Patent Publication Number: US-2015077838-A1

Title: Fresnel Rhomb

Description:
TECHNICAL FIELD 
     The invention relates to a Fresnel rhomb. A Fresnel rhomb enables the conversion of linear polarized light to circular polarized light by double total reflection. 
     A Fresnel rhomb is a transparent body, such as made from glass, which has a cross section in the form of a rhomboid (parallelogram). The acute angle of the rhomb is selected such that linear polarized light which is incident on one of the front ends is totally reflected twice with such angle. The selection of the angle depends on the refractive index of the material used for the body at a selected wavelength. Optical crown glass (refractive index n=1.5), for example requires an angle of 54° 37′. The twice totally reflected light exits the body at the opposite back end in a perpendicular direction also. The ray is shifted by this procedure. 
     If the oscillation plane of the incident linear polarized light forms an angle of 45° with the reflection plane of the rhomb, circular polarized light is generated. A phase difference δ=π/4 is generated with each total reflection, i.e. δ=π/2 between the TE-component which is polarized perpendicular to the reflection plane and the TM-component which is polarized parallel to the reflection plane. The use of two suitable Fresnel rhombs will again provide linear polarized light without a shift. 
     The phase difference generated with a Fresnel rhomb has only a small dependence on the wavelength for large ranges. Accordingly, it is used for applications where only a small wavelength dependence is required. 
     Prior Art 
     On the internet page 
     http:www.wmi.badw.de/teaching/Lecturenotes/Physik3/Gross_Physik_III_Kap — 3.pdf 
     Usually one or two Fresnel rhombs are used in order to achieve an overall delay of 45° or 90°, respectively. 
     Fresnel rhombs are sold on the internet page http:www.halbo.com/fr_rhumb.htm. A graphic representation of the dependence of the phase delay on the wavelength is given for CaF 2 . The phase delay increases with decreasing wavelength. In known assemblies it is assumed that CaF 2  has no birefringent properties. 
     In the publication “Intrinsic birefringence in calcium fluoride and barium fluoride” in Physical Review B. Vol. 64, p 241102 (R) from 29 Nov. 2001 by John H. Burnett, Zachary H. Levine and Eric L. Shirley it is described that there is a small birefringence in CaF 2  and BaF 2  in wavelength ranges below 250 nm. It was found that the birefringence is dependent on the direction of the birefringence. 
     Such small birefringence may not be neglected if light with short wavelengths is used for long optical paths, such as they occur in Fresnel rhombs. Commercially available Fresnel rhombs are, therefore, not suitable for use with short wavelengths of light below 250 nm or can he used only in a limited way. 
     DISCLOSURE OF THE INVENTION 
     It is an object of the invention to provide a Fresnel rhomb according to the above mentioned kind, which can be used in wide wavelength ranges even with light below 250 nm. 
     According to an aspect of the invention this object is achieved in that the orientation of the crystal structure is taken into account during manufacturing and adjusting of the entrance side of the front end in relation to the direction-dependent birefringence. The beam incident on the Fresnel rhomb always forms a set angle of 90° with the front end in order to achieve the desired effect. If the orientation of the crystal structure is taken into account when the front end is manufactured and adjusted the light beam will follow a given direction through the crystal. In such a way non-isotrop properties of the material can he considered and used for the application. One of such non-isotrop properties of the material is, for example, the direction-dependent birefringence when using CaF 2 , BaF 2  or similar materials. 
     Especially with short wavelengths there are several different phase-influencing effects in some materials, such as CaF 2  or BaF 2 , used for a Fresnel rhomb. The light beam travels in a first direction perpendicular to the front end along a first portion of the path. A first phase delay occurs depending on the direction and the length of the path due to birefringence. A further phase delay is effected by total reflection. After total reflection the light beam travels in a second direction along a second portion of the path. A third phase delay is caused by birefringence which also depends on the direction and the length of the path in such second direction. The second total reflection also causes a phase delay. After the second total reflection the light beam travels along a third portion of the path in the first direction. The entire length of the path in the first direction, therefore, corresponds to the sum of the first and the third portion of the path. The length of the path in the second direction corresponds to the second portion of the path. 
     In many materials the delay values for birefringence assume positive values in some directions and negative values in other directions. In other words: the parallely polarized component of the light is faster than the perpendicularly polarized component in some directions and slower in other directions. Therefore, it is provided by a preferred modification of the invention that the birefringence in the first travelling direction of the light, the birefringence in the second travelling direction (B) of the light and the delays caused by total reflections are optimized to a selected delay value. 
     Such an optimization can be achieved in particular by minimizing the deviation of the desired overall delay for all wavelengths of a selected wavelength range. 
     Preferably, the rhomb according to the present invention consists of CaF 2  or BaF 2 , The material is transparent even for short wavelengths from a wavelength range below 250 nm and it is very suitable for the use in ellipsometry or other measuring applications requiring the control of the polarization. 
     Further modifications of the present invention are subject matter of the subclaims, An embodiment is described below in greater detail with reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a cross section of a typical Fresnel rhomb and the corresponding light path. 
         FIG. 2  illustrates typical designations and geometric conditions in a crystal structure. 
         FIG. 3  shows the dependence of the phase delay on the wavelength from an experiment for known assemblies and theoretical values for assemblies where the direction of the front end was optimized. 
         FIG. 4  illustrates the dependence of the delay per mm of material on the direction of the light beam where two directions with fixed distance are marked where the phase delays are compensated along the entire optical travelling path in the Fresnel rhomb. 
         FIG. 5  is a cross section of two consecutive Fresnel rhombs. 
     
    
    
     DESCRIPTION OF THE EMBODIMENT 
     A typical Fresnel rhomb is shown in  FIG. 1  which is generally designated by numeral  10 . In the present embodiment the material is a calcium fluoride (CaF 2 ) crystal. It is understood, however, that the selection of the material depends on the application and the wavelength range which is used and different materials with corresponding properties may be used for different applications. 
     A cross section of the rhomb  10  is shown in  FIG. 1 , the cross section being the same along its entire width. The rhomb  10  has an entrance side front end  12  and an exit side back end  14 . The front end  12  and the back end  14  are parallel planes. The material between the front and back ends is limited by four side faces with each two opposite side faces being parallel, respectively. Two of the side faces, namely side faces  16  and  18 , extend perpendicular to the representation plane. The side faces which are parallel to the representation plane can not be seen in this representation. The front and back ends  12  and  14  form an acute angle  20  and  22  which is in the present embodiment φ=73° 27′. In such a way a rhomb is formed in the shown manner. 
     A beam  26  entering perpendicularly at the front end  12  is incident on the side face  16  at an angle  24  which corresponds to the angle φ with such a geometry. Due to the selected material the beam is totally reflected. The totally reflected beam  28  is incident on the side face  18  at the angle designated with numeral  30 . Since side faces  16  and  18  are parallel, the angle  30  is the same as angle φ. The beam is again totally reflected. The twice totally reflected beam  32  exits the rhomb at an angle of 90° at the exit side back end  14 . 
     A polarization dependent delay occurs with each total reflection at the side faces  16  and  18 . This effect is well known and can be derived from the Fresnel equations. If the incident light, i.e. beam  26 , is linear polarized with an angle of 45°, the TM-component, which is polarized parallel to the reflection plane, is delayed by 22.5° regarding the TE-component, which is perpendicularly polarized with each total reflection. In the present assembly the overall delay is 45°. If the intensities of the components of the incident beam  26  are the same in both polarization directions the exiting beam  32  is elliptically polarized. This is indicated by an ellipse  34 . 
     The above explanations of a Fresnel rhomb assume entirely isotrope material. This, however, is not the case for small wavelengths below 250 nm. The direction dependency of the delay especially for small wavelengths will cause the polarization states of a beam to change in a different way than described above. 
     The beam  26  travels through a Fresnel rhomb along a first travelling path  46  in a first direction designated “A” between the point of entrance  38  at the front end  12  and the point  40  of the first total reflection. Furthermore, the beam  28  travels along a second travelling path  48  in a second direction designated “B” between the point  40  of the first total reflection and the point  42  of the second total reflection. Finally, the beam  32  travels along a third travelling path  50  again in the first direction designated “A” from the point  42  of the second total reflection to the exit point  44  at the back end  14 . In other words: the delay is the sum of the delays along the sum of travelling paths  46  and  50  in the direction A and the delay along the travelling path in the direction B. 
       FIG. 2 . illustrates the geometric conditions of the beam directions relatively to the crystal structure. Direction A is represented by a bold arrow  52 . Direction B is represented by a bold arrow  54 . The cuboid  56  represents the crystal structure. The crystal structure can be represented in known manner by principal directions. In the present embodiment the crystal structure has principal directions forming a Cartesian coordinate system. The crystallographic direction [100] is represented by an arrow  58 . The crystallographic direction [001] is represented by an arrow  60 . The crystallographic direction [010] is represented by an arrow  62 . Such arrows correspond to the directions of the edges of the cuboid  56 . The direction [−111] is represented by arrow  64 . This direction extends along a diagonal of the adjacent cuboid which is not shown in the present representation in order to keep the representation simple. 
     Beam directions A and B are not parallel. The directions A and B define a plane. The plane was selected such that the directions [100] and [−111] also lay in this plane. The plane is represented by a circle  66 . The beam direction B forms an angle α with the principal direction [100]. The beam direction A forms an angle α′ with the principal direction [−111]. In such a constellation the light beam  26  entering the rhomb has a TE-component in the direction [01-1] (dashed arrow) which is polarized perpendicularly to the reflection plane and designated with numeral  68  in  FIG. 2  and a TM-component in the direction designated with numeral  70  (dashed arrow) which is polarized parallely to the reflection plane. 
     Additionally to the delay caused by total reflection, a weak direction dependent birefringence occurs in the crystal. It is particularly strong for small wavelengths below 250 nm and may not be neglected.  FIG. 3  shows experimental results of the measurement of the phase delay δ for a commercially available Fresnel double rhomb made of a CaF 2  crystal as a function of the wavelength. The measuring points are designated with  72 . It can be recognized that phase delays above 250 nm are in the range of 90° as described above for a single Fresnel rhomb with 45° phase delay. The phase delay δ strongly drops below 250 nm and is only about 40° at 170 nm. 
     The effect depends on the direction.  FIG. 4  shows the delay δ caused by the direction dependent birefringence per mm of material in the direction of various angles α, i.e. for different directions in the plane  66 . In the representation α=0° corresponds to the principal direction [100] in  FIG. 2 . 
     Negative ranges, such as the range  74 , are ranges where the refractive index for the perpendicularly polarized component  68  is smaller than for the parallely polarized component  70  and therefore causes a negative delay. In the positive range, such as range  76 , the opposite applies. The refractive index for the perpendicularly polarized. component  68  ( FIG. 2 ) is larger than for the parallel polarized component  70  thereby causing a positive delay. 
     In the present example the direction A is about −115°. It can be recognized that the beam in the direction A has a delay of δ≈−1°/mm. Direction B has, as can be derived from  FIG. 1 , a set angle which is shifted by 2*73° 27′ at about 30°. The beam in the direction B has a delay of about δ≈1°/mm. The angular difference 2*φ=2*73°27′ between direction A and direction B is set by the used material to achieve the properties of the Fresnel rhomb. The direction of the crystal, however, can be selected to achieve a value which is as suitable as possible. A change of the crystal direction corresponds to a shift of the two arrows A and B in  FIG. 4  with identical distance. 
     A crystal direction can be found where the effects of birefringence in the direction A and birefringence in the direction B just compensate. In the selection shown in  FIG. 4  the delay in the direction A is negative and in direction B it is positive. The optimum results are designated with numeral  76  in  FIG. 3 . it can be seen that by suitably adjusting the crystal in the right direction, i.e. by suitably selecting the direction of the front end  12  and the back end  14  relative to the crystal structure the wavelength dependency of the phase delay can be minimized. In the present embodiment the phase delay was optimized to a value of 90° for the entire wavelength range. 
     Depending on the application it can make sense to generate a phase delay without beam shift. For such an application two Fresnel rhombs are arranged in series.  FIG. 5  illustrates how the beam  80  travels through two consecutive Fresnel rhombs  82  and  84 . The direction of the polarized radiation is changed by 90° and the beam keeps its direction.