The Power of Collimation I: “I’m going to focus like a laser beam…” November 07 2016
Bill Clinton and George W Bush both promised to 'focus like a laser' on the economy. I'll leave the politics to others and focus like a lens on the lack of scientific rigor for this turn of phrase. At risk of appearing pedantic, I have to point out that lasers aren’t actually focused at all. In fact, collimation (parallelism) is one of the characteristics of laser light that make it unique and useful. Lenses are required to focus laser light.
You may ask yourself, “So what? It’s a minor exploitation of poetic license.” I agree, but I needed an entrée suitable for segue to my laser surgical device topic; so please grant me license as well.
In order to produce sufficient power for surgical utility, lasers like the holmium lasers used in laser ureterorenoscopy (laser URS – or more commonly laser lithotripsy) use a cylindrical crystal that is about 4 mm to 6 mm in diameter. Such a 'laser rod' produces a beam that is also 4 mm to 6 mm in diameter and the beam emitted is essentially collimated -- meaning it stays about the same diameter over short distances instead of spreading out like a flashlight.
We need to get that light into a tiny, flexible glass fiber of about 0.2 mm diameter in order to get the laser energy into the kidney. Surgical lasers use one or more lenses and almost accomplish this feat. I say ‘almost’ because no surgical holmium lasers focus to a spot that small. They get close, e.g. the Quanta Litho laser focal spot is roughly 0.275 mm, but 0.275 is not 0.2. In my blog series, “All Holmium Laser Fibers are the Same, Right?”, I’ve described various ways fibers have been designed to work around this problem so I’ll not delve into that subject matter here. At least I'll try not to do so, not in this first chapter…
We have shared experience with focusing light: using a magnifying glass to focus sunlight happens to be fairly analogous to focusing laser light because the portion of the Sun’s light that reaches Earth is pretty well collimated. (In fact, compared to the output of a holmium laser rod, the Sun is very well collimated indeed.) The warmth of the Sun becomes a painful burn at the focal point of the magnifying lens because the light gathered by the lens diameter is concentrated onto a tiny spot.
Have you ever wondered what would happen if you could focus that energy to a much smaller spot? Or better yet, have you ever wondered why the sunlight doesn’t focus to an infinitely small spot? It would cut through just about anything so that would be useful. Without getting deep into the weeds, sunlight is composed of many wavelengths and each wavelength behaves slightly differently in the lens. Each wavelength is also subject to the Abbe diffraction limit. (In 1873, Ernst Abbe found that the minimum spot size one could focus a wavelength of light is roughly 2.8 times the wavelength in diameter. This means the Abbe diffraction limit focal spot for holmium laser light is about 6 μm.)
Briefly, another characteristic of laser light that is unique is that the wavefronts are in sync. This is because the totality of a (single mode) beam originates with a single photon that, as it passes the length of the laser medium (rod) causes excited state atoms to produce more photons perfectly in sync with the original photon (see figure, below). It’s sort of like tossing pebbles into a pond, in precisely the right places, at precisely the right times, such that the ripples all add together to make a wave instead of mixing all together into a jumble of overlapping wavelets. To build a strong enough wave to be useful, the wavelets in a laser rod have to bounce off the ends of the rod and make many passes back and forth, building and building until the wave is strong enough to punch through a special window that acts like a dam, or better, as flood gates that open at the right moment.
While holmium laser energy is fairly monochromatic (not a bunch of different wavelengths like sunlight), using the large diameter rod to scale the power for surgery has a consequence of producing lots of slightly different laser modes. A simple way to think of this is as slightly different wavelengths, wavefronts and angles of output being supported by the stimulated emission within a finite length and diameter rod (LASER being an acronym for Light Amplification by Stimulated Emission of Radiation); mostly like the image at right (above), but with a soupçon of the image at left.
A well collimated laser beam is produced when only the photons traveling perfectly along the axis of the laser medium continue the stimulated emission cascade. Larger laser rods suffer more defects, dopant concentration variability, larger temperature differences between the center of the rod and the ends and cylindrical wall, etc. that induce small variations in the wavelength, wavefronts and angles of the emitted beam so the output is not as perfectly collimated as it might be a lower power laser. These small differences, similar to the different wavelengths of sunlight in the magnifier, make it impossible to focus the laser beam to as small a spot as one might hope.
There is another problem for focusing holmium energy that relates to the focal lengths of lenses. Holmium laser fibers can only transmit relatively low angles of light. The highest angle that may be transmitted within a fiber is dependent upon the refractive indices of the core and cladding and is described by its Numerical Aperture (NA) where the maximum off-axis angle compatible with the fiber is the arcsine of the NA.
Holmium energy resides just at the ragged edge of the window of transparency of fused silica and it interacts strongly with most plastics. These characteristics limit the type of fiber that may be used with these lasers to constructions that are ‘silica clad silica’ (aka 'all fused silica or AFS fiber) that are typically low NA -- meaning the angles the fiber can deliver are small or low. (The highest angle that a standard 0.22 NA AFS fiber can accept and transmit is 12.7 degrees off the fiber axis.)
The laser rod is pink; the laser beam is dark blue; focused by the light blue lenses; a long focal length lens in the top illustration and a short focal length in the bottom.
I’ll not get into why, here, but the computer ray trace generated figure above illustrates the phenomenon that a short focal length lens produces a smaller spot than a long focal length lens. Short focal length, small spot lenses produce angles that are too high to be transmitted by the fiber. (We often call the ‘focal spot’ of a holmium laser the ‘beam waist’, for obvious reasons.)
Θ is the maximum angle the fiber can support; the fiber input is placed at the focal spot.
In the real world, engineers must design for variances in fiber NA, laser rod and lens parameters, positioning errors, wear and tear, etc. so they choose lenses that produce angles even lower than the maximum the fiber can support, but not too much lower or the focal spot would be huge (like the 500 μm diameter spot of a DEKA Smart 2100 holmium laser). The comfort level the design engineer has with the other components reproducibility and stability colors his/her choices. Add in the fact that there are multiple laser rod types that produce what we call ‘holmium laser’ wavelengths and it is not surprising that there are a host of different conditions and issues when coupling small core fibers to holmium lasers, issues that vary with the laser model. (See my blog titled, “Ho:YAG Fibers: One 'Size' Does Not Fit All.)
I have been known to say that surgical holmium lasers are just about the lousiest lasers you’ll ever encounter. Some of the reasons for this should now be apparent, but I’ll elaborate a bit more. If the goal is to reach the lower pole of the kidney with sufficient energy to fragment a stone, but without burning through the fiber or blowing the laser connector to smithereens, holmium lasers would be just about your last choice. They produce a low quality beam that is highly attenuated by all but expensive and difficult to work with optical fiber, and even then 1% to 3% of their energy is lost per meter of fiber traversed. Holmium laser rods are very susceptible to overheating in protracted use, making the output bloom and dance on the lens (see crude animation) . We’re stuck with holmium lasers because they uniquely produce sufficient power at a wavelength of light that interacts strongly with kidney stones and in a manner that is very effective at breaking them to pieces in a relatively short timeframe.
I hope that you found something in this post that was of interest to you, independent of my need to build upon your knowledge base for the next chapter in this short series, “The Power of Collimation: Bullets, Balls & Skipping Stones”, where it begins to gel. Thanks for reading.
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