PHGN-480 Fall-2011

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Course Information

Professor: Dr. Chip Durfee

Office: Meyer Hall 330

Meeting Times: T Th 11:00-12:15 AM

Location: Meyer Hall 357

Announcements

18 November 2011

Lab 7 is posted below.

14 November 2011

Do-over for midterm plots: I'm giving you extra time to do the plots for the midterm do-over. You can turn them in by the end of the day on thursday. Reminder: these are for the plots for problems 1g and 2c on the take-home midterm. You can make use of the solutions I handed out (come and get a copy if you don't have them), and any other resources except working together. In particular, you can come to me for advice on the programming aspect of things. The offer for extra credit as posed at the end of problem 1 still stands. The amount of extra credit will be related to how much you do (and how correct it is). Ask me for details.

9 November 2011

Next lab: The next lab will be to set up the HeNe resonators again, but this time to look at different cavity length, to look at the multimode output, and to get the cavity to run single transverse mode. It will be due in 2 weeks. I'll post the instructions today or tomorrow.

4 November 2011

Midterm results: Midterms are graded. A hard exam, some did well, others not so well. Come to see me to get yours back. As a way for you to make up some points, you should do the two problems that asked for plots: 1(g), energy build up for the Nd and Yb amplifiers, and 2(c), the plot of output power vs frequency. You may make use of the solutions I handed out (come get a copy if you don't have one) plus any resources you want except working together. Several of you are not skilled in using Mathematica to do loops and to use lists. Come to me with your questions, and I will help you. This is a relatively easy way to bring your grade up, so take advantage of it. No one in the class will get less than a C on the midterm if they do these plots. You can bring your grade up further if you do the extra credit model, where you take into account the gain saturation within the pulse. I will give extra credit according to how far you get with it.

Final project: Instead of a final exam, takehome or otherwise, you will be doing a research project. There are a number of forms this can take, but typically, it will involve finding an interesting journal article, and working through some calculations that explore the laser system described in the paper. If you happen to be doing a senior design or masters project related in some way to lasers, then it is best if you pick a project related to that. Please come to me with your ideas, and I can help point you to some papers to look at.

ABCD resonator notes: Notes on resonator stability posted below.

HW problem on astigmatism corrected beam expander: To reiterate what I discussed in class, for a curved mirror that is tilted, the angle that goes into the formula for the focal length is the the angle of incidence. If the beam is normally incident on the curved mirror, the center line of the beam will return directly on the incident path. If we then tilt the mirror by an angle theta, theta is now the angle of incidence. Note that in this case, the centerline of the beam will move by 2 theta, just as it does for a flat mirror.

3 November 2011

ABCD resonator analysis: I posted the link to the LaserCanvas program I showed you in class below in the course links area.

29 October 2011

Lab 6: Lab 6 is posted below. I hope you enjoy this one - I think it's pretty cool.

ABCD gaussian beam propagation code is posted below. You'll use this for your homework. Try opening and running the examples before coming to class tuesday.

28 October 2011

Lab 6: Lab 6 is ready to go, I'm going to finish writing it up and post it, but if anyone wants to work on it this afternoon, let me know. It will be due a week from this Tuesday in class.

27 October 2011

Homework 7: I'm pushing back the due date for HW7 to next Friday. Tuesday in class we'll work on the homework, so bring your computers if you have a laptop.

26 October 2011

Saturation fluence: just to reiterate on my comment from 22 Oct, the saturation fluence is just the laser photon energy divided by the stimulated emission cross-section (i.e. the gain cross-section). There is no factor of 2, since we'll assume that the lower level is depleted quickly.

Nd:YAG data: Table 9.4 also has some Nd:YAG information, but that is for a different transition that lases at 976nm. You want to use Table 9.3 for Nd:YAG and 9.4 for Yb:YAG.

My approach to grading: I know that it's possible for a mistake to propagate through to later parts of the test. As long as your approach is right, using what information (or assumptions) you have from earlier parts, you'll be fine and I'll give partial credit. If you are getting results that don't seem physical, but you can't figure out the mistake, say so, and that will help. I know this is a challenging exercise, but it is also very realistic since these are exactly the kind of steps you would have to take if you were going to design a laser or an amplifier yourself.

A couple of hints and tips for problem 1: The scenario is similar to how we design laser amplifiers. We start with a given amount of pump energy from the pump laser, and we want to absorb a fraction of that energy into the crystal. So we choose the crystal thickness to ensure that we absorb that energy. Given that absorbed energy, that sets a theoretical limit on how much could be extracted into the amplified beam, i.e. this is the amount of energy stored in the crystal. "Theoretical" because in practice, it is very hard to get all of that out - that's why we set a target of around 50% extraction. When you do your model where you calculate the amplification assuming small-signal gain throughout the whole buildup, that ignores the fact that you are actually removing energy from the crystal, thereby limiting the gain. But it does give a feel for how many passes will be required. This motivates your next model, in which you account for the energy that is removed from the crystal on each pass. Be sure that in your calculations that energy is conserved - the sum of the pulse energy and the stored energy should always be the same.

The motivation for working this through for two active media is to show you how different they can be in practice - this accounts for very different system architectures for different gain media.

Optional background reading on ABCD matrices for gaussian beams. As I mentioned in class, there is a section in Siegman's Laser book where he derives the formula for how a Gaussian beam is modified an optical system described by an ABCD matrix. Since I'm not supposed to post copyrighted pdf's here, you can either come by to get a hardcopy, or if you send me an email, I'll send you the PDF directly.

Next lab: Gaussian beam focusing and resonators. I'm working on setting this new lab up this afternoon, after which I'll write a page up for you. If anyone wants to work on it this afternoon, you can meet me down there.

25 October 2011

Problem 1f and 1g: In problem 1, the problem is structured to work you through the amplifier design step-by-step. So in parts "f" and "g", the system starts the build-up process with the small-signal gain that you have in part "e". That is G= 3 for Nd:YAG, while for Yb:YAG, G = some other value that you calculate for the same spot size and pump energy that you had for Nd:YAG.

24 October 2011 Not that you're ready yet to work on it, but HW7 is posted. The next lab will be ready by wednesday morning.

Due to popular demand, you can have till thursday in class to finish your midterms. I assume this will be what most people want. I've only gotten a few questions to clarify, so I'm assuming that you all understand what I'm asking for. But again, I'm open to clarifying the questions if I can. Please pass on the news, since not everyone may read this or their email.

Problem 1c:

"in terms of these parameters" Here I'm referring to the parameters listed in the previous paragraph. Of course, not all of them will figure into the expression for the small signal gain.

Lecture notes are all posted. You may find some of the sections useful. Also posted a few of the mathematica demos that I've used in class, though these probably won't be useful for the midterm.

23 October 2011

Comment: the exam is not meant to stump you over terminology, so feel free to ask questions. If I can't answer, I'll say so.

Problem 2: Normally, the quoted gain linewidth (e.g. Δν0 would be a full-width at half maximum (FWHM) number. So the Lorentzian line function should have an extra factor of two to correctly reflect this:

 \sigma ( \nu ) =  \frac{{\sigma _{21} }}{{1 + \left( {\frac{{2\left( {\nu  - \nu _0 } \right)}}{{\Delta \nu _0 }}} \right)^2 }}

Note that this form of the Lorentzian is normalized to be = 1 at the peak, rather than to make the integral over the lineshape = 1.

So in problem 2c, I'm looking for the new tuning range FWHM.

22 October 2011

Problem 1b: gain saturation fluence is just photon energy / gain cross section.

Problem 2a: in making your calculations, assume that this Nd:YAG laser is monolithic, that is, the end mirrors are coated right on the ends of the crystal.

21 October 2011

The take home midterm is now posted. It is important that you read through it soon and make sure you understand what I'm asking for. If there are any clarifications, I will post them here. the midterm is due in class next tuesday.

12:30pm. 1st comment: you should do part 1e before 1d.

19 October 2011

Welcome back from break! I will have your next lab ready after I finish getting your take-home midterm ready. The midterm will be posted no later than friday morning, and I'll try to get it up sooner. It will be due in class on Tuesday.

10 October 2011

No class on Thursday, 13 Oct. This is to make up for the lab time that you've been doing during the semester. I'll be available for anyone who wants to work in the lab or has questions on their homework, which is due on Friday. Also, note that the following tuesday is fall break. I'll be out of town that day at a conference.

7 October 2011

HW6 is posted.

HW5: a typo in problem 1. The "problem 2" referred to is problem 2 of homework 2. That expression connects the spontaneous lifetime to the cross-sections.

5 October 2011

Lab 5 is posted. This should be a short lab. To help make up for some of the time you spend in lab, we will finish class early most days from now on. I'll aim to finish around 12noon, but will stay around in class to answer questions. Let's see how this works and you can give me feedback.

30 September 2011

Lab 4 is posted.

28 September 2011

HW 5 is posted. There are just two problems, but each one is involved, so I advise getting going on it soon enough that you can ask questions. For the second problem, I tried to find a real laser system that we could analyze with relatively simple equations. We'll return to this system for later homeworks.

26 September 2011

No HW this week - HW5 will be due 7 Oct. I should have it posted later today.

16 September 2011

HW4 is posted

HW3:

problem 1

For the gaussian beam, the intensity follows the gaussian function I[r] = I0 exp[ - 2 r^2/ w^2 ], and is in W/m^2.

The parameter w is the 1/e2 radius.

Integrating this over a surface gives the power. Of course you can integrate in polar or x, y coordinates. Total power is when you integrate over + and - infinity on both directions in x,y. As we discussed in class a while ago, power past the knife edge or iris means you integrate over the open surface.

problem 2

Remember that the pump rate Rp has units /m3/s, which is, for example the same units as N2/tau21.

9 September 2011: HW 3 is posted. Feel free to use Mathematica to help you on this set.

Problem 4: shift theorem. I mistakenly thought this was something you'd have seen in your math physics class. If you know the Fourier transform F(w) of a function f(t), then the fourier transform of the combination f(t) exp[-i w0 t ] is simply F( w - w0 ). You can see this by putting f(t) exp[-i w0 t ] into the integral, then combining w - w0 = w'.

Extension for the lab: not many have had a chance to do the lab yet, so you can have another week. Please have the lab done by a week from next monday, and turn in your write up in class the following tuesday. Try not to save it for the last minute though.

8 September 2011: Lecture notes posted and up to date.

Revised lab handout posted - you can finish the lab by end of day tuesday.

7 September 2011: HW2: There is information that we'll cover in class thursday that will help with your homework, so you can turn your homework in on Friday (by 5pm) instead of tomorrow in class.

Some specific responses to some questions:

problem 2: This is simply a matter of finding the right expressions in the book and combining them.

problem 3: First part of this problem uses the result of problem 2. For the second part, see the section on non-radiative decay channels, specifically that if there are two pathways for going from an upper to lower level, then the total rate is the sum of the individual rates.

Lab 2 is posted. finish measurements Monday, turn in brief write-up in class Tuesday.

2 September 2011: Homework 2 is posted, due thursday 8 September, end of day (5pm)

1 September 2011: Scheduling lab time: We have two sets of optical mounts for people to use, and to date, only five of you have been through the lab. While there is still plenty of time, it would be helpful to schedule your time in the lab, to be sure that we don't have any conflicts for parts or table space. I sent each of you an invitation to a Google calendar for the course. Put the time block your team want to work into the schedule. If two groups are working at the same time, they can either split space on the thick optical table that is directly across from the advanced lab door, or use one of the two optical tables in the other room.

Reading: for today, you should read up through section 2.3 in Svelto.

New links added below for laser building resources.

Remember: homework is due tomorrow by 5pm in my mailbox.

26 August 2011: Homework 1 and tentative office hours are posted.

23 August 2011: Welcome to Laser Physics!

Office hours

Times - M1-3, W1:30-4:30

TA: Rezwan Rahman (rrahman@mines.edu)

TA hours: M3-5, F1:15-3:15

Look for us either in our offices or in the advanced lab on the second floor.

Course Material

Syllabus and Reading List

Pdf.png These downloads require Adobe Acrobat Reader
Syllabus

Homework Assignments and Midterm:

Grading policy:

We are aiming for a 1 week turn around on grading homework. At the time we give them back to you, solutions will be available in printed form in a binder that I'll keep, but you can make a copy. Turn in howework on time for full credit. If you turn it in within a week late, we take off 20%. Once the solutions are available and others have theirs graded, then it's too late. If there are extenuating circumtances, please let me know.

Pdf.png These downloads require Adobe Acrobat Reader
Homework 1: due 1 Sept
Homework 2: due 8 Sept
Homework 3: due 16 Sept, by 5pm
Homework 4: due 23 Sept, by 5pm
Homework 5: due 7 Oct, by 5pm
Homework 6: due 14 Oct, by 5pm
Take home midterm: due 25 Oct, in class
Homework 7: due Friday 4 Nov, by 5pm

Lab exercises:

Pdf.png These downloads require Adobe Acrobat Reader
Lab 1: alignment of beams through irises, beam expander setup. Due 5 Sept, end of day
Lab 2: measuring beam sizes. Finish lab by monday 19Sept, turn in sheet in class the following tuesday. Procedure updated thursday.
Lab 3: alignment of HeNe tube, measure gain. Turn in write-up end of day tuesday 27 Sept
Lab 4: getting the HeNe to lase. Turn in write-up end of day tuesday 4 Oct
Lab 5: imaging Turn in write-up end of day tuesday 11 Oct
Lab 6: Resonator and mode-matching. Turn in write-up in class, tuesday 8 Nov
Lab 7: HeNe laser optimization. Turn in write-up in class, tuesday 28 Nov

Final project

Pdf.png These downloads require Adobe Acrobat Reader

Take-home midterm

Pdf.png These downloads require Adobe Acrobat Reader

Lecture Notes

While these notes are primarily to help me give my lectures, I'm posting them to help you fill in things you may have missed in class or to show the details of calculations we don't have time to work through. If you have any constructive input on how to make these more useful to read, let me know.

Pdf.png These downloads require Adobe Acrobat Reader
lecture1: basic laser intro
lecture2: emwaves and simple resonator
lecture3: energy density and BB radiation
lecture4: Einstein A, B quantum transitions
lectures 5, 6: cross-sections and line-broadening
topic 7: non-radiative transitions, degenerate states
topic 8: atomic structure and spectroscopic notation
topic 9: selection rules
topic 10: spectroscopy of HeNe and Nd lasers
topic 11: gain saturation
topic 12: amplifier gain
topic 13: oscillator rate equations
topic 14: oscillator operation - Pthresh, critical pump power, slope_efficiency
topic 15: ray tracing and geometric optics
topic 15a: extra notes on geometric optics
topic 16: ABCD matrices for raytracing, Fabry-Perot interferometer
topic 17: diffractive beam propagation
topic 18: gaussian beams
topic 19: gaussian ABCD resonators


Mathematica Demos

These aren't actually pdf's. Do a "save link as" to save these to your computer, then open with Mathematica.

Pdf.png These downloads require Adobe Acrobat Reader
Spectral_shapes.nb : shows BB radiation curves vs frequency and wavelength, also compare Gaussian and Lorentzian shapes
OC_optimization.nb : Optimizing output coupling in a CW oscillator
ABCD_raytracing.nb : ABCD matrices for raytracing, including functions for plotting rays and setting up a sequence
Etalon.nb : interactive plots relating to the Fabry-Perot etalon
ABCD_cavity_analysis.nb : ABCD matrices for raytracing, Gaussian beam propagation and resonators.

Course Links

Students: when you post links, mark your name and the date of the post

Online Demo's

JavaOptics: a nice collection of optics-related demonstrations

Fabry-Perot demonstration

diffraction by slits

propagating waves, including waveguides (demo in class)

ABCD Gaussian beam tracing (for windows OS)

LaserCanvas: a free ABCD gaussian beam program for resonator design

Lecture notes:

Lectures from GaTech (Rick Trebino): a very useful collection of graphics and worked examples in optics

Laser building resources:

Sam's Laser FAQ: A great resource on hands-on info for building and troubleshooting laser systems.

Homebuilt Lasers

General cool stuff:

A new laser made from biological cells...

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