Part 1 of this series was mostly a review of Snell's law and Fresnel reflections as they explain the weird output of bevel polished fibers. Here we see some more Snell and Fresnel issues and the earliest Band-Aid® treatments designed to mitigate these issues.
Part 2: Abe's Solution(s)
Before we get into what Abe saw as solutions to the issues outlined, we should probably address the problem that I alluded to in Part 1: the disappointing results of polishing a fiber at the calculated TIR angle for lateral redirection of the output. In so doing, you’ll more fully understand why I went through Snell’s law as much as I did in the introduction.
The general design of all side fiber fibers based upon total internal reflection is the same: a beveled fiber within a protective cap. The most common error you’ll see in diagramming side fire fibers (particularly on whiteboards during meetings) is a depiction of the light refracting at the bevel surface rather than reflecting as illustrated below.
Abe even used "refracted" to describe the redirection of the light within his patent, but only once, and I'd venture that I have made this error on at least one or two occasions in presentations. But if this were how side fire fibers worked, the problems that vexed Abe would have been about an order of magnitude smaller and all side fire fibers would have worked much better these last 30 years. The light is not refracted at the bevel, though, it is reflected. We also saw that the rays in the fiber are not parallel, as is often depicted.
Depicting parallel rays is not uncommon and the why of it is fully understandable: the true complexity of the optics is not critical to understanding the basic concepts, particularly at the management level and above. Ignore the protective capsules (like tiny test tubes) on these fibers -- we’ll discuss them in due time -- and for the next illustration I’ll remove them for clarity.
This next illustration is from the perspective of the eyeball icon in the illustration above and the stacked fibers correspond to the INCORRECT ("Fantasy") drawing and the corrected one ("Still Fantasy"). The point of the illustration is to show what the classical depictions of side fire fibers omit in oversimplification, even when mostly correct.
In the illustration above, I’ve indexed the rays horizontally so they don’t overlap one another and I've adopted both shades of pink and arrow size to generally reflect magnitude. You see, in the "INCORRECT"/"Fantasy" version, both above and below, the light exits the flat, beveled surface so that the Fresnel reflections are relatively minor at ~4% (smaller, light pink arrows). In the "Still Fantasy" version below, most of the light exits the curved side of the fiber, and because Fresnel reflections scale with higher angles the reflections are larger. But in these fanciful, classical depictions we fail to consider that the light is going in every direction possible within up to a ~19° solid angle. Recall from Part 1 that the highest NA ray of propagation was 9.5° so rays exist at either extreme off of the axial ray (called the zeroth order mode) and contact the TIR bevel at every point from every possible direction. But even this is simplified because it only considers meridional rays: rays that cross the central axis of the fiber.
It should be noted that even the "Reality" view is highly simplified.There are other sets of modes in large core fibers and, in fact, these skew modes likely dominate at the tip of most side fire fibers where holmium and thulium lasers are used, perhaps even for GreenLight™ lasers. The illustration gives an example of a skew mode in the "Reality" cross-section, but only as induced by the TIR bevel: those rays that are bouncing around the periphery are skew modes. Skew modes need not be THAT skewed; they just don’t cross the central axis of the fiber: they spiral around it instead. Considerations of skew modes become very complex very quickly so I am going stop considering them unless there is a specific reason to bring them up again. Just be cognizant that they exist for the purposes of understanding side fire fibers.
It is the why of the skew mode conversion in the "Reality" cross-section that we are here to examine and that's Snell’s law again. Russell Pon, in US Pat. No. 5,428,699 described how Snell's law, while fundamentally enabling TIR side fire fibers, also raises problems in their execution. Patent contents are not protected by copyright in the US, but credit is due the source, anyway: the patent drawings used below are taken directly from Pon without alteration. Figure 5a form the patent illustrates the Snell's law problem.
The rays in Figure 5a are originating from the reflection at the TIR bevel, all at the center line of the fiber (for simplicity) and all rays are parallel to the zeroth order ray (α) in the center of the fiber: 5a is still a fantasy. For prior side fire fibers, Pon recognized that rays reflected by the TIR bevel at the edge of a standard 1.1 CCDR fiber (Cladding to Core Diameter Ratio, e.g. 600 μm core, 660 μm cladding or 30 μm glass cladding thickness fiber, a standard material of the era), rays like gamma (γ) and delta (δ) that are close to the outer edge of the core impart the glass:air interface at angles greater than the critical angle, so they are totally reflected rather than refracted. This causes the rays to skew about the periphery of the fiber until they intersect the flat plane (TIR bevel) a second time. Then, in refracting from the TIR, similar to the rays in the INCORRECT side view, above (not the horizontal rays, but the ones deflected upward) they escape, but in the wrong direction. The zeroth order ray alpha (α) passes through the core:clad interface and into the air without refracting, but there is a Fresnel reflection of roughly 4% that goes in the other direction (not shown) like the pink arrows of my earlier illustrations). Alpha (α) is the best case ray. The beta (β) ray represents rays near the maximum distance from the central axis that do not suffer inadvertent total internal reflection; these rays are merely refracted.
NOTE: Should you go to the trouble to read Pon's patent, be aware that he also (apparently) had issues with the nomenclature and, as such, he mixes “greater than the critical angle” and “less than the critical angle” in describing the fates of the gamma and delta rays. There are also errors in labeling of refracted rays and Pon’s handwritten Greek characters leave something to be desired, but all in all, his was a brilliant observation that had eluded the rest of us.
Figure 5c from Pon is also imperfect in illustrating the sum total of the distortions in the output (for the intended output direction), but it does a good job in illustrating the scatter in the generally undesirable directions, as a function of the total energy involved. The actual output “spot” (520 in the illustration) is not at all as concentrated as depicted by Pon. It is really more kin to the scatter, though not scattered at such wide angles off of center. The take home lesson from this is that only about 70% of the light goes in directions that are useful. The rest is diffuse and exits in useless and potentially harmful directions, where diffuse emissions facilitate tissue adhesion because they are below the vaporization threshold of tissue.
I apologize for getting a bit out of order here, but since we are on the subject, Pon’s solution was highly successful and merits discussion. It was marketed first as the Laserscope ADD-Stat™ fiber and later became the Model 2090 fiber, essentially the same one used on GreenLight™ 80 watt and 120 watt lasers to this day. It is elegantly simple but horrifically expensive to execute (as done by Laserscope, then American Medical Systems, and now Boston Scientific – owners of the aforementioned trademarks). Simply by substituting the highest available CCDR fiber made -- 1.4 CCDR -- the glass:air interface is moved outward far enough that most of the core edge rays no longer see angles at, or higher than, the critical angle as shown in Figure 9a, albeit using a cladding thickness that is about twice as thick as was ultimately used.
The reason that the device is horribly expensive is that the bulk of the cost of a large core, glass clad, multimode fiber (raw material) is the cost of the fluorine-doped cladding. For example, if a pure fused silica rod costs $X, a 1.1 CCDR "perform" (so called because the waveguide is “pre-formed” rather than the cladding being added in a rod-in-tube draw or as a plastic coating) costs $8X and a 1.4 CCDR preform costs some $40X. With the fiber raw material representing the single largest expense in producing a side fire fiber, you can imagine the impact to materials costs where that fiber now costs 5-fold more.
The commercial success of the 2090 fiber was not just due to Pon's innovation, though. Laserscope also locked out all other suppliers on the very popular GreenLight™ laser. In fact, as we will see in blog entries to come, there were fibers contemporary with the Add-Stat™ and 2090 that were better but these did not succeed in the marketplace for lack of the captive customer base. In fact, prior to Pon, we’d aimed to solve the same problem of unwanted back reflections without recognizing the true sources and, in so doing we repaired more than Pon had.
I do not mean to diminish Pon’s insight: it was seminal and his solution was elegant. But we are here to discuss Abe’s fiber, almost 10-years prior to Pon. We will return to Pon in chronological order, later in the series.
Abe’s fiber had a protective cap, but that’s not Abe's innovation. Caps were an obvious requirement for surgical applications of bevel-tipped fibers because surgery is messy and often performed under water, within a saline-flooded surgical field like the prostatic urethra. Water’s refractive index is too close to that of fused silica to produce a TIR angle that can actually be manufactured: 1.33 versus 1.457 for silica. You can now do the math to find the critical angle θc, add the maximum angle of propagation and take the complementary angle to get to the 14.6° as depicted below. Yikes, that's a pointy fiber....
Not only is this tip almost impossible to fabricate, in quantity, it’s just too delicate to work with in surgery and even if you could do so, the center of the output “beam” is less than 30° off the axis: it not really a side fire fiber at all. This same issue is one reason why the much lower cost, plastic clad fiber materials are not used in making side fire fibers; with NAs in the 0.35 to 0.42 range, the maximum angle of propagation that one must add to the critical angle is much larger than it is for 0.22 NA fibers. The resulting 30° TIR angle and 60° output is too difficult to make and too low an output angle to compete with 37° and a 74° output for reasons that will become clear as we progress through this series.
Addition of a protective cap to the fiber serves to preserve the glass:air interface needed to support the TIR and it protects the delicate (and ideally sharp) fiber tip. At least those were the recognized functions in 1985, when Abe sought to improve performance. Refraction and reflection at the cap inner wall, and to a lesser extent, on the cap outer wall, further reduce efficiency and throw even more of the energy in directions that nothing useful. A “rule-of-thumb” for estimating the magnitude of Fresnel reflections is 4% minimum per surface, for glass:air, increasing with higher angles of incidence regardless of polarization. Because refractive indices are wavelength dependent, Fresnel reflection magnitudes are as well, but the rule-of-thumb holds.
In the real world, Fresnel reflections are bouncing all over the place. The illustration below is (again) grossly oversimplified because to do otherwise would completely obscure the point. In this cartoon, we are looking at only three meridional rays and we are not considering the three dimensional nature of the reflections from cylindrical surfaces, the total internal reflections for the rays imparting the TIR bevel near the edge of the core or their Fresnel reflections, or any refractions. In short, in order to aid in visualizing the complexity of what is actually happening, we are not considering the vast bulk of the complexity; just keep in mind that there is all the mess of the "Reality" cross-section, with new reflections and refractions due to the cap surfaces, and every possible angle within the fiber NA is involved.
Abe primarily considered the “back reflections” but he failed to identify their true (principal) source. In 1985, the consensus was that the back reflections were mostly Fresnel with some additional scatter likely due to polishing defects and scratches on the cap outer diameter. Axial emission was also commonly seen in the early days, at up to 5% to 10% of the total light in the fiber and this was also believed to be a result of defects in the angled tip. There was some truth to this.
There commonly were scratches on the bevel faces chips at the fiber edges -- in particular the pointed tip were commonly compromised -- and caps definitely were scratched on the outer surface, but the contribution of these defects to the “scatter” observed was minimal. The tiny scratches and digs on the TIR bevel were fairly common because the specialized polishing techniques used today had not been perfected. These small defects were difficult to detect with imaging methods of the era, within the manufacturing environment, but even these defects were only partial contributors to axial emission.
The true culprit for axial emission was due to incorrectly calculated angles and/or poor precision and accuracy in reproduction of those angles. Even with digital imaging and edge detection, measuring bevel angles on sub-millimeter fibers can be challenging: it was very problematic 30-years ago.
This is Abe's fiber and it is a series of Band-Aids. He placed flat surfaces on the output side of the cap and the side opposite the output, upon which he applied an antireflective coating and a reflector (depicted here as a gold mirror coating), respectively. The latter was intended to reverse all emissions and reflections that were going the wrong direction and the former was intended to minimize reflections at the output surface. He also called for a mirror coating on the round bottom of the test tube cap, to block the axial emissions.
Note:Optical fiber of the day was not actually available with blue buffer. I added the color to the fiber buffer to make the cap more distinct. Unfortunately, the reflector on the flat opposite the output flat did not come out very shiny.
The inclusion of the flat and anti-reflective coating on the output side offered little or no benefit in that this surface typically offers minimal reflections (due to contact with saline irrigation). It is impossible to judge whether or not Abe calculated the TIR angle correctly in that he does not specify a laser wavelength and the bevel angle range specified is relatively wide at 35° to 40°. To Abe’s credit, he did recognize that eliminating the air gap between the cylindrical side of the fiber and the cylindrical inner wall of the glass cap would “…eliminate the interface reflection caused by the above-described air layer...” but proposed that the precision of manufacturing tolerances needed was incompatible with mass production and that “…in inserting the fiber, made of quartz or the like, and having a sharp forward end inclined at about 45°, straight into the tubular member..." would chip the fiber bevel in most cases. (It's actually worse than that due to ovality issues that Abe was unaware existed in drawn quartz tubing materials.)
While Abe recognized some deficiencies in TIR-based side fiber fibers and his solutions likely provided some improvement at the low laser powers and forgiving wavelengths of 30 years past, none of the two dozen or so side fire fiber designs that followed during the Nd:YAG ‘laser-TURP’ boom incorporated any aspects of his work. Thin film dielectric reflectors did make a comeback in about 2006, but only for a limited use. We will take a look at that laser TURP boom and the fiber technologies that were involved in Part 3 of this series.
Thanks for reading,
Stephen Griffin
@doctorsilica
#LDD85Duet
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