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On the Possibility of Manipulating Lightwaves via Active Electric Charges

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‧ Can TEM waves be affected by the presence of electric charges?
‧ We’ve seen role of passive charges → dipoles → dielectrics
‧ Can EM waves/ lights be manipulated meaningfully by
active charges instead?
‧ Exact solution in the presence of still and moving charges
→ useful?
‧ E. T. Whittaker’s two potential general solution → useful?
‧ Feynman’s versatile formula → intuitive and useful?
‧ Scope reduction to steady-state → effect of interfacial & surface active charges
‧ Experiments & results

‧ Can TEM waves be affected by the presence of electric charges?
‧ We’ve seen role of passive charges → dipoles → dielectrics
‧ Can EM waves/ lights be manipulated meaningfully by
active charges instead?
‧ Exact solution in the presence of still and moving charges
→ useful?
‧ E. T. Whittaker’s two potential general solution → useful?
‧ Feynman’s versatile formula → intuitive and useful?
‧ Scope reduction to steady-state → effect of interfacial & surface active charges
‧ Experiments & results

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On the Possibility of Manipulating Lightwaves via Active Electric Charges

  1. 1. On the Possibility of Manipulating Lightwaves via Active Electric Charges Chungpin Liao1,2,* Li-Shen Yeh,2 Wen-Bing Lai,1,2 Jyun-Lin Huang,1,2 (廖重賓) (葉立紳) (賴玟柄) (黃均霖) 1Graduate School of Electro-Optic and Materials Science, National Formosa University (NFU), Huwei, Taiwan 632, ROC. 2Advanced Research & Business Laboratory (ARBL), Taichung, Taiwan 407, ROC. *Corresponding Author: cpliao@alum.mit.edu 2015/8/13 1Chungpin Liao et al.
  2. 2. 2015/8/13 2Chungpin Liao et al. Outline • Can TEM waves be affected by the presence of electric charges? • We’ve seen role of passive charges  dipoles  dielectrics • Exact solution in the presence of still and moving charges  useful? • Feynman’s versatile formula  intuitive and useful? • Scope reduction to steady-state  effect of interfacial & surface active charges • Can EM waves/ lights be manipulated meaningfully by active charges instead? • Experiments & results • E. T. Whittaker’s two potential general solution  useful?
  3. 3. 2015/8/13 Chungpin Liao et al. 3 • Can TEM waves be affected by the presence of electric charges? The TEM solution is from the source-free wave equation: Hence, the answer should be YES, especially when the charges are responsive to the EM wave/ light frequency. But … 2 2 2 0 E E t       02 2 2     t B B   
  4. 4. 2015/8/13 Chungpin Liao et al. 4 Q: How come in fully-ionized dense plasmas, which is full of positive and negative charges, TEM waves are normal modes? A: Would the quasi-neutrality property of plasma convince us?  i.e., net charge ~ 0 Q: What about the situations where charge number density ne falls between those of vacuum and dense plasma? ? 1. Self-consistent in terms of charges and fields? 2. Even motionless charges, any clue to wave-guiding?
  5. 5. 2015/8/13 Chungpin Liao et al. 5 • We’ve seen role of passive charges  dipoles  dielectrics Matters respond to impinging lights via passively induced charges, i.e., induced dipoles, in ways against the incoming EM fields.  Cluster of induced electric dipoles  dielectrics However, there is essentially NO magnetic dipoles responsive to light frequency.
  6. 6. Chungpin Liao et al. 6 • Due to Doyle [1985],* the whole set of Fresnel equations could be written in its “scattering form”, i.e., D  S: (D – single dipole, S – collective dipoles oscillation pattern)                            t iti itrrrr r p i p t E E     sin sincos2 cos11 (a)                                    it it itrrrr itrrrr p i p r E E     sin sin cos11 cos11 (b)                            t iti itrrrr r s i s t E E     sin sincos2 cos11 (c)                                    it it itrrrr itrrrr s i s r E E     sin sin cos11 cos11 (d) • S  0, D = 0 for (b), (d)  Brewster’s angle, e.g.   1 tan2    rr rrrp B      1 tan2    rr rrrs B    2015/8/13 rrti nn  ,1 * W. T. Doyle, “Scattering approach to Fresnel’s equations and Brewster’s law,” Am. J. Phys. 53 (5), 463-468 (1985).
  7. 7. Chungpin Liao et al. 7                  iti t it p ip P E     sincos2 sin cos 0                  iti t it p rp P E     sincos2 sin cos 0 electric dipole p-wave                 iti tp im M E     sincos2 sin 0 0                 iti tp rm M E     sincos2 sin 0 0 p-wave magnetic dipole Total:                     iti t it p i MP E       sincos2 sin cos 0 0 0                     iti t it p r MP E       sincos2 sin cos 0 0 0 • Induced dipole sources revealed mNMpNP   2015/8/13 p im p ip p i EEE  p rm p rp p r EEE 
  8. 8. Chungpin Liao et al. 8                     iti t it p i MP E       sincos2 sin cos 0 0 0                     iti t it p r MP E       sincos2 sin cos 0 0 0 Putting    p tr EP  10   and   p t r r r EM     0 0 1 into: we obtain:                                it it itrrrr itrrrr p i p r E E     sin sin )cos(11 )cos(11 (b) i.e., Scattering form of one of the Fresnel equations • Checking: p-wave as an example Source equations 2015/8/13
  9. 9. Chungpin Liao et al. 9 • Similarly, for s-wave, with total P and M contributions:                   iti t it s i MP E       sincos2 sin cos 0 0 0 Putting    p tr EP  10   and   p t r r r EM     0 0 1 in, to obtain:                   iti t it s r MP E       sincos2 sin cos 0 0 0                                it it itrrrr itrrrr s i s r E E     sin sin )cos(11 )cos(11 (d) i.e., Scattering form of one of the Fresnel equations Source equations 2015/8/13
  10. 10. Chungpin Liao et al. 10 E.g., adding permanent dipoles for novel applications • By generalization of the types of involved dipoles in source equations • Namely, in general, optically-responsive permanent dipoles (P0 and M0) embedded in the original material can vary optical properties, such as the Brewster angle. • This is, now P = P0 + Pind, M = M0 + Mind (with Pind and Mind as induced dipoles) • However, still, how exactly do the dipoles affect the optical properties, physically? • See e.g., p-wave, unmagnetized case (i.e., P  0, but M = 0) 2015/8/13
  11. 11. Chungpin Liao et al. 11                  iti t it p ip P E     sincos2 sin cos 0                  iti t it p rp P E     sincos2 sin cos 0 So, the P (of whatever origin) contributes only its component along the relevant E. || P All induced P (so || Et) 2015/8/13     itit PP   coscos
  12. 12. Chungpin Liao et al. 12 • Adding P0 into an unmagnetized host and look at the p-wave case: 2015/8/13                       iti t iti p tr p ip P EE      sincos2 sin coscos1 0 0 0    ti p tr E   cos1~                     iti t iti p ip PP E       sincos2 sin coscos 0 0 0 0    ti p tr E   cos1
  13. 13. 2015/8/13 Chungpin Liao et al. 13 • Can EM waves/ lights be manipulated meaningfully by active charges instead? H E t          ( curl on Faraday’s )  u = = = = uniform ε Ampere’s Gauss’E uniform μ H E t      E)E( 2    H t      u E J t    2 2 2 u uJE E tt                 The answer should be YES, even though it is nontrivial.
  14. 14. 2015/8/13 14Chungpin Liao et al. • Exact solution in the presence of still and moving charges  useful? The formal approach is as follows: A tt B E          AHB    (Faraday’s law)          0 t A E   t A E      t J E t E u                   2 2 2
  15. 15. 2015/8/13 Chungpin Liao et al. 15 Now, according to Ampere’s law: E t JH u                                    t A t u AA A B E t JH   2 uJ t A A t A                 2 2 2 Now, let t A      (Lorentz gauge) So, we have: uJ t A A         2 2 2
  16. 16. 2015/8/13 Chungpin Liao et al. 16 On the other hand, we work on Gauss’ E law: uE          u t u A tt A                   2 We reach:    u t     2 2 2 So, we have: AHB    t A E      uJ t A A         2 2 2    u t     2 2 2 t A      Using (Lorentz gauge)
  17. 17. 2015/8/13 17Chungpin Liao et al. The formal general solution: (see, e.g., Feynman Lecture Notes –II)   2 12 12 4 ,2 ,1 dV r c r t t u              2 12 2 12 4 ,2 ,1 dV rc c r tJ tA u             Q: Is it helpful in regard to the purpose of guiding lightwaves? TEM Light in vacuum , J  0 ? 2’ 2 1r’ r12 Position at t -r’/c Position at t q q v Again, self-consistency problem here, unless for motionless charges. Secondly, any practical clue provided for EM wave guiding?
  18. 18. 2015/8/13 Chungpin Liao et al. 18 • E. T. Whittaker’s# two potential general solution  useful? 2 2 22 22222 1 , 1 , 1 t F cz F D tx G czy F D ty G czx F ED zyxx                    2 2 2 22222 , 1 , 1 y G x G H zy G tx F c H zx G ty F c H zyx                             ),,( cos,sinsin,cossinˆ ˆ ,,, ,,, 2 0 0 2 0 0 zyxr k rkct gddtzyxG fddtzyxF                   F & G are: arbitrary functional of   Nontrivial to put to use # Whittaker, E. T., "ON AN EXPRESSION OF THE ELECTROMAGNETIC FIELD DUE TO ELECTRONS BY MEANS OF TWO SCALAR POTENTIAL FUNCTIONS," Proceedings of the London Mathematical Society, Vol. 1, p. 367-372 (1904).
  19. 19. 2015/8/13 19Chungpin Liao et al. • Feynman’s+ versatile formula  intuitive and useful?              'ˆ 1 ' 'ˆ' ' 'ˆ 4 2 2 222 r dt d cr r dt d c r r rq E   For a charge q in whatever motion ErBc   'ˆ Q: How to arrange so many q’s in motion such that the desired E & B fields are secured for light-guiding purposes? + Feynman R., Leighton R. B., Sands M., The Feynman lectures on physics, Vol. II, Sec. 21, Addison-Wesley, Boston, MA, USA (1971).
  20. 20. 2015/8/13 Chungpin Liao et al. 20 • Scope reduction to steady-state  effect of interfacial active charges  Experiment 1 0   J t  Charge conservation law: Steady state: .vv0 ee constEEenJJ eee    At interface between two conducting media:         0  t tEtEtE sb n a nn 
  21. 21. 21 2 0 0 02 0u p uE J                    .const 0  0 0   spsu Pu   no source of E 2 0   Note that the distrib. of ε plays no part in shaping the E lines, but σ can. Conduction and EQS Charge Relaxation ba   terminates or originates on it )1(ˆ 0 b aa spsu En     0 spsu  En  ˆ& ab   < 0 E excluded from high σ 0 0 up  E  & terminates or originates on them (it) 20     uup J  increasing)r(   E attenuates < 0 2015/8/13 Chungpin Liao et al.
  22. 22. V 0 ITO ZnO DC current glass s < 0 2015/8/13 22Chungpin Liao et al. • Experiments & results + -+ - Laser beam spot  more focused E direction
  23. 23. 2015/8/13 23Chungpin Liao et al. 56.0 58.0 60.0 62.0 64.0 66.0 0.0 5.0 10.0 光功率(µW) Time (minute) 2015.07.24_measured intensity at edge DC power supply turned off Spot bottom edge, ITO(+)/ZnO(-) 4V Spot bottom edge, ZnO(+)/ITO(-) 4V Residual charges - undesirable
  24. 24. 2015/8/13 24Chungpin Liao et al. 417.5 420.0 422.5 425.0 427.5 430.0 0.0 1.0 2.0 3.0 4.0 5.0 light intensity (µW) Time (minute) 2015.07.31_Face to face_Top Edge_ITO (+)/ZnO(-)_1.0V to 4.0V Unbiased reference 4 V 1 V 2 V 3 V The repeatability was poor so far, possibly due to varying interfacial states.
  25. 25. 2015/8/13 Chungpin Liao et al. 25 405.0 410.0 415.0 420.0 425.0 430.0 0.0 1.0 2.0 3.0 4.0 5.0 light intensity (µW) Time (minute) 2015.07.31_Face to face_Top Edge_ITO(+)/ZnO(-)_4.0 V to 1.0V reference 1 V 2 V 3 V 4 V There were likely hysteresis effect due to residual charges.
  26. 26. Experiment 2: charge-influenced light reflection 2015/8/13 Chungpin Liao et al. 26 Dielectric: paper Solid-state Argon laser, with E vertical to the laser beam Light power measurement per 300 ms Smooth and shiny stainless steel E Biased Capacitor
  27. 27. 0.00174 0.00176 0.00178 0.0018 0.00182 0.00184 0.00186 0.00188 0 2 4 6 8 10 12 14 16 18 20 W Time(min) No bias Biased at -15V Turning off -15V Biased at +15V Turning off +15V Measured results: 2015/8/13 Chungpin Liao et al. 27
  28. 28. 2015/8/13 Chungpin Liao et al. 28 Summary & conclusions • Active electric charges were found to be responsive to incident lightwaves and to affect the propagation/reflection of lightwaves. • Guiding of lightwaves by active charges is valid in principle, but putting it to work practically would need more creativity and efforts. • In the future, such active ingredients may assist the traditional passive dielectric approach for more meaningful optical and photonic purposes.

Notizen

  • Mainly to ask two questions: 1. Will active charges be responsive to incident lightwaves? 2. If so, how to use active charges for the manipulation of lightwaves?
  • TEM mode is picked up for ease of elaboration only.
  • The important thing in the light diffraction: E_in, E_ref, and E_tran can all be viewed as results of the induced E and M dipoles, as envisioned from the latter.
  • We will be talking about nearly vacuum or nearly uniform cases, where the medium is isotropic, linear, and memoryless.
  • An inhomogeneous wave equation for the vector potential
  • An inhomogeneous wave equation for the scalar potential
  • One scalar potential, one vector potential to suffice the full solution; The bottom part: what about self-consistency?
  • Mathematically easier, but practically harder for our purposes
  • Again, what about the self-consistency?
  • To create steady-state interface charges, unpaired and paired.
  • Residual charge effect might be due to the interface traps.
  • The results were varying from time to time, but the charge influence on light was obvious.
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