History of Ben(Open) (No. 16)

• History
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• View the source.
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  • 1 (2014-06-09 (Mon) 11:49:19)
  • 2 (2014-06-09 (Mon) 14:12:51)
  • 3 (2014-06-09 (Mon) 17:33:03)
  • 4 (2014-06-10 (Tue) 12:18:15)
  • 5 (2014-06-10 (Tue) 15:43:25)
  • 6 (2014-06-11 (Wed) 10:36:12)
  • 7 (2014-06-13 (Fri) 11:10:08)
  • 8 (2014-06-13 (Fri) 15:55:53)
  • 9 (2014-06-16 (Mon) 12:40:39)
  • 10 (2014-06-17 (Tue) 11:09:30)
  • 11 (2014-06-18 (Wed) 10:34:30)
  • 12 (2014-06-18 (Wed) 17:09:37)
  • 13 (2014-06-19 (Thu) 09:22:20)
  • 14 (2014-06-19 (Thu) 13:04:34)
  • 15 (2014-06-20 (Fri) 17:27:02)
  • 16 (2014-06-23 (Mon) 09:51:04)
  • 17 (2014-06-23 (Mon) 16:46:44)
  • 18 (2014-06-25 (Wed) 17:58:52)
  • 19 (2014-06-26 (Thu) 14:51:36)
  • 20 (2014-06-30 (Mon) 11:55:29)
  • 21 (2014-07-02 (Wed) 10:45:12)
  • 22 (2014-07-02 (Wed) 16:04:12)
  • 23 (2014-07-10 (Thu) 16:23:45)
  • 24 (2014-07-14 (Mon) 10:44:35)

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

Daily schedule†

• 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.†

• To describe the coupling between plasmons in graphene and EM waves. The result of this coupling is a wave called a surface plasmon polariton (SPP).
• Keywords: Surface plasmon, graphene, coupling, surface plasmon polariton.

Schedule for Discussion†

• 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

Questions and Answers†

• 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†

Hello! I don`t 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 I`m not very familiar with Latex either. Thanks.

Answer: Equations on Pukiwiki†

• For a basic guide on Latex, please read this: http://tobi.oetiker.ch/lshort/lshort.pdf 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: &tex(): Error! The expression contains invalid characters.;
• Some practical examples:
  • velocity:

    $v = \frac{dx}{dt}$

    gives: &tex(): Error! The expression contains invalid characters.;
  • magnetic dipole:

    $\nabla \times \vec{B} = 0$

    gives: &tex(): Error! The expression contains invalid characters.;
  • work

    $W = \int_{a}^{b} F \cdot d\vec{r}$

    gives: &tex(): Error! The expression contains invalid characters.;

Report†

June 20†

• 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†

• 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†

• 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†

• 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.
• Met with Saito-sensei and talked about what I have learned about surface plasmons with Shoufie-san. Homework is to read an article and answer some questions about M. Faraday.

June 16†

• 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†

• 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†

• 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†

• Managed to make it to lab on my own and on time (yay!).
• Shirakura-san and Inoue-san gave me a lecture on Maxwell`s 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†

• 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-san`s 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†

• 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.