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I received quite a bit of encouragement in my first blog post, so I am super excited to bring to you guys the first post in a series that will hopefully teach you cool things about quantum sciences, while challenging me to figure out how to explain physics without throwing math everywhere.
On that note… many quantum mechanics textbooks start with advice along the lines of “abandon intuition and just do the math”, but unless I assume that you have a pretty advanced math background, that’s really not going to work here. Math is definitely necessary to do quantum mechanics, but we should be able to understand, at least at a conceptual level, several fun quantum phenomena. I’ll try to avoid equations altogether and we’ll see where that gets us. If you have any opinions on this, please say so in the comments! If you really want to learn the details, let me know and I can give you excellent references and offer my assistance.
As requested in the comments on my first post , we can start by defining “quantum optics”, since it isn't exactly a mainstream field, then we’ll get into lesson 1: the laser!
To put it simply, quantum optics is the study of the interaction of light with matter, where both the electromagnetic field (light) and the matter are treated quantum mechanically. Maxwell’s equations, which describe classical light, are insufficient to explain several interesting (and useful!) phenomena, so we have to include Schrodinger’s equation, field theory, and quantum electrodynamics to explain some of the weird things we can observe experimentally. This leads to some very complicated models but they give us tools such as lasing, electromagnetically induced transparency, quantum entanglement, quantum control, etc. etc. etc.
Lesson 1: The Laser
We begin this venture into the world of quantum sciences by developing an understanding of one of the simplest, and by far the most important invention in early optics: the laser.
Quantum mechanics teaches us that light is composed of many quanta of energy: photons. It also teaches us that electrons in an atom are only allowed to have certain discrete energies. Consider a photon and a simple atom that only has two energy levels (the two level atom is your best friend in laser physics, it’s like the mass on a spring of classical mechanics). The photon and the atom (or you can consider it the electron, since we’re talking about electronic transitions) can interact in three different ways:
1. Absorption
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(Note: Ea and Eb are energy levels, with Eb>Ea; photon is blue, electron is yellow)
When light is absorbed by an atom, it is excited into a higher energy state. Quantum mechanics only allows transitions to certain energy levels, so only photons of particular energies can be absorbed (and emitted).
2. Spontaneous emission
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Spontaneous emission occurs when an atom is in an excited state and emits a photon in order to go back to the preferred lower energy level. Just a general concept to keep in mind- nature prefers to minimize energy. An atom in an excited state is not stable, so it’ll seek a way of getting back to its ground state eventually.
3. Stimulated emission
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This is the fun one! Stimulated emission occurs when you have an atom in an excited state and it interacts with a photon that, ideally, has an energy that is identical to the transition energy between the atom’s current state and a lower energy state. The atom’s response is to emit a photon that is exactly identical to the incident photon; you send in one quantum of light, you get out two. This is the fundamental phenomenon that gives us lasers.
So what is a laser? As you probably know, “LASER”= Light Amplification by Stimulated Emission of Radiation. A laser requires 3 things: an energy source, a gain medium, and a cavity.
As you see in the stimulated emission picture, the electron starts in the upper (excited) state. How does it get there? Well, for a traditional laser, we have to put it there. Lasing requires a “population inversion”, meaning that more atoms are in the excited state than are in the lower state. (Spoiler: You can lase without inversion! I spent a lot of time studying this phenomenon and our lab group was the first to demonstrate it experimentally! We’ll definitely cover this topic!)
To get the population inversion required, we need some sort of energy source. This is usually an electrical current or another light source. The addition of energy into the gain medium is called “pumping” the medium.
The next thing you need is the gain medium- a bunch of atoms. The gain medium can be matter of any state. These days most lasers are diode/solid state lasers, but gas lasers are also very popular. The external energy source pumps this material so that most atoms are in an excited state. These excited atoms are going to decay by either spontaneous or stimulated emission.
Consider, for example, a laser diode. We apply an electric current to try to make it lase; if we adjust the current to justtt the right amount, we can pump more atoms into one particular excited state than there are total atoms in lower energy states. Then, if one of these atoms just happens to undergo spontaneous emission (and many of them will), the emitted photon will interact with neighboring atoms via either absorption or stimulated emission. If the neighbor atom is in the same excited state as the first, it’ll undergo stimulated emission (it’s already in a high energy level, it most likely does not want to gain more energy by absorbing a photon). Therefore, if there are more total atoms in the same excited state than in the lower states, stimulated emission will happen more often than absorption, and we’ll get a net increase in light.
Now, these stimulated emission photons all have the same properties; the same energy, polarization, and they travel in the same direction. The gain medium portion of the laser we call the “optical amplifier”. We amplify the light, but usually not enough to do anything useful with it. That’s why we put the amplifier inside an “optical cavity” or “resonator”.
A typical resonator is composed of two mirrors between which the light travels in a coherent beam. This allows each photon to pass through the gain medium multiple times before it exits the cavity through a small hole. As long as the gain remains higher than the loss of photons to absorption/escaping the system, this leads to an exponential increase in the light, and we have a laser!
Lasers are used in so many areas of science and engineering, and come in myriad of flavors. We have continuous wave lasers which produce steady beams and pulsed lasers which shoot fast, high power bursts of light. Lasers come in light of any color, extending from the ultraviolet to the infrared (and beyond), and the power levels used in a typical optics lab range from pathetic to excitingly dangerous.
If you’re interested, the history of the laser is a good read and worth Wikipedia-ing. Unsurprisingly, it’s littered with the names of many famous physicists. Shameless namedropping incoming: My advisor is the Ph.D. student of Willis E. Lamb, who won the Nobel Prize for his work in optical sciences. Together they wrote the first quantum theory of the laser. I also had the great privilege of hosting a former optics Ph.D. student of Gordon Gould a couple months ago, where I got to hear his first-hand accounts of the invention of the laser. Advice to any current college students: make good grades and talk to professors about your interests. Make them your friends, because they can award you so many unique research and networking opportunities that will really kick-start your entrance into the field. I wouldn't be half the physicist I am today without the help of some of the most caring, passionate professors at my university.
So I think that’s it for this lesson. Please please let me know if you like this approach, what changes I should make, if it was too simple, complex, boring, etc. Do you like this “conceptual” approach, or are you more interested in actually seeing the equations and such?
Definitely ask questions if anything was unclear, and call me out if I ever make any mistakes.
I'm also happy to take requests for future topics! I'll try to make this a weekly thing for as long as I can/as long as people retain interest.
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Really great read. I've already had a working understanding of lasers and a background in quantum dynamics myself, and I still learned quite a bit. The write-up definitely explains the way a laser works.
In my opinion, It misses:
- What's so special about a laser beam versus a light bulb?
- A diagram of a working laser cavity, and where the light comes out, and where the gain medium is, and where the initial source is.
- More Math!
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what's quantum optics actually used for in the real world? you just make laser pointers all day while secretly trying to develop a death ray? or are you doing a lot of things that impact other fields and the lives of common people without them even knowing about it?
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Thanks for such fast feedback guys! I want to go ahead and address your questions so future readers have them available.
What's so special about a laser beam versus a light bulb?
I really should have addressed this point. 
In short, laser light is special because it has one single wavelength/color, whereas a lightbulb has all the colors. The laser beam is “coherent”, meaning all of the photons have similar, controlled behavior; in a light bulb they kind of do their own things. Laser light is also mono-directional, while light from a bulb diffuses uniformly in all directions. Also the way in which light is generated is different, but that's a large digress... Anyway, the ability to focus light of one wavelength into a high power beam allows us to do things such as spectroscopy, study transitions in atoms, burn things, etc.
A diagram is also a good idea. My paint skills are lacking, I'll try harder for the next blog. Also, instead of there being a "hole" through which the beam exits, since we're talking about a mirror-based cavity, the light will exit from a partially transmitting mirror. The mirror on the right is coated in such a way that some of the light escapes to create the useful part of the laser beam.
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what's quantum optics actually used for in the real world?
There are a lot of applications for the results of quantum optics. The first thing that comes to my mind is laser spectroscopy, since I’m up to my eyes in it at the moment. I talked a little about my research in the last blog post, which is very application oriented. Lasers are used to obtain detailed molecular information by looking at the light a particular sample reflects/transmits/absorbs.
This is kind of a cool example- remember in the US after 9/11 there was a huge anthrax in the mail scare? There was a big demand for being able to rapidly detect anthrax without opening the envelope or sending it to a lab for testing that would take quite a bit of time (you’d get the results of whether or not the powder was anthrax after it was too late, basically). So our lab group developed a special laser spectroscopy technique that was able to do just that. You hit the envelope with a laser and look at the resulting spectrum; if it matches the spectrum for anthrax, don’t open it. For more info: click here
A project that a few students in our lab are working on right now involves developing a “sky laser”. They’ve figured out a way to send out a laser beam traveling away from the ground, the light reflects from particles in the atmosphere, and they somehow figured out a way to increase the strength of the reflected signal so it’s detectable. The idea is we can use this to detect poisonous gases from miles away using this sky laser spectroscopy. I don’t know many details, but once they publish something I can throw up the reference.
There are millions of medical applications for optical techniques- many imaging and diagnostic systems rely on technologies developed in the field of quantum optics. This is the direction I’m taking my research for my Ph.D. work; optical techniques for early cancer diagnostics. Optical spectroscopy techniques have insanely high sensitivity- they can distinguish between cancerous and non-cancerous cells relatively easily. That makes them really great for detecting cancer super early, before any other diagnostic method could even give you a guess as to what’s going on. The difficulty lies in the fact that the size of the laser beam, when focused on a cell, is much smaller than the actual cell... so unless you know exactly where to look, you might not find the cancer. We're working on that. 
This answer is getting kind of long so I’ll stop there, haha. But yes, there are millions of real-world applications for the work we do. Admittedly we do a lot of physics for the sake of physics, and it’s absolutely beautiful stuff if you’re into theory, but not always useful.
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Very cool, thanks for doing this. I would like it if equations were included too, even if I can't understand them. If you could break down the equation itself into what it is expressing, that would be cool.
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FREEAGLELAND26781 Posts
Bookmarking this for reading tomorrow after a few exams are finished~
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1001 YEARS KESPAJAIL22272 Posts
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On April 29 2014 10:42 lichter wrote:
I bet you play Protoss
It's obvious.
4/5 needs more kitteh.
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how come some lasers damage our eyes if pointed at directly while also there's lasik(?) that fixes eyesight?
awesome blog btw!
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The only thing that bugged me about this was the explanation of stimulated emission using a two level system.
Population inversion is impossible with a two level system!
There's also a lot of other cool stuff with optomechanics, optical cooling (if you know anything about optical tweezers...), and quantum information that you could get into. (Currently writing my senior thesis on quantum dot based VCSEL-like devices)
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Thanks again for the replies, and thanks for wanting math!
how come some lasers damage our eyes if pointed at directly while also there's lasik(?) that fixes eyesight?
My laser safety knowledge is good enough to get me through training (so not extensive), but I think I can sufficiently answer this question, haha. The eye focuses visible/NIR light onto the retina, and this focusing effect can increase the intensity of the light arriving at the retina by several orders of magnitude. This light gets absorbed by some parts of the eye/surrounding stuff and can cause burns. IR light typically causes thermal damage (as can the other wavelengths, too), and UV light tends to get absorbed at the front part of the eye, where it can cause photochemical damage. Really it’s the intensity of the light that matters most; your eyes won’t be damaged by looking at a laser below a certain intensity, but this threshold changes for different wavelengths.
LASIK uses a special kind of laser called an excimer laser. It’s a UV laser that produces tiny pulses of light, and they’re able to use these tiny pulses to remove just a small portion of the cornea tissue at a time. Small, as in fractions of a micron (<10^-6m). They use these tiny pulses to reshape the cornea, and the light doesn’t really touch anything that they aren’t intentionally trying to remove. So really all lasers can damage your eyes, but lasik uses them to cause damage in a way that ends up being convenient.
The only thing that bugged me about this was the explanation of stimulated emission using a two level system.
Population inversion is impossible with a two level system!
Fair enough  I totally didn't catch that when I wrote this up. The 3 interactions are easy to understand if you’re just looking at 2 levels, but I should have mentioned that this model wouldn't support laser operation. Explanation for those who want to know why: in this 2 level system you will eventually reach an equilibrium between pumping the medium, absorption, and emission. This can let you “break even” with light generation, but you won’t get the exponential increase in photons we need. To get a non-equilibrium system we need at least a 3 level atom. I will introduce this model in all its glorious detail when I talk about lasing without inversion, and we'll see how traditional lasing works from a mathematical perspective then, too.
Also, what an awesome senior thesis! I've always wanted a nano-laser, so I hope you figure out how to make one.
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Thanks for your efforts Ideal26, cool read.
I am already familiar with the idea of lasers but your story helps make things more clear. I suck at the more advanced math things and your writing is really easy to follow. If you can connect the math to the easiness that you provide, it could really elucidate stuff. If you're willing
I can chime in on laser eye damage:
When I was a wee lad, I was stupid enough to try and find out just what a laser looked like .. but not on the outside but for real. Or that was my thought pattern I imagine. I was sitting in a small laser show at some amusement park and I found that I could reach with my head where a laser would shine periodically. Of course that setup is nowadays frowned upon obviously.
The result: My right eye can't see that sharp anymore. My yellow spot has been degraded, I believe, but I have never let a doctor look at it. So, nothing too serious, I have two eyes.
What did it look like, you ask? It was a red laser light, I believe. When I looked in it, I saw just a big red circle (or my one eye vision completely filled, not sure). And the color was .. boiling. Not monotone. I realize now that what I "saw" was my retina burning up and my brain interpreting the color thus. It's an experience that you can skip because you pay for it with little reward.
Ideal26, some thoughts: Does incandescence (or black body?) radiation fall in quantum mechanic realm for explanation? Now I am intrigued how the light is sourced versus the atomic model and the electron energy states story. Also the concept of infrared radiation being linked to body heat in general is one of those concepts that sound easy on the surface but probably have very interesting stories behind them.
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On April 29 2014 13:03 icystorage wrote:
how come some lasers damage our eyes if pointed at directly while also there's lasik(?) that fixes eyesight?
awesome blog btw!
lasik is not a special laser, it just means laser eye surgery. Its still a laser, but its operated by a trained medical professional that uses the destructive properties to help you.
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hey a physics blog seems like an awesome idea.
I am looking forward to deeper quantum mechanical topics, I am currently doing a master level course on lasers physics, but most of the course we have been using a semi-classical treatment.
I assume your group has found a way to lase with Ralleigh scattering? that would seem interesting,
as a note as far as I know know raman(inellastic scattering) lasers don't use a population inversion and have been discovered in 1962(though i can't say i am an expert on raman lasers i just superficially know how they work and read some articles for an assignment). As i understand it there is some ground state that can absorb photons to be excited to some virtual energy level from which it instantly decays to a vibrationally excited state emitting a photon in the process.
these photons have a different energy compared to the pump beam photons equal to the energy difference between the ground state and the vibrational excited state(and apparently you can have stimulated emission with this process but i am not sure how that works, maybe its just the picture i normally use is too classical).
The reason you don't have to have population inversion in this case is that the effective lasing transition is from the groundstate to the excited state instead of from some excited state to the ground state.
And for the lasing transition to be more likely then the reverse transition,
the ground state must be more populous instead of the excited state.
they have almost never been used however as raman scattering is much less likely to occur (Raman lasers are bad, usually Raman scattering is just something that screws up your normal laser system)
however recently there has been some renewed research into silicon raman lasers as silicon is hard to make lase normally(as it has an indirect bandgap, which means the allowed excited energy states have higher momenta then the groundstate,
and each transition needs to conserve energy and momentum, which it can do through sound wave(phonon) emission but it makes the transitions far less likely).
The reason they want to make silicon lase is that is the cheapest semiconductor used in electric devices and they would like to make silicon lasers to easily integrate optical circuits in chips, as optical information transportation is about 10.000 times faster then electrical information transportation. and another interesting feature of these lasers are highly tunable because in principle any photon can be absorbed and by choosing the wavelength of the pump laser you can change the wavelength of the output light(although only long wavelengths are convenient to prevent electrons to be excited to the conduction band which amounts to losses).
ps i hope my great wall of text and ramblings are atleast somewhat readable.
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On April 30 2014 07:40 annedeman wrote:
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The reason they want to make silicon lase is that is the cheapest semiconductor used in electric devices and they would like to make silicon lasers to easily integrate optical circuits in chips, as optical information transportation is about 10.000 times faster then electrical information transportation. and another interesting feature of these lasers are highly tunable because in principle any photon can be absorbed and by choosing the wavelength of the pump laser you can change the wavelength of the output light(although only long wavelengths are convenient to prevent electrons to be excited to the conduction band which amounts to losses).
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Sorry but you've made an error. Electrical information transport is measured at a significant fraction of the speed of light. source
Computing with light is currently an unresolved problem (citation needed) so for most functions of a chip you'd need to work with electrons. Converting between photon and electron will have prohibitive overhead when it has to be done at millions of places in a chip so a chip would have to be either electric or fully optic.
For transport however, over the motherboard, I could see the appeal. This is hearsay but I understand that a great difficulty in motherboard design nowadays is electrical interference and that the high speeds/frequencies turns every data and clock line on the motherboard into antennas. Photons don't have that problem so it would help with interfacing in the larger gaps.
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In response to annedeman:
You literally just brought up the next 2 blog topics I was planning. So I’m not going to go into detail here, but I wanted to point out a couple of things:
Rayleigh and Raman are types of scattering effects, they are not the same as laser light. You don’t make lasers using these phenomena, you use a standard laser to observe them. And don't you say bad things about Raman scattering! Normal lasers screw it up! Haha, I have been up to my eyes in all things Raman for the past two and a half years, and it is a beautifully powerful spectroscopic technique. I’m really looking forward to writing that post, it should give you a really good understanding of what exactly Raman scattering is and why I love it.
That said, lasing without inversion is an entirely different beast not necessarily related to the energy levels exclusively. LWI in the way that it has been demonstrated thus far relies on “quantum coherence” effects, which we’ll discuss in that post. You have to prepare the atomic system in a very particular way to get LWI, but you don’t need the usual population inversion requirement. So nothing is free, you just pay a different price.
About Si lasers... The band gap structure of Si isn't compatible with the production of light, so I don't see how it would be possible to make it into a laser. The transitions just don't produce light. However there are many other materials that make excellent diode lasers because of their bandgap structure, and you can buy them in bulk for a few dollars each these days.
Quantum communication is an interesting subject, but outside of what I personally think about day to day. My office is next to a professor who specializes in that area, so maybe I’ll grab some of his papers and see if I can find something that would make for a nice entry here. At this moment though, I can't give you any enlightening insights into that field. Except that quantum encryption is crazy awesome.
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United States24666 Posts
Although this focus of your blog series is quantum optics, this seems like the best place to ask my more classical question:
Why is it so difficult to get a solid state laser to hold a constant intensity? I did some classical optics research last year with solid state lasers, and by far the biggest challenge was normalizing my data to the intensity of my source lasers (which were always varying tremendously in output). I'm not talking 1-2% here... like 25% plus over a number of seconds/minutes.
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This is pretty awesome.
My only request in future posts would be double spacing between paragraphs. Helps me separate out ideas, and find my place if some small child should scroll my mouse mid reading.
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On April 30 2014 08:14 Badjas wrote:Show nested quote +On April 30 2014 07:40 annedeman wrote:
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The reason they want to make silicon lase is that is the cheapest semiconductor used in electric devices and they would like to make silicon lasers to easily integrate optical circuits in chips, as optical information transportation is about 10.000 times faster then electrical information transportation. and another interesting feature of these lasers are highly tunable because in principle any photon can be absorbed and by choosing the wavelength of the pump laser you can change the wavelength of the output light(although only long wavelengths are convenient to prevent electrons to be excited to the conduction band which amounts to losses).
... Sorry but you've made an error. Electrical information transport is measured at a significant fraction of the speed of light. sourceComputing with light is currently an unresolved problem (citation needed) so for most functions of a chip you'd need to work with electrons. Converting between photon and electron will have prohibitive overhead when it has to be done at millions of places in a chip so a chip would have to be either electric or fully optic. For transport however, over the motherboard, I could see the appeal. This is hearsay but I understand that a great difficulty in motherboard design nowadays is electrical interference and that the high speeds/frequencies turns every data and clock line on the motherboard into antennas. Photons don't have that problem so it would help with interfacing in the larger gaps.
your probably right, this was just me interpreting an article on a subject(chips) i am not that familiar with, one article of a research group linked to Intel was talking about a "significant milestone for optoelectronic devices" which does sound to me like they want to be integrating them to me.
Rong, Haisheng; Jones, Richard; Liu, Ansheng; Cohen, Oded; Hak, Dani; Fang, Alexander; Paniccia, Mario (2005). "A continuous-wave Raman silicon laser". Nature 433 (7027): 725–728. Bibcode:2005Natur.433..725R. doi:10.1038/nature03346. PMID 15716948.-<article by intel
^ Jalali, Bahram (2007). "Making silicon lase". Scientific American 296: 58–65. doi:10.1038/scientificamerican0207-58.
<-this was the article i got the 10k number from, where they compared to the transport speed of cable modems
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On April 30 2014 18:51 annedeman wrote:Show nested quote +On April 30 2014 08:14 Badjas wrote:On April 30 2014 07:40 annedeman wrote:
...
The reason they want to make silicon lase is that is the cheapest semiconductor used in electric devices and they would like to make silicon lasers to easily integrate optical circuits in chips, as optical information transportation is about 10.000 times faster then electrical information transportation. and another interesting feature of these lasers are highly tunable because in principle any photon can be absorbed and by choosing the wavelength of the pump laser you can change the wavelength of the output light(although only long wavelengths are convenient to prevent electrons to be excited to the conduction band which amounts to losses).
... Sorry but you've made an error. Electrical information transport is measured at a significant fraction of the speed of light. sourceComputing with light is currently an unresolved problem (citation needed) so for most functions of a chip you'd need to work with electrons. Converting between photon and electron will have prohibitive overhead when it has to be done at millions of places in a chip so a chip would have to be either electric or fully optic. For transport however, over the motherboard, I could see the appeal. This is hearsay but I understand that a great difficulty in motherboard design nowadays is electrical interference and that the high speeds/frequencies turns every data and clock line on the motherboard into antennas. Photons don't have that problem so it would help with interfacing in the larger gaps. your probably right, this was just me interpreting an article on a subject(chips) i am not that familiar with, one article of a research group linked to Intel was talking about a "significant milestone for optoelectronic devices" which does sound to me like they want to be integrating them to me. Rong, Haisheng; Jones, Richard; Liu, Ansheng; Cohen, Oded; Hak, Dani; Fang, Alexander; Paniccia, Mario (2005). "A continuous-wave Raman silicon laser". Nature 433 (7027): 725–728. Bibcode:2005Natur.433..725R. doi:10.1038/nature03346. PMID 15716948.-<article by intel ^ Jalali, Bahram (2007). "Making silicon lase". Scientific American 296: 58–65. doi:10.1038/scientificamerican0207-58. <-this was the article i got the 10k number from, where they compared to the transport speed of cable modems
Ah with cable modems... I assume the 10k number refers to total bandwith then (rather than latency), and cable is an analog environment where multiplexing is perhaps the basis for the difference.
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