EXPERIMENTAL CHALLENGES INVOLVED IN MEASURING POLARIZATION CHANGES OF LIGHT PROPAGATING THROUGH A MAGNETIC FIELD IN VACUUM
EXPERIMENTAL CHALLENGES INVOLVED IN SEARCHES FOR AXION-
LIKE PARTICLES AND NONLINEAR QUANTUM ELECTRODYNAMIC 
EFFECTS BY SENSITIVE OPTICAL TECHNIQUES 
Christopher C. Davis1*, Joseph Harris2, Robert W. Gammon3, Igor I. Smolyaninov1 
and Kyuman Cho4 
1Department of Electrical and Computer Engineering University of Maryland, College 
Park, MD 20742 
2Department of Physics, University of Maryland, College Park, MD 20742 
3Institute for Physical Science and Technology, University of Maryland, College Park, 
MD 20742 
4Department of Physics, Sogang University, Seoul, Korea 
We discuss the experimental techniques used to date for measuring the changes in 
polarization state of a laser produced by a strong transverse magnetic field acting in a 
vacuum. We point out the likely artifacts that can arise in such experiments, with 
particular reference to the recent PVLAS observations and the previous findings of the 
BFRT collaboration. Our observations are based on studies with a photon-noise limited 
coherent homodyne interferometer with a polarization sensitivity of 2×10-8 
rad Hz 1/2 mW-1/2. 
P.A.C.S. numbers: 42.15.Eq, 14.80.Mz, 12.20-m, 13.40.-f 
Introduction 
 The most important magneto-optical interactions that can occur in material media 
are the Faraday effect, magnetic dichroism, and magnetic birefringence (the Cotton-
Mouton effect). Quantum electrodynamics predicts that because of photon-photon 
interactions even the vacuum becomes birefringent in the presence of a strong magnetic 
field [1-5]. Further, the interaction with an axion-like particle and two photons via the 
Primakoff effect will also lend optical properties to the vacuum in the presence of a 
strong magnetic field [6-10]. The occurrence of an apparent magnetic dichroism of the 
vacuum would imply the preferential disappearance of left- or right circularly polarized 
photons from a light beam. To conserve mass and energy this would imply either the 
production of particles, or photon-splitting.  
The QED effect and the axion effect are treated in terms of an effective 
Lagrangian [1-7], in units where 1c= =h and . 2 / 4 1/137eα π= ≈
 ( ) ( ) ( )
2 22 2 2
1 7 1
4 90 4 2 4ae
L F F F F F F a a m a F F
µν µν µν µ µν
µν µν µν µ µν
α ⎡ ⎤
= − + + + ∂ ∂ − +⎢ ⎥⎣ ⎦
% %1 a  (1) 
Where the first half of the expression is the Euler-Heisenberg effective Lagrangian, 
which is appropriate to the QED effect, and the second half is the effective Lagrangian, 
which is appropriate to the Primakoff effect and accounts for the axion.  Here,  is the 
axion field,  is the axion mass, and 
am M is the inverse axion coupling constant.  Raffelt 
and Stodolsky [7] synthesize the results of Adler [4] and solve for the equations of 
motion.  Analysis of the classical wave solutions of the equations of motion produces a 
picture of mixing between photon and axion modes in a polarized laser experiment with a 
static transverse magnetic field and an optical cavity to increase path length.  In such an 
experiment, CP arguments predict that the axion will only couple to the parallel 
components of the beam. Thus, two main effects are predicted.   The first effect is a phase 
difference ∆φ=φ||-φ⊥ between the parallel and perpendicular components of polarized 
light interacting with the magnetic field. This arises from both QED and the preferential 
mixing of axion and photon modes.  In the mixing part of this picture, a photon mode 
oscillates into an axion mode before turning back into a photon and gets out of phase.  In 
both cases, this phase difference causes an apparent birefringence. 
 The second main effect, is an apparent linear dichroism which manifests itself as a 
rotation,ψ ,of the polarization and attenuation.  This is caused by the fact that mirrors do 
not reflect axions and, hence, any axion modes that do not oscillate back to photons 
before hitting the mirror will appear as lost parallel photon modes.  For small axion 
masses, the theory predicts: 
                  
φ ω∆ =  ,  
ext a
∆ =  and  
lψ = , (2) 
where l is the length of the cavity, N is the number of passes and L Nl=  is the total path 
length of the beam through the interaction region.  The subscripts QED and a, refer to the 
origin of the effects.  In terms of index of refraction, ∆φ=kL(n||-n⊥).  Choosing the limit 
of small axion masses is justified by several experimental results and astrophysical 
observations [6 -11] which bound the axion mass to and 3 610 10aeV m eV
− −> >
1010M GeV> .  This result also takes into account Adler’s analysis of the E-H 
Lagrangian which predicts the following vacuum birefringence: 
                                 n⊥=1+2ξsin2θ, n||=1+ θξ 2sin
7  with
= .                          (3) 
Here,θ  is the angle between and k .[4,7] extB
 The expected birefringence, as a function of extB in Tesla, due to the QED effect, is 
∆n=n||-n⊥=4×10-23Bext2.  The phase shift between the two orthogonal components of a 
light beam is 2 /L nφ π∆ = ∆ λ . For input light linearly polarized at 45o to the field 
direction, this translates into an induced ellipticity of the light /L nε π λ= ∆ , for a path 
length L. For a 1m path and a 1T field the induced ellipticity is expected to be 1.2×10-16.  
No experiment to date has achieved this sensitivity. 
The BRFT and PVLAS Experiments 
 Two important experiments have attempted to detect the phenomena that would 
result from the Primakoff effect. In the BRFT experiment [12] an upper limit of 3.5×10-10 
rad was determined for the possible rotation angle for a 2.2km path in a 3.25T field, 
equivalent to 1.5×10-14 rad m-1T-2, and an ellipticity of 1.6×10-9 was measured on a 299m 
path in a 3.25T field. The PVLAS experiment [13] claims a rotation of 1.7×10-7rad for a 
44km long path in a 5T field, equivalent to 1.55×10-14 rad m-1T-2. The BRFT and PVLAS 
experiments differ in several important specific ways, although from the standpoint of 
applying a modulated magnetic field they are similar. BRFT uses a transverse magnetic 
field modulated at a frequency of 32mHz about a background level of 3.25T. PVLAS 
uses a transverse magnetic field that rotates around the light propagation axis at 
1.89rad/s. This field is equivalent to the simultaneous application of two orthogonal 
transverse field components oscillating at 0.3Hz, but in quadrature.  Neither the BRFT 
nor PVLAS experiments operated at the photon noise limit. The BRFT experiment used a 
200mW argon ion laser and achieved a sensitivity of 4.7×10-7 rad Hz ½ m W -1/2. The 
PVLAS experiment used a 100mW 1.06µm Nd:YAG laser and achieved a sensitivity of 
10-6 rad Hz-1/2 mW-1/2. The photon noise limit at 1.06µm for a detector with a responsivity 
of 0.4 A/W (a typical value for a Si photodiode at this wavelength) is 2×10-8 
rad Hz 1/2 mW 1/2. 
Discussion 
 We have for several years operated a balanced coherent homodyne polarization 
interferometer for the study of the Faraday and Cotton-Mouton effects in condensed 
matter [14], and have achieved a photon noise limited sensitivity of 2×10-8 rad Hz-1/2 
mW-1/2 at 632.8nm or 1.06µm. Because we have only a 1kGauss modulated transverse 
field magnet with 0.1m pole pieces we could not compete with the BRFT and PVLAS 
experiments in overall sensitivity since we were a factor of 2.3×104 mT2 below BRFT and 
a factor 109mT2 below PVLAS in terms of path length and field strength. However, our 
experience with a very sensitive system for measuring elipticity has taught us much about 
the potential pitfalls of these experiments from an experimental optics standpoint. It is 
clear to us that the PVLAS experiment suffers from artifacts, as has already been pointed 
out by Melissinos [15], that the BRFT experiment suffers from artifacts has been 
acknowledged by its authors, although they do not specify all the sources of these 
spurious signals. A primary source of spurious signals in sensitive experiments of this 
kind is motion of optical components caused by a time-varying or a rotating magnetic 
field. The BRFT experiment acknowledges this and used a feedback system to attempt to 
minimize its effects. The PVLAS data show clear sideband peaks corresponding to the 
rotation frequency of their magnet, which should not be present for an effect proportional 
to B2. Indeed these peaks are approximately 18 times larger than the “real” signal at twice 
the magnet rotation frequency. They do not explain the origin of the fundamental signal 
but interpret the second harmonic signal as resulting from  an interaction involving a 
light, neutral, spin-zero particle.   
 In both the BRFT and PVLAS experiments optical components are either close to 
the magnet or mechanically coupled to the magnet and its cryostat. A primary component 
of the experiment that is strongly affected by the magnetic field is the evacuated tube 
passing though the magnet. This tube extends to the cavity end mirrors. All components 
in the experiment that experience any modulated field or field gradients will experience 
time-varying diamagnetic or paramagnetic forces. For example, any stainless steel or 
aluminum optical mounts will experience paramagnetic forces. There are torques acting 
on induced magnetic dipoles, especially in any components exposed to the field that are 
not absolutely symmetrically placed with respect to the field direction. A quartz sample 
tube in the magnet will experience the strongest forces in the regions where it leaves the 
magnet and experiences the largest field gradients, and will be pulled into the magnet 
bore. In general time-varying forces all result from any changes in magnetic stored 
energy that occur as the field is modulated. This generalized force on an object is 
F= ∫ ⋅∇− .21 dVHB   
 In our sensitive magneto-optical experiments we have verified that significant 
artifacts can result from any modulated feedback of light into the laser [16]. It has been 
shown that if a part of its own field is fed back into a laser by an optical component 
vibrating with small amplitude, then in the weak feedback regime, phase and amplitude 
of the output beam from the laser are synchronously modulated [17]. This effect is so 
efficient that when the source laser is influenced by the feedback the modulated light can 
cause interference in a sensitive measurement even for a balanced homodyne 
interferometer measuring an extremely small signal. We have performed a rigorous study 
of the feedback effect for the case of a balanced homodyne polarization interferometer. 
As a result, we have been able to detect phase and/or amplitude modulation produced in a 
balanced homodyne polarization interferometer when light from a mirror oscillating with 
an amplitude of only 9nm is fed back into the laser with 120dB of attenuation. This effect 
is still present even if the laser is an extremely low phase noise Nd:YAG ring laser [17]. 
The BRFT experiment is less sensitive to this feedback effect because it uses a multipass, 
zig-zag Herriott type cavity [18,19] rather than a spherical Fabry-Perot cavity. It is 
possible for light scattered by any of the optical components in these experiments to 
cause feedback, even if no specific optical component is used in the normal direction, and 
this includes scattered light that reflects off the inside walls of the evacuated tube inside 
the magnet.  The BRFT experiment uses a single optical isolator, which probably does 
not provide sufficient isolation to prevent feedback modulation effects. It appears that, 
according to the experimental arrangement shown in ref [11], the PVLAS experiment 
does not use an optical isolator after its laser. In principle, the Fabry-Perot resonator 
might not reflect significant incident light if the source laser is perfectly frequency locked 
to the resonator. In practice, however, even for a very high-Q resonator, it is impossible 
to avoid the feedback due to imperfectness of mirrors and locking electronics. Therefore, 
in the PVLAS experiment, the feedback modulation effects may cause major interference 
in measurements. 
 In principle, any correlated intensity noise can be rejected in a balanced 
homodyne interferometer. However, because of the imperfect performance of real optical 
and/or electronic components, overall common mode rejection ratio of the interferometer 
used in our study was approximately 40dB. Synchronous feedback can cause interference 
in a sensitive experiment even when the signal level is very low. In the case of the 
PVLAS scheme, by including the feedback effect synchronized at twice the rotating 
frequency of the magnet, the representation for the light intensity transmitted through the 
crossed polarizers of the ellipsometer given in Eq (2) of Ref. [11] can be rewritten as 
                                      2 20 ,2( ){ [ ( ) ( ) ( )] }mNI I I t t tν σ α η= + + + +Γ  
where 0I , 
2σ , α , η , and Γ  have the same meaning as in Ref [11] and ,2 mNI ν  is the 
intensity modulation caused by the feedback. The frequency of this synchronized 
modulation is given by the vibration frequency of a feedback element, twice the 
frequency of the rotating magnet. Small misalignment between the polarization 
components must be included in the quasi-static, uncompensated rotation and ellipticity, 
, which is much larger than the rotation caused by the Primakoff effect. Thus the term Γ
,22 ( )mN ( )I t tν η Γ  in the above equation has not only the same Fourier frequency as 02I αη  
but also has the same phase relationship when the quarter-wave plate is rotated by 90o. 
The synchronous interference, thereby cannot be distinguished from the magneto-optical 
effect being sought.  
 An important, but subtle distinction between the BRFT and PVLAS experiments 
is that the BRFT uses a mode-matched mirror cavity while the PVLAS apparently does 
not. Consequently, in the PVLAS experiment as the light beam oscillates between the 
two cavity mirrors its spot size and radius of curvature both oscillate and the radius of 
curvature does not match the mirror curvatures. This mismatch in radius leads to local 
non-normal incidence on the cavity mirrors (except on axis) and causes the local P-and S- 
polarization components of the beam to suffer different phase shifts, which vary radially 
on the mirror. A calculation for a typical very high reflectance multilayer mirror shows 
that this phase difference can be easily 10-11 rad per reflection for an incidence angle of 
1.5mrad. The PVLAS cavity is subject to these effects, which would be modulated if the 
cavity mirrors move, although the BRFT cavity is not. 
 A potential confounder in a search for vacuum magneto optic effects is the 
Faraday effect resulting from residual axial field components and trace gas. There are 
residual axial field components in both the BRFT and PVLAS experiments, since the 
local wave-vector directions in a Gaussian beam are only nominally perpendicular to a 
transverse field at the beam waist, or on axis. We do not however, believe that these were 
the sources of sidebands at the magnet oscillation or rotation frequency ωm. Nonetheless, 
an experiment in which there is no obvious modulation of the effect at frequency ωm is 
desirable, since an effect proportional to Bext2 only shows up at frequency 2ωm. In an 
experiment in which the entire field is modulated at frequency ωm a Faraday effect signal, 
or spurious signal, at ωm is distinguished from the desired signal at frequency 2ωm, which 
should be further checked by verifying that the desired signal is proportional to Bext2. A 
complication can arise if the magnet modulation is not a pure harmonic at frequency ωm. 
Any second harmonic of the magnetic field can produce a spurious signal at 2ωm, but this 
can be identified since it will be linear in Bext.  
Features of an Improved Experiment 
 It is our belief that a balanced coherent homodyne interferometer is a better 
instrument to use than an extinction-based ellipsometer in a search for vacuum magneto-
optical effects. Such a system is almost guaranteed to achieve the photon noise limit and 
provides excellent common mode rejection of laser noise. We also believe that any effect 
observed should be demonstrated to scale with Bext2 [14]. It will also be desirable to use 
the largest magnetic field possible, but not to modulate this. An experiment similar to 
PVLAS can then be performed by rotating the optical train at angular frequency ωm.  
Conclusions 
 We believe that we have identified the likely causes of artifacts in the PVLAS 
experiment, and therefore suggest that the case for an interaction involving an axion-like 
particle has not been made. Furthermore, the PVLAS experiment contradicts the findings 
of the BRFT experiment, and a series of astrophysical observations that restrict the range 
of axion particle masses that are possible. An improved experimental arrangement is 
needed to pursue vacuum magnetic birefringence and polarization rotation effects. With 
an improved system, detection of the QED- predicted magnetic birefringence [4,5] should 
be possible, and a more sensitive examination of the existences of any axion-like 
interactions. 
* Corresponding author 
Email address: davis@umd.edu
                                                 
[1] W. Heisenberg and H. Euler, Z. Phys. 98, 714 (1936). 
[2] V.F. Weisskopf, K. Dan. Vidensk.Selsk.Mat.Fys.Medd, 14, 6 (1936). 
[3] J. Schwinger, Phys.Rev. 82, 664 (1951). 
[4] S.L. Adler, Ann Phys. (N.Y.) 67,599 (1971). 
[5] S. L. Adler, J. Phys. A 40, F143 (2007). 
[6] P. Sikivie, Phys. Rev. Lett. 51, 1415 (1983).  
[7] G. Raffelt and L. Stodolsky, Phys. Rev. D 37, 1237 (1988). 
[8] S.J. Asztalos et al. Ann.Rev.Nucl.Part.Sci. 56, 293 (2006). 
[9] P. Sikivie, arXiv:hep-ph/0701198v1 (2007).  
[10] G. Raffelt, arXiv:hep-ph/0611350 (2006). 
[11] J. Jaeckel et al, Phys.Rev.D 75, 013004 (2007) 
[12] R. Cameron et al. Phys Rev. D 47, 3703 (1993) 
[13] E. Zavattini et al. Phys. Rev. Lett. 96, 110406 (2006) 
[14] K. Cho, S.P. Bush, D.L. Mazzoni,  and C.C. Davis, Phys. Rev. B 43, 965 (1991). 
[15] A.C. Melissinos, arXiv:hep-ph/0702135v1 13 Feb 2007. 
[16] K. Cho, Ph.D Thesis, University of Maryland, 1991. 
[17] M. Sargent III, M.O. Scully and W.E. Lamb, Laser Physics, Addison-Wesley, 
Reading. Mass, 1974. 
[18] D. R. Herriott, H. Kogelnik, and R. Kompfner, Appl. Opt. 3, 523 (1964) 
[19] D. R. Herriott and H.J. Schulte,  Appl. Opt. Aug. 4, 883 (1965) 
mailto:davis@umd.edu

  We discuss the experimental techniques used to date for measuring the changes
in polarization state of a laser produced by a strong transverse magnetic field
acting in a vacuum. We point out the likely artifacts that can arise in such
experiments, with particular reference to the recent PVLAS observations and the
previous findings of the BFRT collaboration. Our observations are based on
studies with a photon-noise limited coherent homodyne interferometer with a
polarization sensitivity of 2x10^-8 rad Hz^(1/2) mW^(-1/2).

Introduction 
 The most important magneto-optical interactions that can occur in material media 
are the Faraday effect, magnetic dichroism, and magnetic birefringence (the Cotton-
Mouton effect). Quantum electrodynamics predicts that because of photon-photon 
interactions even the vacuum becomes birefringent in the presence of a strong magnetic 
field [1-5]. Further, the interaction with an axion-like particle and two photons via the 
Primakoff effect will also lend optical properties to the vacuum in the presence of a 
strong magnetic field [6-10]. The occurrence of an apparent magnetic dichroism of the 
vacuum would imply the preferential disappearance of left- or right circularly polarized 
photons from a light beam. To conserve mass and energy this would imply either the 
production of particles, or photon-splitting.  
The QED effect and the axion effect are treated in terms of an effective 
Lagrangian [1-7], in units where 1c= =h and . 2 / 4 1/137eα π= ≈
 ( ) ( ) ( )
2 22 2 2
1 7 1
4 90 4 2 4ae
L F F F F F F a a m a F F
µν µν µν µ µν
µν µν µν µ µν
α ⎡ ⎤
= − + + + ∂ ∂ − +⎢ ⎥⎣ ⎦
% %1 a  (1) 
Where the first half of the expression is the Euler-Heisenberg effective Lagrangian, 
which is appropriate to the QED effect, and the second half is the effective Lagrangian, 
which is appropriate to the Primakoff effect and accounts for the axion.  Here,  is the 
axion field,  is the axion mass, and 
am M is the inverse axion coupling constant.  Raffelt 
and Stodolsky [7] synthesize the results of Adler [4] and solve for the equations of 
motion.  Analysis of the classical wave solutions of the equations of motion produces a 
picture of mixing between photon and axion modes in a polarized laser experiment with a 
static transverse magnetic field and an optical cavity to increase path length.  In such an 
experiment, CP arguments predict that the axion will only couple to the parallel 
components of the beam. Thus, two main effects are predicted.   The first effect is a phase 
difference ∆φ=φ||-φ⊥ between the parallel and perpendicular components of polarized 
light interacting with the magnetic field. This arises from both QED and the preferential 
mixing of axion and photon modes.  In the mixing part of this picture, a photon mode 
oscillates into an axion mode before turning back into a photon and gets out of phase.  In 
both cases, this phase difference causes an apparent birefringence. 
 The second main effect, is an apparent linear dichroism which manifests itself as a 
rotation,ψ ,of the polarization and attenuation.  This is caused by the fact that mirrors do 
not reflect axions and, hence, any axion modes that do not oscillate back to photons 
before hitting the mirror will appear as lost parallel photon modes.  For small axion 
masses, the theory predicts: 
                  
φ ω∆ =  ,  
ext a
∆ =  and  
lψ = , (2) 
where l is the length of the cavity, N is the number of passes and L Nl=  is the total path 
length of the beam through the interaction region.  The subscripts QED and a, refer to the 
origin of the effects.  In terms of index of refraction, ∆φ=kL(n||-n⊥).  Choosing the limit 
of small axion masses is justified by several experimental results and astrophysical 
observations [6 -11] which bound the axion mass to and 3 610 10aeV m eV
− −> >
1010M GeV> .  This result also takes into account Adler’s analysis of the E-H 
Lagrangian which predicts the following vacuum birefringence: 
                                 n⊥=1+2ξsin2θ, n||=1+ θξ 2sin
7  with
= .                          (3) 
Here,θ  is the angle between and k .[4,7] extB
 The expected birefringence, as a function of extB in Tesla, due to the QED effect, is 
∆n=n||-n⊥=4×10-23Bext2.  The phase shift between the two orthogonal components of a 
light beam is 2 /L nφ π∆ = ∆ λ . For input light linearly polarized at 45o to the field 
direction, this translates into an induced ellipticity of the light /L nε π λ= ∆ , for a path 
length L. For a 1m path and a 1T field the induced ellipticity is expected to be 1.2×10-16.  
No experiment to date has achieved this sensitivity. 
The BRFT and PVLAS Experiments 
 Two important experiments have attempted to detect the phenomena that would 
result from the Primakoff effect. In the BRFT experiment [12] an upper limit of 3.5×10-10 
rad was determined for the possible rotation angle for a 2.2km path in a 3.25T field, 
equivalent to 1.5×10-14 rad m-1T-2, and an ellipticity of 1.6×10-9 was measured on a 299m 
path in a 3.25T field. The PVLAS experiment [13] claims a rotation of 1.7×10-7rad for a 
44km long path in a 5T field, equivalent to 1.55×10-14 rad m-1T-2. The BRFT and PVLAS 
experiments differ in several important specific ways, although from the standpoint of 
applying a modulated magnetic field they are similar. BRFT uses a transverse magnetic 
field modulated at a frequency of 32mHz about a background level of 3.25T. PVLAS 
uses a transverse magnetic field that rotates around the light propagation axis at 
1.89rad/s. This field is equivalent to the simultaneous application of two orthogonal 
transverse field components oscillating at 0.3Hz, but in quadrature.  Neither the BRFT 
nor PVLAS experiments operated at the photon noise limit. The BRFT experiment used a 
200mW argon ion laser and achieved a sensitivity of 4.7×10-7 rad Hz ½ m W -1/2. The 
PVLAS experiment used a 100mW 1.06µm Nd:YAG laser and achieved a sensitivity of 
10-6 rad Hz-1/2 mW-1/2. The photon noise limit at 1.06µm for a detector with a responsivity 
of 0.4 A/W (a typical value for a Si photodiode at this wavelength) is 2×10-8 
rad Hz 1/2 mW 1/2. 
Discussion 
 We have for several years operated a balanced coherent homodyne polarization 
interferometer for the study of the Faraday and Cotton-Mouton effects in condensed 
matter [14], and have achieved a photon noise limited sensitivity of 2×10-8 rad Hz-1/2 
mW-1/2 at 632.8nm or 1.06µm. Because we have only a 1kGauss modulated transverse 
field magnet with 0.1m pole pieces we could not compete with the BRFT and PVLAS 
experiments in overall sensitivity since we were a factor of 2.3×104 mT2 below BRFT and 
a factor 109mT2 below PVLAS in terms of path length and field strength. However, our 
experience with a very sensitive system for measuring elipticity has taught us much about 
the potential pitfalls of these experiments from an experimental optics standpoint. It is 
clear to us that the PVLAS experiment suffers from artifacts, as has already been pointed 
out by Melissinos [15], that the BRFT experiment suffers from artifacts has been 
acknowledged by its authors, although they do not specify all the sources of these 
spurious signals. A primary source of spurious signals in sensitive experiments of this 
kind is motion of optical components caused by a time-varying or a rotating magnetic 
field. The BRFT experiment acknowledges this and used a feedback system to attempt to 
minimize its effects. The PVLAS data show clear sideband peaks corresponding to the 
rotation frequency of their magnet, which should not be present for an effect proportional 
to B2. Indeed these peaks are approximately 18 times larger than the “real” signal at twice 
the magnet rotation frequency. They do not explain the origin of the fundamental signal 
but interpret the second harmonic signal as resulting from  an interaction involving a 
light, neutral, spin-zero particle.   
 In both the BRFT and PVLAS experiments optical components are either close to 
the magnet or mechanically coupled to the magnet and its cryostat. A primary component 
of the experiment that is strongly affected by the magnetic field is the evacuated tube 
passing though the magnet. This tube extends to the cavity end mirrors. All components 
in the experiment that experience any modulated field or field gradients will experience 
time-varying diamagnetic or paramagnetic forces. For example, any stainless steel or 
aluminum optical mounts will experience paramagnetic forces. There are torques acting 
on induced magnetic dipoles, especially in any components exposed to the field that are 
not absolutely symmetrically placed with respect to the field direction. A quartz sample 
tube in the magnet will experience the strongest forces in the regions where it leaves the 
magnet and experiences the largest field gradients, and will be pulled into the magnet 
bore. In general time-varying forces all result from any changes in magnetic stored 
energy that occur as the field is modulated. This generalized force on an object is 
F= ∫ ⋅∇− .21 dVHB   
 In our sensitive magneto-optical experiments we have verified that significant 
artifacts can result from any modulated feedback of light into the laser [16]. It has been 
shown that if a part of its own field is fed back into a laser by an optical component 
vibrating with small amplitude, then in the weak feedback regime, phase and amplitude 
of the output beam from the laser are synchronously modulated [17]. This effect is so 
efficient that when the source laser is influenced by the feedback the modulated light can 
cause interference in a sensitive measurement even for a balanced homodyne 
interferometer measuring an extremely small signal. We have performed a rigorous study 
of the feedback effect for the case of a balanced homodyne polarization interferometer. 
As a result, we have been able to detect phase and/or amplitude modulation produced in a 
balanced homodyne polarization interferometer when light from a mirror oscillating with 
an amplitude of only 9nm is fed back into the laser with 120dB of attenuation. This effect 
is still present even if the laser is an extremely low phase noise Nd:YAG ring laser [17]. 
The BRFT experiment is less sensitive to this feedback effect because it uses a multipass, 
zig-zag Herriott type cavity [18,19] rather than a spherical Fabry-Perot cavity. It is 
possible for light scattered by any of the optical components in these experiments to 
cause feedback, even if no specific optical component is used in the normal direction, and 
this includes scattered light that reflects off the inside walls of the evacuated tube inside 
the magnet.  The BRFT experiment uses a single optical isolator, which probably does 
not provide sufficient isolation to prevent feedback modulation effects. It appears that, 
according to the experimental arrangement shown in ref [11], the PVLAS experiment 
does not use an optical isolator after its laser. In principle, the Fabry-Perot resonator 
might not reflect significant incident light if the source laser is perfectly frequency locked 
to the resonator. In practice, however, even for a very high-Q resonator, it is impossible 
to avoid the feedback due to imperfectness of mirrors and locking electronics. Therefore, 
in the PVLAS experiment, the feedback modulation effects may cause major interference 
in measurements. 
 In principle, any correlated intensity noise can be rejected in a balanced 
homodyne interferometer. However, because of the imperfect performance of real optical 
and/or electronic components, overall common mode rejection ratio of the interferometer 
used in our study was approximately 40dB. Synchronous feedback can cause interference 
in a sensitive experiment even when the signal level is very low. In the case of the 
PVLAS scheme, by including the feedback effect synchronized at twice the rotating 
frequency of the magnet, the representation for the light intensity transmitted through the 
crossed polarizers of the ellipsometer given in Eq (2) of Ref. [11] can be rewritten as 
                                      2 20 ,2( ){ [ ( ) ( ) ( )] }mNI I I t t tν σ α η= + + + +Γ  
where 0I , 
2σ , α , η , and Γ  have the same meaning as in Ref [11] and ,2 mNI ν  is the 
intensity modulation caused by the feedback. The frequency of this synchronized 
modulation is given by the vibration frequency of a feedback element, twice the 
frequency of the rotating magnet. Small misalignment between the polarization 
components must be included in the quasi-static, uncompensated rotation and ellipticity, 
, which is much larger than the rotation caused by the Primakoff effect. Thus the term Γ
,22 ( )mN ( )I t tν η Γ  in the above equation has not only the same Fourier frequency as 02I αη  
but also has the same phase relationship when the quarter-wave plate is rotated by 90o. 
The synchronous interference, thereby cannot be distinguished from the magneto-optical 
effect being sought.  
 An important, but subtle distinction between the BRFT and PVLAS experiments 
is that the BRFT uses a mode-matched mirror cavity while the PVLAS apparently does 
not. Consequently, in the PVLAS experiment as the light beam oscillates between the 
two cavity mirrors its spot size and radius of curvature both oscillate and the radius of 
curvature does not match the mirror curvatures. This mismatch in radius leads to local 
non-normal incidence on the cavity mirrors (except on axis) and causes the local P-and S- 
polarization components of the beam to suffer different phase shifts, which vary radially 
on the mirror. A calculation for a typical very high reflectance multilayer mirror shows 
that this phase difference can be easily 10-11 rad per reflection for an incidence angle of 
1.5mrad. The PVLAS cavity is subject to these effects, which would be modulated if the 
cavity mirrors move, although the BRFT cavity is not. 
 A potential confounder in a search for vacuum magneto optic effects is the 
Faraday effect resulting from residual axial field components and trace gas. There are 
residual axial field components in both the BRFT and PVLAS experiments, since the 
local wave-vector directions in a Gaussian beam are only nominally perpendicular to a 
transverse field at the beam waist, or on axis. We do not however, believe that these were 
the sources of sidebands at the magnet oscillation or rotation frequency ωm. Nonetheless, 
an experiment in which there is no obvious modulation of the effect at frequency ωm is 
desirable, since an effect proportional to Bext2 only shows up at frequency 2ωm. In an 
experiment in which the entire field is modulated at frequency ωm a Faraday effect signal, 
or spurious signal, at ωm is distinguished from the desired signal at frequency 2ωm, which 
should be further checked by verifying that the desired signal is proportional to Bext2. A 
complication can arise if the magnet modulation is not a pure harmonic at frequency ωm. 
Any second harmonic of the magnetic field can produce a spurious signal at 2ωm, but this 
can be identified since it will be linear in Bext.  
Features of an Improved Experiment 
 It is our belief that a balanced coherent homodyne interferometer is a better 
instrument to use than an extinction-based ellipsometer in a search for vacuum magneto-
optical effects. Such a system is almost guaranteed to achieve the photon noise limit and 
provides excellent common mode rejection of laser noise. We also believe that any effect 
observed should be demonstrated to scale with Bext2 [14]. It will also be desirable to use 
the largest magnetic field possible, but not to modulate this. An experiment similar to 
PVLAS can then be performed by rotating the optical train at angular frequency ωm.  
Conclusions 
 We believe that we have identified the likely causes of artifacts in the PVLAS 
experiment, and therefore suggest that the case for an interaction involving an axion-like 
particle has not been made. Furthermore, the PVLAS experiment contradicts the findings 
of the BRFT experiment, and a series of astrophysical observations that restrict the range 
of axion particle masses that are possible. An improved experimental arrangement is 
needed to pursue vacuum magnetic birefringence and polarization rotation effects. With 
an improved system, detection of the QED- predicted magnetic birefringence [4,5] should 
be possible, and a more sensitive examination of the existences of any axion-like 
interactions. 
* Corresponding author 
Email address: davis@umd.edu
                                                 
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