Tapered Fibers and Specialty Fiber Microcomponents

This is a continuation from the previous tutorial - Multimode, large-core, and plastic clad fibers

 

 

1. INTRODUCTION

In applications that utilize specialty optical fibers, very often there are requirements placed on the optical fiber design that are not conducive to the launch or delivery requirements placed on the proximal and distal ends of the fiber.

For example, in high-power medical applications, such as laser angioplasty or laser lithotripsy, a small-fiber diameter may be required so the fiber probe assembly will be able to bend easily inside the small blood vessels of the body.

However, this may cause difficulty on the laser input launch (proximal) end of the fiber because the smaller core diameter offers a smaller target for the laser. Adjusting the optical path via lenses can make compensation, but this often increases the cost of the system and makes the laser-to-fiber alignment less robust for day-to-day use. 

Shaped fiber microcomponents are useful devices for medical and industrial applications that require high-power laser delivery (material or tissue cutting), even light distribution over a broad area (tissue ablation or photodynamic therapy), modified beam divergence or spot size (materials processing and communications links), or optical power redirection from the axis of the fiber in an area with small space restrictions (tissue ablation or perforations inside the human body).

Fiber microcomponents have been successfully used for many years. Various fiber microcomponent shapes and sizes can be used to reshape the beam pattern of the light entering or exiting an optical fiber.

The fiber core diameters used range from 200 to more than \(1000\mu\text{m}\) and are typically fabricated from fibers with glass core–glass clad designs, although glass core–plastic clad silica \(\text{(PCS)}\) designs can also be used. Most commonly the fiber end tips themselves are machined or sculpted using the glass material of the fiber itself.

No additional glass material is needed in the process. The process can be either mechanical or thermal, with the latter being primarily but not limited to laser machining. Because the fiber end shapes are fabricated directly from the glass material of the fiber, the interface between the shape and the fiber itself is eliminated.

Thus, there are no coupling losses between the microcomponent and the fiber. They are materially continuous. Furthermore, having no interface, there is no potential for contamination that might exist if the shape were bonded by fusion splicing or epoxy to the fiber. This serves to reduce optical losses and dramatically increase the mechanical strength and durability of the device.

A wide variety of fiber microcomponents have been used. The basic fiber microcomponent design categories are

• Tapers
• Lenses
• Diffusers
• Side-fire and angled ends

There is, of course, a great deal of design variations within these categories (Fig.1).

Common factors in the target application that may dictate the use of any of these microcomponents include 

• Minimum bend radius the fiber must be capable of achieving
• Space restrictions in the laser work area
• Launch numerical aperture \(\text{(NA)}\) of the source
• Size, shape, and optical power density of the input spot
• Wavelength of operation
• Output pattern required 
• Direction of output beam 

 

The operational parameters first depend on whether the fiber microcomponent will be used as an input or an output device. Obviously, the launch conditions will be most critical when the tip is used on the proximal (input) end and output conditions more critical when used on the distal (output) end. The key operational parameters of concern are summarized in Table 1. 

A detailed explanation of each microcomponent design and function follows. Emphasis is made on tapers, because they are most commonly used with specialty optical fibers. 

 

Table 1. Key operational parameters for proximal and distal fiber microcomponents

A discussion of specialty fiber microcomponents would not be complete without commenting on their roll in microfluidic detection technologies. Of key interest here is the application of fiber microcomponents for detection, identification, and quantification of biomolecules. Inclusive to this is the microfabrication of the detection window itself, which results in a flow cell.

 

 

2. TAPERS

A taper is either an enlargement or reduction in the fiber core diameter over a length of the fiber and can be used on either the proximal or the distal end. The purpose of the taper can be to passively alter the input or output divergence (i.e., \(\text{NA})\) with regard to the optical fiber or to alter the optical power density at the fiber’s proximal surface or output target area. 

Despite the funnel-like appearance of the taper, the well-known optical concept of conservation of brightness prevents the taper from behaving as a magical light ‘‘funnel’’ that forces light from a large fiber into a small fiber. There is a price to be paid in transmission through the taper, and this price is paid in \(\text{NA}\).

The tapers actually change the \(\text{NA}\) of the light as it travels down the taper, losing light that exceeds the critical angle for total internal reflection in the optical fiber. When light travels down a taper from larger to smaller diameter (‘‘down’’ taper), the angle the light makes with the fiber axis will increase (Fig. 2).

In most cases, the tapers are fabricated from a fiber with a glass core and glass cladding (glass/glass). The clad diameter–to–core diameter ratio generally remains constant through the taper and the fiber, so the taper actually has a glass cladding layer. Tapers can also be made on \(\text{PCS}\) fibers.

In this case, the plastic cladding is removed in the taper area. Because the cladding around the taper is, therefore, air or epoxy, these tapers tend to be more limited in power capability, transmission, and spectral range as compared to a comparably sized glass/glass fiber. However, in many cases the performance of the \(\text{PCS}\) fiber tapers is good enough and the cost of the \(\text{PCS}\) fiber can be 2–10 times less expensive as compared to the glass/glass.

 

 

 

 

Conversely, as light travels up a taper from smaller to larger diameter (‘‘up’’ taper), the angle will decrease (Fig. 3). This is important when considering the \(\text{NA}\) of the other components of the system and the desired output \(\text{NA}\). 

Laser systems, which produce high peak powers, can be difficult to couple into fiber because of the high-power densities involved. Typically, the bulk fiber material can withstand the high-power density, but the fiber end surface is the weak link and may become damaged due to surface contamination, end-face defects, or dielectric breakdown of the surrounding medium, initiating breakdown of the fiber surface. The degradation can occur very rapidly with nearly instantaneous catastrophic failure of the fiber end. 

Therefore, the most common fiber microcomponent used in medical and industrial applications is the enlarged core taper on the proximal fiber end (Fig. 2). Proximal end tapers are useful in medical and industrial applications where high-power density yet small flexible fiber sizes are desirable.

This type of taper allows a reduction in power density at the fiber end-face and increases the size of the fiber core ‘‘target’’ for the incoming laser power. 

Using a proximal end down-taper, the spot size of the incoming optical power can be enlarged proportionally to the taper. Adjusting the focal point to be inside the taper can perform this. This results consequently in a reduction of the optical power density impinging on the front surface of the taper without a reduction in the total power.

The power density at the larger input surface can be reduced to levels well below the damage threshold, thereby avoiding catastrophic failure of the fiber end. It should be noted that power may be lost as light travels through the taper because of high angle input modes further increasing in angle, eventually exceeding the fiber \(\text{NA}\) and refracted out of the fiber.

The launch optics can be designed to minimize this loss. The loss, however, is typically less than the power gained by being able to increase or maintain the total power input into a taper versus the smaller fiber core without a taper. 

 

Design of a Fiber Taper 

The well-known concept of conservation of brightness states that if light losses are negligible, the spatial and angular content of the light anywhere within or at either end of a taper are described by  

\[\tag{1}A_in^2_i\sin\Theta_i=A_on_o^2\sin^2\Theta_0,\]

where subscript \(i\) refers to the input and o refers to the output of the taper and 

\(A=\) cross-sectional area of the light distribution normal to the taper or fiber axis 

\(\Theta=\) maximum angular extent of the light distribution 

\(n=\) refractive index of the medium, where \(\Theta\) is measured (Fig. 4).

Because \(n\sin\Theta=\text{NA}\) and \(A_i/A_o=d^2_i/d^2_0\), where 

\(\text{NA}=\) numerical aperture 

\(d_i=\) input taper diameter 

\(d_0=\) input taper diameter,

it follows that as light transmits through a sufficiently long taper, the following equation applies:

\[\tag{2}\frac{NA_0}{NA_i}=\frac{d_i}{d_0}.\]

However, in the case discussed here where the taper is integral with the optical fiber, if the product of the input \(\text{NA}\) and the ratio of the diameters exceeds the greatest \(\text{NA}\) that the taper can support (which can occur in the case of the proximal end down-taper when the input \(\text{NA}\) is too high), light will escape into the cladding and be lost. In this situation, this relation will no longer be valid. 

Therefore, if one applies an input \(\text{NA}\) to the end of the taper that would be equal to the \(\text{NA}\) for the base fiber, the light throughput would be inversely proportional to the square of the taper ratio. For a \(2:1\) diameter ratio taper, the throughput would be 25%, exactly the same as butting a large fiber directly to the small fiber with no taper at all!

 

 

 

Therefore, the recommended maximum input \(\text{NA}\) is 

\[\tag{3}NA_i\leq NA_o(d_o/d_i).\]

If this relationship is adhered to, the NA increase down the length of the taper will not exceed the \(\text{NA}\) of the fiber, thereby minimizing loss in the taper. For example, if the source applied to the large end of the \(2:1\) taper has an \(\text{NA}\) half that of the base fiber, then perfect transmission can be expected through a perfect taper.

Of course, the \(\text{NA}\) of the light in the fiber will now be twice that of the original source. Note that there still may be optical losses from imperfections in the taper geometry or taper surface plus anyFresnel losses from the front surface of the taper. 

As another example, with a down-taper with a \(3:1\) diameter ratio attached to a fiber with a \(0.22\) \(\text{NA}\), the maximum input \(\text{NA}\) can be calculated as 

\[\quad\; NA_i=0.22^*(1/3)\]

\[NA_i=0.073.\]

Therefore, to obtain the best possible coupling efficiency into the fiber, the launch \(\text{NA}\) must be 0.073 or less. This relationship can also be used to calculate the required taper ratio if the launch and fiber \(\text{NA}\) are already established.

Therefore, to obtain the best possible coupling efficiency into the fiber, the launch NA must be 0.073 or less. This relationship can also be used to calculate the required taper ratio if the launch and fiber \(\text{NA}\) are already established.

Note that fiber microcomponent tapers are typically manufactured in taper diameter ratios of 1.1–5.0 on fibers that are 200-\(\mu\text{m}\) core diameter or larger. It is possible but difficult to fabricate tapers with good geometrical tolerancing on smaller fibers, because of the fiber easily overheating in the tapering process, causing the glass material of the fiber to quickly flow and making it difficult to control the geometry of the taper.

As expected from the previous equations, the performance of the taper is relatively independent of taper length. This was confirmed in actual measurements in which the taper loss was found to depend strongly on input \(\text{NA}\) but to be relatively independent of taper length and fiber diameter.

This work was supported by an optical modeling ray trace model, which agreed with the general trends of loss being strongly dependent on input \(\text{NA}\) and relatively independent of fiber diameter and taper length, even for very long length \((>1\)-m) tapers. Figure 5. displays these ray trace model results for a \(2:1\) taper (core diameters of 400–200\(\mu\text{m})\) with the actual measured results overlaid.

However, for launch conditions that use significantly non-uniform beam profiles, the model does predict that a longer taper will help to smooth (homogenize) the beam profile of the output power.

Figure 6. is a diagram showing some important taper parameters. The most significant of the physical parameters is the ratio of the diameter of the taper end to the diameter of the base fiber.

 

 

The discussion, thus far, has concentrated on the use of proximal end down-tapers for the purpose of reducing the optical power density impinging on the optical fiber surface. In some cases, the same type of taper is used not for reducing the optical power density, but for cases in which the minimum beam waist from the laser is larger than the fiber diameter or the laser system is difficult to maintain in focus.

The use of a taper can make the coupling tolerances much more forgiving with minimal compromise to coupling performance and allow a loosening of tolerances in the optical system. 

An optical taper can also be used on the output end of an optical fiber using its angle-changing property to alter the angular distribution of the output

 

 

intensity. For example, if a lower output divergence (smaller spot size) than the fiber normally exhibits is desired, an up-taper (Fig. 7.) can be used.

Alternately, if a larger divergence is required, a down-taper (Fig. 8.) can be used. 

In situations in which it is desirable for the optical power to spill out of the fiber abruptly at a spot size larger than the fiber \(\text{NA}\) alone can attain, but there is only a short distance to the target (such as a laser scalpel), a very short taper length can be used.

This decreases the output spot size versus the design shown in Fig. 9, and thereby increasing the power density of the spot. In addition, the shorter tip is mechanically more robust and the sharp point can be used for perforating membranes. 

 

 

3. LENSES 

Various lenses such as concave, convex, and spherical (ball) can be fabricated as fiber microcomponents. These lenses are useful for modifying beam divergence and spot size.

The shaped lenses are used for improved coupling from laser diodes to fibers, reduction in overall Fresnel losses, reducing or increasing the depth of focus, increasing or decreasing output spot size, and collimating or decollimating light. Applications are very broad, from low-power communications links to

 

 

 

 

 

 

 

 

high-power industrial lasers. The lenses can be combined with other shaped tips as well, such as a convex lens on the end of a taper. 

Convex and ball lenses can be fabricated on the end of an optical fiber by simply heating the fiber end until the glass softens and surface tension rounds the fiber end. Precise control of the heating conditions will result in a good piece-to-piece repeatability. Concave lenses can also be fabricated but often entail more complex machining processes. 

The design of the simple fiber lens is similar to the normal design of a Plano convex or Plano concave lens, with the flat side obviously being the optical fiber itself. Because there is no interface between the lens and the fiber, there will be no Fresnel losses to account for in the system optical budget. 

Standard lens design equations also apply to the design of fiber microcompo-nents. In the case of a spherical lens on the fiber end, the radius, \(R\), of the lens surface must be determined. Starting with the thin lens equation: 

\[\tag{4}1/d_o+1/d_i=(n_2/n_1-1)(1/R_1-1/R_2),\]

where Fig. 10 defines the equation’s parameters. 

In the case of collecting collimated light from a source and coupling it into the optical fiber (Fig. 11), the lens must be designed so that the coupled light does not exceed the fiber \(\text{NA}\) and thereby become lost. 

In this situation, 

\(d_o=\) infinity 

\(R_2=\) infinity, 

 

 

 

 

 

 

 

and assuming \(n_1=1\) (air), the thin lens equation reduces to 

\[\tag{5}1/d_i=(n_2-1)/R_1.\]

The distance \(d_i\) can then be calculated through the definition of \(\text{NA}\): 

\[\tag{6}NA_2=n_2\sin\Theta_2\]

Because the \(\text{NA}_2\) of the fiber and the glass fiber core index of refraction, \(n_2\), are both known, \(\sin\Theta_2\) can be calculated. Assuming a (thin) lens where the lens thickness is insignificant, per Fig. 10,

\[\tag{7}d_i=h/\sin\Theta_2,\]

where \(h\) is the input beam radius. The radius of curvature of the lens, \(R_1\), can then be calculated by inserting \(d_i\) and \(n_2\) into the reduced thin lens equation, above. Similar calculations can be performed for light either entering or exiting at various angles.

In some cases in which there is an input \(\text{NA}\) greater than the fiber \(\text{NA}\), coupling efficiency can be increased by the use of a concave lens (Fig. 12).

In cases in which the collection efficiency of the lens is limited by the lens (fiber) diameter, a ball lens can be utilized (Fig. 13). Again, the thin lens

 

 

 

 

equation can be used for calculating the ball lens radius. A common application of such a ball lens is in coupling to laser diodes. The ball lens transforms the light emitted by the laser at a high acceptance angle (high \(\text{NA})\) to a smaller angle that will be accepted by the fiber \(\text{NA}\). Coupling improvement of three to five times are typically obtained over straight fibers (0.16 \(\text{NA})\) butt-coupled to the laser diode.

For comparison, a separate ball lens and fiber can achieve an 18–20 times coupling improvement over straight fibers, but this can be offset by higher material and assembly costs. 

Lenses described here are not typically good for absolute beam collimation. The spherical aberration of the lenses creates a diffuse focal point, thereby making it extremely difficult to absolutely collimate the beam (Fig. 14).

Note that more complicated designs are possible, where tapers and lenses can be combined, although such structures are rarely cost effective because of the complexity of fabrication.

 

 

4. DIFFUSERS 

Diffusers are generally used on the distal end as a means of redirecting and scattering the optical power in an even 360-degree cylindrical output along the length of the tip (Fig. 15). This is typically performed by machining grooves or threads into the glass of the fiber deep enough to extract and scatter light traveling through the fiber core.

The scattered light bathes an area with the optical power, making it useful for applications such as photodynamic therapy or tissue ablation (e.g., prostate reduction and urology procedures) (Fig. 16). 

 

 

 

 

 

Because coupling into a diffuser would be very high loss, they are generally limited to distal end use only. The diffuser tip, having the rather deep grooves, often has a silica cap placed over it for additional mechanical durability and protection from contamination. 

The design of diffusers varies depending on the output length and uniformity required. There are no straightforward equations (as in the case of lenses or tapers) that can calculate the design of the diffuser.

A detailed ray diagram can be used as a first approximation however. It is important to ‘‘budget’’ the amount of optical power being withdrawn versus diffuser length. As the light traveling down the fiber approaches the diffuser, it can be assumed that the light occupies the full \(\text{NA}\) of the fiber. The light at the higher order modes exits the diffuser tip preferentially over the modes traveling at low angle or straight down the fiber core.

If the diffuser design is uniform down its length, then the output intensity will be higher at the beginning of the diffuser than at the end. If this is not acceptable in the application, the output from the diffuser can be made more uniform down the length of the diffuser by adjusting the diffuser design so that 

 

 

 

the light traveling at low angles is progressively stripped more severely down the diffuser length. This can be performed by progressively increasing the groove depth, width, and pattern so light is more aggressively stripped (scattered) from the fiber as it travels down the diffuser. 

 

 

5. SIDE-FIRE AND ANGLED ENDS

The side-fire consists of an angle machined into the distal end of the fiber. In most side-fire designs, this angle is 40–43 degrees from the fiber axis. Optical power impinging on the angle is redirected approximately 90 degrees from the fiber axis. Note that an angle slightly less than 45 degrees is most optimal.

This is because at 45 degrees or more, a significant portion of the light impinging on the angled end exceeds the critical angle for total internal reflection and then exits the fiber in an undesirable direction. 

The side-fire microcomponents are made by first machining in the desired angle into the fiber, then attaching a glass cap over the angled end. The side-fire requires a medium of lower refractive index around the backside of the angled end to operate.

Commonly, a glass cap is placed over the diffuser. The cap provides mechanical protection and an area of low index (i.e., air) on the backside of the angled end, thereby creating the conditions necessary for reflection out the side of the fiber. 

The side-fire is particularly useful in invasive surgical procedures in which the optical power needs to be redirected in a very confined space, such as tissue ablation, cutting, and perforations (e.g., transmyocardial revascularization \(\text{[TMR]})\).

The side-fire is primarily used for such in vivo medical applications, so the protective glass cap also serves to protect the fiber end from damage and contamination of the angled fiber end (Fig. 17). 

Angled fiber ends are also very useful in reducing back-reflection down the fiber. Putting a 7- to 10-degree angle (depending on fiber \(\text{NA})\) into the fiber will cause the Fresnel back-reflection off the fiber end-face to reflect at an angle that will not be accepted by the fiber \(\text{NA}\) and, therefore, not be propagated back down the fiber. In high-power laser cutting and welding applications, this

 

 

back-reflection can cause the fiber distal end termination or a sharp bend point in the fiber itself to overheat and self-destruct. Similarly, when used on the input end, the angle can dramatically reduce back-reflection into the source laser. Such back-reflection can damage optical components, generate signal noise, and create instability in the laser source.

In either case, the reflected power is dumped into some type of absorbing heat sink, which effectively dissipates the energy without destroying the optical fiber assembly or creating a safety hazard (Fig. 18). 

 

 

6. OPTICAL DETECTION WINDOWS FOR MICROFLUIDIC FLOW CELLS

Optical detection windows are used in microfluidic flow cell spectroscopy. Although not necessarily optical fibers in nature, optical detection windows are produced in a similar fashion to many of the fiber microcomponents and are often partnered with specialty optical fibers to complete the flow cell device. In this application, a fluid (gas or liquid) to be analyzed is transferred down a small glass capillary similar in size to an optical fiber.

While traveling down the capillary, the fluid is transformed or reacted or otherwise undergoes a separation process. The fluid then passes through the optical detection window through which the fluid is scanned for fluorescence or spectral absorbance. In some cases, specialty optical fibers discussed earlier in this chapter are added to serve as 

 

 

 

either the conduit for the exciting radiation wavelength(s) of light from the source to the window or the conduit for the output radiation from the window to the analyzing spectrometer. Figure 19. shows a schematic of a typical design that comprises an optical detection window being used as a microfluidic flow cell. 

The detection windows themselves are typically composed of a 2- to 10-mm region of the glass capillary where the exterior protective plastic coating has been carefully removed (Fig. 20), or it can be an enlarged length of the capillary (Fig. 21) where the fluid speed decreases and the illumination volume increases, thereby increasing the sensitivity of the flow cell. 

The advantage of these optical detection windows and flow cells include the following: 

• Small sample sizes
• High sensitivity and throughput speed 
• Low dead volume, as no flow cell connectors are typically needed 
• Analyte processing in a confined, controlled, and safe area (within capillary) 
• Continuous sample processing versus batch 
• Compact flow cell footprint for multiplexed sample processing 

An application that greatly benefited from such detection window technology is DNA sequencing. Many of the \(\text{DNA}\) sequencing instruments are capillary based and use optical detection windows in 1- to 384-channel arrays for very 

 

 

 

 

 

 

 

high throughput processing. This is an obvious requirement for efficient sequencing of a genome and was of particular significance during the Human Genome Sequencing Project, as the human genome contains more than 3 billion base pairs. 

An interesting new technology is using a fiber capillary (a specialty optical fiber with a small hole down its center) as a high sensitivity fluidic sensor cell. The fiber capillary (light-guiding capillary) consists of a core, which is an annulus around the \(\text{ID}\) of the capillary. Designing an appropriate (low) refractive index layer of glass around the \(\text{OD}\) of the annular glass core creates an outer cladding.

The \(\text{ID}\) of the annular core interfaces with the (lower index) fluid in the capillary. Because there is material of low index on either side of the annular core, light launched into the fiber end will travel via total internal reflection down the annular core. The evanescent field of the light impinging on the surface of the \(\text{ID}\) interacts with the fluidic material, creating a high efficient evanescent field sensor microcomponent.

The output of the annular core is monitored for spectral absorbance through the fiber end or through an optical detection window cut into the fiber plastic coating (as discussed earlier). Figure 22. shows a cross-section of such a microcomponent.