Laboratory #3: Measuring Index Profiles
Purpose
This lab experiment shows how to determine the index profile of GRIN and SI fibers using scanning techniques.
Method
To measure the index profile of a fiber, one end is illuminated with a Lambertian light source. All the modes of the fiber will be excited. By scanning a pinhole across the magnified image of the core, one can measure the index profile of the test fiber. This way you can tell if a fiber is step-index (SI) or graded-index (GRIN).
Primary Equipment
Tungsten-Halogen lamp with focusing lens
Beam Scan beam profiler ($6000)
SMF-28 fiber, 100/140 GRIN fiber, 50/125 (GRIN or SI?) fiber, and SI 980/1000 polymer optical fiber (POF).
XYZ positioning stage for manual scanning of image ($650 each)
Si PIN photodetector with aperture
PAR 124A lock-in amplifier
Optical chopper to chop beam for use of lock-in amplifier
Background Information
Index profiling:
A Lambertian source produces light in all directions. This experiment uses a tungsten filament lamp to approximate a white light Lambertian source. The lamp is focused into one end of the optical fiber being measured at an angle overfilling the NA of the fiber if possible. [Note: Another, similar, method illuminates the opposite end of the fiber from the side. See Hatton, et al, “Measuring the refractive-index profile of optical fibers by the cladding-mode near-field technique,” Optics Letters, 22, pp 738-740, September 1987.]
The relationship between the power measured by the detecting aperture/detector and the index of the core is given by
(3)
where r is the radius out from the center (r = 0) of the fiber and a is the core radius.
The most commonly used construction for the refractive index variation in a GRIN fiber is the power law relationship:
, r ≤ a (4)
= n2 r > a (5)
where Δ, from equation (5), is Δ = (n12 – n22) / 2n12. For the usual case in which the two indices are nearly the same, this reduces to the approximate result Δ = (n1 – n2) / n1. Then equation (3) reduces to
. (6)
Note that α here is not the acceptance angle of the fiber. These equations are all valid for SI fiber as well when α → ∞.
Procedure
You will find the experimental setup shown below with a tungsten lamp focused onto the end of a fiber. The opposite end of the fiber is magnified and focused onto a detector covered with a small aperture (small with respect to the magnified fiber core image). An optical chopper converts the CW light source into a square-wave optical signal that can be easily detected using the lock-in amplifier*. Move the small aperture across the center of the image of the fiber core taking 10-20 data points across the image. The intensity of the light follows the radial variation in the index of refraction of the fiber core.
Turn on the chopper (switch on back). “Reference out” goes into “reference in” of lock-in. Check the phase of the signal to make sure it is in phase with the reference. Look at the 0.5 mm polymer fiber (SM) and the 100/140 GRIN fiber. Plot the signal vs. distance across the imaged core for both fibers. [You have to be careful here not to introduce diffraction effects with the lens. You might try just measuring the expanding beam from the end of the fiber without a lens to avoid these artifacts.] Try the 50/125 glass fiber and an SMF-28 fiber if time permits.
Answer the following questions in addition to your mode sketches and plots of n(r):
1. Use equations (3) and (4) and the definition of Δ to derive equation (6).
2. What is one advantage GRIN fibers have over SI fibers? (Check in your book)
3. What is one advantage SI fibers have over GRIN fibers? (Check in your book)
4. In words, describe what a “mode” in a fiber is.
5. In the index experiment, why didn’t we use a HeNe laser (without a coupling lens)?
If we had done so (instead of the W-halogen lamp), do you think we would have noticed (in the case of the GRIN fiber) a larger or smaller core radius? Explain. [I’m more interested in your thinking than in any certain answer here.]
6. What was your evidence for the GRIN fiber being GRIN and the plastic fiber being SI?
* Lock-in Amplifier: The lock-in amplifier (LIA) is a very useful tool for measuring small, regularly repetative signals. Small DC signals, such as from a CW laser signal, are chopped by a stablized frequency mechanical chopper (usually a rotating wheel with equal slots/blocks) to make them square wave signals. A reference signal from the chopper is fed into the LIA “reference in” port. The LIA is a narrow-band, phase-locked amplifier that amplifies only signals that are at the same frequency and “in-phase” with the reference signal. This eliminates all other noise signals. LIAs are able to detect nV levels in the presence of large random noise or other signals at other frequencies (for example, 60/120 Hz from lights, etc.).
T.K. Plant April 2011