Single Mode Optical Fiber
Sarah Campbell
SUNY Stony Brook
Optics Rotation Project 2, Fall 2002
Advisor: Dr. John Noe
Project Goal
In this project, I hope to measure the far field radiation of a single mode step
index optical fiber to a high degree of precision, with an angular precision of half
a degree and intensity precision of 10^-12 Watts. These measurements are important
because fiber optics are used in a variety of communication applications and these
additional modes could cause anomalies in the fiber's output, especially when the
fibers are bundled together.
Far-Field Radiation
The goal of this project is to study the far field radiation of a single mode step
index optical fiber. Studying the far field radiation means studying the light
intensity profile of the beam from the fiber far away from the fiber, a distance of
around 10 inches. This profile is expected to have a gaussian distribution about the
center of the beam. However, additional modes or fringes are expected. These fringes
are rings of light around the bright spot of the beam. These modes are the result of
interference because the end of the fiber optic acts as an aperature. Below is a
picture of the fiber optic output. In this picture the first fringe, a
red ring is visible. The center of the beam is blocked inorder to prevent the center
of the beam from washing out the first fringe. This picture was taken by John Noe.
The far field radiation can be shown graphically by looking at a intensity versus angular
position graph. A very nice graph of the far-field radiation is shown as an example
in the image below.
Experimental Set Up
Two lasers, a metrologia Helium-Neon laser (shown above) and a Helium-Neon from
Meredith Instruments, both at 633nm, were directed into the fiber during the course
of this experiment. The alignment of the laser light into the fiber is aided by 2
mirrors and the PAF fiber port. The light travels through the fiber (yellow) from
the right side of the picture to the output end of the cable on the left side of the
picture. A dectector (silver with black cord) measures the intensity of the light
once is has past through a slit (not shown), 1.25 inches in front of the dectector.
The dectector is on a black metal arm of length, 10.625 inches. This arm pivots at
the end of the fiber allowing the dectector to cover an angular range of around 25
degrees on each side. A white grid is taped to the table under the arm, to allow
angular measurements. The grid has 20 boxes per inch and the slit with a width of
1mm allow an angular precision of less than half a degree.
The detector produces an current proportional to the intensity of light. This current
passes through a resistor and the voltage is read off of a multimeter. The voltage
measurements consist of the average voltage reading over a minute of measurement.
Fiber Optics
A fiber optics is a transmission channel that carries a beam of light. A fiber optic
consists of a glass, plastic or silica core surrounded by cladding. Cladding is an outer
covering with a lower index of refraction than the core. Fiber optics transmit light via
total internal reflection. The light inside of the fiber optic completely reflects off of
the cladding and back into the core. The light then travels down the fiber by bouncing off
thecladding until it reaches the end of the fiber. The benefit of an optical fiber is that
it can bend and travel fairly long distances without losing energy or distorting the light.
A diagram of total internal reflection in a fiber optic is shown in the picture below.
The physics of total internal reflection will be presented shortly, but it relies on a
boundary, such as the core-cladding boundary, where the initial material, the core, has a
higher index of refraction than the second material, the cladding. Without this boundary
total internal reflection would not occur. A nice animation of the difference between
total internal reflection and regular reflection and transmission can be seen at the Schott
website. Just click on "click here for flash animation" after clicking the link below.
http://www.us.shott.com/fiberoptics/english/allaboutfiberoptics.html
For this experiment, I used a step index single mode optical fiber. Step index means that
the optical fiber has a constant index of refraction in the inner core and a different
constant index of refraction in the outer core. This is in contrast to other types of
optical fibers that have gradations in the index of refraction of the core.
A single mode optical fiber means that only one mode of light can propagate in the optical
fiber. In contrast, a mulitmode optical fiber allows several modes to propagate.
A single mode fiber is able to prevent other modes from propagating by operating above
the cutoff frequency, thus cutting off all other modes. Since the fundamental mode of the
fiber can not be cut off, the single mode fiber only allows the fundamental mode.
explain modes
Click here for a brief
history of fiber optics provided by Jeff Hecht
Total Internal Reflection
Fiber optics work by using a electromagnetic phenomena called total internal reflection.
Normal reflection and transmission happens when light or an electromagnetic wave hits
the boundary of two media, with indices of refraction n1 and n2. Total internal
reflection is characterized by the lack of a transmitted wave, meaning that the incident
wave was completely reflected, thus total reflection. The word internal signifies that
the index of refraction of the initial medium is larger than that of the second medium.
Total internal reflection occurs when the incident angle of the wave, theta1, is
greater than or equal to the critical angle, thetaC, where the critical angle is defined
as
It presents the profile of the far-field radiation of
the optical fiber.
The total internal reflection is due to Snell's law.
If theta1 equals the critical angle then sin(theta2) = 1, this means that theta2 = 90
degrees. This represents the transmitted wave traveling parallel to the surface of the
boundary. Since energy can not flow on the boundary, no energy can propagate from this
wave. Therefore, all of the energy must propagate in the reflected wave; this is
total internal reflection.
If theta1 is greater than the critical angle, then there exists an A such that
sin(theta1) = A*(n2/n1), where A > 1. Using Snell's law, this implies that
sin(theta2) = A, and therefore sin(theta2) must be greater than 1. In order to obtain
sin(theta2) greater than 1, theta2 must be a complex angle. In electromagnetic theory,
it is given that an electromagnetic wave has the form
For the transmitted wave, the propagation factor, exp(ik*x), can now be calculated using
the information from Snell's law.
k*x = k(x*sin(theta2) + y*cos(theta2))
where x is the horizontal direction
and y is the vertical direction
k*x = k(x*(n1/n2)*sin(theta1) + iy*sqrt((sin(theta1)*(n1/n2))^2 - 1)
since sin(theta2) = sin(theta1)*(n1/n2)
and cos(theta2) = 1 - (sin(theta2))^2
exp(ik*x) = exp(ikx*(n1/n2)*sin(theta1) * exp(-k*sqrt((sin(theta1)*(n1/n2))^2 - 1))
So propagation in the vertical, or y, direction is exponentially damped below the surface.
This means that no energy can flow beyond a few wavelengths on the other side of the boundary.
This is total internal reflection
Aligning the Fiber Optic
I found aligning the laser into the fiber optic to be an exceedingly frustrating and
time consuming process. This is because the laser beam must be directed into the PAF fiber
port, which is shown below. The PAF fiber port not only holds the fiber optic (yellow)
in place, but it also contains a lens that focuses the laser light. This lens allows
the whole of the laser beam's cross-section, which can be larger than the fiber optic,
to be directed into the fiber. Alignment is very difficult because the laser beam and
the fiber optic need to be directed and positioned appropriately so that an optimal
amount of laser light gets into the fiber optic.
PAF Fiber Port
I used a method to align the laser beam into the fiber optic that was shown to me by Dr.
John Noe. This method involved using the detector to measure the intensity of light that
travels through the fiber optic as I adjust the alignment. Occassionally, the detector
would be unable to register any light and I would have to look into the fiber optic
directly in order to see any fluctuations in the transmitted light intensity.
Alignment Method
- With the fiber removed, line the laser beam through the coupler. This alignment is done
by moving the mirrors to get the beam through the coupler without it bouncing off of the
coupler's sides. The beam must also be parrallel to the table top. To verify this, I marked
the position of the beam on a card held perpendicular to the table and moved the card back and
forth, making sure that the laser beam always hit the card in the same spot.
- Slide the fiber into the coupler, but do not screw the fiber in all the way. See if any
light is transmitted. By adjusting the two mirrors, try and maximize the amount of light
output.
- Slowly move the fiber inwards and readjust the mirrors to find another maximum.
- Lock the fiber's position in the coupler.
The reason that I started with the fiber farther back in the coupler is because the beam
covers a larger area farther away from the focus. So it's benefitial to start farther back
and work your way further up by finding the maxima. Hal Metcalf likened the iteration of
adjusting the mirrors and moving the fiber forward are to moving up a 'hill' in a
four-dimensional phase space. I found this to be the frustrating aspect of this project,
like Sisyphus I wondered whether I would ever get the laser beam up the hill.
Procedure for Taking Data
As mentioned in the Experimental Set-Up section, the data is obtained by recording
the average, minimum and maximum voltage values from the multimeter over a minute
timespan. Because these voltage values correspond to light intensity, all
measurements are performed in the dark. Between each measurement, the lights are
turned on, in order to record the values and reposition the detector at the next
angle for measurement.
Gaussian Approximation/Theory
The center of the profile of a fiber optic should be approximated by a Gaussian
curve, I(x) = I(0)*exp[-a*x^2], where x is the angular position of the detector,
I(0) is the central maximum power of the beam and a = 2/(sigma^2) where sigma is
the standard deviation of the curve.
M.Young provides a similar equation, I(theta) = I(0)*exp[-2*(sin(theta)/sin(thetaO))^2],
where I(0) is the same and thetaO is the angular radius. ThetaO is then shown to equal
lambda/(pi*omegaP) where lambda is the wavelength and omegaP is half of the mode-field
diameter. The correct omegaP for a fiber is chosen to fit a given far-field profile.
For this project, I have used the first theory in my data analysis.
Data for Metrologia Helium-Neon Laser
Initially a Metrologia Heluim-Neon Laser was used as a source for the fiber optic.
This laser has a wavelength of 633 nm and a intensity of 988 microWatts. We were
able to obtain an alignment producing 564 microWatts at the output of the fiber.
This corresponds to 57.14 percentage of the laser light traveling through the fiber
optic. Two different resistors were used to take this data a 2.028 MOhm resistor and
a 1.994 MOhm resistor.
Since the multimeter measures voltages, a resistor is used between the detector and
the multimeter. Using the V=IR law, I obtained a current (mAmp) value. Then, I used
the responsivity of the detector at the 633nm wavelength, 0.425 Amps/Watts, to find the
power of the light from the detector-multimeter measurements.
Far-Field Radiation Profile
This is a graph of the power of light from the fiber optic(nW) versus the off center
angle of the detector (degrees). Because the fiber optic was not perfectly directed to
the center of the detector arm, the data curve was shifted to the right so that the
maximum power would occur on the y axis. The theoretical curve was generated using the
Solver application in Excel, and follows the equation
y = 1952799.6 * exp[-0.0817457 * x^2]. This implies that the standard deviation,
sigma, of the Gaussian curve is 2.47316230583728.
This graph presents the profile of the far-field radiation of the optical fiber. The first
ring of the diffraction pattern is almost visible. The intensity range is 10^4 but the
intensity range is only 10^-7 Watts, not a precise as I was hoping to find. Because of
this failure, I continued my experiment using the Meredith Helium-Neon laser.
Data for the Meredith Helium-Neon
We then switched to the Meredith Helium-Neon laser, a more powerful laser. We did
this hoping that the Meredith would allow us to have a higher intensity of light
through the fiber optic so that we could have more precise measurements.
This laser has a wavelength of 633nm and has an intensity of 19 mWatts.
Unfortunately, after the first mirror only 15mWatts of light still exists. I am
unsure exactly the cause of this drop but I think it is that the mirror is scratched
and dirty. Because the mirrors that we use are gold, they can not be cleaned. The
space between the second mirror and the PAF fiber port is too tight to allow for a
measurement of the light after the second mirror. We were able to obtain an alignment
of 6 mWatts. This corresponds to 39.99 precentage of the laser light after the
first mirror traveling through the fiber optic.
Three different resistors were used to take these measurements, a 2.033 MOhm, a
1.022 MOhm, and a 9.87 kOhm. In this instance, different resistors were used in order
to measure the current provided by the detector to a the highest available precision
while maintaining the voltage in a measureable range. Using these different resistor
values, the same form of calculations as with the Metrologia Helium-Neon Laser were
done inorder to get the power of the light emitted from the fiber optic from the
measured voltage values.
Far-Field Radiation Profile
This is another graph of the power of light from the fiber optic (nW) versus the off
center angle of the detector (degrees). Again the fiber optic was not perfectly
directed to the center of the detector arm, and the data needed to be shifted to the
left in order to have the maximum power intersect the y axis; this also explains why
there is more data in the negative angles. The theoretical curve was generated using
the Solver application in Excel, and has the equation
y = 24964.424839048 * exp[-.074121* x^2]. This implies that the standard deviation of
the Gausssian curve, sigma, is 2.59725054884501.
This graph is another view of the profile of the far-field radiation of the optical fiber.
This time the first ring in the diffraction pattern is definately visible and the second
ring might be the cause of the small bump near -30 degrees. The intensity range is 10^6 and it has an intensity precision of 10^-10.
Conclusion
In conclusion, I studied the far field radiation of a single mode step index
optical fiber. I was able to measure this radiation with less than half a degree of
angular precision and an intensity precision of 10^-10 Watts using the Meredith laser.
The Meterologia results were not as good; a precision of 10^-7 Watts was obtained. The
first of the additional modes are visible in both the Meterologia and the Meredith
graphs, although the Meredith results are much clearer. The data from both lasers
were used to calculated Gaussian approximations of the peak of the far field
radiation.
I attempted to use an amplifier to improve the precision of the Meterologia
measurements. However, I ran into complications, specifically, when using the
amplifier for small voltages a negative number would result. In order to study this
phenomena, I used a voltage box and measured the output of the amplifier at a variety
of values. But the negative outputs did not occur in this test despite the fact that
they were produced repeatedly while taking measurements both before and after the
tests with the volt box.
This project introduced me to the process of aligning a laser into a fiber optic. I
must admit that I am not very proficient at this task. However, I have been able to
improve my alignment ability and I am still working on refining this skill.
Special Thanks
John Noe, Luis Orozco, Harold Metcalf, Xiyue Miao, Matt Eardley
Main References
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