This chapter of this blog series explains how we routinely measure greater than 100% transmission in our ProFlex brand holmium laser fibers and why ProFlex is virtually impervious to burn through.
Light is often described as interacting with materials like billiard balls. It’s a useful, if limited model. Personally, I prefer golf balls on a miniature golf course, where the lane is long and narrow like an optical fiber. I can make the curbs into inclined planes to make the balls back curve into the lane, rather than have them bounce elastically from bumpers. The lane is the fiber core and the curbs are the cladding (Figure 1).
Figure 1: Miniature Golf Model of an Optical Fiber
You have likely heard of “particle-wave duality”: sometimes light acts like a particle and sometimes it acts like a wave. Light is not a particle, as modeled by balls, but it is not a wave either. It is just convenient to describe in these familiar terms since there is nothing in our familiar, macroscopic existence that resembles what light actually is. My miniature golf model is far from perfect but it does allow you to escape the confines of the elastic collisions in billiards.
Some of the light in an optical fiber is carried in the cladding and while this aspect is usually modeled using waves, wave models are difficult for non-mathematicians to understand. My model makes it easy… the ball’s path extends into the ‘cladding’ in the figure above: the evanescent field. You may have heard of the evanescent field before…it’s the part of the light that is carried in the cladding as represented by the gray shading in Figure 2, a simplified wave propagation depiction.
Some wavelengths transmit along an optical fiber with almost no loss, but this only happens where the core and the cladding are almost perfectly transparent to the wavelengths involved. In cases where the core is almost perfectly transparent, but the cladding is not so clear, you’ll see attenuation that increases as the wavelength is absorbed more strongly by the cladding. Even moderate attenuation is fine over short distances like those in holmium laser URS.
Figure 2: Electromagnetic Field Distribution in a Step Index Optical Fiber in Bending (if this figure makes no sense, don't worry, that's kinda the point)
When the light is absorbed by the core material things go south much faster because the bulk of the light is carried in the core. The effective attenuation is calculated by weighting the fraction of the optical power transmitted in each material, core and cladding, and the relative absorptions of these materials (or more correctly, the attenuation coefficients within those materials).
Figure 3: Exceeding Fiber NA
One aspect of attenuation in optical fiber that is often overlooked is related to the amount of the light that is carried within the cladding (relative to the core) as a function of the angle of propagation within the fiber. The depth of penetration of the evanescent field into the cladding increases with the angle of incidence on the cladding surface. For a fiber where the cladding has a higher attenuation coefficient than the core (such as holmium laser fibers), an upper attenuation boundary condition (worst case scenario) is the entire field escaping (zero transmission where the angle exceeds the fiber NA). See Figure 3. The lower boundary condition (theoretical best case scenario) is a minimum field in the cladding where a fiber that is carrying light like a bullet in a rifle barrel – straight down the axis – for the lowest possible attenuation.
The angle of propagation does not matter for most applications of optical fiber, but holmium laser energy delivery is not among “most applications”. The cladding of the holmium laser fiber has a significantly higher attenuation coefficient than the core; the more energy that is propagating in the cladding, the greater the loss. It is also true that the deeper the penetration of the field into the cladding, the less of a bend will be needed to get leakage from the fiber, like the hashed area in Figure 2 or the red ray in Figure 3.
If the wave model is difficult to follow, you can see these same effects with the miniature golf model. The steeper the angle of approach to the inclined plane curb (cladding), the higher (deeper) the ball (energy) will rise (penetrate) up the curb (cladding). The golf ball model also holds for the sensitivity of the fiber to bending loss (leakage). As illustrated in Figure 4, a high angle of approach predisposes the ball to escape.
Now that we’ve dispensed with the mechanisms, let’s summarize the ramifications:
- the lower the angle of propagation of energy within a holmium laser fiber, the lower the total attenuation of that energy within the fiber -- more power will get to the stone -- and
- the lower the angle of propagation within the fiber the more the fiber must be bent in order to leak – the fiber does not burn through.
I’ll save the explanation of how we do what we do for the next chapter of this series and I’ll close this one with the explanation for why we measure greater than 100% energy transmission in ProFlex™ fibers.
Simply put, the industry standard method of measuring percent transmission for a holmium laser fiber is based upon comparison to a reference fiber that has mechanically polished input and output faces on a large core fiber that is 3 meters long. The large core is used to eliminate the possibility of spatial overfill losses in the reference fiber. The 3 meter length is an artifact from the days when all holmium laser fibers were that length (most of our ProFlex fibers are now longer than this). The mechanically polished ends are used for consistency of performance by eliminating any artifacts that may arise from non-traditional finishes (and because just about everyone makes their fibers with a mechanical polish).
Totaling the theoretical losses for such a reference fiber is pretty easy, but it is also a waste of time since we can’t really measure what we’ve put into the fiber so we can't compare theory to practice. It's really hard to measure the power at the focal spot without some compromises. Instead, the energy that the reference fiber delivers is taken to be 100% (no defects) as a matter of convenience and because reference fibers have always been more efficient than small core production fibers in the past -- a lot more efficient -- and matched the efficiencies of perfectly produced large core fibers. Those days are past us, now.
Some of you already know why we measure greater than 100% for ProFlex™ fibers these days. The reference fiber is not actually delivering 100%; it’s just the best that could be done when the practice was adopted. We’ve now developed (and patented) new technology to make all sizes of fibers more efficient than the reference, as foreshadowed by blog series title.
If it is still unclear how collimation reduces bulk fiber attenuation, try this analogy on for size. Skipping a flat stone across a pond is an example of an inelastic collision: the stone loses momentum with each bounce. Photons bounding along a fiber core can be thought of as behaving like the skipping stone, where some of the energy is lost on each bounce, albeit far less loss than a skipping stone. The lower the angle of propagation within the fiber, the less bounces off the fiber cladding so the lower the attenuation.
For those who like math -- probably all of you, I'm thinking -- we can calculate the number of 'bounces' a photon has to make at the maximum angle of a full NA launch for the old standard length of 3 meters. (We now make them longer that that...to make them a bit easier to use, but I'll stick to the old length for this slightly esoteric calculation.) It comes to 2308 bounces in a true 200 micrometer core, 1695 bounces in a 273 micrometer core, 1265 bounces in a 365 micrometer core, 922 bounces in a 550 micrometer core and 557 bounces in a 910 micrometer core fiber.
In other words, it is not just small core fibers where we see > 100% transmission (with respect to a standard reference fiber). And in point of fact, collimation benefits large core fibers at least as much as small core fibers, in terms of getting energy to the stone.
You’ll have to wait until the next Chapter to find out how we do it, so keep a weather eye out for “The Power of Collimation: Moses’ Enthalpy”. Thanks for reading.
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Smooth Passage™, Pulsar™ HPC, ProFlex™, ProFlex™ LLF, ProTrac™ and ProFlex™ SPY are trademarks of InnovaQuartz LLC. ProFlex products are protected by two US Patents. © 2016 InnovaQuartz