• F. Leyvraz added an answer:
    Does accelerated charge emit photons to all observers?

    We know that a decelerated charge emits photons. So you can visualize an observer in a stationary frame of reference that detects these photons.

    However for another observer in an accelerated frame of reference that is moving, at the same pace as the charge, the charge appears stationary and apparently should not emit photons.

    How do we reconcile these two apparently contradictory positions?

    F. Leyvraz · Universidad Nacional Autónoma de México

    @Eric Baird: even in the peculiar case you consider, there is no symmetry, in the sense that the damage to the observer and the damage to the car are unrelated. But what I had in  mind, obviously, was a car running, say, into a tree: someone looking at the car observes an acceleration of the car. On the other hand, if one puts oneself in the frame of the driver, the driver undergoes no acceleration, but the onlooker does, indeed he undergoes an acceleration altogether identical to that undergone by the driver from the onlooker's viewpoint. Nevertheless, in both reference frames, the onlooker does not suffer any major consequences, whereas the driver does.

    Indeed, I did not consider the case in which the car's mass is such as to cause accelerations in the onlooker of the same order of magnitude as the accelerations caused by the accident. I was essentially concerned with arguing in a way as clear as possible that, under normal circumstances, in a space that is reasonably flat, there is no symmetry between accelerated and inertial frames, which seems to me to be the essential issue in answering the question.

  • Craig Scott added an answer:
    How to determine the negative refractive Index of metamaterials?

    Dear all, how I can determine the negative refractive index of the metamaterials by CST studio suite or by using S-Parameters?

    Craig Scott · Northrop Grumman

    And a related question - is it possible to tell if a material is a NIM based on its dispersion relation, since that's what many 3D codes compute... something like negative slope for example.

    I found out the answer - if the slope of the band diagram is negative near the origin (i.e., about the Gamma point, along the Gamma-K or Gamma-M lines), then the index is negative for that band and is related to the (negative) slope of the dispersion curve, dw/dk.

  • Vladimir Lvovich Bychkov added an answer:
    Why displacement current is necessary in Ampere's law?

    Maxwell modified the ampere's law by the introduction of displacement current and was presented as 4th of the famous Maxwell equations. But I am always not clear about this term. Can any one help in this regard?

    Vladimir Lvovich Bychkov · Lomonosov Moscow State University

    Ampere's Laws are not connected with the displacement currents. They use only the law of full current. It can be proved from the hydrodynamic analogy between the hydrodynamics and electrodynamics. There is a great doubt in existence of the displacement currents. There is the opinion that Maxwell introduced them only for derivation of the wave equation,  Details can be found in ISSN 19907931, Russian Journal of Physical Chemistry B, 2014, Vol. 8, No. 2, pp. 212–220. © Pleiades Publishing, Ltd., 2014.
    Original Russian Text © V.L. Bychkov, 2014, published in Khimicheskaya Fizika, 2014, Vol. 33, No. 3, pp. 75–83.

  • Feng Ouyang asked a question:
    Was the conclusion (2) of Theorem 9 in the paper by Bresler et al, IEEE Tran Information Theory, Vol. 60, 9, p 5574, justified?

    I have a question about the paper "Feasibility of Interference Alignment for the MIMO Interference Channel" by Bresler, Cartwright and Tse, IEEE Tran Information Theory, Vol. 60, Issue 9, page 5574.

    In proving Theorem 1, they invoked Theorem 9.  But it seems to me that conclusion (2) of Theorem 9 was used but the conditions for such conclusion was not justified in the proof.

    Does anyone understand that part?  I wish to discuss further about that proof.

  • Frank Gräbner added an answer:
    What is the formula for calculating reflection loss in EMI SE?

    Dear researchers and friends, please tell me the formula for calculating Reflection loss in EMI SE? I used 20 log [S11], is it correct?

    Frank Gräbner · Hörmann IMG

    Dear Sir,

    the Definition of the shielding loss is D(dB) = 20 log ( Eo(f)/Ei(f) ).

    Eo is field outside and E i is inside a material. If you have only a Absorption material ( not any reflections ) you can use S11 für E.

    Yours Sincerely

    F. Gräbner

  • Sachin Gupta added an answer:
    Why do Ce^3 and Yb^3 differ largely in their magnetic moment values?

    Although both Ce^3[ 4 f^1] and Yb^3[4 f^13] possess only one unpaired electron, yet their magnetic moments differ largely.

    Please suggest a suitable relation to calculate their magnetic moments. 

    Magnetic moments of trivalent lanthanides.

  • Stephen O. IKUBANNI added an answer:
    Does E10.7 take geomagnetic sources into consideration?
    Tobiska (1993, 2000) developed and validated a solar EUV flux model named E10.7 and argued that the long-term variation is identical to the age-long F10.7 while it performed better on a short-term scale. How true is this?
    Stephen O. IKUBANNI · Landmark University

    Prof. R. G. Rastogi! Thank you for the short but massive information. I will appreciate it if you could send me some useful published literature in reference to your answer.


  • Sara Zolfaghar Tehrani added an answer:
    How do I apply continuity in 3D Voltage induced a coil by a moving magnet in COMSOL?

    I try to simulate 2D voltage induced in coil by moving magnet which is COMSOL example in 3D but I get error that Failed to evaluate variable Jacobian.
    - Variable: comp1.tAx_lmTy
    - Geometry: 1
    - Boundary: 11 12 16 17? 

    Sara Zolfaghar Tehrani · University of Wollongong

    the model find in http://www.comsol.com/model/voltage-induced-in-a-coil-by-moving-magnet-14163

    forum discussion:http://www.comsol.com/community/forums/general/thread/37104/

  • Orin Laney added an answer:
    Where can I find the hysteresis curve (and if possible the demagnetizing curve) of Hiperco 50 A and other high magnetic saturation soft materials?
    Soft magnetic materials such as Hiperco 50 A offer outstanding magnetic performance but a lack of information, in particular relative to the B-H curve, and considerably slow down use in the development of an electromagnet. In particular, I am looking for free access bulk magnetic properties of Hiperco 50 A after high temperature treatment for optimized magnetic performance.
    Orin Laney · Atwood Research

    You got it right.  Now you probably know more than the manufacturer about this particular alloy.

  • Abdelhakim El Ouadih added an answer:
    Measurements vs simulation of Antenna efficiency?
    Can current EM simulation tools can accurately predict Antenna efficiency and radiation pattern compared with actual anechoic chamber measurements? Any references for such a research comparing both results?
    Abdelhakim El Ouadih · Cadi Ayyad University

    Dear Asraf,

    A full wave EM simulator results can be accurate as experimental results. Nearly any type of losses can be modeled now by a simulator. The problem is difference between simulators because there are  2 families of simulator. the simulators using solvers of differential form of Maxwell's equations (FEM, FDTD, FIT, FVM...) and others using solvers of integral form of Maxwell's equations (MoM, Rayman,...) . The results can be valid as the experimental ones when you use two simulators from different families and you find concordance. I advise to look to this paper. it's very interesting. 

  • Sara Liyuba Vesely added an answer:
    Is there a theoretical modeling of permittivity?

    The dielectric properties of the composites are influenced not only by the relative permittivity of the components but also by other factors such as the morphology, dispersion as well as the interaction between the two phases. According to this there are N number of theoretical models for measuring relative permittivity of the polymer ceramic composites. Some of the examples are Lichtenecker equations, Modified Lichtenecker, Maxwell-Wagner, Maxwell-Garnet, Jayasundere-Smith, Effective Medium Theory etc ?

    I am planing to write a review on this models Please help me to find out new suggestions to these topics?

    I am planing to use N number of composites that already published by explaining those models.. with our systems ?

    Anyone can join me those who are interested in this topics ?

    Sara Liyuba Vesely · itb cnr

    Dear Jobin, as you didn't  mention


    explicitly, maybe it could be a suggestion. Originally it was tested also on solids.

  • Zelimkhan Khakiev added an answer:
    How can I rotate a solid component in CST Design Studio?


    Zelimkhan Khakiev · Rostov State Transport University

    There are general rules for designing the electrical circuits. One of them is that you use only 90 degrees angles everywhere. So it's not common to place the elements at an angle 45 degrees. According to these general concepts CST Design doesn't allow you to arbitrarily rotate the elements in a circuit, only at an angle 90 degrees.

    Why do you whant exactly 45 degrees? I believe it doesn't make a sense for the physics of your task. 

  • Charles Francis added an answer:
    Can we relate Classic Electromagnetism to quantum physics?

    Can someone explain the procedure by which we can view classic electromagnetism through quantum mechanics? Are we able to look at any field as an ensemble of particles (photons), and how can we develop classic field theory assuming quantum mechanics, such as beamforming .

    Charles Francis · Jesus College, Cambridge

    That is not what I mean by a particle, and it is not the concept of a particle which I have used in my construction of qed. I mean a pointlike entity, but one for which position may be indeterminate because there is no background space. The wave aspect just appears in the maths and is not real. Fields are operators used in the description of interactions between particles.

  • Ken Toyama added an answer:
    Phase velocity inside a waveguide?

    In physics law it is said that one can not exceed the speed of light then the why phase velocity of wave inside the wave guide is greater than the speed of light?

    Ken Toyama · Juniper Networks, Inc.

    Another way is to look at a pulse propagation in a waveguide. The pulse envelope moves at the group velocity, which is certainly slower than the speed of light. We argue that we need a pulse or something similar to carry information and thus the information is not moving faster than the speed of light.

  • Aleksandr A. Tarasov added an answer:
    Why does the refractive index for an extraordinary ray vary with the propagation direction?

    In a birefringent crystal, the incident light gets split into two beams. One is ordinary and the other is extraordinary rays. The ordinary ray experiences constant refractive index n_o but the extraordinary ray experiences refractive index that varies with the direction of propagation of the light in the crystal. Why does it happen? Please explain the physical interpretation of the index ellipsoid.

    Aleksandr A. Tarasov · LaserOptek Co. Ltd.

    I shall say the same as Ioseph Gurwich said, but in other words:

    At first necessary to understand, what is refraction index of the material and the relation between refraction index and polarization of the material. See, for example, F. L. Pedrotti and L. S. Pedrotti "Introduction to Optics", 1993, p. 568-575. There is clear physical description of interaction between light and dielectric.

    If you understand the relation between refraction index and material polarizability, then it is easy to understand optical properties of different materials, particularly, of anisotropic crystals, when consider the atomic structure of the crystal (following to Radoslaw Chrapkiewicz post).

     Refraction index ellipsoid is convenient, but  formal tool for the description of light propagation in crystals. It does not explain physical nature of birefringence.

  • Eric Lord added an answer:
    What is the significance of the Poynting vector in a static electromagnetic field?
    In an electromagnetic field the flow of energy is given by the Poynting vector. For an electromagnetic wave, this vector is in the direction of propagation and accounts for radiation pressure. However, in a static electromagnetic field the Poynting vector can of course be non-zero. It's not easy to understand how there can be a 'flow' of energy in a static situation. Please discuss.
    Eric Lord · Indian Institute of Science

    Rajat ~

    Thanks for your answer. What you say is very like the conclusion I eventually arrived at: If E and B are static nothing is happening (nothing 'flows') until an object is placed in the field. Then a force will be exerted on the object - analogous to radiation pressure. I'm surprised that I know of no experimental attempt to test this. Your analogy with the static E-field is an interesting one. We have divE = ρ − charge is the source of E.  The static Maxwells equations imply divP = −E.j; the 'source' of the Poynting vector is provided by the currents j required to set up the static field.

  • Antoine J.H. Acke added an answer:
    Does a uniformly accelerated charge radiate?
    In classical electromagnetism, any accelerated charge should radiate. The back reaction on the charge due to radiation is given by radiation reaction which depends on time derivative of acceleration. However for uniformly accelerated charge there is radiation but no radiation reaction. I would appreciate any comment on this apparent paradox.
    Antoine J.H. Acke · Katholieke Hogeschool Sint-lieven

    We can approach  the problem by starting from the idea that the source of electromagnetic radiation is oscillating charge.

    The time function describing the acceleration of a uniformly accelerated point charge is: a(t) = 1 for all values of t.   Its Fourier transform is the Dirac delta function, what means that a(t) doesn't contain harmonic components.

    So, from  our starting point it follows that a uniformly accelerated charged particle cannot be a source of an EM wave (nor an emitter of photons).

    Let's note that a uniformly accelerated particle is a purely theoretical concept.  In reality, a constant acceleration can only exist during a limited time interval.  In that case the Fourier spectrum of a(t) does contain harmonic components and the particle can be a source of EM radiation.

  • Mohammad Naser Hashemnia added an answer:
    Can anyone suggest why I get different values from these two methods for Torque calculation by energy-coenergy method?

    Dear all,

    I have come to a question regarding what has been extensively studied in electromagnetic energy conversion principles.

    Assume a single coil in a magnetic circuit. It we consider the instantaneous energy flow we write:



    Thus: v=Ri+Lp(i)+ip(L)=Ri+Lp(i)+i*dL/dteta*omega

    Then the input power will be:

    The right hand side has 3 terms; the first is the copper loss, the second is the rate of change of the stored magnetic energy and finally, the last one is the output mechanical power (Pmech).



    Therefore: T=i2*dL/dteta

    This is in contrast with the coenergy method which gives:


    Why is the result of one method double the other one?

    I would appreciate if any one gives me their valuable points of view.

    Mohammad Naser Hashemnia · Sharif University of Technology

    Can you derive Md taking it into account as an inductance?

    Moreover, I criticized this statement: " L AF is the mutual inductance between the fi eld and the rotating armature coils" .I believe that the mutual inductance is zero for the reason you correctly mentioned.

  • Orin Laney added an answer:
    Can any one help me reduce a magnetic field?

    Recently, we have designed a new electrical device with the output power 3v. We need to transfer internet data from this device to another one using a four terminal electrical cable (not twisted. i.e. like the four parallel cables assembled in one shielded cable ) with diameter 0.55 mm. The problem is the magnetic field that generated from the power over the cable is diminished the data (there is no data in the end of another device).
    Can anyone help with this problem where we don't need to make this cable as a twisted cable, not using the earthing point and we don't need to increase the power from the output device.
    Note: The distance is between one device and another is 92 meters.

    Orin Laney · Atwood Research

    To make this 4 conductor flat style cable work, you will need to place balanced data on the two center conductors and power on the outside conductors.  The hot side power conductor must have a high frequency bypass cap right at the connector on both ends and the ground conductor termination should also be right at the connectors.  Use a proper connector that cannot be inserted reversed.  Notwithstanding that the conductors are not themselves twisted, include some rotation in the cable lay (3 to 4 times per meter) to help maintain balance of ambient noise pick up.

    Since your power is apparently coming from a switching supply such that the ripple is the problem, this must be addressed directly.  Either use linear regulation at the sending end, or insert a differential mode choke, which is nothing more than a common mode choke with a winding reversed.  But, it will have to be a large one of the sort intended for power line filtering and not some tiny surface mount part.  Best practice is actually to use two in series, one in standard common mode configuration and the other differential, because neither mode is helpful.  Common mode radiates noise and diff mode couples into your data.  The usual HF bypass cap directly across the choke output should be included.

    I have concerns regarding bandwidth over the distance quoted and mention termination again, but the above  will at least keep power noise out of the data.

  • M. K. Olsen added an answer:
    Spontaneous Parametric Down-Conversion is a classical or quantum phenomenon?

    I have seen that both classical and quantum theories are developed for this phenomenon. So please explain me the need for this.

    M. K. Olsen · University of Queensland 

    There is much discussion about where the boundary between classical and quantum phenomena lies. At some level, everything is quantum, but a classical description often suffices, depending on what we want to measure.

    One operational measure of the boundary comes from phase-space stochastic integration. The truncated Wigner representation is equivalent to stochastic electrodynamics, a classical theory. The Positive-P representation captures all the quantum nature of the problem. When we look at SPDC, the truncated Wigner gives accurate answers, but not for everything we wish to calculate. Some high order correlations, and especially two-time correlation functions are only found accurately when we use the full positive-P.

    My answer is then that it is a quantum phenomenon, but a classical analysis manages to describe most of what happens. I hope this helps.

  • Muhammad Waqas Baig added an answer:
    What should be the direction of force in the coil of my electromagnet?

    I am designing a 1.5 T electromagnet. It is C shaped electromagnet, having two coils at two ends. Image is attached for reference.  When i am considering force between two coil, which should be attractive, as direction of current in both these coils are same. But in simulation direction of force coming is repulsive. I have shown Direction of current with black ink, direction of force as blue and red.  Please give your valuable suggestion. I want to know weather i am doing some blunder of not.

    Muhammad Waqas Baig · University of the Punjab

    Repulsive behavior is really a strange thing because Iron behaves as a dependent magnet and it filed lines produced by Iron Magnet are due to the Coils, so how would it be a dominant factor. Unless, an AC source to Coils I can't figure out a repulsive behavior.

  • Panagiotis Michalis added an answer:
    How can I measure the permittivity value and permeability?
    I have powder sample and thin film sample
    Panagiotis Michalis · University of Strathclyde

    There are plenty of commercial sensors that can provide dielectric permittivity measurements. As already mentioned  they are costly and most of the them are based on the Time Domain technique but also the last few years are also using the Frequency Domain method. You could also measure permittivity in the lab using 2 calibrated capacitor electrodes.

  • François Waelbroeck added an answer:
    What interactions does a flux tube, with frozen in magnetic field, have with a background flow of ionized plasma??

    I need to know the changes in the energy equation and in the Navier-Stokes equations for that matter.

    François Waelbroeck · University of Texas at Austin

    I presume that by "background flow of ionized plasma" you mean the flow of the plasma surrounding your flux tube, which is also threaded by a frozen-in field but with a different topology, so that your flux tube is like a plasmoid.

    One important consideration is whether your background plasma has a pressure gradient. If it does then the ions and electrons have opposite drift velocities and in steady state the plasmoid will generally flow at a velocity intermediate between that of the ions and electrons, depending on its size compared to the ion Larmor radius. Another consideration is the propagation velocity of the tube, since it can excite wakes that exert forces on the tube, just like the wakes of ships.

  • I. G. Richardson added an answer:
    Is there any database available for Magnetic clouds up to 2014?

    As I think only few papers  are available on this field also very few database I found which is also up to 1990 or 1995. Does someone know about these data or other available database or recent research on this topic.

    I. G. Richardson · University of Maryland, College Park

    Response to Crhistine's answer:  The LASCO list is of CMEs at the Sun observed by the coronagraph, not of magnetic clouds in the solar wind.

  • Hossein Javadi added an answer:
    To understand the relationship between gravity and electromagnetism, we should explain blueshift by using quantum mechanics. What do you think?

    The Pound–Rebka experiment is a well-known experiment to test Albert Einstein's theory of general relativity in 1959. The result confirmed the predictions of general relativity. Proponents of the theory of general relativity offer three different conflicting explanations of these results that are said to be equivalent to each other and therefore are all equally correct. The main problem with this explanation lies in the conceptualization of a physical process by which mass, momentum and energy could be either added to or subtracted from a photon without changing its velocity or angular momentum. Such a mechanism has never been proposed except for a mathematical description of a four-dimensional substance called a “space-time continuum.” This is a non-Doppler explanation of the shifts in which both source, observer and all photons are in the same inertial reference frame and the photons move at exactly c relative to both source and observer.
    Apparent Weight of Photons; Physical Review Letters - PHYS REV LETT , vol. 4, no. 7, pp. 337-341, 1960

    Hossein Javadi · Islamic Azad University

    Dear Robert
    What I understood the both special and general relativity are explaining what observers can observe. For example, according to special relativity the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source. There is not any reason why the speed of light is constant. See;

    On the constancy of the speed of light: a nature law or a natural accident!?


  • Chetan R. Kathad added an answer:
    Why the permittivity of free space has non zero value while the sucseptibility is zero?

    The electrical permittivity of free space has constant value of the order of 10-12 F/m while the susceptibility has the exact zero value...The basic physical explanation is sought rather than mathematical..

    Chetan R. Kathad · Saurashtra University

    Mircea Pop, The definition suggests that epsilon is a dissipation factor similar to dielectric constant of dielectrics that forms an opposite field to reduce the original one..And naturally we can think putting all the mathematics aside that if any material susceptible to field than it should not permit it 100%, we taught that susceptibility of a vacuum is zero, than it should permit  the field 100% without any dissipation..

  • Robert Shuler added an answer:
    Is it possible to derive the constant & uniform velocity of light & the Lorentz transform without starting from the principle of relativity?
    Originally the Lorentz transform was developed to explain the Michelson-Morley experiment in terms of length contraction due to motion through an ether. Some work was done on how this might produce distortions of electromagnetic forces and interatomic bonds to produce length contraction. Einstein postulated a fully symmetric (i.e. relative) form with no preferred frame of reference, and gave a different derivation based on the principle of relativity, that the laws of physics including the velocity of light should be the same in all inertial frames. It is a pretty large assumption and gives no insight into mechanisms.

    In years of searching I've found only two papers that claim to derive something like the relativistic Lorentz (not the ether one) from more fundamental principles, one by Yilmaz using de Broglie waves which has received no follow up discussion that I can find, and one by Matthew Brown using pseudo-measurement interaction counting which is only on arXiv (and RG in his profile). Are there any others?

    Does it make any difference if relativity can be derived from some mechanism-like postulates? Does it have any implications for understanding things like spooky action at a distance (entanglement)? Or inertia/gravity?
    Robert Shuler · NASA

    In my view, time is controlled by inertia, and whatever interaction determines inertia is more likely to be akin to entanglement than to QFT.  While QFT interactions are limited to lightspeed, it is well known that entanglement interactions have no regard for relativistic limits.  Think of inertia as position entanglement of multiple masses. 

    Over the course of several papers which I have referenced variously in these discussions, I have shown how gravity can be formulated as emergent from inertia, explaining its weakness.  That implies gravity is probably not a QFT type of force (and therefore there are no conventional gravitons).  Direct evidence for this comes from the way the strength of gravity varies in relation to relativist quantities.  Recall the discussions of the sonic world and the characterization of what an effect with Lorentz stiffness greater than c would look like.  It would not be subject to relativistic slowdowns and limits.  Therefore it could maintain a constant acceleration in spite of relativistic time slowdown (which gravity exactly does, and this amount of acceleration leads to the correct orbit for mercury) and it would be able to push things beyond relativistic limits, or horizons, which depending on the views of Stephen Hawking at any given moment, gravity may or may not be able to do (you couldn't actually push sonic objects beyond their limits, but if there were other objects not made of sound, or EM waves, gravity could push them further than sonic or EM forces in whichever case).

    Thanks for bringing this up.  I forgot to include this very important conclusion (about the Lorentz stiffness of gravity) in my summary.

  • Laurent Damois added an answer:
    How can I generate an azimuthal or axial magnetic field whose strength is proportional to 1/r^2?
    The behavior of surfaces described by the Heisenberg model in the presence of an external magnetic field have like solution skyrmions. However, it is necessary that the magnetic field is proportional to 1/r^2. Does anybody know how this kind of field can be generated?
    Laurent Damois · Institut National des Sciences Appliquées de Lyon

    If you know the equation of the B Field you want, and if the B Field is a static Field, the current density distribution is: j = Curl(B)/µ

  • Marek Wojciech Gutowski added an answer:
    I need to build a setup for generating a dense magnetic field and would like to know if an assembly of solenoids is a good option?
    I am working on the concept of 'force on a current carrying conductor in magnetic field' for which I need to generate approx. 1-D magnetic field. Would an assembly of solenoids be a good option or is there an alternative?
    Marek Wojciech Gutowski · Institute of Physics of the Polish Academy of Sciences

    Suppose your experiment is designed for presentation purposes only, and usage of the expensive equipment should be avoided.  The field generated by a solenoid (perhaps two Helmholtz coils would be preferred, as they generate much more uniform field between them) will be, for all practical reasons, of order 30-50 mT or less.  Inserting a  soft magnetic core inside your solenoid should improve the field 10 times or even more.  Next you should think about your "current carrying conductor".  Perhaps a single copper wire (ribbon?), with, say 1A current, may appear insufficient.  Instead of DC current in your solenoid you can consider a pulsed mode of operation with much higher current (by discharging a capacitor).  Then, however, you should be ready for making such a discharge unidirectional, not oscillating.

  • Ivan Fernandez-Corbaton added an answer:
    Is there any good method that can be used to detect the polarization of the field near focus?
    If the polarization is changed dramatically near the focus, can we image the polarization in an experiment?
    Ivan Fernandez-Corbaton · Karlsruhe Institute of Technology

    Dear Xiaoyang,

    I will give you a theorists answer. This may not be what you are looking for, but I hope you find it useful in some way.

    First of all, there is one thing that you can do if you are content with getting an idea of how the field looks in the focus, even though is only numerical. You can extract the map of polarization in coordinate space (a numerical result is not necessarily an observable quantity). For this to work, you need to have a very good idea of what the beam is at the plane of the input of the lens. You then use the aplanatic lens aproximation to compute the plane wave decomposition of the focus field. You can find a nice description of the procedure in section 3.5 of this book


    Now for the discussion. I would say that, strictly speaking, there is no way to measure the polarization of a focused field in coordinate space. By "polarization in coordinate space" I mean the spatially varying polarization vector. I assume that this is what you want to measure.

    The reason why I say that there is no way to mesure it is because it is not an observable of the field. Observables of the field are its frequency, its angular momentum, its linear momentum, etc ... . Now, there is an observable related to polarization in momentum space. It is called the helicity of the field. By polarization in momentum space, I mean the polarization of each and every plane wave composing the field. If all of the plane waves composing a field are left hand polarized, the helicity of the field is 1,  and it is -1 if they are all right hand polarized. You can of course have fields with mixed helicity.

    In theory, you can measure the power in each helicity component of a field. In practice, at optical frequencies, this is not trivial since it is hard to have objects that respond to just one of the helicities. At lower frequencies such objects exist, for example helical conductors


    I do not know of such objects at optical frequencies, but some nanostructure materials may do the job some day.

    At this point you may be thinking that all the above must be wrong because you can measure the polarization of a beam with just waveplates, linear polarizers and a CCD camera or powermeter. You can of course do that, but this is not a general field. The difference there is that you are working with a special type of light, collimated light.  For proper operation, the waveplates must be aligned so that the collimated beam hits them perpendicularly. They do not work in the expected same for non perpendicular incidence. This is why, even if you place a small piece of waveplate in the focus, it will not do the job for you. What you want is a filter of polarization whose operation is independent of the direction of incidence on the device. That, is related to helicity (the polarization of all the planewaves impinging on the device).

    If you are interested in the use of helicity in focusing experiments, you can check out chapter 4 of my thesis (available in RG and the arxiv).

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