TOP LATERAL REFRACTION AND REFLECTION OF POLARIZED LIGHT IN LENSES

Transcription

1 Journal of Scientific Research in Engineering & Technology Volume (1) Issue (1) Year (2016) ISSN: TOP LATERAL REFRACTION AND REFLECTION OF POLARIZED LIGHT IN LENSES Miranda Díaz Lázaro J. Electronic Design Center of Technological Applications and Nuclear Development (CEADEN), Ciudad Habana, Cuba. ABSTRACT This effect is significant only looking at the lens laterally. Therefore, a lens acts as a lateral analyzer when the polarization plane of polarized light incident on the lens is rotated. Following this principle that in the spherical surface of a lens fit n circles of radius r, where n is inversely proportional to r, and each circle is a lens itself. Then if a beam of light is shined in one of these areas, the phenomenon is expressed lateral side and diametrically opposite to where the incident linearly polarized light, the lens acting as a waveguide for the light beam polarized. Received: 08 Jan Accepted: 22 Jan Published: 31 Jan Corresponding author: miranda@ceaden.edu.cu

2 Miranda Díaz Lázaro J INTRODUCTION The intersection between a plane and a spherical surface take place, when a linearly polarized light beam incident on a lens. A polarised light beam is composed of electromagnetic waves to oscillate in planes parallel to each other and in the same direction. Taking one of these planes to affect orthogonally on the spherical surface of a convex lens, the light is reflected and refracted without leaving the plane which belongs, as shown in Figure 1 where only the central portion of the lens i s s h o w i n g for a better understanding. Now if we rotate the polarisation plane of polarised light beam, not the lens, then also changes the reflected and refracted ray s direction and remain within the plane of polarisation of light. Fig. 1. Representation of refraction and reflection to affect polarised light in a convex lens Fig. 1.a. Representation of intensity light variation When a non-polarized light and or a light circularly polarized incidents on a lens, the light will be reflect and refract inside the lens body in all directions. But a linearly polarized light beam incident on a lens, the light will be reflect and refract inside the lens body only in the same direction that polarise plane (Figure 1.a), the light can not through out from the polarize plane that it belong. Them, polarize plane acts like filters that only permit the maxim light intensities in only one direction, that is polarize plane orientation. In other directions the intensity will be equal to the maxim light intensity by the Cosβ, where β is the angel between a deferent position that polarize plane position and the position of polarize plane.

3 Miranda Díaz Lázaro J. 41 When a linearly polarized beam incident on a lens, will be reflect and refract inside the lens body following the interception between a plane (plane of polarization) and a sphere (lens surface), maintaining the orientation of the beams refracted and reflected within the polarization plane. On both sides of the lens are forming two pairs of fans on opposite edges to the lens diameter. The higher intensity of the resulting beams will take place at opposite ends to the diameter of the lens, so that this phenomenon is noticeable only by observing the lens laterally, i.e., placing parallel to the optical axis. 2. EXPERIMENT Take two observers situated one on the right and one on the left of Figure 1. The observer on the left sees the right side of the image of the light source, because the rays that reach it are refracted and reflected within of the lens from the side opposite the light source. While the right observer sees the left side of the image of the light source. Turning to the position as seen in Figure 1, both are observed to reduce the light intensity of the image completely when the plane of polarization is orthogonal to the plane of the paper, or it is parallel to the two observers. But at the same time each plane of the polarize light beam is a light beam too, and it is refracting and reflecting, but to 90 0 of another reflection and refraction that was axial to the polarized plane of the polarize light beam. In Figure 2 at the right a is the orientation of the polarized plane of the light beam incident, b and c is the axial reflection and refraction polarized plane oritation, d is the 90 0 reflection and refraction polarized plane oritation. d b a c Fig. 2. At the left reflection and refraction axial to the polarized plane of the polarize light beam. At the right a is the orientation of the polarized plane of the light beam incident, b and c is the axial reflection and refraction polarized plane oritation, d is the 90 0 reflection and refraction polarized plane oritation. Therefore, a lens can be used like analyser of polarised light, which gives information about the orientation of the plane of polarisation, shows this effect, as shown in Figure 3.

4 Miranda Díaz Lázaro J. 42 Fig. 3. The reflection and refraction at a convex lens representation Figure 2 represents the entire lens and the beam of polarized light. With this figure can be seen together as discussed earlier and conclude the greatest refraction and reflection takes place where the geometric central plane of the beam impinges on the diametric line of the circumference defined by the beam on the surface of the lens. Fig. 4 Intensity vs Angel β The intensity light distribution around the lens has sinusoidal shape according of polarise plane orientation and the angel β between a select position and the polarise plane. If we know β for a point, we can know the light intensity for that point. Then, if I=0, polarise plane position is 90 0 from that point. In this way we can use this principle to a polarymetric detection method (Figure 4). Figure 5 is a sequence of rotation of plane polarized light beam. In the centre of the lens side, a light spot is observed that its light intensity varies depending on the spatial position of the plane of polarization relative to the position of the observer. Hence, an observer who turns laterally around the lens with the same speed to the plane of polarization will always see the same intensity Fig. 5. Polarize plane rotation sequence

5 Miranda Díaz Lázaro J. 43 The lens being a spherical surface, over it can be placed perfectly n circles of radius r, the number n is inversely proportional to the radius r. Each circle can be seen as a lens. Taking this into account, if the linearly polarized light incident is on the lens edge, it will pass all explained above, but in the region of incidence, the light will exit the edge of the lens diametrically opposed to the incident beam and it just shows the image at that point and not in any other region of the lens. Figure 6 shows what has been explained here, including an equation to determine the number of reflections that occur within the geometry of the lens and selecting the appropriate lens. This permit us select the geometrical dimensions of the lens that we most use in our optical design, the reflections must be lest than or equal 3, with more than that, we lost many intensity of light in that reflections and this is to bad to design results for. Fig. 6. Reflections on the lens to make an impact on its edge beam perimeter If the beam of polarized light is shinning in the lens edge, rotate the plane of polarization of light along the diametrical opposite of the lens coinciding with the orientation of the polarization plane, it will have a very bright image of the light source. To rotate the plane, the intensity will decrease Figure 7 shows a sequence in which can be seen how to change the outgoing light when the polarizing plane is rotated Fig.7. Sequences that shows how changes the out coming light lens in a lens side view

6 Miranda Díaz Lázaro J. 44 In other words, when beams of polarize light pass through of a biconvex lens, occurred refraction and reflections inner the body lens with out of the beam light polarization plane that it belong. Then there are two beams go out of the lenses in the same direction that polarize plane and opposite to the diameter (Figure 8). Fig. 8. Representation of refraction and reflection to affect polarized light in a convex lens The lateral beam out 1 is the lower part of the object s image. The lateral beam out 2 is the upper part of the of the object s image. If the polarize plane of polarize light beam is rotated, both lateral beams out (1 and 2) will be rotated too around the external lens s circle, following polarize plane position. This is the reason for what is very difficult use this phenomena in order to build measurements instruments. 3. Coplanar lens system Taking two identical lenses and placing them in the same plane. The intercept between the lines extending perpendicular where the edges of the lens join, with a line tangent to the upper edges of the two lenses, will be the centre of the light beam. The two points diametrically opposite light emerging in each of the lenses will be 90 o to each other. Figure 9 is the geometric representation of this phenomenon. Fig. 9. Parallel lens system By rotating the light beam linearly polarized, when the diametrical path of the lens coincides with the orientation of the polarization plane, a bright image of light source is obtained in the side diametric position, while the position diametrically

7 Miranda Díaz Lázaro J. 45 opposite in the other lens there be not light. If we rotate the plane of polarization in the direction of the lens with a lower intensity of light, this will grow in intensity and the other will decrease. There is 90 o of difference between the points. Using this principle is possible to get very good results with two lenses in coplanar position. In this case the input beam of polarize light must be projecting between the two lenses and not to lenses center (Figure 10). Fig. 10. Parallel lens system For both lenses polarize light beam touch the external circle of each lens and polarize light beam is reflecting and refracting along the lens diameter and get out for the opposite side. If the polarize plane have the same position of lens diameter, the lateral beam out will be very strong, but if it is orthogonal to the lens diameter, the lateral beam will be very weak. When the polarization plane of the polarize beam is rotated, the lateral beam 1 and 2 don t change its positions, but change its intensity in opposite form. This is due to that is the same light beam for the two lenses, but the polarize plane position not is the same for both lenses, and this deference produce that the lateral beam out 1 and the lateral beam out 2 shining in deferens forms. When the light beam polarize plane is orthogonal to both lenses, the shining of both lateral beam out will be the same; this occur too when polarize plane is parallel to the both lenses. In this two positions is possible considering there is not polarize plane rotation, then, this will be the cero of the polarizing measurement instrument. At this point, if an active optically substance is putt on in the light polarization beam trajectory, one of the lateral beams out will increase its shining and the other decreases its shining. The differences of shining between both lateral beams out will be polarize plane rotation value. In order to make this most easy, the source of the light polarization beam is pulse modulated. In this form is possible compare the rise time of both lateral beams out pulses signals

8 Miranda Díaz Lázaro J. 46 If the rise time of the both lateral beams out occurs at the same time there is not polarizing plane rotation. If the one rise time occurs before the other, then there is polarizing plane rotation (Figure 11). Fig. 11. Electronic circuit letters time It is possible to know if the rotation was a clockwise or not, depending which rise time was occur first. For the first rise time, its lateral beam out shining more than that rise time produced by the other lateral beam out. For that the first optic-electronic sensor respond before that the second because it receive more than light that the second opticelectronic sensor which receive less than light (Figure 12) Fig. 12. Operational amplifier output following the pulse signal in each output amplifier, according to the Malus`s Low.rise time of the Fig. 13. Vista fixed to an experiment made media screens on which projects the light emerging from the lens which are the white-bluish halos. On the left of the spot of light

9 Miranda Díaz Lázaro J. 47 of greater intensity on the screen is dark in the left and the right is in the right display as a consequence of the rotation of the polarization plane. Figure 13 is the capture of two still pictures taken from a media conducted in the laboratory. At the bottom is a hole through which passes the polarized light beam, downwards for the back and sides of the orifice are positioned two lenses, and the bottom two black Using an optimal modulation frequency of the light polarization beam, according to the optic-electronic sensors uses, is possible obtain polarize plane rotation in hexadecimals degrees (Figure 14). 360 t 2 O f t Wild a Wild b Fig. 14. Graphic method to obtain polarizes plane rotation value in hexadecimals degree. After this point is very easy make a microprocessor program, which does the measurement; wild of both pulses and after that do the rest in order to get t and 360 multiplication by 2 O f. The result is showing in a digital display (LCD). 4. Applications The optical system and the phenomenon can be used in various applications. 1) It can be used in data transmission. Using polarised light in which the variation of the polarisation plane position can represent ones and zeros. This is very advantageous because it would avoid the loss of information, because it does not matter the levels of light intensity does not remain constant, only interested the angles of the plane of polarisation, who would take the information corresponding to ones and zeros. 2) Use in sea and air signalling. 3) In weighing systems in which rotation of the polarization plane would be proportional to body weight.

10 Miranda Díaz Lázaro J. 48 4) In polarimetry instruments. 5) In determining if a beam of light is polarized or not (astronomic). 5. An application Abstract: When a pulsing beam of polarize light (light emitter diode (LED) or a semiconductor laser) passing through an optical system, and two photodiodes spatially arranged at 90 0 to each other and both with their detection surfaces parallel to the transmission shaft of light, and polarization axis oriented at 45 0 of the vertices of the edges where the photodiodes join, in the outputs of two operational amplifiers, we have two signals with the same shape in time, i.e. a pulse train with the same phase, but when you turn the polarization plane, change the radiance of the light projected onto the photodiodes, being out of phase signals to the outputs of the amplifiers, where the difference between the fronts of the pulses is proportional to the angle of rotation of the plane of polarization light. In a digital circuit phase discriminator, a pulse is obtained equal to the time difference between two sides of the rise time in the output of two amplifiers. The width of this is directly proportional to the value of rotation the plane of polarization of light, that is, the greater the rotation, the greater the width of this Introduction It is possible determined the polarized light plane rotation in very comfortable and precise form. Using a very simple optic system, a luminous source (light emitting diode (LED)), as sensor two Optic-Electronic Amplifiers, associated to front wave differentiating digital circuits, Without the necessity to use analyzers, rotational modulators, neither magnetic coil that are those more commonly employees for the polarized light plane measure. This outlined method has the advantage that there is not having a mobile mechanical part; and not having to use big currents densities in induction coils. Its precision depending of the pulses modulation electric sign stability and the optic system alignment precision, including the photodiodes spaced to 90 0 degrees among them incidence faces. When you affect linearly polarized light in a lens, it will reflect and refract along the curves lines arising from the interception of a plane with a sphere on the surface of the lens while maintaining the orientation of the plane of polarization. This effect is significant only looking at the lens side. Therefore the lens is like a side analyzer if we rotate the polarization plane of polarized light that falls on it.

11 Miranda Díaz Lázaro J System with only one lens Figure 15. Sequence showing how two photodiodes spatially to 90 0 are illuminated when the polarize plane change. To use this phenomenon in the construction of an instrument to determine the value of the rotation of the plane of polarization of light, would have two light sensors placed parallel to the optical axis 90 0 spaced from each other and on the sides of the lens. In Figure 15, the green color circles are the photodiodes and when the plane of polarization of light rotated, the light over photodiodes detection surface change. But this has two disadvantages, one is the light intensity is low and the other is the absorption effect of distorting information because there is a lighted space between the sensors would not touch the surface of both System with two lens Using a geometric study of the lenses we find out the solution to this problem. As is the spherical surface lens on it can be matched perfectly circles of radius r, the amount will be inversely proportional to that radius. Each circle may be regarded as a lens. A linearly polarized light beam (with a diameter more little than the lens diameter) shine on the edge of the lens, the light will go over the edge and go out diametrically opposed to incident beam. It can only be observed at that point and do not in any other region of the lens. In this way we will not have a cone-shaped beam on the side of the lens, but a point where we will get the whole picture and therefore with greater intensity. In this case the sequence is showing in Figure 7; where the out coming light intensity is polarize plane incident position function over the border lens surface. But we still have a problem and we have to use two sensors to polarized light to come on as a light source. The solution to this problem is to use a system of two identical lenses placed in the same plane. Its may be positioned so that they cross a line where you play two of its edges with another drawn from the edges that touch the two lenses and orthogonal to the first, is the center of the beam. This ensures that the two points of light coming out diametrically opposed in each of the lenses are at 90 0 from each other. Figures 9 and 10 is the geometric representation. By rotating the linearly polarized light beam, the lens diameter path coincides with the orientation of the polarization plane will have a very bright image of the light

12 Miranda Díaz Lázaro J. 50 source, while the diametrically opposite position of the other lens will not shining. If we continue to rotate the plane of polarization in the direction of the lens with less intensity than light, it will grow in intensity and decreasing the other, when both intensities are equal will be in the place where the instrument has its zero. There will be a gap of 90 0 between the points. Now the light sensors are always under the light field (see Figure 16), recording exactly light variations that are proportional to the rotation of the polarization plane of light. Modulating the polarized light with a train of pulses and use as sensor photodiodes, an electric current will be generated in them (photodiodes). This current will be directly proportional to the amount of light reaching them, there is a gap between rising fronts amplified signal pulses obtained in photodiodes if they do not receive the same amount of light and that is the value of rotation of the polarization plane. Figure 16. With two lenses the light sensors are always under the light fie 6. Low of Malus If between a pulsating light source and a radiometer put in two polarizing sheets, with their polarization axes at The radiometer will measure zero or minimal candle power, then if one the polarizing sheet is rotated, will go increasing the light intensity reading in the measuring instrument, until a maximum that will correspond when we have rotated it 90 0 (Malus`s law). Now retired the polarizing sheet utilized as analyzer and used instead of the radiometer our amplifier. The amplifier exit, view in an oscilloscope, a pulse will appear. The pulse width will go increasing until a maximum valor, and starting from there it will begin to diminish until a minimum and a phase shift will take place, increasing the width until a maximum, but now in opposed sense (Figure 17). Fig. 17. Operational amplifier output following the rise time of the pulse signal in each output amplifier, according to the Malus`s Low.

13 Miranda Díaz Lázaro J. 51 Comparing both methods has obtained more information with our amplifier than with the radiometer. When in the oscilloscope appear a minimum, the polarized light plane will be exactly at 45 0 or 45 0 (the lines with double arrow), that is to say that already know in the fact that the sense the polarization plane is oriented of and to identify this in the polarizing sheet. Now place an active optic substance in that trajectory, being the plane of polarization at We will have a pulse that will increase its width toward the right if the substance is levorotary and counter-clockwise if it is not levorotary, being its magnitude in agreement with the angular quantity that the substance has rotated the plane of polarization. If initially the plane of polarization is to 45 0, inferior image gives the drawing in Figure 17, a pulse will increase its width counter-clockwise if the substance is levorotary, and toward the right if it is not levorotary. FD1 and FD2 in the Figure 8 represent the photodiodes space disposition utilized. 7. Wave form at the output electronic amplifier. In the Figure 18 the signs time letters, where we only use the rise time between the pulse signals in each output of both operational amplifiers. That difference is equivalent to the rotation of the polarize axis, this value is equal to signal pulse in the last one line. 8. System Fig. 18. Electronic circuit letters time

14 Miranda Díaz Lázaro J. 52 Fig.19. Equipment block diagram The Figure 20 is the optic system utilized 9. Conclusions Fig. 20. Optic system The optical system and the phenomenon can be used as a new polarimetric detection method, in which the accuracy of alignment of the optical system is essential

15 Miranda Díaz Lázaro J. 53 for accuracy of detection. It's a new polarimetric detection method, based, first, in the new principle of refraction and reflection of light polarized in lenses and the first time use of coplanar optical lens systems that significantly improve the use of the phenomenon analysed. Principle of refraction and reflection of light polarised in lenses: When a linearly polarised light beam incident on a lens, the light will be reflect and refract inside the lens body only in the same direction that the polarise plane, the light cannot throughout from the polarise plane that it belong. The system allows determine the beam of light polarization plane orientation. It also allows to determine the magnitude that has been rotated when introducing an active optic substance and to also know if the same one is levorotary or not. By first time have been used a parallel lens systems and this is a new optical method for polarimetric measurement, with this, extremely simple, sure and precise polarimeters can be built. REFERENCE LINKING Book: [1] G.S. Landsberg, Optic, First Book, MIR, (1976), Light Polarization [2] E. Hecht, Optics, Fourth Edition, 5Geometrical Optics, 5.1Lens, , 8Polarization, Proceedings paper: [3] Va[1] Miranda Díaz L.J., Invention Author Certificate, CU A1, EQUIPO DE POLARIMETRÍA Y MEDICIÓN DE ABSORCIÓN, Note References have been mentioned rather to indicate the field that the subject matter belonging hereof, as the phenomenon is not reflected in the literature