[HN Gopher] What is a zero refractive index material?
       ___________________________________________________________________
        
       What is a zero refractive index material?
        
       Author : _Microft
       Score  : 217 points
       Date   : 2023-12-10 08:28 UTC (1 days ago)
        
 (HTM) web link (skullsinthestars.com)
 (TXT) w3m dump (skullsinthestars.com)
        
       | knob wrote:
       | Fascinating. Thank you for putting it together.
        
       | carterschonwald wrote:
       | This is cool. This is the sort of stuff I like to see on the
       | internet.
        
       | jacobolus wrote:
       | For anyone who hasn't studied electrodynamics or advanced optics,
       | Grant Sanderson (3Blue1Brown) recently made a detailed video
       | explaining what the refractive index really means, probably the
       | clearest reasonably accessible explanation of this topic anywhere
       | to date:
       | 
       | https://www.youtube.com/watch?v=KTzGBJPuJwM
       | 
       | https://www.youtube.com/watch?v=Cz4Q4QOuoo8
       | 
       | The first video is really a tour de force. Too bad it saw such
       | limited traction here:
       | https://news.ycombinator.com/item?id=38482549
        
         | hadlock wrote:
         | For those without a lot of patience, skip ahead to 6:45 or so
         | (in the fist linked video) which is a really cool, "a-ha!"
         | moment of why light "slows down" when it hits light. He also
         | points out that he's really just animating feinman lectures, so
         | giving credit where it's due. Gonna have to go dig out those
         | books. Big thanks to jacobolus for linking these videos
        
           | Kranar wrote:
           | To be clear there are numerous explanations for why light
           | slows down in a medium and they are almost all incorrect in
           | one way or another.
           | 
           | This video uses the explanation that light interacts with
           | electrons in a medium which causes the electrons to produce
           | an electromagnetic wave whose interference pattern changes
           | the phase of the light wave, kicking it back.
           | 
           | The problem is that an interference pattern can never change
           | the speed of a wave, it can change the phase of the wave and
           | adjust it, but that won't explain how light passing through a
           | medium takes longer to traverse that medium than light
           | travelling in a vacuum.
           | 
           | I don't know of a visualization or explanation that captures
           | why light slows down in a medium, and the video linked is
           | still a good way to get a sense of what's happening, but it's
           | worth knowing that there is still a great deal being left out
           | of that explanation.
           | 
           | It is nevertheless better than explanations involving the
           | absorption an reemission of photons or that light bounces
           | around within the internal structure of a medium. Both of
           | those explanations manage to explain how light takes longer
           | to pass through a medium but fails to explain how light keeps
           | a consistent direction as opposed to scattering randomly.
           | 
           | The explanation in the video manages to explain how light
           | maintains a consistent direction but fails to explain how
           | light will actually take longer to pass through a medium
           | compared to a vacuum.
        
             | mikewarot wrote:
             | I thought that Grant's video did a great job of explaining
             | it was all phase kicks, and how it all depended on resonant
             | frequencies of the medium.
             | 
             | [Edit]In the second video above, he notes that phase kicks
             | don't change the speed of the wave, even though the
             | wavelengths can stretch out, it's still lower than the
             | speed of light in vacuum.
        
               | Kranar wrote:
               | Phase kicks don't change the speed of a wave. If you
               | setup a similar experiment with sound or water where you
               | constructed an interference pattern that kicked back the
               | phase of the wave, the wave wouldn't slow down.
               | 
               | If you want an actual non-layman explanation for why
               | light slows down ib a medium you need to express the
               | light and medium interaction in terms of polaritons. Of
               | course this is incredibly difficult to do so for even
               | simple cases, so alas a whole suite of simplified
               | explanations exist that seek to explain some aspect of
               | the situation while failing to explain others.
               | 
               | https://en.m.wikipedia.org/wiki/Polariton
        
               | deely3 wrote:
               | Could you elaborate please?
               | 
               | So, there no slowdown by phase shift at all? But.. are
               | you sure, because it looks like the phase shift is the
               | real effect and logically speaking result of the phase
               | shift will be the effect that look like slowdown for
               | outside observer.
               | 
               | Also, how can you simulate similar effect in water and
               | sound if there no sound polarization?
        
               | mikewarot wrote:
               | The phase shift is dependent on both the resonance
               | frequency of the medium and the incident light. In the
               | case of X-rays, the refractive index can go below 1,
               | resulting in total external reflection for a few tenths
               | of a degree. Even in this case, the speed of the X-ray
               | itself stays below that of C, even though the
               | "wavelength" appears to be longer than in vacuum.
        
               | michaelt wrote:
               | _> logically speaking result of the phase shift will be
               | the effect that look like slowdown for outside observer._
               | 
               | If there was a phase shift but no slowdown, wouldn't we
               | expect individual photons to propagate through a 10km
               | loop of fibre optic cable without any slowdown, which
               | would be measurable?
        
               | Kranar wrote:
               | You would certainly see an apparent slowdown due to phase
               | shift if you consider a continuous wave that spans the
               | entire medium, yes for sure and so this explanation and
               | model does have merit, I don't want to dismiss it
               | entirely.
               | 
               | But this model won't be useful for understanding pulses
               | of light through a medium. For example if I emit a very
               | short pulse of light through a medium and measure how
               | long it takes the head of the pulse to traverse the
               | medium, using this model won't work. A phase shift won't
               | move the head of a pulse of light backwards, it will just
               | adjust the amplitude of the head as it propagates through
               | the medium.
               | 
               | You still need a way to explain how it is that the head
               | of the pulse actually takes longer to travel through the
               | medium and that's not something a phase shift can
               | explain.
        
               | rocqua wrote:
               | The understanding of a refractive index only cares about
               | 'phase speed' in steady state. At least, that is what the
               | video claims to be about. For that case, phase kicks are
               | a sufficient explanation no?
               | 
               | I can imagine things get really weird with pulses, but
               | that's out of scope for the video.
        
               | planede wrote:
               | > Phase kicks don't change the speed of a wave.
               | 
               | "Phase kicks" explain the phase velocity. The speed of a
               | wave is the group velocity. Phase velocity is omega(k)/k,
               | group velocity is omega'(k). So if "phase kicks" explain
               | phase velocity sufficiently so it's valid for a range of
               | frequencies, then it also explains group velocity by
               | taking the derivative of the dispersion relation.
        
               | Kranar wrote:
               | That's true for a steady-state wave, and hence this model
               | is accurate for a steady-state light wave. But if you
               | were to consider short pulses of light then there is no
               | longer a relationship between the group velocity and
               | phase velocity.
               | 
               | The group velocity of these pulses through a medium will
               | still be lower than the speed of light in a vacuum and
               | phase kicks won't influence the group velocity.
               | 
               | Explaining how the group velocity of light can be slower
               | in a medium than in a vacuum requires analyzing the
               | coupling of photons with electrons to form polariton
               | quasiparticles. You can then calculate the mass of these
               | polaritons which in turn gives you the speed and get the
               | full picture. Doing this, however, is incredibly complex
               | and so it's much easier to consider simplified scenarios
               | like either the steady-state case where you can simply
               | reason about the scenario in terms of interference
               | patterns between the light wave and the electromagnetic
               | waves produced by oscillating electrons, or you can
               | consider some non-steady state scenarios involving
               | photons themselves being absorbed and reemitted by
               | electrons but neither of these explanations fully capture
               | the phenomenon.
        
             | gpsx wrote:
             | I'm not sure if this will be satisfying because it is a
             | mathematical explanation rather than an intuitive one. If
             | you combine two of maxwell's equations, you get a wave
             | equation for electric/magnetic fields. However, there is an
             | extra term in there, which is the effect of a time changing
             | current on the magnetic field. In a material, the time
             | changing electric field induces such a current, which in
             | turn has the mathematical effect of reducing the coupling
             | between the electric and magnetic field, creating the
             | equation for a wave that is slower.
             | 
             | Something that might be comforting about light going slower
             | than the speed of light is that the speed of light is not a
             | special property of light, but it is a property of space
             | time. It just so happens that light is the only way we have
             | experience on this magic speed. Light isn't physically
             | bound to go "the speed of light".
        
             | Tazerenix wrote:
             | The actual answer is the assumptions which define a self-
             | propagating wave do not apply once the wave leaves a
             | vacuum. When it becomes incident onto some medium, due to
             | the coupling of electrons within the medium to the
             | electromagnetic field, the pure electromagnetic wave gets
             | transformed into a phonon, which is a combination of
             | electromagnetic and mechanical oscillation within the
             | medium (and therefore has speed <c, depending on the
             | particular properties of the medium). When the phonon
             | subsequently leaves the system, those traveling
             | oscillations induce a new self-propagating wave on the
             | other side, sending the light on its way as usual.
        
               | MichaelZuo wrote:
               | What does it mean for something to oscillate
               | electromagnetically and mechanically simultaneously?
               | 
               | Doesn't mechanical oscillation already occupy all three
               | spatial dimensions plus a time dimension?
        
               | zmgsabst wrote:
               | The phonon oscillates both the electrons and the EM
               | field.
               | 
               | A photon is EM only.
               | 
               | So you're correct that it occupies all four dimensions,
               | but we're discussing an excitation in one field (photon)
               | changing to an oscillation in multiple (phonon) and then
               | back to only one field (photon).
        
               | MichaelZuo wrote:
               | Can you explain this in a step by step manner?
               | 
               | I really can't quite grasp how the photon/phonon switches
               | back and forth like this.
        
               | zmgsabst wrote:
               | 1. The photon moves through free space, where only the EM
               | field is disturbed.
               | 
               | 2. The photon enters a material, where the disturbance in
               | the EM field couples to the electron waves -- creating a
               | phonon.
               | 
               | 3. The phonon travels through the material, as an
               | oscillation in both electrons and EM.
               | 
               | 4. The phonon reaches the edge of the material, where
               | there are no more electrons and reverts to a wave of just
               | EM -- a photon.
               | 
               | 5. The photon continues in free space.
               | 
               | The reason this happens is the photon changes the
               | electron behavior, which in turn changes the photon
               | behavior. This is because EM interacts with charged
               | particles like electrons.
               | 
               | For the time it is in a material, a EM wave can't be
               | separated from the behavior of the electrons present:
               | both and their mutual interaction are required to explain
               | what happens.
               | 
               | That disturbance of both is "coupled" -- and called a
               | phonon.
        
               | cbolton wrote:
               | Is this more than a change of terminology? Is it wrong to
               | say that the electromagnetic oscillation is still there
               | in the medium but coupled to a mechanical oscillation,
               | and the coupled system is called a phonon? (I mean
               | there's still an electromagnetic field in the material,
               | it still gets excited, it's not replaced with a new field
               | that fuses the EM and matter fields). Then the question
               | is by which process exactly is the electromagnetic
               | oscillation slowed down, and is the answer much different
               | from the explanations above? I.e. the moving charges due
               | to the mechanical oscillation add perturbations to the EM
               | field such that the net effect is a slower propagating
               | wave.
        
             | dustingetz wrote:
             | visualized well in "Picture Book of Quantum Mechanics" ch 1
             | (a fairly hardcore physics text that does indeed have many
             | diagrams)
        
           | martincmartin wrote:
           | No need to dig out the books, they're available online, well
           | formatted and a pleasure to read:
           | 
           | https://www.feynmanlectures.caltech.edu/
           | 
           | https://www.feynmanlectures.caltech.edu/II_32.html
        
         | dcreater wrote:
         | Grant has singlehandedly taught me more than all of my elite
         | education combined. Man is an absolute treasure
        
         | platz wrote:
         | One remaining question I had after watching Grant's video was
         | that, although the collective behavior of a bunch of light
         | waves made sense via interference, _how would a single photon
         | 's direction would change upon entering the medium_?
         | 
         | The best answer I could find on physics stack exchange was that
         | the single photon's wavefunction is delocalized, so that the
         | photon's wavefunction, in fact, interacts with the entire
         | medium, instead of at a single point.
         | 
         | Is this the correct way to state this phenomenon or is there a
         | better understanding of how the light emitted from a single
         | photon interacting with a medium would bend?
        
         | SAI_Peregrinus wrote:
         | Huygens Optics (pretty much the only dedicated optics channel
         | on Youtube) also recently made a video on this subject[1].He
         | made some diffractive lenses via photolithography, and shows
         | how the interference caused by variably spaced diffraction
         | patterns causes refraction.
         | 
         | [1] https://youtu.be/SS2AbZVdk2A?si=5KTvkX-KVnxRUN7G
        
       | datadrivenangel wrote:
       | This kind of thing is super important for fiber optics.
        
       | luispauloml wrote:
       | AhnLab Safe Transaction's anti-phishing protection erroneously
       | blocks this domain. The log says:                   Date:
       | <redacted>         Security Threat: Phishing site         Target:
       | skullinthestars.com/         Status: Block         Scan Method:
       | Anti-Phishing
       | 
       | _Sigh._ I wonder how much worse can these South Korean  "security
       | applications" get. For instance, AhnLab's website1 doesn't even
       | list Ahnlab Safe Transaction in their products.
       | 
       | For the curious ones, a related thread: "South Korea's online
       | security dead end" https://news.ycombinator.com/item?id=34231364
       | 
       | 1 https://www.ahnlab.com/
        
       | rendall wrote:
       | > _" Privacy & Cookies: We and our 772 advertising partners store
       | and/or access information on your device and also process
       | personal data, like unique identifiers, browsing activity, and
       | other standard information sent by your device including your IP
       | address..."_
       | 
       | There is no opt-out, which violates GDPR. If my data was
       | collected on landing, I would like my data removed, please.
        
         | uxp8u61q wrote:
         | Have you contacted the owners of the website to get your data
         | removed?
        
           | saagarjha wrote:
           | And give them more personal information?
        
           | rendall wrote:
           | I assumed OP was the website owner. But while my request is
           | serious and legally binding, it was somewhat rhetorical as I
           | do not expect the owners of a site with such a data policy
           | would really be conscientious about contacting me to sort out
           | which data is mine and removing it.
        
             | eru wrote:
             | > But while my request is serious and legally binding,
             | [...]
             | 
             | Posting a comment on HN is somehow legally binding for a
             | third party website whose operator likely never even heard
             | of HN? Or what are you trying to say?
        
               | rendall wrote:
               | As I understand it, the request to have data removed is
               | what's legally binding, not the format in which the user
               | makes the request. If the site owners see it or otherwise
               | become aware of it, they are obligated to remove my data
               | even though it was a post on HN. Whether all of that
               | actually happens is a different story. They could
               | probably claim truthfully they don't know which data is
               | mine. If I were determined, I'd contact them directly.
        
               | uxp8u61q wrote:
               | Don't be absurd. I'm a big proponent of GDPR but you seem
               | to be under the impression that it's a magic spell. You
               | seriously believe that, legally, if you post a comment on
               | HN, you're putting an obligation on someone? I have a
               | piece of the moon to sell you, then!
        
               | rendall wrote:
               | That is a misapprehension of what I wrote.
        
               | rendall wrote:
               | Also, I threw that in there because, if the site
               | operators were to see "I don't expect them to actually
               | remove my data", I do not want them to interpret that as
               | releasing them from the obligation. It does not. It's
               | just my prediction of how things will go.
        
         | groby_b wrote:
         | Yes, there is an opt out, see the fourth sentence: * Otherwise,
         | you can get more information, customize your consent
         | preferences, or decline consent by selecting "Learn More".*
         | 
         | It's a dark pattern to only call it "Learn More", but I
         | wouldn't bet it's a GDPR violation.
        
           | rendall wrote:
           | Thanks for the tip.
           | 
           | The opt out is supposed to be as easy as the opt in, so I'd
           | bet it crosses the line.
           | 
           | Edit: furthermore, even after opting out, you nevertheless
           | "agree" that (that is to say, you cannot opt out of):
           | Certain information (like an IP address or device
           | capabilities) is used to ensure the technical compatibility
           | of the content or advertising, and to facilitate the
           | transmission of the content or ad to your device.
           | Match and combine data from other data sources
           | Link different devices            Identify devices based on
           | information transmitted automatically
        
             | sokoloff wrote:
             | The first of those is surely a valid technical requirement,
             | right? (I'm not a GDPR expert, by any means.)
             | 
             | In order to send you bits via IP, the server needs your IP
             | address. In order to know the type of bits to send, it
             | needs to understand the content-type, encoding, etc that
             | your device supports.
        
               | rendall wrote:
               | From what I understand, GDPR applies only to retention of
               | data, and not such technical requirements. It does not
               | require operators to inform users unless the server will
               | be retaining the IP address.
        
               | sokoloff wrote:
               | In any distributed system, what "retention" means is
               | unclear* and, in the face of that lack of clarity, a
               | company deciding to play it safe and require consent for
               | things that GDPR says needs consent seems reasonable.
               | 
               | * If I put your content-type and IP address onto a queue
               | for processing by another system, that's arguably
               | retaining the data, even if that length of retention is
               | typically measured in seconds. Given that, the safest
               | thing for me to do is to require your consent for the
               | retention of IP address and related data.
        
               | rendall wrote:
               | I suppose? The GDPR is very clear: if you serve European
               | residents, you cannot collect their identifiable data
               | without their informed consent, nor can you make consent
               | the price of viewing your content. If you are found to do
               | so, you are liable to huge fines.
               | 
               | The language of the law itself is not very far from that
               | clarity. Check it out for yourself:
               | https://commission.europa.eu/law/law-topic/data-
               | protection/d...
               | 
               | I find it not credible that a company would read that
               | second part, think "My goodness that sounds awful! Out of
               | an abundance of caution, we better include language
               | around arcane technical edge cases!" but then go on to
               | violate the very, very clearly stated core intent of the
               | law regarding consent and actual data retention and
               | brokering.
               | 
               | So... it is confusing. Probably intentionally so. Perhaps
               | their legal strategy would be to somehow conflate these
               | edge cases? Try to baffle judges?
        
           | 6510 wrote:
           | > The EDPB adopted Guidelines on dark patterns in social
           | media platform interfaces[2]. The guidelines offer practical
           | recommendations to designers and users of social media
           | platforms on how to assess and avoid so-called "dark
           | patterns" in social media interfaces that infringe on GDPR
           | requirements.[1]
           | 
           | There calling it "deceptive design patterns". In short,
           | tricking people is not consent.
           | 
           | [1] - https://edpb.europa.eu/news/news/2022/edpb-adopts-
           | guidelines...
           | 
           | [2] - https://edpb.europa.eu/system/files/2023-02/edpb_03-202
           | 2_gui...
        
         | lm28469 wrote:
         | Just click on "disagree to all", no ?
        
           | rendall wrote:
           | At the time i wrote that, I did not understand that was
           | behind the "learn more" button. However, if their data
           | retention policy is accurate, even clicking "disagree to all"
           | means they will retain data that individually identifies
           | their users and they exchange this data with other brokers.
           | This is strictly against the letter and spirit of the GDPR,
           | opening them up to the possibility of massive fines.
        
       | kazinator wrote:
       | I would love to have a mug that is nearly invisible (when clean)
       | until you pour beer into it.
        
       | johanvts wrote:
       | If you want to play around with different refraction values and
       | see what happens I made a MetaPost script for that once:
       | http://www.hugoblog.onrender.com/post/prism/
        
         | zdimension wrote:
         | I'm getting an SSL error when trying to load that URL
        
           | ipdashc wrote:
           | https://hugoblog.onrender.com/post/prism/
        
       | zppln wrote:
       | > _We and our 772 advertising partners store and /or access
       | information on your device [...]_
       | 
       | > _772_
       | 
       | Seriously...
        
         | lm28469 wrote:
         | A lot sites are like that (most big ones), that's the whole
         | reason they started GDPR. All you have to do is add a few
         | widgets/plugin/third party ads/traffic monitors/tracking and
         | their dependencies and you'll get hundreds of "partners"
         | 
         | arstechnica, cnet, &c. all have 200+ "partners"
        
           | xnorswap wrote:
           | And unfortunately they've all settled on the apparently
           | untested, "legitimate interest" loophole where these hundreds
           | of partners have a "legitimate interest" in serving you
           | personalised adverts.
        
         | ycombinatrix wrote:
         | thanks for the heads up. i wasn't that interested in this topic
         | anyway.
        
       | jeffparsons wrote:
       | I have no physics education beyond high school, but I briefly
       | became obsessed with the idea of efficient collimation of light.
       | I eventually concluded that it must be impossible, because it
       | would imply a global decrease in entropy, much like Maxwell's
       | demon.
       | 
       | But this article seems to suggest that it might still be
       | possible. Have I misread it? Or maybe misinterpreted -- e.g.
       | maybe "efficient" would cover a system that does require energy
       | input, and just doesn't require discarding a lot of the input
       | light?
       | 
       | Can anyone with more of a clue comment on this?
       | 
       | I find the idea exciting because I can imagine endless practical
       | uses for an efficient collimator.
        
         | mnw21cam wrote:
         | It'd be balanced by the difficulty in getting the light _into_
         | the material in the first place. You 're right, you can't
         | change the laws of physics. Light will only enter an object
         | with lower refractive index if its angle of incidence is close
         | enough to straight on that the beam coming through into the
         | material has somewhere to go that satisfies Snell's law. When
         | the object's refractive index is near zero, the object will
         | only accept incoming light across an extremely narrow angle.
         | This solves your concerns about having a global decrease in
         | entropy.
         | 
         | You can fudge this by making the incoming surface of the object
         | match the shape of the incoming waves. Then all the light will
         | be allowed in. However, that surface will only match the shape
         | of the incoming waves for light originating from a tiny point
         | in space. If your light source is larger than a tiny point in
         | space, then the light coming from the larger area will bounce
         | off the material and not enter it. In effect, the magic
         | material will magically collimate a light source, but only if
         | the light source is already fairly magic, and in that case a
         | simple lens would suffice.
        
         | dekhn wrote:
         | it sounds like etendue
        
       | denton-scratch wrote:
       | You can model refraction using waves in a water-tank; the waves
       | slow down in shallow water, and speed up in deeper water. You can
       | do things like make lenses.
       | 
       | So I suppose a near-zero refractive index would be modeled by a
       | region of "infinite depth". Is there a relationship between
       | wavelength and depth, such that for a given wavelength, there is
       | some finite depth that behaves for practical purposes as if it
       | were infinite?
        
       | Jeff_Brown wrote:
       | I don't understand why this does not imply the possibility of
       | faster than light communication. If you had a long tube with a
       | zero refractive index, couldn't you type Morse code into one end,
       | by simply turning the signal on and off, and have the receiver
       | receive the message immediately?
        
         | edgineer wrote:
         | 3blue1brown's video covers this. The effect of "changing speed"
         | is a change to the light's wavelength, not the speed of an
         | impulse through the material--imagine taking a standing wave
         | and pushing the peaks and valleys up and down so the wavelength
         | looks really long. And since the frequency is unchanged,
         | there's your appearance of high speed. This happens because the
         | material changes the phase of the wave continuously.
        
       | gcanyon wrote:
       | For anyone who's interested, Fermilab has done several videos on
       | this topic as well that I found highly informative:
       | 
       | https://www.youtube.com/watch?v=CUjt36SD3h8
       | 
       | https://www.youtube.com/watch?v=NLmpNM0sgYk
        
       | aurizon wrote:
       | There is an old science fiction concept of 'slow glass', where
       | light travels very very slowly, with 1/2 day glass used for
       | windows that allow light to dally for 1/2 day before it exits -
       | also good for street lights. Extending it to week/glass, year
       | glass and so on, with the glass becoming a defacto streaming
       | video display to watch burglars/traffic etc. Interesting concept,
       | smashing a pane of year glass - would it release all that energy
       | as an e=mc2 blast?? https://sf-encyclopedia.com/entry/slow_glass
        
       | JoshGG wrote:
       | This is a great article. Very interesting. Thanks for posting!
       | 
       | I recently developed a new interest in optics and it's cool to
       | see this posted on HN.
        
       | cbondurant wrote:
       | The first application that comes to mind for me, and of course I
       | am not a quantum physicist so its entirely possible that my
       | conceptions here are misguided, would be with creating even more
       | perfectly coherent beams of laser light for use in the high
       | precision environments of quantum laser experiments.
       | 
       | Possibly either at more affordable rates or to allow for an
       | extremely temporally coherent wavefront in other shapes besides
       | just the beam that is most commonly used? I could easily believe
       | that there are potential experiments that are just waiting for
       | the right technology to be viable.
        
       | FireInsight wrote:
       | I'm on my phone, and the privacy banner takes so much space I
       | just see the title, a divider, and then the banner. I started
       | reading the banner thinking it was the article...
        
       | swayvil wrote:
       | Note that the sun produces collimated rays too. And the stars
       | even moreso.
       | 
       | Which is to say, the rays are always parallel if the source is
       | far enough away. Which feels like a good metaphor for something.
        
       | the-mitr wrote:
       | of possible interest: _Discussions on Refraction of Light_
       | 
       | https://archive.org/details/TarasovTarasovaDiscussionsOnRefr...
        
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