Category Archives: Physics

Feathers in my hat, and new beginnings

The 2017 spring semester was an eventful one.
Courses: MA511 😦 and ECE65900 🙂
I began with the plan that I’d finish a math course and a nanoelectronics course by Supriya Datta. The math course was a requirement, but the nanoelectronics course was something I really had to do. I had heard stories about what a wonderful teacher Professor Dutta is. For those who do not know it, Supriyo Dutta is the Father of Spintronics – the person who laid down the theoretical foundation of spin devices. I took the course and was hooked from the beginning to the end. Even though we did not have a solid background in quantum mechanics, Prof. Dutta navigated us through the treacherous currents of quantum mechanics, density functional theories, and vector algebra, and taught us the intricacies of spin transport. The quizzes were more like a formality, easy to solve if you had practiced the past papers. He designed the course to give students the necessary intuition to solve electron transport problems on their own.
I highly recommend this course to students with interest in Nanoelectronics.
The MA511 course, unfortunately, was very disappointing. The lecturer, instead of showing us the applications of linear algebra in real problems, just went on copying math notes from a notebook on to the screen. We completed the first few homeworks on time, but eventually lost interest and dropped the course.
Won the SVC Foundation Scholarship
Our group specializes in discovering and investigating the plasmonic properties of new materials – transition metal nitrides and transparent conducting oxides being a few of them. To develop films with excellent optical properties we possess our very own sputtering system. As a lot of my seniors from our group recently graduated, my colleague Deesha and I got the duty of taking care of the system. As titanium nitride is always in high demand from a lot of our collaborators, the system is always hot in demand and needs to be well maintained at all times. Being the superuser is a tough job. We have to provide samples-on-demand to our fellow labmates and our collaborators, ensure the consistency of the sputtered films, make sure that the machine is operational, and develop and optimize recipes for new materials. It’s a demanding job, but also rewarding. For instance, my close association with the sputtering system landed me the SVC-foundation scholarship, that partially covers books and tuition for a year, and pays for conference travel to any conference related to vacuum technology.
Completed my quota of tours for the Discovery Park Ambassador Program.
I had signed up for the discovery park ambassador program earlier this year. As part of the program, the Ambassadors give tours to visiting faculty and members of the public of the facilities we have here in Discovery Park. As a Birck ambassador, I gave tours of the Birck Nanotechnology Center, which houses the Scifres Nanofabrication Center. It was a really enriching experience. My audience varied from fifth-graders to full professors; so even though I was covering the same material, I had to tune down or expand my descriptions of the cleanrooms and the facilities to suit the knowledge of the audience. And the visitors never ceased to surprise me. For instance, during one of the tours, I was trying to figure out the best way to explain plasmonic tweezers to a work at home mom. The best I could come up with was, “So… when you focus light into a very narrow region, the spot begins to suck in smalls particles and hold them in position.” I didn’t get to the part where plasmonic antennae push the trapping dimensions to the sub-wavelength level. To my surprise, she responded, “Yes, so the dipole force due to the field gradient is what holds it in place. Now the plasmonic antennae enable a high field confinement, and you can trap them in a smaller space, yes?” It turned out that her husband did his PhD in optical trapping.
The following pictures are of a demo of LCDs I was giving to elementary school kids.
Nanodays 2017
Nanodays is a big annual event where all the research facilities open their doors to the public. It’s a three-day long event that features talks by men and women in science, demonstrations of science projects, and x. Representing OSA and SPIE, Deesha, Oksana, Shaimaa, and I manned a table with an assortment
of toys designed to teach people about optical phenomena. The audience this time varied from two to sixty-year-olds. I discovered that I really like explaining elementary science to students. The highlight of the day was when a cute little three year old stole a slinkie from the demonstration set from right under my friend Deesha’s nose.
Became president of the SPIE elections.
Last, but not least, both Deesha and I were nominated for executive committee positions for the OSA and the SPIE respectively, and became the presidents of the respective student chapters.
We look forward to a year full of exciting and enriching events related to optical science.
To get more information about the events and about how to join the groups, comment here, or join the following group.

Paper Review: The third-order nonlinear optical susceptibility of gold – Boyd et. al.


When I started this blog, I decided that I’d regularly post reviews of interesting papers and articles on a regular basis. Then several things (projects, sub-projects, courses, and qualifying exams to name a few) happened, and this issue had to be put on hold. Now that I have a little time, I’ll attempt to give this a shot.

The first paper I’ll review is on nonlinear optics.

I decided to be thorough and wanted to get a permission from the journal to use the figures and tables on my website, for which, I was asked for a sum of $149 dollars. Hence, the review will be devoid of any figures or tables. This presents a challenge, now, because I’ll have to explain the physics without resorting to graphs, which will be interesting.

So, without further ado, here it is.

The third-order nonlinear optical susceptibility of gold

Authors: Robert W. Boyd, Zhimin Shi, Israel De Leon


This is a critique of the paper “The third-order nonlinear optical susceptibility of gold”, by Boyd et. al., published in Optics Communications in 2014. This paper goes over several experimental papers dealing with the nonlinear optics of bulk gold films, points out how largely the measured χ(3) vary with the frequency of the laser used and the pulse duration, and provides a feasible physical explanation for the variance, which has been overlooked in the previous papers. I chose this paper because it is very closely related to part of my Ph.D. work, which involves the characterization of nonlinear optical properties of new plasmonic materials.

Summary of the Paper

The third order nonlinearities of gold can arise mainly from three mechanisms:

  1. The contribution of free electrons

Free electrons do not have a strong contribution to the nonlinear response of bulk gold in the electric dipole approximation. Since there is no restoring force, there can be no nonlinearities in the restoring force. Also, the ponderomotive nonlinearity of free electrons also plays a negligible role in the case of gold because of strong interband transition. When electrons are confined in a small region, e.g. in a nanosphere, they display a nonlinear response because of quantum size effects. But this effect diminishes as the sample gets larger in size.

  1. Interband transitions

This is the dominant effect in bulk gold and arises from the transitions from the 5d valence band to the 6sp band. This provides for the lowest order contribution to the saturation of the absorption associated with this transition.


where A is an angular factor, T1 and T2 are, respectively, the energy lifetime and the dephasing time for the two-level system describing the interband transition, J(ω) is the joint density of states, and P is a constant associated with the momentum operator between the two states. This is the predominant effect that is used to explain the nonlinear coefficients of bulk gold.

2. The hot-electron contribution

This is the contribution to non-linearity that arises from the excitation of the 5d electrons to the 6sp conduction band through laser excitation. This causes the electrons in the conduction band to heat up. This heating causes the population of energies above the Fermi level to increase and that below the Fermi level to decrease, resulting in a change in the dielectric function of gold, in a largely frequency dependent manner. This is also known as the Fermi Smearing contribution. Typical values of this effect range around 10-16 m2/V2.  This has a slower response time because it takes about 500 fs for the electrons to heat up and several picoseconds to relax, after which the effect disappears. This is also highly frequency-dependent (for wavelengths ranging from 300 to 800nm).

Boyd argues that the third effect, namely the effect of hot-carriers excited through laser absorption, is a dominant effect in the cases where the nonlinearity observed was larger than typical values of the χ(3) (10-19 m2/V2).

Ranging from the first reported study of the third order nonlinear responses of gold [1], the authors go through several experiments taking note of the laser power and the pulse duration used in the experiments, and the observed χ(3). For papers which did not have the χ(3) calculated, the authors assumed the real part of the refractive index to be zero and used the formula starting from basic equations of permittivity and refractive index.

It was seen that for experiments where long pulses (tens of picoseconds or higher) of lasers were used, the values of χ(3) obtained were in the order of 10-16 m2/V2. This was seen in the papers of Smith et. al., Xenogiannopolou et. al., and Wang et. al. [2,3,6]. Whereas, when short-duration (lower than 1 ps) pulses were used, the values of χ(3) obtained were in the order of 10-19 m2/V2, several orders of magnitudes smaller. These were seen in the papers of Bloembergen et. al., the van Driel group, and Renger et. al. [1,4,5,7]. 

For the papers reporting very large nonlinear indices, the effect of hot-electrons has not been used to explain the phenomenon. Boyd and his co-authors propose that hot-carrier induced refractive index change may be causing the large value of χ(3). The hot carrier induced χ(3) is also highly frequency dependent, which is also observed in the experiments conducted by the van Driel group, where with a change in the laser wavelength, the χ(3) changed by a factor of 100.


This paper covered the origin of the nonlinear optical properties of bulk gold quite comprehensively and provided an explanation for the large discrepancies of the nonlinearities that are seen across publications by different groups. By looking at the results obtained by a large number of groups, they have also noticed a trend in the dependence of the nonlinearity of a gold film with the energy and the pulse duration of the laser used to characterize it. Their explanation for the phenomenon is supported by several experiments cited in the paper.

All that being said, the paper has some drawbacks which I should point out.

Some of the papers cited in the article do not seem to add any useful information to support the authors’ point. For example, the authors mention that the paper by Wang et. al. has an error in the calculation of the nonlinearities. But this does not serve to push forward their own point regarding hot-electron-assisted nonlinearity. The paper by Smith et. al. involved the z-scan measurement of the nonlinear absorption of gold composite media. The χ(3)  computed in the paper was (-1+5i) x 10-16 m2/V2. Using the same experimental results, Boyd et. al. calculated the real and imaginary parts of χ(3)  = (-9.5+2.3i) x 10-15 m2/V2. There is a large difference between the χ(3) computed by Boyd’s group and Smith’s group although they are based on the same experimental data, but the authors do not make a comment on that.

The authors also do not elaborate on why the sign of the nonlinearity varies between papers.

In conclusion, I believe that a good way to really set the hypothesis regarding hot-electron assisted nonlinearity in gold would be for one group performing an array of experiments on several gold films by varying respectively the pump frequency and the pump width. If the χ(3)  is indeed high for longer pulse durations as well as has a large frequency-dependence, it must have a strong contributing factor from hot-electrons.

Overall, I found the organization of details in this paper to be quite easy to follow, and the background provided was sufficient to give even someone unfamiliar with the topic a clear picture of what was being discussed.


[1] W.K. Burns, N. Bloembergen, Phys. Rev. B 4 (1971) 3437.

[2] D.D. Smith, Y.K. Yoon, R.W. Boyd, J.K. Campbell, L.A. Baker, R.M. Crooks, M. George, J. Appl. Phys. 86 (1999) 6200.

[3] P. Wang, Y. Lu, L. Tang, J. Zhang, H. Ming, J. Xie, F. Ho, H. Chang, H. Lin, Di. Tsai, Opt. Commun. 229 (2004) 425.

[4] T.K. Lee, A.D. Bristow, J. Hübner, H.M. van Driel, J. Opt. Soc. Am. B 23 (2006) 2142.

[5] N. Rotenberg, A.D. Bristow, M. Pfeiffer, M. Betz, H.M. van Driel, Phys. Rev. B 75 (2007) 155426.

[6] E. Xenogiannopoulou, P. Aloukos, S. Couris, E. Kaminska, A. Piotrowsk, E. Dynowska, Opt. Commun. 275 (2007) 217.

[7] J. Renger, R. Quidant, N. van Hulst, L. Novotny, Phys. Rev. Lett. 104 (2010) 046803.


Disclaimer 1: I am responsible for the explanations, interpretations, and opinions presented in the review; these do not reflect the views of my group or my mentors.

Disclaimer 2: I have tried to explain everything to the best of my abilities. Feel free to leave a comment if you think something is unclear or incorrect. I will try to address it as soon as possible.

2016: looking back

It has been a while since I had a chance to blog. Between classes, work, and life, it’s really hard to keep the promise I made to myself about writing regularly.

Anyway, here’s what had happened between my last post and now.

The Qualifying Exam aka The Ph.D. Lottery:

This was perhaps the biggest achievements for this year. My friends and I took the Ph.D. qualifying exams – a daunting, haunting, four-hour long exam that determines whether you are qualified to pursue a Ph.D. in Purdue.
Most of us, including myself, passed by a respectable margin.

The Soham Saha Library:

The West Lafayette Public Library was having a fundraising sale last month. You could get a bag of books For just three dollars. I always dreamed of having my own library. And thus, the Soham Saha Library was born.
I have never been an ardent reader of non-fiction and thought this would be a good time to start reading them. I ended up buying about thirty non-fiction books, and am currently reading whenever I have free time.
Some of the notable ones among the books:
– The Nobel Duel, by Nicholas Wade – a true story about the rivalry between two Nobel Laureates in Medicine. This is for inspiration.
– The Idea Factory, by Jon Gertner – It’s about the inception of Bell Labs and the brilliant innovations that took place there. It’s an interesting book on the research dynamics of one of the best Labs the world has ever seen.
– Writing Science: How to write papers that get cited and proposals that get funded, by Joshua Schimel – for obvious reasons.
If you happen to have an office at the Birck Nanotechnology Center and are walking past Room 1238, drop by and take a look. You might find something you like.


Made some new friends, learned how to kickbox, the usual random things I do.

Oh yeah, also, the Presidential election happened. But that is too much for one post.

So, you want to go to grad school?

This is a email I composed for my brother and sister a couple of years ago, to give them some tips on applying to grad school. These are things I learned the hard way, and wish someone had told me when I was applying. I think they will be helpful to anyone applying to grad school. So, here goes.
Okay. Here’s the list of things you need to do to get into a good university for higher studies – a no-nonsense guide.
1. Have great undergraduate research experience. It isn’t sufficient to say that you’ve worked under so and so for six months. You have to have documented proof that you worked with them. The best case is a publication in a well reputed journal, which takes months and months of hard work in a (sometimes) seemingly hopeless project, which (sometimes) ends in a miracle.
But the normal case is just the Professor’s recommendation. And trust me, it’s hard to get a good one. A recommendation that starts with something like “In the short period of time I have known X for…”, isn’t likely to get you into a single place. To get a good recommendation, you must do consistent, good work, and do 110% of what your advisor has asked you to do. Remember, the professor has nothing, absolutely NOTHING, to gain by giving you a good recommendation. If he’s not responsive, it’s YOUR job to coax him, to goad him, and to convince him into blessing you with a good recommendation. You have to meet with him regularly. It may be months between your working under him and the time you need the recommendation. He will have tens of other students to associate with in the meantime. So, keep in touch. A good way to do this is to send him New Year Cards, Chinese New Year Cards, Christmas Cards, and everything else you can think about, without annoying him. That way, he’ll remember you when the time comes.
2. Recommendation letters: You’ll usually need three letters of recommendation. So better have at least five people ready. Don’t ask for a recommendation a day before the deadline and expect them to do it for you. You need to regularly check is ALL of them have submitted ALL the recommendations. You don’t have any leverage over them, and their lives will be affected by zero amount if you miss an application. So finish your application well before the deadline.
3. Have a great GPA: The median GPA of accepted students in any of the first tier universities is around 3.80/4.00. That’s the median, which means that half the people have a GPA better than that. A good GPA is no guarantee that it’s going to get you in. But a bad GPA is a red flag. Also, if you want to do research in a particular topic, better have A plusses in all the courses you took in that topic.
I shouldn’t be adding this, because if you don’t know this by now, well… you should know this by now. The secret to a good result is – studying. It’s not finding the subject really interesting. It’s not great teachers. It’s not a profound sense of fulfilment that one gets from being enlightened from a lecture. The lecturers are not there to teach you stuff. They are there to stand and give you slides and tutorials. It’s your job to listen and learn, because someone is paying a LOT of money so that you do just that – study. If you can repeat a subject for a better grade, repeat it. And no matter which university you are in, solving past exam papers always helps. Looking at them at the beginning of the term will at least tell you if the questions have any relation with whatever your lecturer teaches in class.
About research
The same goes for good research. When Edison put in a piece of human hair between two electrodes to see if it glows, and when it filled his room with the horrid stench of burnt hair, do you think he was filled with a sense of bliss? No. But he pulled his ass into the lab the next day, and tried again. 
Research is not just finding a great idea in your sleep, and then getting instantly famous. It’s doing the same mundane, trivial thing over and over and over again, until something good happens. It’s also about doing the things faster than others, because a hundred other students are probably doing the same thing day and night to finish it before anyone else.
So if you think that you can’t juggle fun and study, either drop fun and just study, or just quit. A university degree is overrated anyways. 
4. Have good GRE scores: A lot of good universities don’t ask for GRE scores. But still, it’s an added bonus. But the word list is much harder than the SAT word list. And this need about a few months of practice.
5. Take GRE subject tests: If you want to do a PhD in a different subject from your Undergrad, you’ll need to take the relevant subject test. The tests are hard, and need at least 3 months of full time study, unlike the SAT subject tests.
6. Select the right Universities to apply to: This requires a different post entirely.
7. Contact your potential advisor: This also needs elaboration.
So there. Now you have a succinct, yet comprehensive guide to getting into a good school for PhD.
One more thing. Doing each of these things perfectly, gives you about 10% chance of getting accepted. Because there are thousands of students who will apply, hundreds of whom will do everything perfectly.
So better get moving from this minute.
If you have time, here are some great resources that can help you:
1. A timeline for applications.
2. On getting recommendations.
3. A great read at any stage of your life.

Where Newton’s Third Law doesn’t work

In the last post, I talked about some of the basics of Newton’s three laws of motion.
Reiterating them.
1. The first law is about a body’s reluctance to change its state of motion – If it’s not acted upon by an external force, a body undergoing uniform motion will moving, and a body at rest will remain at rest.
2. The second law is about how a body reacts to a force – The rate of change of momentum of a body is proportional to the force acting on it.
3. The third law states that for every action, there is an equal and opposite reaction.
Here’s an instance, however, where the third law does not apply.
For this bit, you’ll need a little bit of background in electromagnetism.
A moving charge creates a magnetic field around it. The direction of the field is given by the right hand rule. If the thumb of your right hand points along the velocity of a positive charge, your fingers curl along the direction of the field.
Right hand rule
A charge moving in a magnetic field experiences a force that is proportional to the charge of the particle, its velocity, and the magnetic field.
F = qv x B.
The direction of the force experienced by the particle can be given by Fleming’s Left Hand Rule, depicted below. If your forefinger points along the direction of the field a positively charged particle is moving through, and your middle finger in the direction of motion , your thumb points along the direction of the force experienced by the charged particle.
Fleming's left hand rule
Now look at this figure where two positive charges are moving in directions perpendicular to each other.

2016-02-20 06_54_02

The red charged particle (Particle 1) is producing a field B1. The blue particle (Particle 2) is moving through the field upwards. As it does so, it experiences F21, which pushes it to the right side, as shown by the red arrow.

According to Newton’s third law, Particle 1 should also feel a magnetic force F12 to the left, created by Particle 2. However, since the field produced by Particle 2 (B2) is zero at point 1, Particle 1 feels no force acting on it when it is directly underneath Particle 2.

So, F12 = 0.

Newton’s Third Law does not apply.

If you want to dig deeper and understand why momentum is still being conserved in this scenario, you can mull over reference 3. It’s explored there in great detail.

[Note: I am omitting the Coulomb forces the particles are exerting on each other. They are equal and opposite. It’s the magnetic forces that aren’t obeying Newton’s Third Law.]


  1. Fig1:
  2. Fig2:


Newton’s Three Laws of Motion – A fun exercise

Let me start with an update on my PhD status. Obvious from the frequency of my blog posts, I have been extremely busy with my projects and coursework. But I am glad to say that, thanks to group mates I can trust and talented lab partners I can rely on when I’m in trouble, things could not have been more productive. And honestly, I don’t mind being under a lot of pressure as long as I am being productive.
Okay, now for the topic of this post. I have been wanting for a long time to write about something that’s very basic in physics – Newton’s Laws.
Before I go into detail, here’s a simple question you can ask your friends. And try to answer it as fast as possible, like, in under ten seconds. Come on, you are a smart guy! You shouldn’t take any more time than that.
While you are asking the question, make sure you contract your arm, and make a throwing motion, providing a visual aid for the innocent victim. If you are lucky, you’ll probably make them give you a wrong answer.
It seems like an easy enough question, but you would be surprised how many get this wrong. Of course, the question lacks a lot of detail. Where in space is the object? How far are the nearest bodies that might exert a force on the object?
The object is not going to slow down. Everyone gets this bit right. There’s no air resistance. So nothing slows the ball down. [Unless your time scale is over millennia and the ball loses its momentum bumping into tiny space particles floating around].
Now, why does the ball not speed up? You did exert a force on it that caused it to accelerate, and as I have established before, there’s nothing there to slow it down, right?
Well, it did accelerate as long as your hand was pushing it forward. But as soon as the ball left your hand, it did not have any force pushing on it anymore. So, it would move in a straight line in a constant speed.
But what about the third law? For every action there is an equal and opposite reaction. So if there is a reaction force, why don’t the two forces cancel each other out and the ball remain at rest?
That’s because the action and the reaction force don’t act on the same body. The reaction force exerted by the ball acted on your hand, and decelerated it, as your biceps tied to pull your hand forward. Since the force by the ball was decelerating your hand, it could not cancel out the force your hand was exerting on the ball.
Sweet. So far we’ve covered high school level physics. But honestly, I have seen Olympiad competitors, engineering students, and even PhD students mess up this simple question. Just needs a little misdirection.
Now, after we have kind of established Newton’s laws and their ‘infallibility’, in my next post, I am going to give you an example where Newton’s third law does not seem to work.