Abstract

This paper introduces Microfluidic Beam Steering (MBS), which is a new technique for electronically steering light having multiple octaves of bandwidth, any polarization state and incidence from any direction of the sky without significant restrictions due to physical area, optical loss and power handling capacity. It is based on optical elements comprising both transparent solids and electronically controllable fluids to control Total Internal Reflection (TIR), refraction and/or diffraction from micro-structured surfaces within a transparent solid. A TIR-based MBS is discussed in the context of solar energy and its potential to significantly increase annual energy harvests from solar arrays situated on fixed areas like roofs. The advantages and challenges associated with analog and digital MBS systems are discussed and early-stage MBS hardware is demonstrated. Finally, an analytic model of sun-tracking is provided to formally establish the potential for MBS to increase annual solar energy harvests by approximately 45% more than conventional 0-Degree Of Freedom (0-DOF) solar arrays, 62% more than 1-DOF arrays and 233% more than 2-DOF arrays, all at 20% atmospheric aerosol scattering.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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  1. NREL, “Best Research Cell Efficiencies Chart,” http://www.nrel.gov/ncpv/images/efficiencychart.jpg
  2. C. W. Forsberg, P. F. Peterson, and H. Zhao, “High-Temperature Liquid Fluoride-Salt Closed-Brayton Cycle Solar Power Towers,” J. Solar Energy Eng. 129, 141 (2007).
    [Crossref]
  3. P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A Review of Phased Array Steering for Narrow-Band Electrooptical Systems,” Proc. of the IEEE 97 (6), 1078–1096 (2009).
    [Crossref]
  4. J. G. Pender, “Motion-Free Tracking Solar Concentrator,” US patent6,958,868B2 (October252005).
  5. J. Heikenfeld, “Tunable Optical Array Device Comprising Liquid Cells,” U.S. patent7,898,740 (March112011).
  6. L. Hou, J. Zhang, N. Smith, J. Yang, and J. Heikenfeld, “A full description of a scalable microfabrication process for arrayed electrowetting microprisms,” J. Micromech. Microeng. 20, 015044 (2010).
    [Crossref]
  7. M. J. Escuti, J. Kim, C. Oh, and S. Serati, “Beam Steering Devices Including Stacked Liquid Crystal Polarization Gratings and Related Methods of Operation,” US patent8,982,313B2 (March172015).
  8. J. Kim, Liquid Crystal Geometric Phase Holograms for Efficient Beam Steering and Imaging Spectropolarimetry (North Carolina State University Ph.D. Disseration, 2011).
  9. C. Oh, Broadband Polarization Gratings for Efficient Liquid Crystal Display, Beam Steering, Spectropolarimetry, and Fresnel Zone Plate (North Carolina State University Ph.D. Disseration, 2009).
  10. L. Shi, P. F. McManamon, and P. J. Bos, “Liquid Crystal Optical Phase Plate With a Variable In-Plane Gradient,” J. Appl. Phys. 104, 033109 (2008).
    [Crossref]
  11. I. W. Smith, M. K. O. Holz, and for Raytheon, “Wide-Angle Beam Steering System,” US patent7,215,472 (May82007).
  12. L. D. DiDomenico, “Active Matrix Sun Tracker,” US patent7,924,495 (April122011).
  13. H. Xie, S. Maley, P. F. McManamon, T. Nelson, L. Wu, A. Pais, and K. Jia, “Micromirror and fabrication method for producing micromirror,” US patent app.20100033788 (February112010).
  14. M. Rabinowitz, “Reflection Dynamic Illumination and Projection,” US patent7,130,102 (October312006).
  15. Y. Chiu, J. Zou, D. D. Stancil, and T. E. Schlesinger, “Shape-Optimized Electrooptic Beam Scanners: Analysis, Design, and Simulation,” J. Lightwave Technol. 17(1), 108–114 (1999).
    [Crossref]
  16. G. F. Marshall, Handbook of Optical and Laser Scanning (Marcel Dekker, 2004).
    [Crossref]
  17. Whispering gallery image cropped from Wikipedia https://en.wikipedia.org/wiki/Whisperinggallery
  18. K. P. Ivanov and M. K. Kalinina, and Yu. I. Levkovich, “Blood flow velocity in capillaries of brain and muscles and its physiological significance,” Microvascular Research 22(2), 143–155 (1981).
    [Crossref] [PubMed]
  19. Fabrication services provided by Controlled Fluidics Corp, http://www.controlledfluidics.com
  20. R. Winston, J. C. Minaño, and P. Benítz, Nonimaging Optics (Elsevier, 2005), p. 139.
  21. S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” App. Phys. Lett. 93, 251108 (2008).
    [Crossref]
  22. NREL, US Solar Radiation Resource Maps http://rredc.nrel.gov/solar/olddata/nsrdb/1961-1990/redbook/atlas/
  23. M. Muller, “Equation of Time — Problem In Astronomy,” Acta Phys. Pol. A. 88, 49 (1995).
  24. P. Lynch, “The Eqn. of Time and the Analemma,” Irish Math Soc. Bulletin 69, 47–56 (2012).
  25. A SolFocus 2-DOF solar array located at Victor Valley College, https://www.google.com/maps/@34.4800707,-117.2579087,224m/data=!3m1!1e3

2012 (1)

P. Lynch, “The Eqn. of Time and the Analemma,” Irish Math Soc. Bulletin 69, 47–56 (2012).

2010 (1)

L. Hou, J. Zhang, N. Smith, J. Yang, and J. Heikenfeld, “A full description of a scalable microfabrication process for arrayed electrowetting microprisms,” J. Micromech. Microeng. 20, 015044 (2010).
[Crossref]

2009 (1)

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A Review of Phased Array Steering for Narrow-Band Electrooptical Systems,” Proc. of the IEEE 97 (6), 1078–1096 (2009).
[Crossref]

2008 (2)

S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” App. Phys. Lett. 93, 251108 (2008).
[Crossref]

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid Crystal Optical Phase Plate With a Variable In-Plane Gradient,” J. Appl. Phys. 104, 033109 (2008).
[Crossref]

2007 (1)

C. W. Forsberg, P. F. Peterson, and H. Zhao, “High-Temperature Liquid Fluoride-Salt Closed-Brayton Cycle Solar Power Towers,” J. Solar Energy Eng. 129, 141 (2007).
[Crossref]

1999 (1)

1995 (1)

M. Muller, “Equation of Time — Problem In Astronomy,” Acta Phys. Pol. A. 88, 49 (1995).

1981 (1)

K. P. Ivanov and M. K. Kalinina, and Yu. I. Levkovich, “Blood flow velocity in capillaries of brain and muscles and its physiological significance,” Microvascular Research 22(2), 143–155 (1981).
[Crossref] [PubMed]

Benítz, P.

R. Winston, J. C. Minaño, and P. Benítz, Nonimaging Optics (Elsevier, 2005), p. 139.

Bos, P. J.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A Review of Phased Array Steering for Narrow-Band Electrooptical Systems,” Proc. of the IEEE 97 (6), 1078–1096 (2009).
[Crossref]

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid Crystal Optical Phase Plate With a Variable In-Plane Gradient,” J. Appl. Phys. 104, 033109 (2008).
[Crossref]

Chhajed, S.

S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” App. Phys. Lett. 93, 251108 (2008).
[Crossref]

Chiu, Y.

DiDomenico, L. D.

L. D. DiDomenico, “Active Matrix Sun Tracker,” US patent7,924,495 (April122011).

Escuti, M. J.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A Review of Phased Array Steering for Narrow-Band Electrooptical Systems,” Proc. of the IEEE 97 (6), 1078–1096 (2009).
[Crossref]

M. J. Escuti, J. Kim, C. Oh, and S. Serati, “Beam Steering Devices Including Stacked Liquid Crystal Polarization Gratings and Related Methods of Operation,” US patent8,982,313B2 (March172015).

Forsberg, C. W.

C. W. Forsberg, P. F. Peterson, and H. Zhao, “High-Temperature Liquid Fluoride-Salt Closed-Brayton Cycle Solar Power Towers,” J. Solar Energy Eng. 129, 141 (2007).
[Crossref]

Heikenfeld, J.

L. Hou, J. Zhang, N. Smith, J. Yang, and J. Heikenfeld, “A full description of a scalable microfabrication process for arrayed electrowetting microprisms,” J. Micromech. Microeng. 20, 015044 (2010).
[Crossref]

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A Review of Phased Array Steering for Narrow-Band Electrooptical Systems,” Proc. of the IEEE 97 (6), 1078–1096 (2009).
[Crossref]

J. Heikenfeld, “Tunable Optical Array Device Comprising Liquid Cells,” U.S. patent7,898,740 (March112011).

Holz, M. K. O.

I. W. Smith, M. K. O. Holz, and for Raytheon, “Wide-Angle Beam Steering System,” US patent7,215,472 (May82007).

Hou, L.

L. Hou, J. Zhang, N. Smith, J. Yang, and J. Heikenfeld, “A full description of a scalable microfabrication process for arrayed electrowetting microprisms,” J. Micromech. Microeng. 20, 015044 (2010).
[Crossref]

Ivanov, K. P.

K. P. Ivanov and M. K. Kalinina, and Yu. I. Levkovich, “Blood flow velocity in capillaries of brain and muscles and its physiological significance,” Microvascular Research 22(2), 143–155 (1981).
[Crossref] [PubMed]

Jia, K.

H. Xie, S. Maley, P. F. McManamon, T. Nelson, L. Wu, A. Pais, and K. Jia, “Micromirror and fabrication method for producing micromirror,” US patent app.20100033788 (February112010).

Kalinina, M. K.

K. P. Ivanov and M. K. Kalinina, and Yu. I. Levkovich, “Blood flow velocity in capillaries of brain and muscles and its physiological significance,” Microvascular Research 22(2), 143–155 (1981).
[Crossref] [PubMed]

Kim, J.

J. Kim, Liquid Crystal Geometric Phase Holograms for Efficient Beam Steering and Imaging Spectropolarimetry (North Carolina State University Ph.D. Disseration, 2011).

M. J. Escuti, J. Kim, C. Oh, and S. Serati, “Beam Steering Devices Including Stacked Liquid Crystal Polarization Gratings and Related Methods of Operation,” US patent8,982,313B2 (March172015).

Kim, J. K.

S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” App. Phys. Lett. 93, 251108 (2008).
[Crossref]

Lynch, P.

P. Lynch, “The Eqn. of Time and the Analemma,” Irish Math Soc. Bulletin 69, 47–56 (2012).

Maley, S.

H. Xie, S. Maley, P. F. McManamon, T. Nelson, L. Wu, A. Pais, and K. Jia, “Micromirror and fabrication method for producing micromirror,” US patent app.20100033788 (February112010).

Marshall, G. F.

G. F. Marshall, Handbook of Optical and Laser Scanning (Marcel Dekker, 2004).
[Crossref]

McManamon, P. F.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A Review of Phased Array Steering for Narrow-Band Electrooptical Systems,” Proc. of the IEEE 97 (6), 1078–1096 (2009).
[Crossref]

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid Crystal Optical Phase Plate With a Variable In-Plane Gradient,” J. Appl. Phys. 104, 033109 (2008).
[Crossref]

H. Xie, S. Maley, P. F. McManamon, T. Nelson, L. Wu, A. Pais, and K. Jia, “Micromirror and fabrication method for producing micromirror,” US patent app.20100033788 (February112010).

Minaño, J. C.

R. Winston, J. C. Minaño, and P. Benítz, Nonimaging Optics (Elsevier, 2005), p. 139.

Muller, M.

M. Muller, “Equation of Time — Problem In Astronomy,” Acta Phys. Pol. A. 88, 49 (1995).

Nelson, T.

H. Xie, S. Maley, P. F. McManamon, T. Nelson, L. Wu, A. Pais, and K. Jia, “Micromirror and fabrication method for producing micromirror,” US patent app.20100033788 (February112010).

Oh, C.

C. Oh, Broadband Polarization Gratings for Efficient Liquid Crystal Display, Beam Steering, Spectropolarimetry, and Fresnel Zone Plate (North Carolina State University Ph.D. Disseration, 2009).

M. J. Escuti, J. Kim, C. Oh, and S. Serati, “Beam Steering Devices Including Stacked Liquid Crystal Polarization Gratings and Related Methods of Operation,” US patent8,982,313B2 (March172015).

Pais, A.

H. Xie, S. Maley, P. F. McManamon, T. Nelson, L. Wu, A. Pais, and K. Jia, “Micromirror and fabrication method for producing micromirror,” US patent app.20100033788 (February112010).

Pender, J. G.

J. G. Pender, “Motion-Free Tracking Solar Concentrator,” US patent6,958,868B2 (October252005).

Peterson, P. F.

C. W. Forsberg, P. F. Peterson, and H. Zhao, “High-Temperature Liquid Fluoride-Salt Closed-Brayton Cycle Solar Power Towers,” J. Solar Energy Eng. 129, 141 (2007).
[Crossref]

Rabinowitz, M.

M. Rabinowitz, “Reflection Dynamic Illumination and Projection,” US patent7,130,102 (October312006).

Schlesinger, T. E.

Schubert, E. F.

S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” App. Phys. Lett. 93, 251108 (2008).
[Crossref]

Schubert, M. F.

S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” App. Phys. Lett. 93, 251108 (2008).
[Crossref]

Serati, S.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A Review of Phased Array Steering for Narrow-Band Electrooptical Systems,” Proc. of the IEEE 97 (6), 1078–1096 (2009).
[Crossref]

M. J. Escuti, J. Kim, C. Oh, and S. Serati, “Beam Steering Devices Including Stacked Liquid Crystal Polarization Gratings and Related Methods of Operation,” US patent8,982,313B2 (March172015).

Shi, L.

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid Crystal Optical Phase Plate With a Variable In-Plane Gradient,” J. Appl. Phys. 104, 033109 (2008).
[Crossref]

Smith, I. W.

I. W. Smith, M. K. O. Holz, and for Raytheon, “Wide-Angle Beam Steering System,” US patent7,215,472 (May82007).

Smith, N.

L. Hou, J. Zhang, N. Smith, J. Yang, and J. Heikenfeld, “A full description of a scalable microfabrication process for arrayed electrowetting microprisms,” J. Micromech. Microeng. 20, 015044 (2010).
[Crossref]

Stancil, D. D.

Watson, E. A.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A Review of Phased Array Steering for Narrow-Band Electrooptical Systems,” Proc. of the IEEE 97 (6), 1078–1096 (2009).
[Crossref]

Winston, R.

R. Winston, J. C. Minaño, and P. Benítz, Nonimaging Optics (Elsevier, 2005), p. 139.

Wu, L.

H. Xie, S. Maley, P. F. McManamon, T. Nelson, L. Wu, A. Pais, and K. Jia, “Micromirror and fabrication method for producing micromirror,” US patent app.20100033788 (February112010).

Xie, H.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A Review of Phased Array Steering for Narrow-Band Electrooptical Systems,” Proc. of the IEEE 97 (6), 1078–1096 (2009).
[Crossref]

H. Xie, S. Maley, P. F. McManamon, T. Nelson, L. Wu, A. Pais, and K. Jia, “Micromirror and fabrication method for producing micromirror,” US patent app.20100033788 (February112010).

Yang, J.

L. Hou, J. Zhang, N. Smith, J. Yang, and J. Heikenfeld, “A full description of a scalable microfabrication process for arrayed electrowetting microprisms,” J. Micromech. Microeng. 20, 015044 (2010).
[Crossref]

Zhang, J.

L. Hou, J. Zhang, N. Smith, J. Yang, and J. Heikenfeld, “A full description of a scalable microfabrication process for arrayed electrowetting microprisms,” J. Micromech. Microeng. 20, 015044 (2010).
[Crossref]

Zhao, H.

C. W. Forsberg, P. F. Peterson, and H. Zhao, “High-Temperature Liquid Fluoride-Salt Closed-Brayton Cycle Solar Power Towers,” J. Solar Energy Eng. 129, 141 (2007).
[Crossref]

Zou, J.

Acta Phys. Pol. A. (1)

M. Muller, “Equation of Time — Problem In Astronomy,” Acta Phys. Pol. A. 88, 49 (1995).

App. Phys. Lett. (1)

S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” App. Phys. Lett. 93, 251108 (2008).
[Crossref]

Irish Math Soc. Bulletin (1)

P. Lynch, “The Eqn. of Time and the Analemma,” Irish Math Soc. Bulletin 69, 47–56 (2012).

J. Appl. Phys. (1)

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid Crystal Optical Phase Plate With a Variable In-Plane Gradient,” J. Appl. Phys. 104, 033109 (2008).
[Crossref]

J. Lightwave Technol. (1)

J. Micromech. Microeng. (1)

L. Hou, J. Zhang, N. Smith, J. Yang, and J. Heikenfeld, “A full description of a scalable microfabrication process for arrayed electrowetting microprisms,” J. Micromech. Microeng. 20, 015044 (2010).
[Crossref]

J. Solar Energy Eng. (1)

C. W. Forsberg, P. F. Peterson, and H. Zhao, “High-Temperature Liquid Fluoride-Salt Closed-Brayton Cycle Solar Power Towers,” J. Solar Energy Eng. 129, 141 (2007).
[Crossref]

Microvascular Research (1)

K. P. Ivanov and M. K. Kalinina, and Yu. I. Levkovich, “Blood flow velocity in capillaries of brain and muscles and its physiological significance,” Microvascular Research 22(2), 143–155 (1981).
[Crossref] [PubMed]

Proc. of the IEEE (1)

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A Review of Phased Array Steering for Narrow-Band Electrooptical Systems,” Proc. of the IEEE 97 (6), 1078–1096 (2009).
[Crossref]

Other (16)

J. G. Pender, “Motion-Free Tracking Solar Concentrator,” US patent6,958,868B2 (October252005).

J. Heikenfeld, “Tunable Optical Array Device Comprising Liquid Cells,” U.S. patent7,898,740 (March112011).

M. J. Escuti, J. Kim, C. Oh, and S. Serati, “Beam Steering Devices Including Stacked Liquid Crystal Polarization Gratings and Related Methods of Operation,” US patent8,982,313B2 (March172015).

J. Kim, Liquid Crystal Geometric Phase Holograms for Efficient Beam Steering and Imaging Spectropolarimetry (North Carolina State University Ph.D. Disseration, 2011).

C. Oh, Broadband Polarization Gratings for Efficient Liquid Crystal Display, Beam Steering, Spectropolarimetry, and Fresnel Zone Plate (North Carolina State University Ph.D. Disseration, 2009).

Fabrication services provided by Controlled Fluidics Corp, http://www.controlledfluidics.com

R. Winston, J. C. Minaño, and P. Benítz, Nonimaging Optics (Elsevier, 2005), p. 139.

G. F. Marshall, Handbook of Optical and Laser Scanning (Marcel Dekker, 2004).
[Crossref]

Whispering gallery image cropped from Wikipedia https://en.wikipedia.org/wiki/Whisperinggallery

I. W. Smith, M. K. O. Holz, and for Raytheon, “Wide-Angle Beam Steering System,” US patent7,215,472 (May82007).

L. D. DiDomenico, “Active Matrix Sun Tracker,” US patent7,924,495 (April122011).

H. Xie, S. Maley, P. F. McManamon, T. Nelson, L. Wu, A. Pais, and K. Jia, “Micromirror and fabrication method for producing micromirror,” US patent app.20100033788 (February112010).

M. Rabinowitz, “Reflection Dynamic Illumination and Projection,” US patent7,130,102 (October312006).

A SolFocus 2-DOF solar array located at Victor Valley College, https://www.google.com/maps/@34.4800707,-117.2579087,224m/data=!3m1!1e3

NREL, US Solar Radiation Resource Maps http://rredc.nrel.gov/solar/olddata/nsrdb/1961-1990/redbook/atlas/

NREL, “Best Research Cell Efficiencies Chart,” http://www.nrel.gov/ncpv/images/efficiencychart.jpg

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Figures (13)

Fig. 1
Fig. 1 MBS is heuristically inspired by three ideas. (A) QWGW propagating along curved whispering gallery surfaces [17]. (B) The depth of injection of fluids in thermometer-like capillaries may be controlled by micro-mechanical, thermal or electrical phenomena independent of gravity. (C) An IMF can hide a solid transparent material and vice versa.
Fig. 2
Fig. 2 A time sequence of MBS figures, which show the relation between IMF injection depth di in capillaries and propagation direction θi. The incident light in each case is the same and passes into the device normally to minimize reflections. In principle, the rays can be reversed and the device becomes 1-DOF tracking receiver instead of a transmitter as shown. Additionally, adding another orthogonal layer (not shown above) for steering light into or out of the image page would provide 2-DOF beam steering.
Fig. 3
Fig. 3 A plot of the output angle of light steered through the optical system of Fig. 2 as a function of IMF injection depth d normalized by the radius of curvature r for n1 = 1 and n2 = 1.5—see Eq. (1). The dashed curves above and below the primary plot represent curvature induced beam spreading for light not perfectly tangent at the input edge of the µFCC. The beam spreading can be eliminated by instead using many short flat segments instead of a continuously curved µFCC as discussed later in this paper.
Fig. 4
Fig. 4 (A) shows a reflector geometry for just a circular arc bc and a flat reflecting extension cd. Ideal performance of the MBS device occurs when tangent rays to the reflector are infinitesimally close to the curved reflecting surface bc so that an infinite number of reflections are required for a ray to move from point b to point c via QWGW. As a tangent input ray moves from point b to point a, a distance Xin (thereby becoming less ideal), and as the input ray deviates from an input tangent direction by θin (again less ideal) then the output light deviates from the ideal output tangent direction by θout and a set of saw tooth angle transfer functions are generated—e.g. blue curves. While the specific shape of the saw tooth characteristic depends on Xin, θin and the steering angle α, the characteristics always stays within the dashed envelope of (B). Figure (C) shows the limiting case of an infinitely long flat reflecting extension cd taking the absolute value of the angle transfer function. Different shaped compact extensions that replace cd can also reduce angular spreading. The spreading of the radiation can actually be seen directly in Figs. 8.
Fig. 5
Fig. 5 A 150× scale model of a µFCC constructed in PMMA. The IMF injection/extraction ports are at the bottom and top of the µFCC. Light input is at the angle-cut corner.
Fig. 6
Fig. 6 A PMMA rod is shown in a beaker with a simple calibration line in the background. Different liquids are shown: (A) pure MPPS, (B) pure EA and (C) a mixture of MPPS and EA in the ratio of approximately 2 grams EA for every 23 grams MPPS (a total of 25 grams). It is clear that the calibration line, as seen through the PMMA rod, appears discontinuous when there is an refractive index mismatch, see (A) & (B), and is continuous in (C) when the proportions of MPPS and EA optically match the cylindrical PMMA rod.
Fig. 7
Fig. 7 A time sequence of photos showing the evolution of a completely transparent medium into one containing a curved TIR-mirror as the distribution of the IMF changes.
Fig. 8
Fig. 8 Using a long exposure-time and small F-number a time-sequence of photos captures the volume scattering of a 532 nm laser within PMMA by QWGW. The direction of the light is changing in response to the spatial extent of the active mirror—compare to Fig. 7.
Fig. 9
Fig. 9 An integrated concentrating solar panel unit cell, which provides a continuous analog MBS system to track the sun and concentrate its radiation onto the multi-junction PV cell shown in yellow. The image depicts an east-to-west cross section of a 20 mm wide and 25mm high unit cell with a 32 times concentration. This is one out of 50 unit cells measuring 2 cm × 100 cm cells in a 1 m2 concentrating solar panel with 1-DOF sun-tracking. An optional 3 rd MBS layer (not shown) for north-south steering (into and out of the page) would allow (32)2 1,000 suns of concentration in a 2-DOF solar panel having (50)2 = 2,500 tracking elements. Note, by using digital (instead of the above analog) steering techniques, which is described later in this paper, the thickness of the MBS section can be further decreased through “folding the optic” and multiplexing optical functions.
Fig. 10
Fig. 10 If circular control channels are segmented, reordered and flattened to ensure zero curvature then the resulting steering device (shown above) contains multiple layers that can be turned off or on by the injection or removal of the IMF. In the above example the MBS device has 12 layers, each layer is multiplexed two-fold for two angular ranges and can provide the angular resolution needed for 1000× solar concentration. Additionally, each layer is 500 µm thick. Blue lines across each layer are IMF reservoirs and piezoelectric (or other) electronic microfluidic pumps provide IMF injection and extraction digitally. Inset image shows an actual 4-layer experiment with only the first mirror layer active. Notice that the remaining three MBS layers do not interact with the redirected light.
Fig. 11
Fig. 11 The instantaneous insolation p(t) is a rectified sinusoidal function, where the rectification occurs each night when p(t) = 0, however at the scale of an entire year the insolation is essentially a fast square wave (dashes) that can be modeled with a 50% duty cycle that is amplitude modulated by a sinusoidal function having a period of a solar year.
Fig. 12
Fig. 12 The yearly average value of the cosine of the angle between an solar receiver and the sun is based on averaging cosψ(t) = q (t) · w (t) when the sun is above the local horizon.
Fig. 13
Fig. 13 A visual comparison of several common solar array configurations by showing 16 solar receivers in each different tracking configurations—actual arrays would usually have many more receivers. In particular, (A) is a flat 0-Degree of Freedom (0-DOF) array similar to silicon PV panels, (B) represents a south-facing 0-DOF array with tilt angle equal to the latitude angle θLAT, (C) is a 1-DOF tracker array where in the receivers scan from east-to-west, (D) same as C except that each tracker is tilted south by the latitude angle θLAT, (E) 2-DOF trackers that always point directly at the sun, (F) heliostat array that are configured to redirect sunlight onto a remote receiver tower. The yellow area between trackers is where light is lost by today’s state-of-the-art trackers.

Tables (2)

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Table 1 Value of 〈cosψ〉 during the periods when the sun is above the local horizon for the reference solar array configurations of Fig. 13. These results are used in the linearized model for the annual energy harvested where E = PATYηrηa〈cosψ(t)〉.

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Table 2 Potential percentage improvement of an MBS system beyound today’s typically configured solar array systems assuming a 35° North latitude. The MBS has an area utilization efficiency of ηaM = 100%, aerosol scattering loss of 20% providing a direct insolation efficiency of ηdM = 80% and concentrating solar cells that are 40% efficient with 10% loss in the optical system so that the receiver’s total efficiency is ηrM = 0.4 × 0.9 = 36%. All numbers in the table are percentages. The bottom line shows the percentage improvement anticipated for annual energy harvesting using a MBS system compared to today’s current state-of-the-art systems having array configurations as those shown in Fig. 13.

Equations (28)

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θ = π 2 sin 1 [ 1 d r csc θ c ] ,
d E d t = p ( t ) A η r η a cos ψ ( t ) .
E = [ 1 T Y 0 T Y p ( t ) cos ψ ( t ) d t ] T Y A η r η a ( P o 2 ) [ 2 T Y 0 T Y cos ψ ( t ) d t ] T Y A η r η a
E P [ ( 2 N T D ) ( N T D / 4 + T D / 4 cos ψ ( t ) d t ) ] T Y A η r η a = P [ 2 T D T D / 4 + T D / 4 w ( t ) q ( t ) d t ] Avg . of cos ψ ( t ) above horizon T Y A η r η a = P A T Y η r η a cos ψ ( t ) .
w ( t ) = cos h ( t ) cos δ ( t ) , sin h ( t ) sin δ ( t ) , sin δ ( t ) .
h ( t ) M 4 ( t ) + 2 e sin M 1 ( t ) + tan 2 [ ε / 2 ] sin 2 M 2 ( t ) EOT
δ ( t ) ε sin M 3 ( t )
M 1 ( t ) = 2 π ( t T p ) / T Y
M 2 ( t ) = 2 π ( t T w ) / T Y
M 3 ( t ) = 2 π ( t T ϒ ) / T Y
M 4 ( t ) = 2 π ( t T 0 ) / T D
w ( t ) q A ( t ) = cos δ ( t ) cos h ( t ) cos θ L A T + sin δ ( t ) sin θ L A T
q A = cos 0 cos θ L A T , + sin 0 cos θ L A T , sin θ L A T
q B = cos 0 cos 0 , sin 0 cos 0 , sin 0
q C = cos h cos θ L A T , sin h cos θ L A T , sin θ L A T
q D = cos h cos 0 , sin h cos 0 , sin 0
q E = cos h cos δ , sin h cos δ , sin δ .
cos ψ ( t ) = 2 T D T D / 4 + T D / 4 w ( t ) q ( t ) d t
sin [ ε sin u ] = 2 n = 1 J 2 n 1 ( ε ) sin [ ( 2 n 1 ) u ] 0
cos [ ε sin u ] = J 0 ( ε ) + 2 n = 1 J 2 n ( ε ) cos [ ( 2 n u ] J 0 ( ε ) ,
w ( t ) q A ( t ) = cos θ L A T J 0 ( ε ) J 0 2 ( e ) J 0 [ tan 2 ( ε 2 ) ] cos 2 [ 2 π ( t T 0 ) T D ] .
cos ψ = 2 T D T D / 4 T D / 4 w q A d t 2 π cos θ L A T J 0 ( ε ) J 0 ( ε 2 / 4 ) J 0 2 ( e ) .
E M = ( P η d M ) A T Y η r M η a M ( 2 / π ) cos θ L A T J 0 ( ε ) ,
E M E A = η a M η r M η d M η a A η r A
E M E B = η a M η r M η d M η a B η r B cos θ L A T
E M E C = 2 π η a M η r M η d M η a C η r C η d C
E M E D = 2 π η a M η r M η d M η a D η r D η d D cos θ L A T
E M E E = 2 π η a M η r M η d M η a E η r E η d E J 0 ( ε ) cos θ L A T .

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