© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

6.4.3.2 Electromagnetic Tethers

Optical energy may be piped from one place to another by allowing light to enter a narrow solid fiber of clear plastic or fused silica. Light undergoes total internal reflection at the glass-air boundary and follows the contours of the light pipe, with losses due to scattering and absorption in the material as each photon undergoes up to ~10⁵ reflections/meter during transit. The scattering minimum in commercial ultrapure silica fiberoptic cable occurs at ~1500 nm, or ~2 x 10¹⁴ Hz, in the near infrared. These losses are roughly equivalent to transmission in clear air, negligible over distances of relevance in nanomedicine: measurable amounts of energy may be transmitted through single fibers ~100 km long.

At the lowest frequencies, the cutoff frequency for electromagnetic waveguides of diameter d_guide filled with material of dielectric constant k_e, below which frequency the waveguide cannot transmit photons (velocity c = 3 x 10⁸ m/sec in vacuo, and slightly lower in various dielectric materials at various frequencies), is n_cutoff = c / 2 k_e d_guide ~ 7.5 x 10¹³ Hz (l = 1000 nm) in the near infrared -- close to the scattering minimum at 1500 nm -- for d_guide = 2 microns and k_e ~ 1. This cutoff applies only to waveguides; coax (shielded single wire) or triax (shielded twisted pair) lines can conduct frequencies all the way down to DC and all the way up to near-infrared (Section 7.2.5.1).

More specifically, if a nonmagnetic weak dielectric (~air) fills the space between two coaxial cylindrical conductors, with inside wire of radius r_in, outer jacket of radius r_out and line current I_line, then the average transmitted power⁷²⁷ is given by:

{Eqn. 6.43}

In coax theory,⁷²⁷ r_out/r_in = 1.65 allows maximum power to be carried at a given breakdown voltage gradient across the dielectric (most appropriate for power transmission), whereas r_out/r_in = 3.6 gives the lowest attenuation due to conductor losses for a given outer diameter (most appropriate for communications applications). Thus for a 1-micron power coax, r_out = 0.5 micron implies r_in = 0.3 micron; assuming I_line ~ 10⁸ amps/m² on the inside wire, P_E ~ 10⁴ pW at ~1 millivolt and the line has a characteristic impedance of 30 ohms.

For the highest frequencies, optical fibers may be as small as ~0.51 micron in diameter, roughly the photon wavelength -- a dielectric rod can serve as a waveguide crudely analogous to the hollow metal pipes used at rf frequencies. Blue photons (~400 nm) carry ~500 zJ of energy, almost enough to break C-C bonds (~550 zJ). Ultraviolet (UV) wavelengths shorter than ~300 nm are greatly attenuated for fiber lengths >1 meter due to heavy absorption, and intense prolonged UV irradiation of silica creates defects (color centers) in the material that lead to further absorption of the laser light in the fiber.

In biomedical applications, silica fibers are used to conduct photons from excimer lasers, the brightest known sources of UV radiation.^3539,3540 Typical maximum continuous power intensities are ~30,000 watts/m² for corneal sculpting, ~10⁵ watts/m² for bile duct cholangiocarcinoma tumor surgery, and ~10⁶ watts/m² for arterial debulking, laser dental machining and laser lithotripsy for kidney stones,^645,646 so ~0.01-1 microwatts may be delivered to medical nanodevices using a single ~1 micron² optical tether transmitting UV photons. The maximum transmittable power intensity is approximated by Eqn. 6.40; taking e_r = 0.80 for silica, A_w^1/2 = 1 mm diameter fiber, L = 1 meter and T_max - T₀ = 20 K at room temperature for a handheld surgical instrument, then P_Aw ~ 4 x 10⁵ watts/m², in line with the above figures for excimer lasers assuming a ~40% duty cycle. For a nanomedical optical power cable with A_w^1/2 = 1 micron diameter fiber, L = 1 meter, T₀ = 310 K and T_max < 373 K, then P_Aw ~ 10⁹ watts/m² and a maximum of P ~ 1 milliwatts may be delivered down the fiber. However, at this high fluence there is tremendous risk of localized tissue incineration, should the fiber detach in vivo and the photon flow is not immediately halted -- a good argument for limiting optical power tether intensities to <10⁵ watts/m² or less. A thin adjacent backchannel fiber could serve as a fuse, rupturing simultaneously with the main fiber and cutting off the feedback control signal.

Last updated on 18 February 2003