Field of the Art

The present invention generally relates, in a first aspect, to a polarimeter based on conical refraction, and more particularly to a polarimeter adapted for the unambiguous determination of any polarization state of an input electromagnetic radiation.

A second aspect of the invention concerns to a method for determining the polarization state of an input electromagnetic radiation using the polarimeter of the first aspect.

Prior State of the Art

Polarimeters are the basic devices to measure the polarization of the light (Stokes polarimeters) or characterizing the polarimetric properties of a polarizing sample (Mueller polarimeters) from radiometric measurements. This polarimetric information is crucial in a large number of applications, such as in medicine, to enhance the image contrast of samples [1]; in material characterization, to determine their thickness and refraction indices [2]; or in astronomy, to obtain quantitative information of stars [3], among others.

Stokes polarimeters determine the polarization of a light beam by projecting the studied incident light over a set of different polarization analyzers, known as Polarization System Analyzer (PSA). If the PSA includes as minimum four linearly independent polarizing analyzers, the polarimetric information of the light beam is fully determined, conforming a complete Stokes polarimeter.

A visual way to determine if a certain polarimeter is able to perform complete polarimetric measurements is to represent the set of polarizing analyzers on the Poincare sphere [4]. When the polarizing analyzers are confined in a plane (i.e. a slide of the Poincare sphere), the resulting polarimeter is incomplete. For instance, if the PSA only contains the polarizing analyzers placed in the sphere equator (i.e. linear polarized states), the elliptical polarizing content is not determined. On the contrary, if the PSA arrangement confines a certain volume in the Poincare sphere, one obtains a complete polarimeter [5,6].

Many polarimeter architectures have been proposed in the literature [1-3,5-13]. Roughly, polarimeters can be classified depending on the acquisition method in which they are based on [14]: time sequential measurements [5,7,8], polarization modulation [9], division of aperture [10] and division of amplitude [1 1 ]. In each one of these categories, there exist different prototypes performing accurate polarimetric measurements. However, as a consequence of the specific acquisition method applied, each category presents certain limitations in the measurement. For instance, time sequential polarimeters and polarization modulator based polarimeters require of mechanical movements of polarizing elements [12] or of electrical addressing to liquid crystal panels [5,7] to generate the different polarization analyzers. Therefore, errors related to misalignments or deviations in phase-voltage Look Up Table (LUT) are always present. In addition, time-sequential polarimeters may present false polarization effects due to scene changes during the data acquisition. Regarding the main drawback in division of aperture polarimeters, it is related to the loss in spatial resolution of their acquisition device [13]. Finally, division of amplitude polarimeters divide the studied beam in different sub-beams, which are simultaneously projected to different polarization analyzers. For complete polarimeters, a minimum of 4 sub-beams are required, leading to a final signal-noise ratio reduction [13].

In Conical Refraction (CR) [15-21], when a focused input Gaussian beam propagates along the optic axis of a biaxial crystal it is transformed into a light ring, as shown in Fig. 1 (a), being this light ring most sharply resolved at the focal plane. The radius of the CR ring, R ₀ , can be obtained from the product of the crystal's length, L, and its conicity, a, i.e. Ro = La. The conicity of the crystal depends on the principal refractive indices of the crystal through a = J(n| - ¾(n - n|)/4n ₁ n ₃ [17]. One interesting peculiarity of the CR light ring is that it splits into two concentric bright rings separated by a dark (Poggendorff) ring under conditions of Ro » wo, where wo is the waist radius of the focused input beam. Additionally, wo is also the width of each of these bright rings.

One of the most interesting features of the CR effect is the polarization distribution along the ring. Each point of the light ring is linearly polarized with the polarization plane rotating along the ring so that every pair of diagonally opposite points have orthogonal polarizations. In other words, at a certain point of the CR ring, given by its azimuthal angle φ, the plane of the electric field, , will be:

where φα is the orientation of the plane of optic axes of the biaxial crystal [18]. Therefore, the biaxial crystal projects the input beam into an infinite number of linearly polarized states. If the input beam is circularly polarized or unpolarized, the azimuthal intensity along the ring is constant. In contrast, for linearly polarized input beams the light ring possesses a point of null intensity and a maximum intensity point placed diagonally opposite to the first one.

To measure states of polarization based on the mapping that conical refraction (CR) phenomenon produces between the polarization of the input beam and the transverse intensity distribution along the light ring of the output beam [15] has been disclosed in US20060193044, which describes a polarimeter based on conical refraction, comprising:

- a refractive arrangement configured for conically refracting an input electromagnetic radiation characterized by a polarization state so as to provide a light spatial pattern corresponding to said polarization state; and

- a light analysis arrangement configured for receiving and analysing said light spatial pattern and for determining the polarization state of the input electromagnetic radiation according to the analysed spatial pattern.

However, with the polarimeter of US20060193044 is not possible to determine all the polarization states of the input electromagnetic radiation, particularly is not possible to distinguish between a circularly polarized and an unpolarized input electromagnetic radiation, as the light spatial pattern provided by both polarization states, as indicated above, is a constantly distributed intensity light ring.

References:

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De Martino, "Ex-vivo characterization of human colon cancer by Mueller polarimetric imaging," Optics Express 19, 1582 (201 1 ).

2. D. N. and E. G.-C. A Lizana, M Foldyna, M Stchakovsky, B Georges, "Enhanced sensitivity to dielectric function and thickness of absorbing thin films by combining total internal reflection ellipsometry with standard ellipsometry and reflectometry," Journal of Physics D: Applied Physics 46, 105501 (2013).

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Lopez Jimenez, V. Domingo, J. L. Gasent, L. Jochum, and V. Martinez Pillet, "IMaX: a polarimeter based on Liquid Crystal Variable Retarders for an aerospace mission," Physica Status Solidi (c) 5, 1041-1045 (2008).

4. D. H. Goldstein, Polarized Light (CRC Press, 2010), p. 808.

5. A. Peinado, A. Lizana, J. Vidal, C. lemmi, and J. Campos, "Optimization and performance criteria of a Stokes polarimeter based on two variable retarders," Optics

Express 18, 9815 (2010). 6. D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S.

Phipps, "Optimization of retardance for a complete Stokes polarimeter," Optics Letters 25, 802 (2000).

7. L. Gendre, A. Foulonneau, and L. Bigue, "Full Stokes polarimetric imaging using a single ferroelectric liquid crystal device," Optical Engineering 50, 081209 (201 1 ).

8. D. H. Goldstein, "Mueller matrix dual-rotating retarder polarimeter," Applied Optics 31 ,

6676 (1992).

9. O. Arteaga, J. Freudenthal, B. Wang, and B. Kahr, "Mueller matrix polarimetry with four photoelastic modulators: theory and calibration," Applied Optics 51 , 6805 (2012).

10. G. Myhre, W.-L. Hsu, A. Peinado, C. LaCasse, N. Brock, R. A. Chipman, and S.

Pau, "Liquid crystal polymer full-stokes division of focal plane polarimeter," Optics Express 20, 27393 (2012).

1 1 . E. Compain and B. Drevillon, "Broadband Division-of-Amplitude Polarimeter Based on Uncoated Prisms," Applied Optics 37, 5938 (1998).

12. D. H. Goldstein and R. A. Chipman, "Error analysis of a Mueller matrix polarimeter," Journal of the Optical Society of America A 7, 693 (1990).

13. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, "Review of passive imaging polarimetry for remote sensing applications," Applied Optics 45, 5453 (2006).

14. R. A. Chipman, "Polarimetry," in Handbook of Optics, 2nd ed. (McGraw-Hill, 1995).

15. M. V. Berry and M. R. Jeffrey, Progress in Optics 50, 13-50, (Elsevier, 2007).

16. A. M. Belskii and A. P. Khapalyuk, "Internal conical refraction of bounded light beams in biaxial crystals," Optics and Spectroscopy 44, 436-439 (1978).

17. T. K. Kalkandjiev and M. A. Bursukova, "Conical refraction: an experimental introduction," Proceeding of SPIE 6994, p. 69940B-69940B-10, (2008).

18. A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, and J. Mompart, "Multiple rings formation in cascaded conical refraction," Optics Letters 38, 1455 (2013).

19. A. Turpin, Y. Loiko, T. K. Kalkandjiev, and J. Mompart, "Free-space optical polarization demultiplexing and multiplexing by means of conical refraction," Optics

Letters 37, 4197 (2012).

20. A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, "Conical refraction Nd:KGd(WO_4)_2 laser," Optics Express 18, 2753 (2010).

21. D. P. O'Dwyer, C. F. Phelan, K. E. Ballantine, Y. P. Rakovich, J. G. Lunney, and J.

F. Donegan, "Conical diffraction of linearly polarised light controls the angular position of a microscopic object," Optics Express 18, 27319 (2010). 22. D. H. Goldstein, Polarized Light, 2nd ed. (Mercel Dekker, 2010).

23. P. Taylor, Theory and Applications of Numerical Analysis, 2nd ed. (Academic Press, 1996). Description of the Invention

It is an object of the present invention to provide an alternative to the prior state of the art, which covers the gaps found therein, and which particularly overcomes the drawbacks and lacks of the proposal of US20060193044.

To that end, the present invention concerns, in a first aspect, to a polarimeter based on conical refraction, comprising:

- a refractive arrangement configured for conically refracting an input electromagnetic radiation characterized by a polarization state so as to provide a light spatial pattern corresponding to said polarization state; and

- a light analysis arrangement configured for receiving and analysing said light spatial pattern and for determining the polarization state of the input electromagnetic radiation according to the analysed spatial pattern.

Contrary to the known polarimeter based on conical refraction, i.e. to that of US20060193044, the polarimeter of the first aspect of the present invention, in a characteristic manner, has the next features:

- it further comprises a division-of-amplitude device configured and arranged for amplitude dividing said input electromagnetic radiation into first and second input electromagnetic radiations,

- said refractive arrangement is arranged in a first arm of the polarimeter configured for receiving said first input electromagnetic radiation,

- the polarimeter further comprises a second arm configured for receiving said second input electromagnetic radiation, where said second arm includes a static polarizing element that modifies in a controlled way the polarization content of the second input electromagnetic radiation, rotating its polarization state on the Poincare sphere, and a further refractive arrangement configured for conically refracting said second input electromagnetic radiation once it has passed through said static polarizing element, so as to provide a light spatial pattern corresponding to its polarization state;

- and said light analysis arrangement is also configured for receiving and analysing said light spatial pattern provided by said further refractive arrangement and for determining the polarization state of the input electromagnetic radiation according to both analysed light spatial patterns. For a preferred embodiment, said static polarizing element is a quarter-wave plate (QWP).

For another embodiment, said static polarizing element is an optical fibre element.

For an embodiment, said input electromagnetic radiations are Gaussian light beams or light beams having at least divergence characteristics similar to the ones of a Gaussian light beam.

For a preferred embodiment, each of said refractive arrangements include at least one conical refraction biaxial crystal configured for providing said light spatial pattern in the form of a light ring projected on a plane, such as the Lloyd plane.

Said light analysis arrangement comprises, according to an embodiment, first and second photo-detectors arranged for receiving the light spatial patterns provided by the refractive arrangements of, respectively, the first and second arms and translating them into corresponding first and second electrical patterns, and the light analysis arrangement further comprises processing means configured and arranged for receiving, processing and analysing said first and second electrical patterns for determining the polarization state of the input electromagnetic radiation.

Generally, said first and second photo-detectors generate said first and second electrical patterns with magnitudes proportional to the light intensities received.

Each of said first and second photo-detectors comprises, for a preferred embodiment, a light sensor array arrangement, such as an image sensor of any image acquisition technology based on a pixelated array, for instance a charge-coupled device (CCD) camera, a Complementary Metal Oxide Semiconductor (CMOS) sensor or an active-pixel sensor.

The polarimeter of the first aspect of the invention further comprises, for an embodiment, calibration means for performing an accurate alignment of the incidence angle of some or all of the above mentioned input electromagnetic radiations and/or for compensating possible polarization defects of the optical elements of the polarimeter.

For a preferred embodiment, the polarimeter is a static polarimeter, having means for avoiding any movement of the elements involved in the polarimeter.

Regarding the refractive arrangements of the polarimeter, these are configured, preferably, for conically refracting an input electromagnetic radiation of any wavelength to which the refractive arrangement is transparent, including wavelengths out of the visible spectra.

A second aspect of the invention relates to a method for determining the polarization state of an input electromagnetic radiation, comprising using the light analysis arrangement of the polarimeter of the first aspect for performing said analysis of said light spatial patterns, or of electrical patterns translated therefrom, and the determination of the polarization state of the input electromagnetic radiation according to the result of said analysis, said analysis including comparing both of said light spatial patterns.

For a preferred embodiment, said light spatial patterns are light rings that exhibit different intensity distributions depending on the input electromagnetic radiation (as for instance, constant intensity distributions or broken light rings with diametrically opposite maximum and minimum intensity positions). The method is able to determine any polarization state of the input electromagnetic radiation, including fully polarized radiation (linear polarization, right and left handed elliptical polarization, right and left handed circular polarization), partial polarized radiation and fully unpolarized radiation. The method determines the polarization of the electromagnetic radiation, by comparing the intensity distributions of the light patterns of the first and second arms of the polarimeter, achieving different pairs of intensity patterns for each particular input polarization.

For distinguishing if the polarization state of the incoming electromagnetic radiation is a non-polarized state or a circularly polarized state (which couldn't be distinguished by the polarizer of US20060193044), the method of the second aspect of the invention comprises:

- determining that the polarization state of the input electromagnetic radiation is a non-polarized state if both light patterns are light rings with constant intensity distributions; or

- determining that the polarization state of the input electromagnetic radiation is a circularly polarized state if the light pattern of the first arm of the polarimeter is a light ring with constant intensity distribution and the light pattern of the second arm of the polarimeter is a broken light ring with diametrically opposite maximum and null intensity positions, and depending on the locations of said maximum and null intensity positions determining that the circularly polarized light is right or left handed.

Brief Description of the Drawings

The previous and other advantages and features will be more fully understood from the following detailed description of embodiments, with reference to the attached drawings, which must be considered in an illustrative and non-limiting manner, in which:

Fig. 1 schematically shows the polarimeter of the first aspect of the invention, for a preferred embodiment; Fig. 2 show the polarizing analyzers (Pas) of both arms of the polarimeter of the first aspect of the invention, represented upon the Poincare sphere, by means of the illustrated lines corresponding to the linear detection arm and to the elliptical detection arm (assuming that the QWP is at 0°);

Fig. 3 are experimental images acquired by cameras of arm 1 (a-g) and arm 2 (h- n) of the polarimeter of the first aspect of the invention, when illuminating with linearly polarized light at 0° (a,h), at 90° (b,i), at 45° (c,j), at 135° (d,k), with circularly polarized light right handed (e,l) and left handed (f,m) and with unpolarized light (g,n); and

Fig. 4 show different simulated intensity profile in continuous line and experimental intensity profile in spots, as function of φ, the position along the ring of arm 1 (a-g) and arm 2 (h-n); when illuminating with linearly polarized light at 0° (a,h), at 90° (b,i), at 45° (c,j), at 135° (d,k), with circularly polarized light right handed (e,l) and left handed (f,m) and with unpolarized light (g,n). Detailed Description of Several Embodiments

By considering all the optical features of the conical refraction phenomenon explained in a previous section, the design of a polarimeter based on two biaxial crystals is proposed, sketched in Fig. 1 , as an embodiment of the first aspect of the invention, and which includes:

- a division-of-amplitude device BS, such as a light beam splitter,

- a first arm A1 including, arranged aligned according to a first optical axis, from a first output of the light beam splitter BS: a focusing lens L1 , a conical refraction biaxial crystal C1 , a magnifying lens L2 arranged beyond the focal plane Pf1 of said conical refraction biaxial crystal C1 for magnifying the light ring projected thereon, and a first photo-detector FD1 , such as a CCD camera, arranged for receiving the magnified light ring,

- a second arm A2 including, arranged aligned according to a second optical axis, from a second output of the light beam splitter BS: a focusing lens L3, a quarter wave plate QWP, a conical refraction biaxial crystal C2, a magnifying lens L4 arranged beyond the focal plane Pf2 of said conical refraction biaxial crystal C2 for magnifying the light ring projected thereon, and a second photo-detector FD2, such as a CCD camera, arranged for receiving the magnified light ring; and

-a light analysis arrangement configured for receiving and analysing the light spatial patterns provided though by both arms A1 , A2, for determining the polarization state of the input electromagnetic radiation Sj _n according to both analysed light spatial patterns, where the light analysis arrangement comprises, for the illustrated embodiment, the first and second CCD cameras FD1 , FD2, which translated the received light patterns into corresponding first and second electrical patterns, processing means SP configured and arranged for receiving, processing and analysing said first and second electrical patterns for determining the polarization state of the input electromagnetic radiation.

Depending on the embodiment, the processing means SP can be local, remote, partially local and/or partially remote, internal and/or external to the circuitry associated to the CCD cameras, and/or wired or wireless communicated therewith.

The operation of the polarizer is as follows: The studied light beam Si _n , by means of a division of amplitude device BS, is split in two sub-beams Sj _n i and Sj _n 2 which are analyzed separately by two different polarizing analyzer arms A1 and A2. Both biaxial crystals were cut with one of the optic axes perpendicular to the slab faces. In both arms A1 , A2, the focusing lens L1 , L3 focuses the beam Sj _n i , Sj _n 2, which passes along the optical axis of the biaxial crystal C1 , C2, forming the C ring at its focal plane Pf1 , Pf2. The magnifying lens L2, L4 images the CR ring into the CCD camera FD1 , FD1 , with a certain magnification. Thus, the intensity distribution acquired by the cameras FD1 , FD1 , will depend on the incident state of polarization Si _n .

Concerning the first arm A1 , the obtained intensity pattern can be understood as the result of projecting the incident beam Sin (in fact sub-beam Sj _n i ) over a set of linear polarizers arranged in a circle. The orientation of the transmission axis of those polarizers is rotated (from 0° to 180°) over the complete circle.

In order to obtain ellipticity information, the second arm A2 is needed, which includes a quarter waveplate QWP before the biaxial crystal C2. In this way, the intensity pattern in the plane Pf2 for the second arm A2 can be understood as the result of projecting the incident beam Sin (in fact sub-beam Sin2) over a QWP and then, over the set of rotated polarizers arranged in a circle.

By using the Mueller matrices of a QWP and a rotated linear polarizer [22], the expressions of the polarizing analyzers (PAs) of both arms can be calculated. These

PAs will be expressed as function of φ, the angular position at the ring. Finally, the intensity distribution measured by the two cameras will be the projection of the incident

Stokes vector (S _in ) over these PAs: cos φ sin φ 0)- (S, o S _x S ₂ S ₃ f , (2)

^CCD2 (ψ) ^\ cos φ 0 sin <p)- {S o _i J, S _t S , (3) where the orientation of the QWP has been fixed at 0° for convenience, although any other angle would have led to a complete polarimeter. In addition, these expressions can be rewritten as function of the total intensity (So), the degree of polarization (DoP), the azimuth (a) and ellipticity (ε) of the incident state of polarization:

I can (<P) = y j ¹ 1 (4)

ccD2 φ) = --^- + — - [cos 2 ε cos 2a cos φ + sin 2ε sin φ\

Note that Eq. (4) describes the intensity distribution along the ring due to the CR phenomenon for any input state of polarization. This equation is a generalization of the equations presented in [18], describing the particular cases of linearly and circularly fully polarized states.

The PAs of both arms are plotted upon the Poincare sphere in Fig. 2. If the orientation of the QWP is rotated an angle Θ, the curve of the PAs represented upon the Poincare sphere corresponding to the arm A2 will be rotated 2Θ over the S3 axis. Note that by using only a single arm, the PAs draw a plane in the Poincare sphere and consequently, they constitute an incomplete polarimeter. In particular, the PAs from first arm A1 (indicated in the Figure as "Linear detection") do not have information about S3 and, the ones from second arm A2 (indicated in the Figure as "Elliptical detection") do not measure the S2 component. However, when the whole system is considered the polarimeter is complete since the PAs represented upon the sphere are enclosing a certain volume.

In general, different quality indicators are used to evaluate the propagation of noise to the measurement in polarimeters, as for instance, the Condition Number (CN) [23], or the Equally Weighted Variance (EWV) [5,6] indicators. The CN (a metric widespread used in polarimeter design) calculated for our PAs arrangement is equal to 2.00, value very close to the theoretical minimum 1 .73 for polarimeters. Besides, the EWV indicator is also calculated for our proposed configuration. From simulations, it can be observed that the EWV value depends on the number of PAs used in the Stokes measurement [5]: the larger the number of PAs used, the smaller the EWV value obtained. For the case of 360 PAs per arm, i.e. 720 in total, the EWV is 0.0153. This value is much smaller than the one reported in [5] for 100 PAs (0.1 ).

To show and prove the measurement principle of the polarimeter design proposed above, the present inventors have experimentally implemented the arrangement of Fig. 1 and different input polarization states are analyzed. In the experimental implementation, the input light is obtained from a 640 nm diode laser coupled to a monomode fiber. The two biaxial crystals C1 , C2 used in the setup were cut from a monoclinic centrosymmetric KGd(W0 ₄ ) ₂ crystal. Their polished entrance (cross-section 6x4 mm ² ) have parallelism with less than 10 arc sec, and they are perpendicular to one of the two optic crystal axes within 1 .5 mrad misalignment angle. Their lengths, L = 23.38 mm (measured with precision of less than 100nm), and their conicity, a = 17 mrad, provide a CR ring of radius Ro = 397 μηη.

Fig. 3 shows the two experimental images acquired by the two cameras FD1 , FD2 when seven particular states of polarization (SOPs) illuminate the system. The used SOPs are linearly polarized light at 0°, 90°, 45° and 135°, right and left handed circularly polarized light and unpolarized light. The first row of Fig. 3 corresponds to the first camera, i.e. projecting over linear polarization analyzers. Thus, when this camera analyzes a linear SOP (Fig. 3(a)-(d)), the intensity patterns consist in broken rings with a maximum and a null of intensity in diametrically opposite positions in the ring. This broken ring rotates as the azimuth of the analyzed SOP is rotated, as it is described in Eq.(4). As explained above, circularly polarized light and unpolarized light (Fig. 3(e)-(g)) result in a ring of constant intensity. In the second row of Fig. 3, the intensity distributions differ from the first row because of the presence of the QWP. When illuminating with 0° or 90° linear SOPs, the polarization is not modified by the QWP (oriented at 0°) and for this reason, the intensity distributions (Fig. 3(h)-(i)) are identical to the ones acquired by the first camera FD1 . In addition, unpolarized light remains unpolarized after the QWP, so that an uniform ring is visualized in Fig. 3(n). Finally, when projecting the linear SOPs at 45°, 135°, right handed and left handed circular SOPs over the QWP, they are respectively transformed to left handed and right handed circular SOPs and linear SOPs at 45° and 135°. Then, by taking into account the actual SOP impinging the biaxial crystal, and considering the effect of the crystal over these SOPs as explained above, the intensity distribution of Fig. 3(j)-(m) can be understood.

By conducting a data analysis of these experimental images, the intensity profile along the rings has been extracted, plotted in points in Fig. 4. Moreover, in Fig. 4, in continuous line, the simulated intensity profiles obtained by using Eq. (2) and (3) have been included. A good agreement between experimental and simulated intensity profiles is observed.

Note that if only the linear arm A1 is used, there is not distinction between unpolarized light and right and left circularly polarized light (see Fig. 4 (e-g)). In the same way, the elliptical arm A2 cannot distinguish between linearly polarized light at 45°, 135° and unpolarized light (see Fig. 4 (j,k,n)). Nevertheless, by using the two intensity profiles corresponding to both arms A1 , A2, it is possible to distinguish each state of polarization, including unpolarized light beams. Thus, the results given in Fig. 3 and 4 constitute an experimental prove of the capability of the presented design to perform polarimetric measurements, as the whole polarimetric content of any input SOP can be determined. In fact, by applying a data reduction procedure [14] to the two intensity profiles obtained (arms A1 and A2), a quantitative estimation of any input SOP can be achieved.

In conclusion, the polarimeter and method of the present invention constitute a new concept for Stokes vector metrology by means of analyzing the characteristic intensity pattern associated to the conical refraction phenomenon occurring in biaxial crystals. This idea is developed by proposing the design of a division of amplitude complete Stokes polarimeter based on two biaxial crystals. Just one division of amplitude is required to completely characterize any state of polarization, including partially polarized and unpolarized light. Besides, the proposed design describes a static polarimeter and thus, no mechanical movements or electrical signal addressing would be needed in a future implementation.

However, since the conical refraction phenomenon is very sensitive to the incidence angle, the necessity of performing a very accurate alignment is expected. Additionally, an experimental calibration of the PAs is strongly recommended in order to take into account possible polarization defects of the elements in the setup [14]. For instance, some differences with the theoretical configuration may be introduced in the experimental implementation due to polarimetric effects related to the division of amplitude device used in the setup, or due to experimental deviations of the quarter waveplate retardance value. To that end, for some embodiments, the polarimeter of the first aspect of the invention further comprises calibration means for performing an accurate alignment of the incidence angle of some or all of the above mentioned input electromagnetic radiations and/or for compensating possible polarization defects of the optical elements of the polarimeter.

A person skilled in the art could introduce changes and modifications in the embodiments described without departing from the scope of the invention as it is defined in the attached claims.