Marin Soljacic

Summary

Affiliation: Massachusetts Institute of Technology
Country: USA

Publications

  1. ncbi request reprint Optical bistability in axially modulated OmniGuide fibers
    Marin Soljacic
    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Opt Lett 28:516-8. 2003
  2. ncbi request reprint Nonlinear photonic crystal microdevices for optical integration
    Marin Soljacic
    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Opt Lett 28:637-9. 2003
  3. ncbi request reprint Enhancement of nonlinear effects using photonic crystals
    Marin Soljacic
    Physics Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Nat Mater 3:211-9. 2004
  4. doi request reprint High-temperature stability and selective thermal emission of polycrystalline tantalum photonic crystals
    Veronika Rinnerbauer
    Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, MA, Cambridge 02139, USA
    Opt Express 21:11482-91. 2013
  5. doi request reprint Photonic Crystals: Enabling Ideal Selective Solar Absorption with 2D Metallic Dielectric Photonic Crystals (Adv. Mater. 47/2014)
    Jeffrey B Chou
    Room 41 211, 77 Massachusetts Ave, Cambridge, MA, 02139, USA
    Adv Mater 26:7922. 2014
  6. pmc Enabling enhanced emission and low-threshold lasing of organic molecules using special Fano resonances of macroscopic photonic crystals
    Bo Zhen
    Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
    Proc Natl Acad Sci U S A 110:13711-6. 2013
  7. doi request reprint Abrupt coupling between strongly dissimilar waveguides with 100% transmission
    André Kurs
    Department of Physics, Massachusetts Institute of Technology, Massachusetts 02139, USA
    Opt Express 19:13714-21. 2011
  8. doi request reprint Transparent displays enabled by resonant nanoparticle scattering
    Chia Wei Hsu
    1 Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA 2 Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
    Nat Commun 5:3152. 2014
  9. pmc Toward high-energy-density, high-efficiency, and moderate-temperature chip-scale thermophotovoltaics
    Walker R Chan
    Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
    Proc Natl Acad Sci U S A 110:5309-14. 2013
  10. doi request reprint TOPOLOGICAL MATTER. Experimental observation of Weyl points
    Ling Lu
    Department of Physics, Massachusetts Institute of Technology MIT, Cambridge, MA 02139, USA
    Science 349:622-4. 2015

Collaborators

  • Mihai Ibanescu
  • Michael Ghebrebrhan
  • Jorge Bravo-Abad
  • André Kurs
  • Liang Jie Wong
  • Zheng Wang
  • Elefterios Lidorikis
  • Peter T Rakich
  • Gang Chen
  • Bjorn Maes
  • John D Joannopoulos
  • Ivan Celanovic
  • Ling Lu
  • Peter Bermel
  • Bo Zhen
  • Chia Wei Hsu
  • Steven G Johnson
  • Yi Xiang Yeng
  • Song Liang Chua
  • Ognjen Ilic
  • Walker R Chan
  • Evan J Reed
  • Nicholas Rivera
  • Dexin Ye
  • J D Joannopoulos
  • Scott A Skirlo
  • Jeffrey B Chou
  • Andrej Lenert
  • Veronika Rinnerbauer
  • Wenjun Qiu
  • Jeongwon Lee
  • Ido Kaminer
  • Rafif E Hamam
  • Yichen Shen
  • Nicholas X Fang
  • Evelyn N Wang
  • Brendan G DeLacy
  • Ofer Shapira
  • Alejandro W Rodriguez
  • Yi Yang
  • Hrvoje Buljan
  • Dafei Jin
  • Liang Fu
  • Lixin Ran
  • Sang Gook Kim
  • Yoonkyung E Lee
  • Jay J Senkevich
  • A Douglas Stone
  • Christopher H Marton
  • Klavs F Jensen
  • David Chester
  • Zhiyong Xu
  • Aristeidis Karalis
  • Chiyan Luo
  • Yaniv Tenenbaum Katan
  • Chen Fang
  • Owen D Miller
  • Josue J Lopez
  • John Joannopoulos
  • Qinghui Yan
  • Yuichi Igarashi
  • Youngsuk Nam
  • David M Bierman
  • Robert C N Pilawa-Podgurski
  • Xiangdong Liang
  • Henry I Smith
  • Lin Lee Cheong
  • Marinko Jablan
  • Michael Harradon
  • Yidong Chong
  • Christine A Caccamise
  • Dane J Phillips
  • Henry O Everitt
  • Mohammad Araghchini
  • Walker Chan
  • Rafif Hamam
  • Erich Ippen
  • Lluis Torner
  • Xunya Jiang
  • Alejandro Rodriguez
  • Richard Gee

Detail Information

Publications50

  1. ncbi request reprint Optical bistability in axially modulated OmniGuide fibers
    Marin Soljacic
    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Opt Lett 28:516-8. 2003
    ..At 1.55-microm carrier wavelength, the in-fiber devices that we propose can operate with only a few tens of milliwatts of power, can have a nearly instantaneous response and recovery time, and can be shorter than 100 microm...
  2. ncbi request reprint Nonlinear photonic crystal microdevices for optical integration
    Marin Soljacic
    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Opt Lett 28:637-9. 2003
    ..Among many possible applications, we focus on an all-optical transistor and integrated optical isolation...
  3. ncbi request reprint Enhancement of nonlinear effects using photonic crystals
    Marin Soljacic
    Physics Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Nat Mater 3:211-9. 2004
    ..Moreover, if these designs are combined with materials and systems that support electromagnetically induced transparency, operation at single-photon power levels could be feasible...
  4. doi request reprint High-temperature stability and selective thermal emission of polycrystalline tantalum photonic crystals
    Veronika Rinnerbauer
    Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, MA, Cambridge 02139, USA
    Opt Express 21:11482-91. 2013
    ....
  5. doi request reprint Photonic Crystals: Enabling Ideal Selective Solar Absorption with 2D Metallic Dielectric Photonic Crystals (Adv. Mater. 47/2014)
    Jeffrey B Chou
    Room 41 211, 77 Massachusetts Ave, Cambridge, MA, 02139, USA
    Adv Mater 26:7922. 2014
    ..On page 8041, J. B. Chou, S.-G. Kim, and co-workers demonstrate a fabricated wafer-scale, omnidirectional, selective solar absorber that is stable at high temperature. ..
  6. pmc Enabling enhanced emission and low-threshold lasing of organic molecules using special Fano resonances of macroscopic photonic crystals
    Bo Zhen
    Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
    Proc Natl Acad Sci U S A 110:13711-6. 2013
    ....
  7. doi request reprint Abrupt coupling between strongly dissimilar waveguides with 100% transmission
    André Kurs
    Department of Physics, Massachusetts Institute of Technology, Massachusetts 02139, USA
    Opt Express 19:13714-21. 2011
    ..Moreover, this technique only requires varying a small number of parameters (two for each waveguide in our example) and the tuning to each waveguide may be done separately, greatly simplifying the computations involved...
  8. doi request reprint Transparent displays enabled by resonant nanoparticle scattering
    Chia Wei Hsu
    1 Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA 2 Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
    Nat Commun 5:3152. 2014
    ..This approach has attractive features including simplicity, wide viewing angle, scalability to large sizes and low cost. ..
  9. pmc Toward high-energy-density, high-efficiency, and moderate-temperature chip-scale thermophotovoltaics
    Walker R Chan
    Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
    Proc Natl Acad Sci U S A 110:5309-14. 2013
    ..The system was demonstrated to operate up to 800 °C (silicon microcombustor temperature) with an input thermal power of 13.7 W, generating 344 mW of electric power over a 1-cm(2) area...
  10. doi request reprint TOPOLOGICAL MATTER. Experimental observation of Weyl points
    Ling Lu
    Department of Physics, Massachusetts Institute of Technology MIT, Cambridge, MA 02139, USA
    Science 349:622-4. 2015
    ..This work paves the way to a variety of photonic topological phenomena in three dimensions. ..
  11. doi request reprint Enabling Ideal Selective Solar Absorption with 2D Metallic Dielectric Photonic Crystals
    Jeffrey B Chou
    Room 41 211, 77 Massachusetts Ave, Cambridge, MA, 02139, USA
    Adv Mater 26:8041-5. 2014
    ..The broadband absorption is due to a high density of optical cavity modes overlapped with an anti-reflection coating. Results allow for large-scale, low cost, and efficient solar-thermal energy conversion. ..
  12. doi request reprint Observation of trapped light within the radiation continuum
    Chia Wei Hsu
    Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Nature 499:188-91. 2013
    ..This method to trap electromagnetic waves is also applicable to electronic and mechanical waves...
  13. pmc Enabling high-temperature nanophotonics for energy applications
    Yi Xiang Yeng
    Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
    Proc Natl Acad Sci U S A 109:2280-5. 2012
    ..Finally, a precise high-temperature measurement technique is developed to confirm that emission at 1,225 K can be primarily confined to wavelengths shorter than the cutoff wavelength...
  14. pmc Tailoring photonic metamaterial resonances for thermal radiation
    Peter Bermel
    Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA
    Nanoscale Res Lett 6:549. 2011
    ..This represents a 250% increase in efficiency and 94% decrease in selective emitter area compared to a standard, angular-insensitive selective absorber.PACS: 42.70.Qs; 81.05.Xj; 78.67.Pt; 42.79.Ek...
  15. ncbi request reprint Purcell effect in nonlinear photonic structures: a coupled mode theory analysis
    Rafif E Hamam
    Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Opt Express 16:12523-37. 2008
    ..Our results agree well with exact finite-difference time-domain (FDTD) results. Therefore, this approach can also in certain circumstances be used as a potential substitute for the more numerically intensive FDTD method...
  16. pmc Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene
    Ido Kaminer
    Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
    Nat Commun 7:ncomms11880. 2016
    ....
  17. doi request reprint Tailoring high-temperature radiation and the resurrection of the incandescent source
    Ognjen Ilic
    Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Nat Nanotechnol 11:320-4. 2016
    ..The ability to tailor the emission spectrum of high-temperature sources may find applications in thermophotovoltaic energy conversion and lighting. ..
  18. doi request reprint Shrinking light to allow forbidden transitions on the atomic scale
    Nicholas Rivera
    Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
    Science 353:263-9. 2016
    ....
  19. ncbi request reprint Topological nature of optical bound states in the continuum
    Bo Zhen
    Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
    Phys Rev Lett 113:257401. 2014
    ..Our findings connect robust BICs in photonics to a wide range of topological physical phenomena. ..
  20. doi request reprint Theoretical criteria for scattering dark states in nanostructured particles
    Chia Wei Hsu
    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
    Nano Lett 14:2783-8. 2014
    ..This is a realization of coupled-resonator-induced transparency in the context of light scattering, which is related to but different from Fano resonances. Explicit examples are given to illustrate these concepts. ..
  21. ncbi request reprint Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials
    Alejandro W Rodriguez
    School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
    Phys Rev Lett 107:114302. 2011
    ..We also find that heat transfer can be further enhanced at selective frequencies when the slabs are brought into a glide-symmetric configuration, a consequence of the degeneracies associated with the nonsymmorphic symmetry group...
  22. doi request reprint Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances
    Song Liang Chua
    Department of Electrical Engineering and Computer Science, MIT, Cambridge, Massachusetts 02139, USA
    Opt Express 19:1539-62. 2011
    ..In addition to their fundamental interest, these findings may affect further engineering of active devices based on photonic crystal slabs...
  23. ncbi request reprint Broadband super-collimation in a hybrid photonic crystal structure
    Rafif E Hamam
    Center for Materials Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Opt Express 17:8109-18. 2009
    ..We also point out the potential importance of our proposed structure in the design of super-collimation-based devices for both monochromatic and polychromatic light...
  24. doi request reprint Optically Thin Metallic Films for High-Radiative-Efficiency Plasmonics
    Yi Yang
    Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
    Nano Lett 16:4110-7. 2016
    ..The enhancement has almost spatially independent efficiency and does not suffer from quenching effects that commonly exist in previous structures. ..
  25. pmc Topological magnetoplasmon
    Dafei Jin
    Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Nat Commun 7:13486. 2016
    ..These findings can be readily verified in experiment, and can greatly enrich the topological phases in bosonic and classical systems...
  26. pmc Controlling Directionality and Dimensionality of Radiation by Perturbing Separable Bound States in the Continuum
    Nicholas Rivera
    Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
    Sci Rep 6:33394. 2016
    ..Such resonances with easily reconfigurable radiation allow for applications such as the storage and release of waves at a controllable rate and direction, as well systems that switch between different dimensions of confinement. ..
  27. ncbi request reprint Cutoff solitons in axially uniform systems
    Elefterios Lidorikis
    Center for Materials Science and Engineering, Massachusetts Institute for Technology, Cambridge, Massachusetts 02139, USA
    Opt Lett 29:851-3. 2004
    ..We term such solitons "cutoff solitons"; they provide an interesting alternative to gap solitons in periodically index-modulated fibers for in-fiber all-optical signal processing...
  28. ncbi request reprint Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air
    Aristeidis Karalis
    Center for Materials Science and Engineering and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Phys Rev Lett 95:063901. 2005
    ..These novel waveguides allow for easy broadband coupling and exhibit absorption losses limited only by the intrinsic loss of the metal...
  29. pmc Invisible metallic mesh
    Dexin Ye
    Laboratory of Applied Research on Electromagnetics, Zhejiang University, Hangzhou 310027, China Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139
    Proc Natl Acad Sci U S A 113:2568-72. 2016
    ..This invisible metallic mesh can improve mechanical stability, electrical conduction, and heat dissipation of a system, without disturbing the electromagnetic design. Our approach is simple, robust, and scalable to higher frequencies. ..
  30. doi request reprint Optical broadband angular selectivity
    Yichen Shen
    Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
    Science 343:1499-501. 2014
    ..Our method enables transparency throughout the visible spectrum at one angle--the generalized Brewster angle--and reflection at every other viewing angle...
  31. ncbi request reprint Three-dimensional photonic crystals by large-area membrane stacking
    Ling Lu
    Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Opt Lett 37:4726-8. 2012
    ..By introducing a linear defect with a nonsymmorphic symmetry into the mesh-stack, we achieved a single-mode waveguide over a wide bandwidth...
  32. ncbi request reprint Overcoming the black body limit in plasmonic and graphene near-field thermophotovoltaic systems
    Ognjen Ilic
    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA
    Opt Express 20:A366-84. 2012
    ....
  33. doi request reprint Optimization of broadband optical response of multilayer nanospheres
    Wenjun Qiu
    Department of Physics, Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
    Opt Express 20:18494-504. 2012
    ..We also show how properly chosen mixture of several species of different nanospheres can have an even larger minimal cross-section per volume/mass over the entire visible spectrum...
  34. doi request reprint Spatio-temporal theory of lasing action in optically-pumped rotationally excited molecular gases
    Song Liang Chua
    Department of Electrical Engineering and Computer Science, MIT, Cambridge, Massachusetts 02139, USA
    Opt Express 19:7513-29. 2011
    ....
  35. ncbi request reprint Wireless power transfer via strongly coupled magnetic resonances
    André Kurs
    Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
    Science 317:83-6. 2007
    ..We present a quantitative model describing the power transfer, which matches the experimental results to within 5%. We discuss the practical applicability of this system and suggest directions for further study...
  36. ncbi request reprint Coherent optical photons from shock waves in crystals
    Evan J Reed
    Center for Materials Science and Engineering and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Phys Rev Lett 96:013904. 2006
    ..The emission frequencies are determined by the shock speed and the lattice constants of the crystal and can potentially be used to determine atomic-scale properties of the shocked material...
  37. doi request reprint Observation of unidirectional backscattering-immune topological electromagnetic states
    Zheng Wang
    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Nature 461:772-5. 2009
    ....
  38. ncbi request reprint Reversed Doppler effect in photonic crystals
    Evan J Reed
    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Phys Rev Lett 91:133901. 2003
    ..In addition to reflection of a single frequency, multiple discrete reflected frequencies or a 10 GHz periodic modulation can also be observed when a single carrier frequency of wavelength 1 microm is incident...
  39. ncbi request reprint Superprism effect based on phase velocities
    Chiyan Luo
    Department of Physics and Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Opt Lett 29:745-7. 2004
    ..We suggest the possibility of realizing agile beam steering based on purely phase-velocity effects. We present designs of photonic crystal prisms that might make experimental observation of this effect possible...
  40. ncbi request reprint Maxwell equation simulations of coherent optical photon emission from shock waves in crystals
    Evan J Reed
    Center for Materials Science and Engineering and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Phys Rev E Stat Nonlin Soft Matter Phys 75:056611. 2007
    ..While this effect is treated classically in our previous work, we present a quantum perturbation analysis showing that it can also occur in the low-amplitude emission quantum limit...
  41. doi request reprint Experimental Observation of Large Chern Numbers in Photonic Crystals
    Scott A Skirlo
    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Phys Rev Lett 115:253901. 2015
    ..We measure the mode profiles and Fourier transform them to produce dispersion relations of the edge modes, whose number and direction match our Chern number calculations. ..
  42. doi request reprint A nanophotonic solar thermophotovoltaic device
    Andrej Lenert
    Device Research Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
    Nat Nanotechnol 9:126-30. 2014
    ..Our device is planar and compact and could become a viable option for high-performance solar thermophotovoltaic energy conversion...
  43. ncbi request reprint Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs
    Jeongwon Lee
    Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Phys Rev Lett 109:067401. 2012
    ....
  44. doi request reprint Design and global optimization of high-efficiency solar thermal systems with tungsten cermets
    David Chester
    Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, Massachusetts 02139, USA
    Opt Express 19:A245-57. 2011
    ..66% at 1000 K using realistic design parameters. The marginal benefit of adding more than 4 cermet layers is small (less than 0.26%, relative)...
  45. doi request reprint Design and global optimization of high-efficiency thermophotovoltaic systems
    Peter Bermel
    Massachusetts Institute of Technology, Cambridge, 02139, USA
    Opt Express 18:A314-34. 2010
    ....
  46. ncbi request reprint Efficient mid-IR spectral generation via spontaneous fifth-order cascaded-Raman amplification in silica fibers
    Peter T Rakich
    Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
    Opt Lett 33:1690-2. 2008
    ....
  47. ncbi request reprint Nonlinear photonic crystals near the supercollimation point
    Zhiyong Xu
    Department of Physics, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Opt Lett 33:1762-4. 2008
    ..Linear stability analysis shows solitons are stable in an existence domain that obeys the Vakhitov-Kolokolov criterium. In addition, we investigate the influence of the nonlinear diffraction on soliton collision scenarios...
  48. ncbi request reprint Multimode one-way waveguides of large Chern numbers
    Scott A Skirlo
    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Phys Rev Lett 113:113904. 2014
    ..We demonstrate a continuously tunable power splitter as a possible application of multimode one-way waveguides. All our findings are readily realizable at microwave frequencies. ..
  49. ncbi request reprint Waveguiding at the edge of a three-dimensional photonic crystal
    Ling Lu
    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Phys Rev Lett 108:243901. 2012
    ..A simple cell counting approach is presented to describe the periodic evolution of the system with interesting interplays among edge, surface, and bulk states...
  50. ncbi request reprint Tailoring optical nonlinearities via the Purcell effect
    Peter Bermel
    Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    Phys Rev Lett 99:053601. 2007
    ..For example, in realistic physical systems, enhancement of the Kerr coefficient by one to two orders of magnitude could be achieved...