WO2013128446A1

WO2013128446A1 - Depolariser

Info

Publication number: WO2013128446A1
Application number: PCT/IL2013/050169
Authority: WO
Inventors: Hagai EISENBERG; Assaf SHAHAM
Original assignee: Yissum Research Development Company Of The Hebrew University Of Jerusalem Ltd.
Priority date: 2012-02-27
Filing date: 2013-02-27
Publication date: 2013-09-06

Abstract

An optical system is described, configured for affecting polarization of input light. The system comprise at least two birefringent modules accommodated sequentially along a light propagation path, wherein said at least two birefringent modules are arranged with a certain first angular relation between them. Each of said at least two birefringent modules comprises at least two birefringent elements having predetermined lengths and oriented in a certain second angular relation between them, at least one of said first and second angular relations being selected for desirably reducing polarization degree of the input light.

Description

DEPOLARISER

TECHNOLOGICAL FIELD

The present invention is in the field of polarization control and relates to polarization modifications.

REFERENCES

References considered to be relevant as background to the presently disclosed subject matter are listed below:

[1] K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, "Dense Coding in Experimental Quantum Communication", Phys. Rev. Lett. 76, 4656 (1996).

[2] N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography", Rev. Mod. Phys. 74, 145 (2002).

[3] P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, "Experimental Verification of Decoherence-Free Subspaces", Science 290, 498 (2000).

[4] G. Puentes, D. Voigt, A. Aiello and J. P. Woerdman, "Tunable spatial decoherers for polarization-entangled photons", Opt. Lett. 31, 2057 (2006).

[5] M. P. Almeida et al., "Environment-induced sudden death of entanglement", Science 316, 579 (2007).

[6] M. Karpinski, C. Radzewicz and K. Banaszek, "Fiber-optic realization of anisotropic depolarizing quantum channels", JOSA B 25, 668 (2008).

[7] A. Shaham and H. S. Eisenberg, "Realizing controllable depolarization in photonic quantum information channels", Phys. Rev. A 83, 022303 (2011).

[8] A. Chiuri, V. Rosati, G. Vallone, S. Pa'dua, H. Imai, S. Giacomini, C. Macchiavello, and P. Mataloni, "Experimental Realization of Optimal Noise Estimation for a General Pauli Channel", Phys. Rev. Lett 107, 253602 (2011). [9] J. B. Altepeter, E. R. Jeffrey, and P. G. Kwiat, "Photonic State Tomography", Adv. At. Mol. Opt. Phys, vol. 52, 107 (2005).

[10] I. L. Chuang and M. A. Nielsen, "Prescription for experimental determination of the dynamics of a quantum black box", J. Mod. Opt. 44, 2455 (1997).

[11] A. Shaham and H. S. Eisenberg, "Quantum process tomography of single-photon quantum channels with controllable decoherence" , Phys. Scr. T147, 014029 (2012).

[12] A. Shaham and H. S. Eisenberg, "Realizing a variable isotropic depolarizer," Opt. Lett. 37, 2643-2645 (2012).

Acknowledgement of the above references herein is not to be inferred as meaning that these are in any way relevant to the patentability of the presently disclosed subject matter.

BACKGROUND

Polarization of electromagnetic radiation (e.g. light) is a fundamental effect and is particularly important in the field of optics. Various optical systems utilize polarized light and polarization filters or polarization rotators to enable control of the polarization of light as well as transforming light of one polarization state to another polarization state.

Recently, there is a significant growth in various fields based on communication and computing utilizing various quantum effects (i.e. utilizing the quantum superposition states of atoms, photons etc.). Some of such applications utilize polarization states of single photons and/or of classical light for encoding information. The ability to control polarization degree of light is useful in various applications, either for complete depolarization and/or for controlled depolarization. For example, controlled depolarization process are required for exploring the effects of noise in quantum information channels, where data is encrypted is polarization states of optical signals (e.g. photons).

The Lyot depolarizer is an example of a device for reducing polarization degree of light passing therethrough. The Lyot depolarizer is composed of two birefringent crystals, where one crystal is twice as long as the other and their principal axes (e.g. fast axes) are specifically oriented at 45° with respect to each other. The Lyot depolarizer can completely depolarize light under a condition that of coherence length t_c of light passing through the depolarizer is shorter than the polarization temporal walk-off τ in the shorter crystal of the two.

Variations of the Lyot depolarizer are described for example in the scientific paper "Realizing controllable depolarization in photonic quantum-information channels" Phys. Rev. A 83, 022303 (2011) by the inventors of the present invention. Such variations enable control of the output polarization degree for known, specific, polarization states of input light. GENERAL DESCRIPTION

The present invention provides a system capable of isotropically and controllably depolarize light of a certain initial polarization degree to a desired polarization degree. The term controllably describes that the depolarization system of the present invention can reduce a polarization degree of light passing therethrough to any desired final polarization degree regardless of its initial polarization orientation. The term isotropically or isotropic used herein describes that the degree of polarization of the output is not affected by the initial polarization state(s) of the input light, i.e. isotropic depolarization occurs when the degree of polarization of the output state is equal for any initial polarization state of the input light.

Generally, each polarization state of polarized light (linear, circular, elliptic polarizations and/or a combination thereof) can be viewed as a superposition, or coherent sum, of two orthogonal polarization states. Non-polarized light is a statistical sum of polarization states (i.e. non coherent sum of polarization states). Such nonpolarized light is desirable for various applications in optical communication, for example for study of noise effects in quantum information channels. To this end, the present invention provides for a technique and a system capable of controllably reducing polarization degree of light to provide output light of any desired polarization degree and orientation.

It should be understood that a polarization state of light (e.g. a single photon or classical light beam), can be represented by a vector of Stocks parameters {Si, ¾, S3 } each presenting a fraction of light being in a certain polarization state. The total light intensity is normalized and represented by So≡l- The Stocks representation of polarizations provides a complete description of the polarization state of light and is well known in the art and thus will not be described here in details but to note that, for simplicity, the present invention is described in the convention where Sj represents linear horizontal IH> and vertical \V> polarizations, i.e. Si=l represents horizontal polarization and Si=-1 represents vertical polarization, ¾ represents linear polarization in ±45°, and S3 represents left and right hand circular polarization respectively.

In this connection, in the following description the term degree of polarization refers to the fraction of polarized light intensity out of the total intensity ¾. This degree of polarization is measured/represented by the length of the Stokes vector D = ^ S ² + S₂ ² + S₃ ² , where D=l represents a fully polarized state and D=0 represents a completely un-polarized state. It should be noted that every polarization state can be viewed as a superposition of two orthogonal polarization states, e.g. the (+45°) polarization state can be described as \p) =

right-hand circular polarization can be described as \ R) = (| H) + /|v))/V2 , etc. On the other hand, non- polarized light (light having polarization degree D=0) is actually a statistical sum of polarization states. This can be seen by transmitting light through a polarization filter (e.g. linear polarizer). When light of certain linear polarization is transmitted through a linear polarizer, the output light intensity depends on an angle between the polarization filter and the polarization axis of the input light and follows the relation

However, when non-polarized light is transmitted through such a polarization filter, the output light intensity will be approximately 50% of the input light intensity regardless of the orientation of the polarization filter.

The present invention provides a novel system for isotropically reducing the polarization degree of light propagating through the system by a certain fraction of the initial polarization degree in a manner enabling control of the decrease of the polarization degree. The system comprises a predetermined number of multiple birefringent modules comprising birefringent elements (e.g. birefringent crystals or optic fibers) with predetermined thicknesses/length. Each birefringent module is configured for affecting polarization of light with respect to at least two intersecting polarization axes, as described by Stokes parameters, e.g. the module comprises at least one pair of birefringent elements of different lengths, and possibly a polarization rotator between them. The birefringent modules are arranged sequentially along a light propagation path of the system and are controllably manipulatable to orient them with certain angular relations between them, wherein the angular relations are selected to desirably decrease a degree of polarization of the output light with respect to the input light irrespective of a polarization state/orientation of the input light.

It should be noted that the birefringent module may be formed by two or more birefringent elements by themselves or by the birefringent elements and a polarization rotator. Accordingly, the term angular relation used herein below with respect to the orientation of the birefringent modules relates to the following. This may be defined by the angular relation between fast and slow axes of the birefringent elements within the module and with respect to the birefringent elements of at least one other module. The angular relation may be determined by physical orientation of the birefringent elements (i.e. rotation of the element to vary angles between its fast axis relative to other birefringent elements of the system), and/or by using a polarization rotator, such as half wave-plate (HWP), for controllably varying polarization of light passing through the system between the birefringent elements.

Also, it should be understood that the present invention provides for manipulating/reducing the degree of polarization of light while maintaining the spatial intensity distribution/spatial modes of the light. For example, the invention enables manipulating a degree of polarization of a single spatial mode of light while preserving said single spatial mode.

As indicated above, the system of the present invention is capable to provide control on the degree of polarization of the output light irrespective of a polarization state/orientation of the input light. It should also be noted that as generally known in the art, it is possible to transform light having certain defined polarization state/orientation to light having any other defined polarization state if the polarization state of input light and the required polarization state of output light are known. However, the system of the present invention operates isotropically with respect to the input light polarization to modify/reduce the degree of light polarization and in this regards may not require any knowledge on the polarization state/orientation of the input light. In general, the system may operate on partially or fully polarized input light (namely light in which the degree D of polarization is D<1). Although, for simplicity, in the following description the operation of the system is exemplified with respect to fully polarized input light (D=l), it should be understood that the invention is not limited to this specific example, and the principles of the invention can be applied to input light of any degree of polarization. It should also be noted that depolarization of light by the system of the present invention may, at times, be reversible. For example, by transmitting partially polarized (or fully unpolarized) light which is output of the system to pass through the system in similar configuration, the de -polarizing effect of the system may be cancelled to provide light having polarization degree similar to the (original) input light.

Thus, according to one broad aspect of the present invention there is provided an optical system configured for affecting polarization of input light. The system comprises at least two birefringent modules accommodated sequentially along a light propagation path, wherein said at least two birefringent modules are arranged with a certain first angular relation between them. Each of said at least two birefringent modules comprises at least two birefringent elements having predetermined lengths and oriented in a certain second angular relation between them, at least one of said first and second angular relations being selected for desirably reducing polarization degree of the input light. Selection of at least one of said first and second angular relations may be such as to desirably reduce the polarization degree of the input light irrespective of polarization orientation of said input light.

The optical system may comprise a mounting module carrying at least one of the birefringent modules and/or at least on polarization rotator located between the modules or within the modules. The mounting module is configured to enable a control over said angular orientation of the birefringent module or therebetween.

Generally, the predetermined lengths of the birefringent elements are longer than a coherence length of said input light. It should be noted that coherence length of light is the distance which the light maintains a defined coherent relation. For pulsed light sources (e.g. pulsed lasers) the coherence length is typically the pulse length divided by the velocity of light (i.e. L=m/c). For continuous light sources the coherence length may be longer and often depends on the spatial mode of the light, e.g. for Helium-Neon laser the multimode coherence length is about 20cm while the single mode coherence length is about 100m.

According to some embodiments of the present invention, at least one of said at least two birefringent modules comprises an intra-module polarization rotator located between the at least two birefringent elements of the respective birefringent module, said intra-module polarization rotator may be configured to alter the second angular relations between said birefringent elements with respect to said input light. Said intra- module polarization rotators may be half wave-plates (HWP's). Additionally or alternatively, the optical system may comprise at least one extra-module polarization rotator located along optical path through the system between said at least two birefringent modules. One of said at least one extra-module polarization rotator may be a HWP, one other of said at least one extra-module polarization rotator may be a quarter wave-plate.

According to some embodiments of the present invention, said at least two birefringent elements of each of said at least two birefringent modules are of different lengths. In such configurations variation of the first angular relation between said at least two birefringent modules may provide for variation in reduction of the polarization degree of said input light. The at least two birefringent modules, which comprises at least two birefringent elements of different lengths each, may be arranged a symmetrical order relative to a central point along said optical path along the system.

The optical system may comprise a first and a second of said birefringent modules, each comprising a pair of the birefringent elements. The four sequentially accommodated birefringent elements may be arranged such that lengths of first and second birefringent elements of each module are different. An extra-module polarization rotator may be located between the first and second birefringent modules; said extra-module polarization rotator is typically configured to controllably vary an angle of polarization rotation.

According to some embodiments of the invention, the optical system may comprise first and second half wave -plates (HWP) located in the first and second birefringent modules between the respective birefringent elements, and an additional HWP located between said birefringent modules. The HWP's are configured to affect light of a selected wavelength range. The birefringent elements are oriented such that fast axes of the birefringent elements of the same module are perpendicular to one another and said first and second HWPs are oriented with a predetermined angle relative to the fast axis of the first birefringent element of the birefringent module thereby defining a zero angle. The additional HWP is rotatable about an optical axis with respect to the zero angle to thereby vary a degree of polarization of output light. The first and second HWP may be oriented with equal or opposite angles with respect to said zero angle. For example, the first and second HWPs may be oriented with opposite angles of 13.68 or 31.32 degrees with respect to said zero angle. In such configuration, rotation of said additional HWP with an angle Θ_ΡΚ with respect to said zero angle varies polarization of light passing through the system to a degree of D '=1/3+2/3 *COS(46PR).

According to some embodiments of the invention, at least one of the first and second birefringent modules is rotatable with respect to the other birefringent module, the angular relation between the birefringent modules provides for desirably decreasing the polarization degree of said input light.

The birefringent elements of each of the first and second birefringent modules may be of different lengths between them, being similar for the first and second modules. The different birefringent elements of the two modules may be arranged in opposite order with respect to a central point of the optical path between them such that when said two birefringent modules are positioned in similar angular orientation with respect to the input light, a polarization degree of light being output from said two birefringent modules is similar to a polarization degree of the input light.

According to some other embodiments of the present invention, the optical system may comprise at least three of said birefringent modules. Each of said birefringent modules comprises the at least two birefringent elements of a similar length, being different from that of the other birefringent modules. The optical system may comprise at least two extra-module polarization rotators, each located in between two of said at least three birefringent modules and being configured to rotate polarization of light passing therethrough to thereby transmute between Stokes parameters defining said polarization state.

Additionally, each of said at least three birefringent modules may comprise an intra-module polarization rotator, located between the at least two respective birefringent elements. An angular orientation of said intra-module polarization rotator provides for desirably reducing polarization degree of light passing therethrough.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to better understand the subject matter that is disclosed herein and to exemplify how it may be carried out in practice, embodiments will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which: Fig. 1A schematically illustrates a depolarization system according to the present invention;

Fig. IB illustrates a polarization reduction map describing Poincare representation radii which may be provided by the system of the present invention;

Figs. 2A-2B illustrate two examples of polarization systems utilizing respectively two and three birefringent modules according to some embodiments of the present invention;

Figs. 3A-3E show Poincare representation of polarization, Fig. 3A illustrate the Poincare representation, and Figs. 3B-3E show experimentally constructed Poincare spheres of light with reduced polarization degree; and

Fig. 4 show experimentally calculated eigenvalues of depolarization matrix illustrating the operation of the depolarizer system of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS

The present invention provides an optical system configured to controllably and isotropically reduce a degree of polarization of input light, i.e. irrespective of the polarization state/orientation of input light. Such system 100 is exemplified schematically in Fig. 1A and includes a predetermined number of multiple birefringent modules BMi-BM_n arranged sequentially along a light propagation axis (optical axis) OA defined by the system 100. Each birefringent module includes at least one pair of birefringent elements and may also include a polarization rotator between the elements. In the present not limiting example, the birefringent modules are shown as being formed only by the birefringent elements BEi-BE_n. The birefringent elements BEi-BE_n may or may not be attached to one another. The birefringent elements BEi-BE_n are preferably oriented such that both the fast and slow axes of each birefringent element are perpendicular to the optical axis OA, in order to provide temporal separation (delay) of polarization components propagating through the element, while avoiding spatial separation of the polarization components.

The system 100 is thus configured as a depolarization system capable of transforming input light IL having certain (unknown) polarization to output light OL having desirably reduced polarization degree D (e.g. being a certain fraction of the input polarization degree). The controllable reduction in polarization degree of input light IL, and the ability to perform it isotropically, i.e. independently from the polarization state/orientation of the input light IL, is achieved by the use of a predetermined number n of the birefringent modules BMi-BM_n and control over the angular relations between them. For example, the control on the reduction in the polarization degree may be achieved by changing the respective angular relations between some of the birefringent elements within the module and/or angular relations between the birefringent elements of one module with respect to those of another module(s), and/or by positioning at least one polarization rotator between at least two of the birefringent elements at desired angle.

Thus, a combination of at least one pair of birefringent elements with appropriate angular relation between them generates a birefringent (depolarizer) module BMi. It should be understood that such a module, while being capable of depolarizing light passing therethrough, provides very limited control on the degree of depolarization or dependence of the degree of polarization on initial polarization state of input light. The inventors have found that using at least two such modules successively affecting light propagating through the system with a predetermined optical length relation between the birefringent elements of the modules enables isotropically and controllably affecting the polarization degree of the input light. This will be described more specifically further below.

Generally, birefringent elements such as birefringent crystals of optical fibers are optically transparent elements having different effective refractive indices for light of different (orthogonal) linear polarization states. Typically a birefringent element can be characterized by orthogonal axes corresponding to fast and slow axes such that light polarized along the fast axis is affected by lower refractive index relative to light polarized along the slow axis. The birefringent elements used in the system of the invention, or at least some of them, may be birefringent crystals formed for example of Calcite (CaCOs) or other non-isotropic crystals. Alternatively or additionally some of the birefringent elements may be polarization preserving optical fibers, which are configured to exhibit different effective refractive indices for different polarization axes of light. As shown in Fig. 1A, the input light IL entering the system 100 at the input facet of the birefringent module BMi has a certain polarization state which can be described by Stokes parameters {¾,¾,¾}. As indicated above, in the present description, for simplicity only, the input light is assumed to be fully polarized, i.e. having polarization degree D²= ¾²+¾²+¾²= . The output light OL emerging from the system 100 through the output facet of the last birefringent nodule BM_n has a certain (generally different) polarization state

which has a desirably reduced polarization degree, i.e. D'²=S'i²+S'₂ ²+S'₃ ²<l. To this end, the birefringent elements within each module are of different lengths, and the birefringent modules of the system are oriented with desired angular relations between them, e.g. by rotating the birefringent element and/or module and/or operating polarization rotator(s) as will be described more specifically further below. It should be noted that the modules may be identical to one another with respect to the relative accommodation of the birefringent elements of different lengths, or may be oppositely identical in this respect to enable full control of the reduction in the degree of polarization i.e. up to substantially not affecting the polarization degree such as 0< D '<\ .

Typically, each birefringent element BEi of the system 100 is configured for de- phasing at least one polarization component/state of a light beam passing therethrough. To this end, each birefringent element BEi is configured with sufficient length/thickness along the optical axis OA, such that a difference in the optical path traversed by polarization components parallel to the fast and slow axes respectively of the birefringent element BEi is greater than a coherence length of the light. This reduces the coherence between those polarization components. Specifically, the length Li of the birefringent element BEi along the optical axis is such that the temporal walk-off τ caused by light passing therethrough is larger than a coherence time (coherence length) to of the input light, i.e. ¾<r=L_;z)«/c, where An=n₀-n_e is the difference between the refractive indices of the birefringent element along the slow and fast axes thereof and c is the speed of light. Accordingly, the elements BEi are sufficiently long to couple between polarization degrees of freedom and temporal degrees of freedom of the light passing therethrough. Additionally, it should be noted that the differences in length between the birefringent elements of the system should preferably also obey the above ratio, i.e. the differences in length between the birefringent elements should be longer than the coherence length of light passing through the system (L_rL_j)An/c>to. It should be noted that although the above described minimal length of the birefringent elements is typically sufficient, a use of longer birefringent elements, e.g. thick birefringent crystals or long polarization preserving optical fibers, for a given refractive index difference An will results in better performance of the depolarizer system. Additionally, the birefringent elements used may be selected as those having larger refractive index difference An. As described further below, several experiments were done using Calcite crystals (Αη-Ο. Π for 2=780nm) of length of 1mm and 2mm while the above described ratio shows that length of 0.3mm and 0.6mm are generally sufficient.

As generally known, light passage through a birefringent element BEi may cause spatial and/or temporal separation of polarization components. When the birefringent element BEi is oriented such that both its fast and slow axes are perpendicular to the direction of light propagation, the two polarization components (ordinary and extraordinary polarization components) continue to propagate along the initial direction of propagation but are separated temporally. A single birefringent element BEi configured and oriented as described above (with respect to its length and orientation of the fast and slow axes) operates to de -phase polarization components of light passing therethrough. Such de -phasing can be described as a projection of the Stokes polarization representation such as to cause two Stokes parameters (e.g. ¾ and ¾) to be zero while maintain a single polarization component. If an additional birefringent element BEi, with similar length and optical properties, is further located along the optical path of light propagation being oriented with 90° with respect to the first element, the initial polarization of the light is restored by cancelation of the temporal de -phasing. A use of a second birefringent element BEi of different length being oriented with an angle other then perpendicular with respect to the first element provides a depolarizer module DMi capable of depolarizing light to a degree of polarization D=0 or in some cases where the input polarization state is known, enables some control on the output degree of polarization. Such depolarizer module may be configured as the known Lyot depolarizer, i.e. an angle of 45° between the birefringent elements, which depolarize all input polarized light to a polarization degree of D=0 after the passage through both birefringent elements. Alternatively, if the angle between the birefringent elements is other than 45°, the final polarization degree depends on the initial polarization orientation (e.g. for an angle of 30° between the birefringent elements input light having circular polarization will be completely depolarized while linearly polarized input light will be only partially depolarized).

Accordingly, the inventors have found that a predetermined arrangement of birefringent elements BEi in the module and in the different modules is appropriately provided. Preferably, the arrangement is such that the at least two pairs of birefringent elements BEi of the at least two modules respectively are identically symmetrical. More specifically, the birefringent two elements of different lengths in one module are arranged oppositely relatively to those of the other module, thus providing symmetrical arrangement with respect to a central plane perpendicular to the optical axis of the system 100. This arrangement by itself (i.e. with no further variation of angular orientation) enables the system to transmit input light without affecting its polarization degree, while enabling, by appropriately varying the angular relation between the birefringent modules (by physical rotation of one module with respect to the other, and/or by using polarization rotators as described above), controlled reduction of polarization degree irrespective of the initial polarization orientation of input light.

Generally, the depolarizer system 100 of the present invention may be configured in the form of at least two depolarizer/birefringent modules arranged along an optical axis of light propagation through the system and respectively defining a light input and output ports of the system 100. Each of the at least two modules may include two or more birefringent elements BEi (defining at least one pair of such elements) oriented with a certain angular relations between them to thereby affect the degree of polarization of light passing therethrough corresponding to all of the Stokes parameters (i.e. Si, ¾ and S3). The degree of polarization of a light beam propagation along the system, between the light input and output ports, is controlled by varying at least an angular relation between the at least two modules BMi.

As noted above, the two depolarizer modules BMi may be similar in respective lengths of the birefringent elements BEi of the module and angular relations between the elements in the module, and may be arranged opposite to one another to provide symmetry of birefringent elements' lengths relative to a central plane along the optical axis. This configuration provides that when the depolarizer modules are positioned in appropriate angular relations a polarization degree of light passing therethrough can be unchanged. Variation of the polarization degree may thus be controlled by variation of angular relations between the two depolarizer modules, which may be achieved by rotating at least one of the depolarizer modules with respect to the optical axis and with respect to the at least one other module, and/or by using one or more polarization rotators to vary angular relations between the depolarizer modules.

Reference is made to Fig. IB showing a map of polarization degree reduction schemes provided by the system 100 of the present invention. The horizontal and vertical axes represent radii of Poincare representation of polarization along the Sj axis (horizontal) and combined ¾ and S₃ axes (vertical) resulting from depolarization of fully polarized light. Region C of the map is not physical, while regions A and B are achievable utilizing various configurations of the system. Isotropic depolarization channel exists along ISO-line and provides for equal radii along the three axes of the Poincare representation. It should be noted that the de-polarization map illustrated in Fig. IB only shows the cases where the ¾ and S₃ radii of the Poincare sphere are equal, a corresponding complete de -polarization map is a three-dimensional map which also includes regions where these radii are different. As will be described below, region A is achievable using the depolarizer configuration of Fig. 2 A while other depolarizer configurations may cover region B of the map and/or additional regions of the complete three-dimensional map.

Reference is made to Fig. 2 A, illustrating an example of the depolarizer system 100 according to some embodiments of the present invention. The system 100 includes two birefringent/depolarizer modules BMi and BM2 which in the present example are defined by four birefringent elements BE1-BE4 such as Calcite crystals, appropriately configured optical fibers or any other birefringent material/element. The birefringent elements BE1-BE4 are arranged in a spaced-apart relationship along an optical axis OA and each is oriented with the fast and slow axes thereof being perpendicular to the optical axis OA. The lengths of the birefringent elements of the modules, defining optical paths through the elements as well as the corresponding walk-off time τ, is selected to provide efficient and controlled depolarization. In this example, showing the symmetric arrangement of the modules, birefringent elements BEi and BE₄ have lengths Lj and elements BE2 and BE₃ have lengths

however it should be understood that a different relation between the lengths of the birefringent element in the module may be used, except for those satisfying the following conditions: L2=Li or 2L2=L]. The use of symmetrical configuration, L;=L^ and L2=L_?, enables an operation state of the system 100 in which no light depolarization occurs, i.e. D '=D. Additionally, the lengths of each one of the birefringent elements BE1-BE4 is preferably longer than the coherence length of the input light. For example, for a depolarizing system suitable for use with 150fms, the birefringent elements may be of length of at least 0.261mm which may be rounded to 0.3mm (for Calcite crystals having An~0A72). For example, in some experiments using the system 100 of Fig. 2A the birefringent elements used are birefringent Calcite crystals of lengths 1mm and 2mm for depolarizing light of coherence time for about 200fms. The angular relations between the fast axes FA of the birefringent elements in the module are selected to appropriately couple temporal and polarization degrees of freedom of input light IL to thereby reduce polarization degree in the output light OL. For clarity, the direction of the fast axis FA of the first birefringent element BEi is referred to herein below as angle 0°.

In some configurations, additional polarization rotators 12 and 14 and/or additional polarization rotator PRi, e.g. half wave plates (HWP's), are located along the optical axis OA and in optical path of light passing through the system 100. Polarization rotators 12 and 14 are located within birefringent modules BMi and BM₂, and polarization rotator PRi is located between the modules. The birefringent elements BE1-BE4 are oriented along the optical axis OA such that the fast axes FAi and FA₃ of the first and third elements BEi and BE₃ and the slow axes of the second and the fourth elements BE2 and BE₄ are parallel; orientation of the fast axis FAi of element BEi defines the zero angle. As indicated above, polarization rotators 12and 14 are used to rotate polarization of light passing between the birefringent elements BE1-BE4 within the birefringent modules of the system 100 and their provision is optional because they may be replaced by appropriate rotation of at least some of the birefringent elements BE1-BE4 themselves. Additionally, polarization rotator PRi is used to rotate polarization of light passing between the birefringent modules, this polarization rotator may also be replaced by appropriate rotation of one module with respect to the other. According to one possible configuration of the system 100, polarization rotators 12 and 14 (in this configuration being half wave plates (HWP) appropriately selected for a wavelength of the input light) are oriented with opposite angles relative to the zero angle (fast axis FA of BEi), i.e. Θη=-θΐ4. This is while the second polarization rotator PRi is rotatable to thereby control degree of depolarizarion of input light IL, i.e. the degree of polarization of output light OL assuming that the input light is polarized (D=l).

To this end, the inventors have found that by setting Θη=-θΐ4 to be 13.68 or 31.32 degrees, rotation of the second polarization rotator PRi enables full control of the output polarization degree. The optical depolarizer 100 thereby reduces polarization degree of light passing therethrough such that output polarization degree of input light having polarization deg D ' = l/3+2/3*∞s(4e_PR) (equation 1) where 6PR is the angle of orientation of the second polarization rotator (HWP) 14 between the optic axis thereof and the zero angle defined by fast axis FAi of ΒΕχ. According to equation 1, for

no depolarization occurs, i.e. the output light OL has similar polarization degree as the input light IL (D '=D). For 0PR=3O°, the output light OL is completely depolarized (D '=0), the output polarization degree D ' in the above described configuration of the system 100 is thus determined according to equation 1. It should be noted that negative D' values resulting from equation 1 correspond to reflection of the polarization state, and thus the polarization degree can be viewed as the absolute value of D ', i.e. \D '\. This configuration of the system 100 provides control over the polarization degree of output light using a single parameter,

Reference is made to Fig. 2B illustrating an additional example of the depolarization system 100 of the present invention capable of operating independently on different polarization components of light. In this example the system 100 includes three birefringent/depolarizer modules BM1-BM₃, each module includes two birefringent elements BEi of similar length, while different birefringent modules include birefringent elements of different lengths. More specifically birefringent elements BEi and BE₂ are of length L_lt2=L, birefringent elements BE₃ and BE₄ are of length L_3i4 (which preferably obeys L3_R4>L+2Li_R2=3L) and birefringent elements BE5 and BEe are of length L5 6 (which preferably obeys L_5:6>L+2L]_:2+2L_3:4=9L). The birefringent elements of each module are oriented such that the fast axes of birefringent element within the module are perpendicular to each other while the fast axes of the downstream elements of the different modules are perpendicular. More specifically the fast axes of birefringent elements ΒΕχ, BE₃ and BE₅ are parallel while being perpendicular to the fast axes of birefringent elements BE2, BE₄ and BEe.

Each of the birefringent modules BM1-BM₃ also include a polarization rotator (typically a half wave -plate (HWP)) located between the birefringent elements, polarization rotator 12 is located in module BMi, polarization rotator 14 is located in module BM2 and polarization rotator 16 is located in module BM₃. Polarization rotators 12-16 are rotatable with respect to the zero angle (fast axis of BEi) and angular orientation of these polarization rotators is designated as θη, Θ14 and θιβ- Within each of the birefringent modules, the orientation of the respective polarization rotator enables certain limited control on the depolarization of light. The appropriate combination described herein provides for simple control on the depolarization of light, and a wide range of de -polarization schemes, including the isotropic depolarization. Two additional polarization rotators PRi and PR2 are located along the optical path of light passing through the system between the birefringent modules. These polarization rotators are used to rotate the polarization state of light passing therethrough to thereby transform between polarization states thus enabling each of the birefringent modules to operate on a different Stokes parameter. For example, PRi may be a half wave -plate oriented at an angle of 22.5° and thus configured to transform between polarization states IH> and \ V> to polarization states IP> and \M> (i.e. from horizontal and vertical to ±45°) and PR2 may be a quarter wave-plate oriented at 45° and thus configure to transform between polarization states IH> and \ V> to polarization states IR> and \L> (i.e. right- and left-hand circular polarization). The polarization rotators PRi and PR2 are fixed in their orientation and are used to enable each birefringent module to operate to depolarize the light mainly with respect to one of the Stokes parameters. More specifically, each birefringent module typically affects a certain Stokes parameter twice as much as the other two Stokes parameters. More specifically, each birefringent module, e.g. consisting of two equal birefringent elements and a half-wave plate located in between them affects polarization of input light by projecting polarization states from Poincare sphere onto an ellipsoid having one short radius and two relatively long radii. Orientation of the fast axis of the birefringent elements defines the primary radius R_\ of the ellipsoid. The primary radii lengths of such ellipsoid are described by

(equation 2) where Θ is the angle of the half wave plate of the birefringent module. Similarly to equation 1, negative values of the radii represent a reflection of the ellipsoid. For example, if the wave -plate is oriented at an angle of 15°, polarization states of input light will be projected onto an ellipsoid with primary radii of Ri=0.5, and R₂=R3=0.75. Thus, as shown in equation 3 below, each Stoke parameter is affected by all three birefringent modules, while in this configuration the effect of each birefringent module over a certain polarization state is greater than over other polarization states.

The control over the reduction of polarization degree of input light is provided by rotation of polarization rotators 12, 14 and 16. This is different from the example of Fig. 2A where all Stokes parameters may be controlled by rotation of one polarization rotator. It should be noted that the system configuration as exemplified in Fig. 2B gives the depolarizer system 100 an ability to easily induce various depolarization schemes and to control the polarization of light with respect to one or more Stokes parameters while substantially not affecting the other Stokes parameters. The polarization rotators PRi and PR2 are tuned to operate on light polarization to thereby rotate the Stokes parameters' space to replace between the corresponding polarization states of light. This enables each of the birefringent modules to operate to de -polarize input light mainly with respect to one Stokes parameter.

Assuming the input light is fully polarized (i.e. D=l) the operation of the system can be described by the radii of Poincare sphere representation with respect to different Stokes parameters. The configuration of Fig. 2B provides that each of the birefringent modules BM1-BM₃ operates to reduce the radius of the Poincare sphere by varying the angular orientation of the respective polarization rotator 12-16 according to the following equations:

R₁=cos(4e₁₂ (cos(4e₁₄)+i (cos(4e₁₆)+i)/4

(4θ₁₄)-(οοί(4θ₁₆)+1)/4 > (equation 3)

R₃=(cos(4e₁2)+i (cos(4e₁₄)+i cos(4e₁₆)/4

where R1-R3 are the radii of Poincare sphere respectively associated with Stokes parameters S1-S3, the Θ12- θιβ are the angular orientations of polarization rotators 12-16 respectively. As shown from equation 3 the depolarization system configuration of Fig.

2B does not necessarily provides isotropic de -polarization but rather provides substantial control over the polarization degree with respect to each of the polarization states (typically described by Stokes parameters). This provides relatively accurate control on polarization reduction and maintains the system's ability to provide isotropic de-polarization utilizing appropriate orientation of the polarization rotators 12, 14 and

16.

It should be noted that the order of the birefringent modules may be changed, as well as the order of polarization rotators PRi and PR2. Additionally, similar to the example of Fig. 2A, each one of polarization rotators 12-16 may be replaced by physical rotation of all proceeding elements by a corresponding angle of 2Θ.

The depolarizer system 100 configured as described above with reference to Fig. 2A, utilizing HWP 12 and 14 within the birefringent modules and PRi between the birefringent modules, where the birefringent elements BE₁-BE₄ are used as Calcite crystals, was constructed to experimentally verify its performance. The Calcite crystals BE₁-BE₄ were configured with lengths of 1mm for ΒΕχ and BE₄ and 2mm for BE₂ and BE₃. The system is configured with

and for experimentally performing Quantum Process Tomography (QPT) for varying the angle θρ of HWP PRi in the range of 0<6PR<45° . The QPT include transmission of separate photons, prepared in the polarization states \H), \P), \R), and \ V), through the system 100. The final polarization of the output photons was characterized using Quantum State Tomography (QST) by transmitting the output photons through a polarization detection system including half- and quarter-wave plates, a polarizer and a single photon detector (SPD).

To this end photon pairs were generated using spontaneous parametric down- conversion of 390nm pulses. One photon of the pair was probabilistically split by a beam splitter, and sent to a single -photon detector (SPD). The second photon was sent to the depolarizer system 100. The photons were spectrally filtered by a 5nm band-pass filter before entering the depolarizer system 100, and were spatially filtered by coupling into a single-mode fiber, and collimated into free space. As noted, the photons were prepared in the polarization states IH), IP), IR), and IV), serving as the initial states for the QPT procedure. After depolarization, the final polarization state of the output photons was characterized at the QST unit. In order to reduce background noises, and to demonstrate the depolarizer applicability to single photons, the detection of the two photons was in coincidence, i.e. the depolarized photon and a control photon both split from the same signal.

Reference is made to Figs. 3A-3E showing some experimentally measured QPT processes in Figs.3B-3E together with a Poincare representation of polarization states in Fig. 3A. The Poincare representation of polarization states shown in Fig. 3A illustrates the various possible polarization states on a sphere, where each axis represents one of the Stokes parameters {¾,¾,¾} and the radius of the sphere is D = -_\]s_l ² + S₂ ² + S₃ ² .

Figs. 3B-3E show the experimentally measured QPT processes at four angular orientations of HWP PRi, i.e. four values of θρη angles being 4°, 15°, 22° and 30°. These orientations of HWP 14 correspond to theoretical polarization degree values of '=0.97, 2/3, 0.36, and 0, respectively. All QPT processes were reconstructed using the standard and known maximal likelihood protocol, in order to restrict their parameters to physically allowed values.

In order to better illustrate the isotropic behavior of the depolarization system 100 according to the present invention, the depolarization process can be viewed in algebraic representation. Given a configuration of the system (certain value of 6PR in the non-limiting example of the system's configuration above), its effect on an input polarization state p can be described as p '= e(p). This can be represented by a Hermitian process matrix χ as:

^Ε (P) =∑ Z_m« ^E _mP^E _« (equation 4) mn

where E_m are matrices spanning the vector space of p and assuming that there are no intensity losses the trace of χ is one (Tr(/)=1).

Fig. 4 illustrates measured eigenvalues of χ experimentally calculated using the above described configuration. When no depolarization occurs, χ has one eigenvalue that equals 1, and the rest eigenvalues are zeros. If two or more eigenvalues of χ are other than zero, the operator/system depolarizes the input light. Isotropic depolarization can be described by a matrix with three nonzero equal eigenvalues; and complete depolarization occurs when all four eigenvalues of χ are equal. Fig. 4 shows measured eigenvalues of the reconstructed matrices as a function of HWP PRi orientation (θρ ). As shown, at

one eigenvalues equals 1 and the others equal zero, i.e. no depolarization and D'=\ . As 6PR grows, one eigenvalue is reduced and the three others increase equally thereby providing isotropic depolarization of input light, and at

all eigenvalues are equal representing complete depolarization.

It should be noted that the depolarization system of the present invention can provide controllable and isotropic depolarization utilizing different setup parameters. Such as different lengths of the birefringent elements, rotation of the birefringent elements instead of the use of polarization rotators etc. The main constrain on the respective birefringent elements' lengths L1-L4 is that the use of

is required in order for the system to be capable for transmitting light with no depolarization. The lengths ratio can be any number, as indicated above, except for exactly 1 or 1/2.

As indicated above, the depolarizer system can be used without polarization rotators (wave plates). To this end, the angular relations between the orientation of the fast axes of the birefringent elements (within the module and between the modules) should vary to provide effective polarization rotation for light passing therebetween. For example, to replace the first polarization rotator 12 when oriented at θ]=31.32° , the second birefringent element BE2 (as well as the proceeding elements) should be rotated by 62.64° to provide similar effect. Generally, to replace a half wave -plate polarization rotator oriented in a certain angle Θ, all the proceeding elements can be rotated by an angle of 2Θ. For example, setting BEi as shown in Fig. 2, orienting BE2 such that a slow axis thereof is oriented at 27.4° or 62.6° and parallel to fast axis of BE₃, and placing BE₄ such that slow axis thereof is parallel to fast axis orientation of BEi, will provide zero depolarization (similar to the above described

In this configuration the degree of depolarization can be controlled by rotating BE₃ and BE₄ together until reaching complete depolarization after 60°. It should however be noted that the polarization state of the output light will vary with different configurations of the system. However polarization orientation of light can be varied using known polarization rotators.

Thus, the present invention provide a novel isotropic depolarizer system capable of that equally reducing the degree of polarization of any input polarization state to any required level. Those skilled in the art will readily appreciate that various modifications and changes can be applied to the embodiments of the invention as hereinbefore described without departing from its scope defined in and by the appended claims.

Claims

CLAIMS:

1. An optical system configured for affecting polarization of input light, the system comprising at least two birefringent modules accommodated sequentially along a light propagation path, wherein said at least two birefringent modules are arranged with a certain first angular relation between them, each of said at least two birefringent modules comprises at least two birefringent elements having predetermined lengths and oriented in a certain second angular relation between them, at least one of said first and second angular relations being selected for desirably reducing polarization degree of the input light.

2. The optical system of Claim 1, wherein said selection of at least one of said first and second angular relations being such as to desirably reduce the polarization degree of the input light irrespective of polarization orientation of said input light.

3. The optical system of Claim 1 or 2, wherein said predetermined lengths of said birefringent elements are longer than a coherence length of said input light.

4. The optical system of any one of Claims 1 to 3, wherein at least one of said at least two birefringent modules comprises a polarization rotator located between the at least two birefringent elements of the respective birefringent module, said polarization rotator being configured to alter angular relations between said birefringent elements with respect to said input light.

5. The optical system of any one of Claims 1 to 4, comprising at least one polarization rotator located along optical path through the system between said at least two birefringent modules.

6. The optical system of any one of Claims 1 to 5, wherein said at least two birefringent elements of each of said at least two birefringent modules are of different lengths.

7. The optical system of Claim 6, wherein variation of the angular relation between said at least two birefringent modules provides for variation in reduction of the polarization degree of said input light.

8. Then optical system of Claim 6 or 7, wherein said at least two birefringent modules, each comprising the at least two birefringent elements of different lengths, are arranged a symmetrical order relative to a central point along said optical path along the system.

9. The optical system of any one of Claims 6 to 8, wherein said polarization rotators are half wave-plates.

10. The optical system of any one of Claims 1 to 5, comprising at least three of said birefringent modules, wherein each of said birefringent modules comprises the at least

5 two birefringent elements of a similar length, being different from that of the other birefringent modules.

11. The optical system of Claim 10, comprising at least two polarization rotators each located in between two of said at least three birefringent modules and being configured to rotate polarization of light passing therethrough to thereby transmute

10 between Stokes parameters defining said polarization state.

12. The optical system of Claim 10 or 11, wherein each of said at least three birefringent modules comprises a polarization rotator located between the at least two respective birefringent elements, an angular orientation of said polarization rotator providing for desirably reducing polarization degree of light passing therethrough.

15 13. The optical system of any one of claims 1 to 9, comprising first and second of said birefringent modules each comprising a pair of the birefringent elements, the four sequentially accommodated birefringent elements being arranged such that lengths of first and second birefringent elements of the module are different.

14. The optical system of Claim 13, comprising a polarization rotator located 20 between the first and second birefringent modules, said polarization rotator being configured to controllably vary an angle of polarization rotation.

15. The optical system of any one of Claims 13 or 14, comprising first and second half wave-plates (HWP) located in the first and second birefringent modules between the respective birefringent elements, and an additional HWP located between said

25 birefringent modules, said HWP being configured to affect light of a selected wavelength range, said birefringent elements being oriented such that fast axes of the birefringent elements of the same module are perpendicular to one another, said first and second HWPs are oriented with a predetermined angle relative to the fast axis of the first birefringent element of the birefringent module thereby defining a zero angle, and

30 said additional HWP is rotatable about an optical axis with respect to said zero angle to thereby vary a degree of polarization of output light.

16. The optical system of Claim 15, wherein said first and second HWP are oriented with equal or opposite angles with respect to said zero angle.

17. The optical system of Claim 15 or 16, wherein said first and second HWPs are oriented with opposite angles of 13.68 or 31.32 degrees with respect to said zero angle, rotation of said additional HWP with an angle Θ_ΡΚ with respect to said zero angle varies polarization of light passing through the system to a degree of D' =1/3+2/3 " os (4θρ ).

18. The optical system of claim 13 or 14, wherein at least one of the first and second birefringent modules is rotatable with respect to the other birefringent module, the angular relation between said birefringent modules provides for desirably decreasing the polarization degree of said input light.

19. The optical system of any one of claims 13 to 18, wherein the birefringent elements of each of the first and second birefringent modules have different lengths between them, being similar for the first and second modules, said different birefringent elements of the two modules being arranged in opposite order with respect to a central point of the optical path between them such that when said two birefringent modules are positioned in similar angular orientation with respect to the input light, a polarization degree of light being output from said two birefringent modules is similar to a polarization degree of the input light.

20. The optical system of any one of the preceding claims, comprising a mounting module carrying at least one of the birefringent modules and configured to enable a control over said angular orientation of the birefringent module.