This is Ben's logbook for Nano Japan project from 2014.6.9-2014.7.31.

#contents

* Daily schedule [#daily]
- 09:00-10:00 Discussion (1)
- 10:00-12:00 Solve the problem and write the progress on pukiwiki
- 12:00-13:30 Lunch
- 13:30-14:30 Discussion (2)
- 14:30-16:30 Solve the problem and write the progress on pukiwiki
- 16:30-17:30 e-mail report and problems

* Goal of the project. [#goal]

- To describe the discrepancy between the value of the calculated group velocity of surface plasmons in graphene compared to the value of the measured group velocity.
- Keywords: Surface plasmon, graphene, group velocity.

* Schedule for Discussion [#discussion]
|Date|Month|Day|Time|Tutor|Topic|
|10|June|Tue|09:00-10:00|Shoufie|Mathematics : Differential Operator & Curvilinear Coord.|
|10|June|Tue|13:00-14:00|Thomas|Dielectric Function of Free Electron Gas(B)|
|11|June|Wed|09:00-10:00|Shirakura&Inoue|Maxwell Equation and EM Wave Function(B)|
|11|June|Wed|13:00-14:00|Hasdeo|Graphene Band Structure|
|12|June|Thu|09:00-10:00|Nugraha|Plot and Programming (band structure)|
|12|June|Thu|13:00-14:00|-|Group Meeting|
|13|June|Fri|09:00-10:00|Mizuno|Programming with mathematica|
|13|June|Fri|13:00-14:00|Pourya|	Mathematics : ODE and PDE|
|16|June|Mon|09:00-10:00|Shoufie|Dielectric function in Real Metals and Interband Transition(B)|
|16|June|Mon|13:00-14:00|Siregar|The Wave Equation (Surface Plasmon Polariton) (TM,TE)(B)|
|17|June|Tue|09:00-10:00|Shoufie|Surface Plasmon Polariton (SPP) in Single Interface(B)|
|17|June|Tue|13:00-14:00|Thomas|SPP in Multilayer System(B)|
|18|June|Wed|09:00-10:00|Shirakura&Inoue|Electrodynamics Problem Solutions|
|18|June|Wed|13:00-14:00|Hasdeo|Prism Coupling  SPP(B)|
|19|June|Thu|09:00-10:00|Pedro|Finite element methods|
|19|June|Thu|13:00-14:00|-|Group Meeting|
|20|June|Fri|09:00-10:00|Mizuno|Mathematica|
|20|June|Fri|13:00-14:00|Shoufie|Plasmon Dispersion Multilayer|
|23|June|Mon|13:00-14:00|Shoufie|Coupling SPP using Total Reflection|
|24|June|Tue|09:00-10:00|Nugraha|Plotting |
|24|June|Tue|13:00-14:00|Thomas|Drude Model of Conductivity|
|25|June|Wed|09:00-10:00|Shirakura and Inoue|Reflection and Transmission of EM Wave|
|25|June|Wed|13:00-14:00|Hasdeo|Graphene|
|26|June|Thu|09:00-10:00|Shoufie|Coupling SPP using Total Reflection|
|27|June|Fri|09:00-10:00|Mizuno|Mathematica|
|27|June|Fri|13:30-14:30|Shoufie|Coupling SPP using Grating or Corrugated Graphene|
- Tutorial takes place in Coffee room, since visitor room will be occupied with many people
-(B) means the topic is taken from book: Plasmonics Fundamentals and Applications

- This section is for posting questions from Ben-san and answers from other group members.
- Please list here with some simple reasons or details.
- For every problem, give a tag double asterisks (**) in the code so that it will appear in the table of contents.
- For the answer, give a tag triple asterisks (***) in the code below the problem in order to make a proper alignment.
- List from new to old.

** Question: Equations on Pukiwiki [#Q-EQ]
Hello! I dont need this information right away, but it might be useful in the future. How do you input equations and formulas into pukiwiki? I heard it is similar to Latex, but Im not very familiar with Latex either. Thanks.

*** Answer: Equations on Pukiwiki [#A-EQ]
You will also need Latex when writing the final report of Nano Japan project.
- Now, for our purpose in this pukiwiki page, you can simply insert Latex equation by inserting "dollar" symbol before and after any Latex code. For example, to show E=mc^2 properly, you need to write:
$E=mc^2$
which will be shown as:
$E=mc^2$
- Some practical examples:
--velocity:
$v = \frac{dx}{dt}$
gives:
$v = \frac{dx}{dt}$
--magnetic dipole:
$\nabla \times \vec{B} = 0$
gives:
$\nabla \times \vec{B} = 0$
--work
$W = \int_{a}^{b} F \cdot d\vec{r}$
gives:
$W = \int_{a}^{b} F \cdot d\vec{r}$

* Report [#report]

**July 16 [#july16]
- Still sick, but came in to lab anyway.
- Started making a powerpoint for the derivation of the two interface system.

**July 15 [#july15]
- Sick again.

**July 14 [#july14]
- Finished finding the dispersion relation for the two interface system.
- Started substituting terms to create the graphene-metal system.
- Finding specific values for terms for silver.

**July 11 [#july11]
- Worked on 3D plotting capabilities with Mathematica with Mizuno-san. Ran into some trouble with defining the size of aspects we were using.
- Added specific values of graphene for finding the dispersion relation to the powerpoint.
- Redid my work on the two interface system, this time with z=-d/2 and z=d/2 as the boundaries of the interface. The result seems more reasonable than the earlier case.
- Presented the updated powerpoint to Saito-sensei. He asked me to add references for the values of terms for the case of graphene.

**July 10 [#july10]
- Still have a bit of a headache, but felt well enough to go to lab.
- Added the Drude Conductivity term derivation to the powerpoint.
- Started the derivation for the two graphene interface system with the conditions of z=0 at the bottom interface and z=d at the upper interface. The result didn't seem to be correct, so I will redo it with z=-d/2 at the lower and z=d/2 at the upper as Shoufie-san recommends.
- Trying to add to the powerpoint the specific values of constants in the dispersion relation for the case of graphene.

**July 9 [#july9]
- Not feeling well, so I stayed in.

**July 8 [#july8]
- Back from Okinawa. We left the day before the category 5 typhoon Neoguri hit.
- Spent the morning making a powerpoint detailing the derivation of the dispersion relation for a single interface of graphene, which basically is the accumulation of my progress thus far.
- Presented the powerpoint to Saito-sensei. He wants me to add the derivation for the Drude conductivity as well as clarify a few things.
- Started on the case of a two interface system of graphene in the afternoon.

**July 2 [#july2]
- Feeling better today, so I came in to lab.
- Now that we are finished for the case of graphene at a single interface with dielectrics, we are now taking a look at the case with graphene and a metal. Shoufie-san also showed me some articles that might be of use.
- In the afternoon, had discussion with Nugraha-san. We were looking at the complex equation of plasmon dispersion in graphnene, and trying to solve it numerically. We were still having a little difficulty plotting it in gnuplot, but it seems I only need to make minor changes.
- Met with Saito-sensei. He wants me to make a powerpoint file with the derivation of the dispersion equation that I have learned over the previous week.
- Tomorrow I will be leaving for the Okinawa midprogram meeting. I will get back on Tuesday, July 8th.

**July 1 [#july1]
- Sick day. Stayed in and rested after letting Shoufie-san know I wasn't feeling well.
- Read some articles that Shoufie-san gave me.

**June 30 [#june30]
- Had both of the day's discussions with Shoufie-san.j
- In the morning, we summed up the previous lectures into two equations, and using these two, got the dispersion relation for plasmons in graphene.
- I continued looking at the dispersion relation, and used it to find the group velocity of plasmons in graphene as a function of frequency.
- After lunch, made plots of the dispersion relation and group velocity functions. I used Microsoft PowerPoint to create the labels.
- Had meeting with Saito-sensei. I talked about what I had gone over with Shoufie-san and showed him the graph printouts. For homework, he wants me to make graphs with error bars for the imaginary, damping component.

**June 27 [#june27]
- Had morning discussion with Muzino-san. I asked about how to refine the dipole plots I had made, and he suggested trying both ListVectorPlot[] as well as StreamPlot[]. I also asked about 3D plotting capabilities. Next I am going to try making a 3D plot of the dipole using the finite element method.
- Made a small sample of the 3D dipole plot.
- Had an afternoon discussion with Shoufie-san. We reviewed the important points of what I had learned over the past three weeks.
- Made a short outline of what I would be discussing with Kono-sensei.
- Met with Saito-sensei. Practiced my discussion for Kono-sensei, and then discussed upcoming plans.
- I updated the sign outside my door for when I will be in Okinawa for the mid-program meeting.
- Sarah-sensei, Packard-sensei, and Kono-sensei came to visit the lab. I had my discussion with Kono-sensei on my research topic and it went well. Afterwards we played ping pong together, and then headed to the restaurant for the party.

**June 26 [#june26]
- Met Hasdeo-san on the way to lab in the morning. Learned that there is another bus line that stops at a nearby bus stop that I can take if I miss the usual one.
- Had a morning discussion with Hasdeo-san. We went over the background of the project first. I asked about interference between plasmons, and whether this could be involved in the velocity discrepancy. He mentioned that Landor damping might be worth investigating.
- Spent the rest of the morning reading part of the article Shoufie-san gave me, as well as making a few powerpoint slides to prepare for my discussion with Kono-sensei tomorrow.
- Was going to see the group discussion where Shoufie-san would give a presentation of progress on his work, but apparently he doesn't present until next week.

**June 25 [#june25]
- The bus was full and had to walk to lab. Because Inoue-san and Shirakura-san have a class soon, we have to reschedule the lecture for later.
- Repeated the dipole calculation, but this time using a k value for the Hemholtz equation. Could not distinguish the result from the previous plot. Will try again with a larger k value.
- Had an incident where I discovered that I had not replied to an important email sent earlier in the week. Thankfully, Saito-sensei brought it to my attention. I am trying to reconfigure the notifications for Thunderbird so that this will not happen again.
- Had an afternoon lecture with Nugraha-san. We looked at the energy dispersion plot for graphene, this time in 2 dimensions. Homework is to focus the plot on the dirac point in preparation for my lecture with Hasdeo-san tomorrow.
- Met with Saito-sensei. He let me know there are problems with my methods of communicating, and that I should always reply to emails to let them know I have received the information. He also pointed out the two crucial points of the lectures I have had, which are finding the group velocity, and finding the plasma frequency as a function of wave vector.
- Saito-sensei has also decided that tomorrow we will stop having lectures. With the information I have received thus far, I will begin making progress. Rather than having lectures, I will continue to meet with the other lab members and discuss what I am currently working on. This will be a good time to ask questions or get advice on anything I am stuck on.
- With the help of Shoufie-san and Nugraha-san, I have my email set up so that all messages to my flex account are automatically forwarded to my Rice University email address. Unfortunately, there is a 15 minute delay, but this shouldn't be a problem, since we usually communicate via Skype while at the lab for anything that is time urgent.

**June 24 [#june24]
- Had a morning lecture with Shoufie-san. We finished our discussion of the situation of graphene between two dielectrics. We then started talking about the Drude conductivity, which is when there is a current running through graphene. Homework is to combine today's lesson with last week to find and graph the real part of the wave vector as a function of frequency.
- Finished making a vector plot of an electric dipole by using the finite elements method in mathematica. Tried to repeat the process but with a much larger conducting sphere in the center, but due to the relative density of the vector plotting, the result was not very useful.
- Due to a scheduling conflict, there was no afternoon lecture.
- Saito-sensei told me he would not be here today, so there was no afternoon meeting.
- Need to start on a presentation for Kono-sensei's visit.

**June 23 [#june23]
- Came in around 10.00 in the morning. No morning lecture.
- Finished setting up the math for programming the dipole for Saito-sensei's homework after getting stuck over the weekend.
- Had lunch in the coffee room and we finished the leftovers from the party last Thursday.
- In the afternoon, had lecture with Shoufie-san on Prism-coupling to make surface plasmon polaritons. It was similar to the case of a two interface system, but with the electric field in the top material coming from the incident and reflected light. It was a total-reflection system, so there was no transmitted light.
- Had my meeting with Saito-sensei at 3. There was some confusion over the direction we are taking with Shoufie-san's lecture. After much discussion with Saito-sensei and Shoufie-san, it seems we will be focusing more on plasmons created by alternating currents in a graphene-dielectric interface.

**June 20 [#june20]
- Had a lecture with Mizuno-san on how to program with Mathematica. I asked him a lot of questions pertaining to how I could use Mathematica to do the finite element method for the homework Saito-sensei gave me. It has the capabilities, but having to do many iterations may be a problem.
- At lunch there were donuts. Not sure if this happens every Friday or just today for some reason. They were good.
- Had a lecture with Shoufie-san. We continued on the previous topic of plasmons at an interface, now addressing the condition of having a multilayer interface. It was a fairly straightforward extension of the previous method, but the math gets a little more complicated now that you have additional terms.
- Played ping pong with Yang-san.

**June 19 [#june19]
- Made the bus today and didn't have to walk.
- Had a lecture with Pedro-san on the Finite element method. Basically just derived the theory of the method using the definition of a derivative. Did this for both the Poisson equation and the Hemholtz equation.
- There was a misunderstanding and Nugraha-san thought he was supposed to give me a lecture today. Instead, he linked me several resources in order to further explore the capabilities of gnuplot.
- Met with Saito-sensei. Homework is to map a 2d electric dipole with and incident E-field from a lightwave. Will try to do this using mathematica, and if that doesn't work, will try using C++ in conjunction with gnuplot.
- Had a lab party and potluck dinner at night. Got to try lots of Japanese, Chinese, Indonesian, and Brazilian food.

**June 18 [#june18]
- Was a little late and rescheduled the lecture with Inoue-san and Shirakura-san for the afternoon.
- Had lecture with Hasdeo-san on Graphene Energy Structure. We took the hamiltonian matrix we saw last week and used it to find an equation for the dielectric function, which we then used to to plot the conduction and valence bands. We then reviewed Bloch Theory and used this to derive the Brillouin zone of graphene. Homework is to find the high symmetry points, make a Taylor expansion near K point, and plot starting from gamma to M to K back to gamma.
- Met with Saito-sensei and talked about my lecture with Hasdeo-san. Found the area of the Brillouin zone of graphene. Homework is to find the comparison between the real space unit cell area and the Brillouin zone area in a general case.
- Had a lecture with Inoue-san and Shirakura-san on Electrodynamics. We talked a lot about identities with the Kroniker delta. Homework is to find the equation of motion of a charge in a uniform magnetic field.

**June 17 [#june17]
- Had a lecture with Shoufie-san on the dispersion relation of surface plasmons on a single interface. Using the transverse magnetic wave equations from yesterday's lecture with Siregar-san, we derived the electric and magnetic fields for a metal-dielectric interface. When making boundary conditions, we added the assumption that there was no surface charge and no current, and then we were able to find the requirement of a surface plasmon. From this we derived the wave vector of a surface plasmon. Homework is to show that there is no transverse electric mode for a surface plasmon.
- Had a lecture with Thomas-san on Fourier integrals. We did a few basic integrals and saw Fourier transforms. He also explained the difference between k-space and the real space. Homework is to evaluate the Fourier integral that Thomas-san gave me.

**June 16 [#june16]
- Had a lecture on the dielectric function in real metals and interband transition with Shoufie-san. It was a lot of mathematics. We did not have enough time to cover everything and will finish up on Friday. No homework.
- After lunch, had a lecture with Siregar-san on the Wave Equation. He taught me the derivation of the Hemholtz Equation, and we went on to use Maxwell's equations to get the equations to describe Transverse Magnetic and Transverse Electric waves. Homework is to isolate the different components of the Electric and Magnetic fields in the x and z directions.
- At the meeting with Saito-sensei, I had a little trouble answering the questions involving parts of Shoufie-san's lecture, so we did some more review until I was more comfortable with the subject. Homework is to explain why the electric field and wave vector are perpendicular in EM waves.

**June 13 [#june13]
- It's Friday!
- Had a lecture on using mathematica with Mizuno-san. Learned basic inputs, solving equations, extracting solutions, and how to input matrices and vectors. Homework is to look up material on using mathematica for solving differential equations. More programming will be covered next week.
- Had a lecture on ordinary differential equations and partial differential equations with Pourya-san. Homework is to read more on Laplace equation.
- In meeting, Saito-sensei gave me recommendation of traveling to Yamadera over the weekend if the weather is good.
- Managed to fix gnuplot code with help of sensei and Nugraha-san. Turns out ^ is not used for exponents, but double astrisks are. Was also missing a single multiplication sign that was causing a misleading error.
- Saito-sensei gave me homework to solve Laplace's equation on a circle.

** June 12 [#june12]
- Arrived a little late after being mistaken about bus times.
- Nugraha-san introduced me to gnuplot as well as the flex-network interface. Learned to plot from both arranged data sets as well as plotting equations. Learned to export plots into eps files and use inkscape to edit files. Homework was to plot the Energy dispersion equation I found as part of Hasdeo-san's homework.
- No afternoon lecture, there was a group meeting which I didn't need to attend. I worked on homework instead. I think I will attend next week, though.
- Had Nugraha-san help me learn to convert plots to .pdf files and he helped me set up printing from my office desktop. Printed out Energy dispersion homework plot to show to Saito-sensei.
- Met with Saito-sensei, and discussed both this morning's lectures and yesterday's lectures as well, since we could not meet on Wednesday. He gave me homework to 'create the gap' by altering the Energy equation and make a plot of it.
- Played ping pong with the lab. I started off not so good, but improved near the end.
- Had tea and mochi with lab members. They want me to make country-fried steak for them next week.

** June 11 [#june11]
- Managed to make it to lab on my own and on time (yay!).
- Shirakura-san and Inoue-san gave me a lecture on Maxwells equations and EM waves. It was largely review, but it was good practice for communicating with non-native English speakers.
- Hasdeo-san taught me about Graphene Band Structure. He began by teaching me about Schrodinger's equation, then went on to 1-D chain Band structure, and tight binding wave functions. We then went on to 2D configurations with alternating atom types, and derived the Hamiltonian matrix form. Homework was to find the Hamiltonian for graphene and use this to find the Energy dispersion equation.
- No meeting with Saito-sensei, he had to go to a conference meeting.

** June 10 [#june10]
- Hasdeo-san picked me up from Urban Castle and showed me another bus stop nearby.
- Shoufie-san gave me a lecture on differential operators, generalized so that they can be used in curvilinear coordinates. He assigned me some homework problems due in the afternoon, mostly taking the curl or divergence of different functions in different coordinate systems.
- Met Sumino-san.
- Finished Shoufie-sans homework before going to lunch. Will try to upload to pukiwiki soon.
- Had lecture on the dielectric function with Thomas-san. Homework is to describe physically and derive the plasma frequency, as well as give the relation between the dielectric function and the complex refractive index.
- Had my discussion with Saito-sensei. He asked me to calculate the plasma frequency of 1 cm^3 of Copper, and to use this to find the typical plasmon energy in Copper.

** June 9 [#june9]
- Thomas-san picked me up from Urban Castle Kawauchi (UCK). He showed me how to get to the lab, and the location of the bus stop.
- I was introduced to the other lab members, Saito-sensei, and the secretaries.
- Saito-sensei, Hasdeo-san, and Thomas-san set up a computer for me to use in the guest office.
- Hasdeo-san and Thomas-san helped me set up an account on Xming and helped me get a Thunderbird email account.
- Looked up material regarding plasmons, plasma oscillations, phonons, and polaritons.
- Saito-sensei gave me homework of describing what is a plasmon, and to describe using equations.
-- A plasmon comes from a plasma oscillation in a metal.
-- It is a quasi-particle that is the quanta of these oscillations.
-- To describe plasmons, we use the plasma model of free electrons.
-- The equation of motion of an electron in a plasma sea is:
--- mx + m(lambda)x = -eE , where we assume E(t) = E0 * e^(-iwt)
-- The particular solution is
--- x(t) =  e / [m(w^2 + i(lambda)w)] * E(t)
-- will try to write these equations using LaTex code soon.
`