**Nanomedicine,
Volume I: Basic Capabilities**

**©
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 ~10^{5} reflections/meter
during transit. The scattering minimum in commercial ultrapure silica fiberoptic
cable occurs at ~1500 nm, or ~2 x 10^{14} 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 10^{8} 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 10^{13} 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 power^{727}
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}
~ 10^{8} amps/m^{2} on the inside wire, P_{E} ~ 10^{4}
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/m^{2}
for corneal sculpting, ~10^{5} watts/m^{2} for bile duct cholangiocarcinoma
tumor surgery, and ~10^{6} watts/m^{2} 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 micron^{2} 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} - T_{0} = 20 K at room temperature
for a handheld surgical instrument, then P_{Aw} ~ 4 x 10^{5}
watts/m^{2}, 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, T_{0} = 310 K and T_{max}
__<__ 373 K, then P_{Aw} ~ 10^{9} watts/m^{2}
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 <10^{5}
watts/m^{2} 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