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Birefringence is a property of certain materials where the refractive index of the material is dependent upon the polarization and direction of propagation of light through it. I recently learned about it while reading a book on lasers.

Reflection and refraction are phenomena that arise from changes in relative permittivity, and they are exactly the same physical concepts as we see in electromagnetic wave propagation through transmission lines. Fundamentally speaking, they are both aspects of wave impedance, and the calculations used in both arenas are identical.

It therefore occurs to me that birefringence is not limited solely to the domain of optics, and we might also observe the behaviour in electronics - perhaps as some sort of transmission line where the characteristic impedance differs depending on the direction of wave propagation through it.

I suspect that a very tiny amount of birefringence is observable in all conductors, e.g. due to variation in crystalline structure within the metal, but I'm more interested in examples where the magnitude of birefringence is significant enough to be a factor worthy of consideration in practical applications.

Are there any significant examples of birefringence's appearance or exploitation within electronics, specifically in the electrical domain rather than the optical domain?

texnic
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Polynomial
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    I am baffled by the "opinion based" close vote on this question. Surely the question of whether or not the physical phenomenon of birefringence is observed in the electrical domain is, by the very definition of the word, objective? – Polynomial Sep 21 '22 at 12:12
  • You are asking if there are any significant examples and either the answer is "yes" (which makes your question not very good) or, you are asking for examples in electronics and that is asking for opinions because no single answer is right or wrong. I mean, how would you decide which answer is best? Also, what will happen to this list of examples in a week or a month or a year when some new use is found? In other words, you are asking for opinions and your question is not focussed enough to yield answers that stand the test of time. That's two reasons to vote to close as I see it. – Andy aka Sep 21 '22 at 12:19
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    @Andyaka By that second argument one could close almost any question on this site, since new understandings and technologies are always possible, and future developments are a fundamental tenet of the scientific process that should be implicitly assumed. As for whether or not the answer may be a bounded yes (one or two examples given our current understanding and technologies), or an unbounded yes (it's everywhere), or a no - I could not possibly know which it is before receiving an answer, so to argue that this question should be closed because one of those _might_ be the case is a tautology. – Polynomial Sep 21 '22 at 12:35
  • Electric fields in conductors (even carrying AC) are parallel to the conductors, not perpendicular. There is only one direction of propagation. You can look at waveguides that are used for microwave frequencies and higher - but I'm not sure if those count as "electronics" – user253751 Sep 21 '22 at 12:37
  • @user253751 I'm not sure that the electric fields being parallel precludes the possibility of birefringence effects, though, given the existence of biaxially birefringent materials and more general observations around changes to characteristic impedance when the εr of nearby dielectrics is altered. Perhaps this is a limitation in my understanding, though, and I'd appreciate any insight you can offer. Regarding waveguides, I'd consider RF to be within the domain of electronics insofar as it pertains to the implementation of radio transceivers. – Polynomial Sep 21 '22 at 12:56
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    Basically all flexible waveguides are anisotropic if you bend them, so it appears as a nuisance in cabling. I'm not sure of productive uses. In optics, material birefringence is widely used in free space optics (splitters, attenuators, isolators), whereas free space electronic components are not so common due to the longer wavelengths. – user1850479 Sep 21 '22 at 13:07
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    @user1850479 Any scenario where birefringence constitutes an electrically relevant phenomenon, whether it be wanted or unwanted, would be of interest to me. – Polynomial Sep 21 '22 at 13:41
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    Unwanted anisotropy shows up in lots of places, especially at high frequencies. PCBs are made of fiberglass and so have birefringence between the fiber axis and perpendicular axes. Bending any waveguide does something similar. For very high frequency interconnects (PCIe 5, USB4, DDR5, etc), a lot of effort goes into manufacturing devices (PCBs, coaxial cables, etc) that have relatively uniform, isotropic properties. – user1850479 Sep 21 '22 at 14:04
  • Polarization-maintaining optical fiber makes use of birefringence to, well, do what its name says, maintain the polarization of incident light. – Hearth Sep 21 '22 at 14:45
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    @user1850479 If you could put together an answer explaining how the birefringent behaviours arise in that situation, with an overview of the challenges involved and how they are mitigated, I'd very much appreciate that! – Polynomial Sep 21 '22 at 14:58
  • @Hearth Yeah, it's also used in LCDs, and in Pockels cells, and for SHG in DPSS lasers, but in this case I'm specifically interested in the electrical domain rather than the optical domain. – Polynomial Sep 21 '22 at 15:07
  • @Polynomial An argument could be made that optical stuff is electrical, since it's all EM waves. But I suppose you're looking for stuff to do with static electric fields, or something like that? At least lower-frequency than anything involving a waveguide like an optical fiber? – Hearth Sep 21 '22 at 15:09
  • My expertise is in optics, so I was hoping someone who knows more about high frequency RF could answer this. – user1850479 Sep 21 '22 at 15:17
  • @Hearth The distinction is certainly fuzzy, since the two things are fundamentally identical. I'm not sure I'd specifically draw the line at a particular frequency boundary, since I wouldn't _necessarily_ want to exclude things like Ka-band radio transceivers. I'm having trouble coming up with the right language to use here. For the purposes of this question I'm primarily interested in behaviours that occur in what we would traditionally describe as an electronic circuit, or on a PCB, where we'd describe things in terms of impedance, rather than behaviours in the realm of optoelectronics. – Polynomial Sep 21 '22 at 15:25
  • @user1850479 Honestly any information you could give about the relation between the issues you mentioned and birefringence would be much appreciated. I'm aware of factors like plane roughness and weave effects in PCB manufacturing for high speed digital interfaces (e.g. designing for 100G+ Ethernet), but I'm lacking a conceptual bridge in understanding between birefringence and those challenges in the electrical domain. – Polynomial Sep 21 '22 at 15:31
  • I think you're going to have the problem that, whereas fields exist in 3D, and have degrees of freedom arising from that (namely, the matrices or tensors that express material properties, like birefringence), circuits are at best 1D (TLs, transmission lines), and usually 0 (abstract networks with either zero length, or infinite speed of light). As a result, you get phase and amplitude, or I and Q (the complex components of a signal), and frequency response and interference and dispersion (general networks, which may involve TLs), but not polarization or direction. – Tim Williams Sep 21 '22 at 17:17
  • (That is, direction any further than that which results from Telegrapher's Equations: forward or reverse, no other spacial axes. We could do a parallel-plane layout on a PCB and get anisotropy with respect to incident direction, but I'm not aware of any practical use -- a more traditionally synthesized network would be more compact.) – Tim Williams Sep 21 '22 at 17:20
  • This is absolutely not my field of expertise, but does [skin effect](https://en.wikipedia.org/wiki/Skin_effect) count as exhibiting birefringence under any conditions? Skin depth decreases with frequency, akin to refractive index. Skin effect in large PN junctions, eg solar panels? In the pixels of a CCD sensor ([800 nm](https://semiconductor.samsung.com/newsroom/news/introducing-two-new-0-point-8-micrometer-isocell-image-sensors/), very close to red at 650nm). – jonathanjo Sep 22 '22 at 11:29
  • @jonathanjo No, that's more of a filtering effect, and not dependent on direction, other than the orientation of the surface (but importantly, incident signals have no directionality beyond simply how they're wired to it). Another interesting example could be laminated iron transformers, which are very anisotropic to B-field: but the windings specifically apply it in the parallel direction, so you wouldn't know just from probing the response of one or a few windings. – Tim Williams Sep 22 '22 at 13:11
  • @Polynomial. "Are there any significant examples of birefringence's appearance or exploitation within electronics, specifically in the electrical domain rather than the optical domain?" Yes, one would guess applications in radar detection etc and yet they remain highly classified for good reasons ... – citizen Jan 03 '23 at 09:39

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As @user1850479 mentioned, birefringence is a well-known issue in traces on high-speed PCBs. If you are searching for references, just call it "anisotropy" since that's how the signal integrity literature refers to it. It's also an issue in microstrip patch antennas.

If you want a paper in more depth look at "Pulse propagation on Microstrip transmission-line Using an anisotropic substrate" by Awasthi and Verma at the 2008 International Conference on Recent Advances in Microwave Theory and Applications, or "Modal Analysis of Microstrip Antenna on Fiber Reinforced Anisotropic Substrates" by Yang and Hung in IEEE Transactions on Antennas, vol 57, 792-796, 2009. Those papers have earlier references.

In high speed buried PCB traces, the issue is that you want a dispersionless line to avoid spoiling the rising and falling edges of pules. Dispersionless in turn requires a transverse electromagnetic wave, which in turn requires a homogeneous substrate material.

In circular polarization microstrip patch antennas (e.g. low cost GPS antennas) pure circular polarization (called low axial ratio in antenna specs) is achieved by closely matching the x and y electric dimensions, that is, the dimension in wavelengths should be the same in x and y. Birefringence messes that up, and since the bandwidth of a microstrip patch is only a few percent, it doesn't take much of it to create a problem.

Eeyn
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