photonic band gaps. Proc. Natl. Acad. Sci. U.S.A. 106, 20658–20663 (2009)
Gao, J., Liu, Y.-Y., D’Souza, R.M., Barabási, A.-L.: Target control of complex networks. Nat. Commun. 5, 5415 (2014). https://doi.org/10.1038/ncomms6415
Garanovich, I.L., Longhi, S., Sukhorukov, A.A., Kivshar, Y.S.: Light propagation and localization in modulated photonic lattices and waveguides. Phys. Rep. 518, 1–79 (2012)
Ge, L., El-Ganainy, R.: Nonlinear modal interactions in parity-time (PT) symmetric lasers. Sci. Rep. 6, 24889 (2016)
Ge, L., Stone, A.D.: Parity-time symmetry breaking beyond one dimension: the role of degeneracy. Phys. Rev. X 4, 031011 (2014). https://doi.org/10.1103/PhysRevX.4.031011
Golshani, M., Akhavan, O.: Bohmian prediction about a two double-slit experiment and its disagreement with standard quantum mechanics. J. Phys. A 34, 5259 (2001)
Guo, A., Salamo, G.J., Duchesne, D., Morandotti, R., Volatier-Ravat, M., Aimez, V., Siviloglou, G.A., Christodoulides, D.N.: Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103 (2009). https://doi.org/10.1103/physrevlett.103.093902
Hahn, K., Kärger, J., Kukla, V.: Single-file diffusion observation. Phys. Rev. Lett. 76, 2762 (1996)
Haus, H.A.: Waves and fields in optoelectronics. In: Solid State Physical Electronics. Prentice-Hall, Englewood Cliffs, NJ (1984)
Heisenberg, W.: Physics and Philosophy: The Revolution in Modern Science. George Allen & Unwin Ltd., London (1958)
Hilgetag, C.C., Goulas, A.: Is the brain really a small-world network? Brain Struct. Funct. 221, 2361–2366 (2016)
Hodaei, H., Miri, M.-A., Heinrich, M., Christodoulides, D.N., Khajavikhan, M.: Parity-time-symmetric microring lasers. Science 346, 975–978 (2014)
Holland, P.R.: The Quantum Theory of Motion: An Account of the De Broglie-Bohm Causal Interpretation of Quantum Mechanics. Cambridge University Press (1995)
Horsley, S., Artoni, M., La Rocca, G.: Spatial Kramers-Kronig relations and the reflection of waves. Nat. Photonics 9, 436–439 (2015)
Hsieh, P., Chung, C., McMillan, J., Tsai, M., Lu, M., Panoiu, N., Wong, C.W.: Photon transport enhanced by transverse Anderson localization in disordered superlattices. Nat. Phys. 11, 268 (2015)
Hsu, C.W., Zhen, B., Lee, J., Chua, S.L., Johnson, S.G., Joannopoulos, J.D., Soljacic, M.: Observation of trapped light within the radiation continuum. Nature 499, 188–191 (2013). https://doi.org/10.1038/nature12289
Hsu, C.W., Zhen, B., Stone, A.D., Joannopoulos, J.D., Soljačić, M.: Bound states in the continuum. Nat. Rev. Mater. 1, 16048 (2016)
Huang, X., Lai, Y., Hang, Z.H., Zheng, H., Chan, C.: Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials. Nat. Mater. 10, 582–586 (2011)
Iudice, F.L., Garofalo, F., Sorrentino, F.: Structural permeability of complex networks to control signals. Nat. Commun. 6, 8349 (2015). https://doi.org/10.1038/ncomms9349
Joannopoulos, J.D., Johnson, S.G., Winn, J.N., Meade, R.D.: Photonic Crystals: Molding the Flow of Light. Princeton University Press (2011)
Keil, R., Pressl, B., Heilmann, R., Gräfe, M., Weihs, G., Szameit, A.: Direct measurement of second-order coupling in a waveguide lattice (2015). arXiv:1510.07900
Lagendijk, A., Van Tiggelen, B., Wiersma, D.S.: Fifty years of Anderson localization. Phys. Today 62, 24–29 (2009)
Lahini, Y., Avidan, A., Pozzi, F., Sorel, M., Morandotti, R., Christodoulides, D.N., Silberberg, Y.: Anderson localization and nonlinearity in one-dimensional disordered photonic lattices. Phys. Rev. Lett. 100, 013906 (2008)
Lawrence, M., Xu, N., Zhang, X., Cong, L., Han, J., Zhang, W., Zhang, S.: Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces. Phys. Rev. Lett. 113, 093901 (2014)
Lee, H., Chen, T., Li, J., Yang, K.Y., Jeon, S., Painter, O., Vahala, K.J.: Chemically etched ultrahigh-Q wedge-resonator on a silicon chip. Nat. Photonics 6, 369–373 (2012)
Liang, G., Chong, Y.: Optical resonator analog of a two-dimensional topological insulator. Phys. Rev. Lett. 110, 203904 (2013)
Liberal, I., Engheta, N.: Near-zero refractive index photonics. Nat. Photonics 11, 149–158 (2017). https://doi.org/10.1038/nphoton.2017.13
Lidorikis, E., Sigalas, M., Economou, E.N., Soukoulis, C.: Tight-binding parametrization for photonic band gap materials. Phys. Rev. Lett. 81, 1405 (1998)
Lin, Z., Ramezani, H., Eichelkraut, T., Kottos, T., Cao, H., Christodoulides, D.N.: Unidirectional invisibility induced by PT-symmetric periodic structures. Phys. Rev. Lett. 106, 213901 (2011). https://doi.org/10.1103/PhysRevLett.106.213901
Longhi, S.: Bloch oscillations in complex crystals with PT symmetry. Phys. Rev. Lett. 103 (2009a). https://doi.org/10.1103/physrevlett.103.123601
Longhi, S.: Quantum‐optical analogies using photonic structures. Laser Photon. Rev. 3 243–261 (2009b)
Longhi, S.: Invisibility in PT-symmetric complex crystals. J. Phys. A 44, 485302 (2011). https://doi.org/10.1088/1751-8113/44/48/485302
Longhi, S.: Talbot self-imaging in PT-symmetric complex crystals. Phys. Rev. A 90, 043827 (2014)
Longhi, S.: PT phase control in circular multi-core fibers. Opt. Lett. 41, 1897–1900 (2016)
Longhi, S., Della Valle, G., Ornigotti, M., Laporta, P.: Coherent tunneling by adiabatic passage in an optical waveguide system. Phys. Rev. B 76, 201101 (2007)
Louisell, W.: Amplitude and phase uncertainty relations. Phys. Lett. 7 (1963)
Mahler, D.H., Rozema, L., Fisher, K., Vermeyden, L., Resch, K.J., Wiseman, H.M., Steinberg, A.: Experimental nonlocal and surreal Bohmian trajectories. Sci. Adv. 2, e1501466 (2016)
Makris, K.G., Musslimani, Z.H., Christodoulides, D.N., Rotter, S.: Constant-intensity waves and their modulation instability in non-Hermitian potentials. Nat. Commun. 6, 7257 (2015)
Makris, K.G., Brandstötter, A., Ambichl, P., Musslimani, Z.H., Rotter, S.: Wave propagation through disordered media without backscattering and intensity variations. Light Sci. Appl. 6, e17035 (2017)
Marinica, D., Borisov, A., Shabanov, S.: Bound states in the continuum in photonics. Phys. Rev. Lett. 100, 183902 (2008)
Martin, L., Di Giuseppe, G., Perez-Leija, A., Keil, R., Dreisow, F., Heinrich, M., Nolte, S., Szameit, A., Abouraddy, A.F., Christodoulides, D.N.: Anderson localization in optical waveguide arrays with off-diagonal coupling disorder. Opt. Express 19, 13636–13646 (2011)
Molina-Terriza, G., Torres, J.P., Torner, L.: Twisted photons. Nat. Phys. 3, 305–310 (2007)
Monticone, F., Alù, A.: Do cloaked objects really scatter less? Phys. Rev. X 3, 041005 (2013)
Mrejen, M., Suchowski, H., Hatakeyama, T., Wu, C., Feng, L., O’Brien, K., Wang, Y., Zhang, X.: Adiabatic elimination-based coupling control in densely packed subwavelength waveguides. Nat. Commun. 6 (2015a)
Mrejen, M., Suchowski, H., Hatakeyama, T., Wu, C., Feng, L., O’Brien, K., Wang, Y., Zhang, X.: Adiabatic elimination-based coupling control in densely packed subwavelength waveguides. Nat. Commun. 6, 7565 (2015b). https://doi.org/10.1038/ncomms8565
Nagarajan, R., Joyner, C.H., Schneider Jr., R.P., Bostak, J.S., Butrie, T., Dentai, A.G., Dominic, V.G., Evans, P.W., Kato, M., Kauffman, M.: Large-scale photonic integrated circuits. IEEE J. Sel. Top. Quantum Electron. 11, 50–65 (2005)
Nassar, A.B., Miret-Artés, S.: Bohmian Mechanics, Open Quantum Systems and Continuous Measurements. Springer (2017)
Papasimakis, N., Fedotov, V.A., Fu, Y.H., Tsai, D.P., Zheludev, N.I.: Coherent and incoherent metamaterials and order-disorder transitions. Phys. Rev. B 80, 041102 (2009)
Pendry, J.: Off-diagonal disorder and 1D localisation. J. Phys. C 15, 5773 (1982)
Pendry, J.B., Schurig, D., Smith, D.R.: Controlling electromagnetic fields. Science 312, 1780–1782 (2006)
Peng, B., Özdemir, Ş.K., Lei, F., Monifi, F., Gianfreda, M., Long, G.L., Fan, S., Nori, F., Bender, C.M., Yang, L.: parity-time-symmetric whispering-gallery microcavities. Nat. Phys. 10, 394–398 (2014)
Piao, X., Yu, S., Park, N.: Design of transverse spinning of light with globally unique handedness. Phys. Rev. Lett. 120, 203901 (2018)
Poddubny, A.N., Rybin, M.V., Limonov, M.F., Kivshar, Y.S.: Fano interference governs wave transport in disordered systems. Nat. Commun. 3, 914 (2012)
Regensburger, A., Bersch, C., Miri, M.A., Onishchukov, G., Christodoulides, D.N., Peschel, U.: Parity-time synthetic photonic lattices. Nature 488, 167–171 (2012). https://doi.org/10.1038/nature11298
Rivet, E., Brandstötter, A., Makris, K., Rotter, S., Lissek, H., Fleury, R.: Constant amplitude sound waves in non-Hermitian metamaterials. J. Acoust. Soc. Am. 142, 2684–2684 (2017)
Rivet, E., Brandstötter, A., Makris, K.G., Lissek, H., Rotter, S., Fleury, R.: Constant-pressure sound waves in non-Hermitian disordered media. Nat. Phys. 14, 942 (2018)
Rüter, C.E., Makris, K.G., El-Ganainy, R., Christodoulides, D.N., Segev, M., Kip, D.: Observation of parity-time symmetry in optics. Nat. Phys. 6, 192–195 (2010)
Schwartz, T., Bartal, G., Fishman, S., Segev, M.: Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007)
Scully, M.O.: Do Bohm trajectories always provide a trustworthy physical picture of particle motion? Phys. Scripta 76, 41–46 (1998)
Shafiei, F., Monticone, F., Le, K.Q., Liu, X.-X., Hartsfield, T., Alù, A., Li, X.: A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance. Nat. Nanotech. 8, 95–99 (2013)
Skardal, P.S., Arenas, A.: Control of coupled oscillator networks with application to microgrid technologies. Sci. Adv. 1, e1500339 (2015)
Smith, D.R., Pendry, J.B., Wiltshire, M.C.: Metamaterials and negative refractive index. Science 305, 788–792 (2004)
Song, W., Gatdula, R., Abbaslou, S., Lu, M., Stein, A., Lai, W.Y., Provine, J., Pease, R.F.W., Christodoulides, D.N., Jiang, W.: High-density waveguide superlattices with low crosstalk. Nat. Commun. 6, 7027 (2015). https://doi.org/10.1038/ncomms8027
Takesue, H., Matsuda, N., Kuramochi, E., Munro, W.J., Notomi, M.: An on-chip coupled resonator optical waveguide single-photon buffer. Nat. Commun. 4, 2725 (2013). https://doi.org/10.1038/ncomms3725
Teimourpour, M.H., Ge, L., Christodoulides, D.N., El-Ganainy, R.: Non-Hermitian engineering of single mode two dimensional laser arrays. Sci. Rep. 6, 33253 (2016)
Teimourpour, M., Khajavikhan, M., Christodoulides, D.N., El-Ganainy, R.: Robustness and mode selectivity in parity-time (PT) symmetric lasers. Sci. Rep. 7, 10756 (2017a)
Teimourpour, M., Rahman, A., Srinivasan, K., El-Ganainy, R.: Non-Hermitian engineering of synthetic saturable absorbers for applications in photonics. Phys. Rev. Appl. 7, 014015 (2017b)
Torquato, S., Zhang, G., Stillinger, F.: Ensemble theory for stealthy hyperuniform disordered ground states. Phys. Rev. X 5, 021020 (2015). https://doi.org/10.1103/PhysRevX.5.021020
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998a)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998b)
Wiersma, D.S.: Disordered photonics. Nat. Photonics 7, 188–196 (2013)
Wiersma, D.S., Bartolini, P., Lagendijk, A., Righini, R.: Localization of light in a disordered medium. Nature 390, 671–673 (1997)
Xu, L., Chen, H.: Conformal transformation optics. Nat. Photonics 9, 15–23 (2015)
Yu, S., Piao, X., Mason, D.R., In, S., Park, N.: Spatiospectral separation of exceptional points in PT-symmetric optical potentials. Phys. Rev. A 86, 031802 (2012)
Yu, S., Mason, D.R., Piao, X., Park, N.: Phase-dependent reversible nonreciprocity in complex metamolecules. Phys. Rev. B 87, 125143 (2013)
Yu, S., Piao, X., Hong, J., Park, N.: Progress toward high-Q perfect absorption: a Fano antilaser. Phys. Rev. A 92, 011802 (2015a)
Yu, S., Piao, X., Yoo, K., Shin, J., Park, N.: One-way optical modal transition based on causality in momentum space. Opt. Express 23, 24997–25008 (2015b)
Yu, S., Piao, X., Hong, J., Park, N.: Bloch-like waves in random-walk potentials based on supersymmetry. Nat. Commun. 6, 8269 (2015c)
Yu, S., Piao, X., Hong, J., Park, N.: Metadisorder for designer light in random systems. Sci. Adv. 2, e1501851 (2016a)
Yu, S., Park, H.S., Piao, X., Min, B., Park, N.: Low-dimensional optical chirality in complex potentials. Optica 3, 1025 (2016b). https://doi.org/10.1364/OPTICA.3.001025
Yu, S., Piao, X., Park, N.: Acceleration toward polarization singularity inspired by relativistic E × B drift. Sci. Rep. 6, 37754 (2016c)
Yu, S., Piao, X., Hong, J., Park, N.: Interdimensional optical isospectrality inspired by graph networks. Optica 3, 836–839 (2016d)
Yu, S., Piao, X., Park, N.: Dynamical phase diagram of parity-time symmetry with competing saturable channels (2017a). arXiv:1707.07096
Yu, S., Piao, X., Park, N.: Target decoupling in coupled systems resistant to random perturbation. Sci. Rep. 7, 2139 (2017b)
Yu, S., Piao, X., Park, N.: Disordered potential landscapes for anomalous delocalization and superdiffusion of light. ACS Photonics 5, 1499 (2018a)
Yu, S., Piao, X., Park, N.: Bohmian photonics for independent control of the phase and amplitude of waves. Phys. Rev. Lett. 120, 193902 (2018b)
Yu, S., Piao, X., Park, N.: Designing non-Hermitian dynamics for conservative state evolution on the Bloch sphere. Phys. Rev. A 97, 033805 (2018c)
Yu, S., Piao, X., Park, N.: Chirality in non-Hermitian photonics (2019a). arXiv:1904.11662v2
Yu, S., Piao, X., Park, N.: Neuromorphic functions of light in parity-time-symmetric systems. Adv. Sci. 6, 1900771 (2019b)
Zhu, X., Feng, L., Zhang, P., Yin, X., Zhang, X.: One-way invisible cloak using parity-time symmetric transformation optics. Opt. Lett. 38, 2821–2824 (2013). https://doi.org/10.1364/OL.38.002821
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 The Author(s), under exclusive license to Springer Nature Singapore Pte. Ltd.
About this chapter
Cite this chapter
Yu, S., Piao, X., Park, N. (2019). Designing Modes in Disordered Photonic Structures. In: Top-Down Design of Disordered Photonic Structures. SpringerBriefs in Physics. Springer, Singapore. https://doi.org/10.1007/978-981-13-7527-9_3
Download citation
DOI: https://doi.org/10.1007/978-981-13-7527-9_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-7526-2
Online ISBN: 978-981-13-7527-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)