Dispersion Compensation in Mode-locked Thulium/Holmium Doped Fiber Lasers

Kelley Daenzer

Supervisor:  Brian R. Washburn

AFG-081203-004.jpgKansas State University Physics Department  REU Program


This work is partially funded by the National Science Foundation (NSF) and the Air Force Office of Scientific Research (AFOSR) through NSF grant number PHYS-1461251.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF or AFOSR.



Project Overview

We are using an all-fiber laser with thulium/holmium doped gain fiber. When mode-locked, the light inside this laser travels in pulses. Short pulses of light are useful for measuring things that happen on short timescales – chemical reactions, biological functions, etc. Our goal is to get these pulses as short in duration as possible, so that they can be used to measure over shorter and shorter timescales. However, due to dispersive effects caused by the fiber, the light experiences group velocity dispersion and third order dispersion, which distorts and lengthens the pulses. Both types of dispersion can be managed by using several varieties of fiber whose dispersive components cancel each other. We will try a type of ultra-high numerical aperture fiber called UHNA-7 to compensate for both.


Group Velocity and Third Order Dispersion

Group velocity dispersion is a change in the velocity of spectral components of a wave pulse with respect to the carrier frequency. Specifically, different spectral components of the pulse reach a given point at different times, causing the pulse to distort in what is called “chirping”. A simplified example of chirping can be seen below:

chirp good-

Because of this separation of spectral components, the pulse becomes longer in duration than it was initially. The goal is to create shorter and shorter pulses of light, which means we need to find a way to compensate for this dispersion.

The parameter which determines group velocity dispersion is β2, which is related to the second derivative of the Sellmeier equation for index of refraction. The graph of β2 for bulk fused silica appears as

betta beta 2

although the graph shifts to the right inside optical fiber. As is seen here, β2 can be either positive or negative.

Third-order dispersion is the rate of change of group velocity dispersion with respect to frequency; i.e. β3 is the derivative of β2.


Net Cavity Dispersion

The thulium/holmium doped fiber that we are using in our laser cavity has a positive β2, while the standard single-mode fiber that makes up the rest of the cavity has a negative β2. Net dispersion in the laser cavity is found by adding the products of the β2 value of a fiber and that fiber’s length. The net cavity dispersion for our current setup, with only these two types of fiber, is

net cavity dispersion

Finding a third fiber with a positive β2 value that will compensate for this dispersion is difficult. At 2µm light, where our laser operates, most β2 values are highly negative. Some fibers with an ultra-high numerical aperture, however, have a positive β2. We have chosen a fiber of this type, called UHNA-7 and having a β2 value of 0.13ps2/m, to add to our laser.

When group velocity dispersion is near zero, then third-order dispersion dominates, so we need to compensate for that as well. Luckily, UHNA-7 fiber has a β3 value which is also opposite to that of SMF, so it can compensate both group velocity dispersion and third-order dispersion simultaneously. The equation for net third-order dispersion, with UHNA-7 fiber included, is:

net cav tod eqn

laser diagrams



Calculating Fiber Lengths

The length of existing Tm/Ho fiber in the laser is known: it was measured at the same time it was inserted into the laser, and that length has not been altered. The length of SMF, however, has been altered as time goes on to aid in mode-locking. The existing length of SMF fiber can be found two ways. The first is by direct measurement with a tape measure. The second is by measuring the repetition rate of the laser cavity – that is, how many times the laser pulse travels around the laser cavity per second. The length can be found from this value by solving for L in the relationship

rep rate eqn

where 1/T is the repetition rate. The length of SMF fiber can be found by subtracting the length of Tm/Ho fiber from the length given by the above equation.

Using the formula for net cavity dispersion, we can solve for the length of UHNA-7 fiber needed to compensate the dispersion caused by the other two:

uhna7 length eqn

We have selected 0.03ps2 as our desired net dispersion value – this is the value at which we have taken successful data in the past. Then, LUHNA7=3.05m. We can use even less of this fiber if we alter the amount of single-mode fiber in the cavity.


Spectral Data

Once the laser is mode-locked, we can take measurements to find out what wavelength(s) it is lasing at. We were able to successfully mode-lock the laser with only Tm/Ho and SMF fibers in the cavity. Since the gain fiber is doped with both thulium and holmium atoms, it can lase at 2 wavelengths, as seen by the two distinct spectra below:


The two wavelengths are found by mode-locking the laser in different polarization states.

The spectral width (FWHM) is approximately 10nm. If the UHNA-7 fiber successfully compensates for dispersion, that should get wider by about a factor of three.


We added 2.889m of UHNA-7 fiber to the laser and successfully mode-locked it – something that has not been done before with this type of compensation fiber.

To check our numbers, we did a length comparison. Using the repetition rate of the cavity (26.56MHz), we found that the total fiber length in the laser was 7.85m, which corresponds to the measured length of 7.76m.

We took some spectral measurements:




The spectrum is wider, which is what we predicted, but it is an odd shape. We are still trying to understand why the spectrum looks the way it does.


Next Steps

Our next step will be to take an interferometric autocorrelation trace in order to find the temporal pulse duration. We will also cut back the amount of UHNA-7 fiber in the laser cavity to see how that affects the pulse. Both of these tasks will be done in order to find out whether the UHNA-7 is adequately compensating for group velocity dispersion and third-order dispersion.



I would like to thank Drs. Kristan Corwin and Bret Flanders, Ms. Kim Coy, and Kansas State University for preparing and hosting the physics REU program during the summer of 2016.



[1] R. Kadel and B. R. Washburn, “All-fiber passively mode-locked thulium/holmium laser with two center wavelengths,” Applied Optics, vol. 51, no. 27, pp. 6465-6470, Sept. 2012.

[2] R. Kadel and B. R. Washburn, “Stretched-pulse and solitonic operation of an all-fiber thulium/holmium-doped fiber laser,” Applied Optics, vol. 51, no. 4, pp. 746-750, Feb. 2015.




About Me

I am working towards a physics degree at University of Colorado, Colorado Springs. At the conclusion of this program, I will have three semesters left, after which I intend to pursue a graduate degree.

Physics has always made the most sense to me out of any field of science, and the more I learn, the more I am convinced that this is the closest thing we have to magic. There is so much mystery in the universe, and it’s exciting! I first became interested in physics because of my high school physics teacher – he was excellent at finding new ways to explain concepts, and tried to help everyone understand in their own way, even if he had to find ten different ways to explain it before it clicked. I believe that anyone can understand physics at least on a basic level, if they have it explained to them in a way they can wrap their head around. I would love to teach undergraduate physics for this reason; so many people are so intimidated by physics and I want to help make it more accessible to people with different learning styles.

Outside of physics, I love reading, playing and listening to music, writing poetry, knitting, going to church, and practicing parkour.




You can download my poster here.

You can download my final presentation here.



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