Tapered Waveguide Answers Perplexing Question

Breck Hitz

There are occasions in medicine — dentistry, in particular — when it is desirable to focus a laser beam to a small, intense spot some distance behind a small aperture. Root canal surgery is one example, and the treatment of dental caries is another.

Figure 1. The inside diameter of this hollow taper was 700 μm at the input end and 200 μm at the output. Reprinted with permission of Optics Letters.

Even with high-quality beams from today’s lasers, a simple lens cannot perform the task. In practice, a fiber optic tip commonly is used to get the light into the small opening, but these are expensive and they introduce a high insertion loss. Recently, scientists at Tohoku University and at Sendai National College of Technology, both in Sendai, Japan, demonstrated that a hollow, tapered waveguide can provide the necessary focusing with very small insertion loss.

Tapered waveguides have been explored previously as focusing elements but proved too lossy for many applications. The scientists in Sendai performed a ray-tracing analysis of various taper shapes and found that a straight linear taper is more efficient than the exponential taper created when a glass capillary is stretched under a steady heat source. To form the linear taper, they scanned a torch back and forth across the length of the taper as they stretched it from a glass capillary.

Figure 2. Calculated and measured insertion losses are shown as a function of taper length for three tapers: one with a 100-μm opening at the small end, one with a 200-μm opening and one with a 320-μm opening. All three tapers had a 700-μm opening at the input end.

They fabricated tapers with 700-μm-diameter input openings down to apertures as small as 100 μm, over taper lengths from 10 to 30 mm. They maintained a linear taper to within a 3 percent tolerance. After fabricating the tapers, they coated the inner surface with a thin silver film (Figure 1).

The scientists measured the loss of the tapers at 2.94 μm with a pulsed Er:YAG laser. The measured losses for the tapers were larger than the losses they calculated by ray tracing, but otherwise were in good agreement (Figure 2). The discrepancy between measured and calculated losses resulted from imperfections in the taper and the silver coatings inside the tapers. The losses, as low as 0.7 dB, are well within the acceptable range for nearly all applications.

Figure 3. The scientists increased the energy of pulses injected into the tapers until they observed damage. (They were not able to damage the largest taper.) The tapers can deliver energy densities significantly greater than those required for dental surgery (d_o = output diameter).

To calibrate the power-handling capability of the tapers, the scientists increased the pulse energy injected into the tapers until they observed damage (Figure 3). From these data, they calculated that the damage threshold for the 200-μm taper was 278 J/cm², and 290 J/cm² for the 100-μm-diameter one. The energy density necessary to ablate even hard dental tissue and dentin is between 50 and 180 J/cm², well below the tapers’ damage threshold.

Optics Letters, April 15, 2007, pp. 930-932.