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An interferometric array generator with polarizing elements
Opdcs und Lasers in Engmeering, 28 (1997) 457A51 0 1997 Eisevier Science Limited
AI1 rights reserved. Printed in Northern Ireland 0143-8166197 $17.00 + 0.00 ELSEVIER
PII:
SO143.8166(97)00057-2
An Interferometric Array Generator with Polarizing Elements l? Seut~i~ku~aran Physics ffepartment,
Indian Institute of Technology, Guwahati, Panbazar, Guwahati 781 001, Assam, India
(Received 20 December 1996; accepted 17 July 1997)
ABSTRACT Interferometric methods for array generation offer various advantages over the detractive methods, but the eficiency of such i~zterferometric methods so far retorted are very low, making its applicability very low. In view of this, an experimental setup using poiar~zing elements for an eight-.~o~d increase in the eflciency of an interferometric array generator-the Michelson interferometers in tandem setup (I? Senthilkumaran and R. S. Sirohi, Optics Communications, IO.5 (1994) 158)-is presented in this paper. 0 1997 Elsevier Science Ltd.
1. INTRODUCTION An array generator, as its name implies, splits an incoming beam into an array of large number of beamlets. Such a device is useful in optical data processing systems for various applications. A wide variety of optical array generators have been proposed in the past based on various optical phenomena. A review of various types of array generators is given in Ref. 1. Recently proposed interferometric methods2,3 for array generation have poor light efficiency, but these interferometric methods for generation of arrays have certain advantages. The spot size, the array size and compression ratio can be varied in real time unlike other methods where real-time manipulations are not possible. Generation of large array patterns is simple compared with the other existing techniques. In the Michelson Interferometers in Tandem (MIT) setup3 the loss of light at the beam splitters reduces the achievable light efficiency to 6.25%. The experimental setup proposed in this paper makes use of polarizing elements to reduce these losses for better efficiency. 457
P.Senthilkumaran
4.58
2. MICHELSON
INTERFEROMETERS SETUP
IN TANDEM
(MIT)
The schematic of the Michelson interferometers in tandem for array generation is given in Ref. 3. For the sake of completeness a brief account of that technique is given below. Two Michelson interferometers are arranged in tandem as shown in Fig. 1. A collimated beam from a laser is launched into the set-up which results in the interference of four beams at the output plane. With appropriate tilts given to one of the mirrors of each Michelson interferometer setup, the complex amplitudes of the four light beams which form array at the output plane are given by (a/16), (a/16) exp ( - j2rr pux), (a/16) exp ( - j2rvy), (a/16) exp ( - j2+ux + my)), where a is the amplitude of the incident beam, and ,!L and Y are the spatial frequencies which are related to the tilts & and & given to mirrors M2 and M4, respectively. ,X= (sin @#A and Y= (sin &)/A, where A is the wavelength of the light. The intensity distribution at the observation plane is given by2: II = (a2/64)[1 + COS(~~~XUX)] [l + cos(27rvy)l equation spots.
(1) represents
a two-dimensional
(1) array of equal intensity light
1
M4 Fig. 1.
MIT setup for array generation. Ml, M2, M3 and M4 are mirrors. beam splitters; O-output plane.
BSl and BS2 are
An interferometric array generator with polarizing elements
459
In the MIT setup, assuming 100% reflections at the mirrors Ml, M2, M3 and M4, the loss of light amplitude is mainly due to the beam splitters. Each time light encounters the beam splitter, 50% of the incident light is wasted, since it is not taking part in array formation. This results in a poor light efficiency of 6.25%.
3. MIT SETUP WITH POLARIZING
ELEMENTS
The following experimental setup shown in Fig. 2 results in higher efficiency. Here, the use of the polarizing elements reduces the loss of light. The complex amplitudes of the four beams in this new setup now become (a/2), (a/2) exp ( - j27.r +x), (a/2) exp ( - j2rvy), (u/2) exp ( - j2n(px + VY)), with ,u and Y as explained in Section 2. The incident light is assumed to be plane polarized with amplitude a. The intensity pattern at the output plane due to the interference of these four beams is now given by 12 = (a’ls)[l + cos (2 7r/Jux)][l + cos (2 ?Tvy)]
0
PLl hi3
(2)
P2
” PBs1
_P3
PL2
-
0 9 PBS2
Fig. 2. Experimental setup to improve the efficiency of the MIT setup for array generation. Ml, M2, M3 and M4 are mirrdrs; Pl, P2, P3 and P4 are quarter-wave plates. PLl and PL2 are polarizers. PBS1 and PBS2 are polarizing beam splitters; O-output plane.
460
P. Senthilkumaran
Equation (2) represents the same type of array pattern given by equation (1) but with higher intensity profile, i.e. Z, = 8 Z,. Let us now see how the loss of light is minimized in the present proposed setup. The plane polarized laser beam incident on the polarizing beam splitter PBS1 (Fig. 2) is split up equally in the two arms of the first Michelson setup. Note that, in the MIT setup3, ordinary beam splitters were used instead of polarizing beam splitters. In the present setup, in each of the arms of the MIT setup a quarter-wave plate is inserted. All these four h/4 plates Pl, P2, P3 and P4 are oriented in such a way that the optic axis of the plate makes 45” to the plane of vibration of the light from the beam splitter. Thus each quarter-wave plate and the mirror combination will rotate the plane of polarization of the incident light by 90” by the time the light reaches back to the PBS. The result is that the light from two arms of the Michelson interferometer will enter the second Michelson interferometer setup without any wastage. Polarizer PLl placed between the beam splitters picks up the components of vibrations from the two orthogonally polarized lights that arrive from the first Michelson interferometer setup, so that the light will be split into two equal amplitudes at the second polarizing beam splitter PBS2. The quarter-wave plate and the mirror combinations in the second Michelson interferometer eliminate the wastage of light at the beam splitter (PBS2) in a similar way to that explained earlier. The light reaching the output plane will have two types of vibrations which are at right angles with each other. To have interference, E-vector vibrations of the light should be brought to the same plane. This is done by using a polarizer PL2, which picks up the components of the two orthogonally polarized states. Both the polarizers PLl and PL2 are oriented in such a way as to enclose 45” with the two orthogonal light vibrations so as to pick equal amplitudes from them. Each traversal through the polarizer results in the reduction of the amplitude of the light beam by a factor (l/q2). It can be seen that the efficiency of this setup is 50%, which is eight times higher than that of the setup proposed in Ref. 3. It may be noted that the efficiency is calculated as the ratio of the intensity of light arriving at the output port to the intensity of the light incident on the MIT setup, assuming no tilt is given to any of the mirrors. 4. SUMMARY The interferometric method of array generation reported in Ref. 3 is briefly given. The reason for poor efficiency in that method is due to the loss of light at the beam splitters. In the present paper, the use of polarizing elements is proposed to reduce this loss. This results in improved efficiency.
An interferometric array generator with polarizing elements
461
REFERENCES 1. Streibl, N. Beam shaping with optical array generators. Optics, 36 (1989) 1559
Journal of Modern
2. Senthilkumaran,
generation
P., Sriram, K. V., Kothiyal, M. P and Sirohi, R. S. Array using double wedge plate interferometer. Journal of Modern
Optics, 41 (1994) 481 3. Senthilkumaran, P and Sirohi, R. S. Michelson interferometers array generation. Optics Communications, 105 (1994) 158
in tandem for
AI1 rights reserved. Printed in Northern Ireland 0143-8166197 $17.00 + 0.00 ELSEVIER
PII:
SO143.8166(97)00057-2
An Interferometric Array Generator with Polarizing Elements l? Seut~i~ku~aran Physics ffepartment,
Indian Institute of Technology, Guwahati, Panbazar, Guwahati 781 001, Assam, India
(Received 20 December 1996; accepted 17 July 1997)
ABSTRACT Interferometric methods for array generation offer various advantages over the detractive methods, but the eficiency of such i~zterferometric methods so far retorted are very low, making its applicability very low. In view of this, an experimental setup using poiar~zing elements for an eight-.~o~d increase in the eflciency of an interferometric array generator-the Michelson interferometers in tandem setup (I? Senthilkumaran and R. S. Sirohi, Optics Communications, IO.5 (1994) 158)-is presented in this paper. 0 1997 Elsevier Science Ltd.
1. INTRODUCTION An array generator, as its name implies, splits an incoming beam into an array of large number of beamlets. Such a device is useful in optical data processing systems for various applications. A wide variety of optical array generators have been proposed in the past based on various optical phenomena. A review of various types of array generators is given in Ref. 1. Recently proposed interferometric methods2,3 for array generation have poor light efficiency, but these interferometric methods for generation of arrays have certain advantages. The spot size, the array size and compression ratio can be varied in real time unlike other methods where real-time manipulations are not possible. Generation of large array patterns is simple compared with the other existing techniques. In the Michelson Interferometers in Tandem (MIT) setup3 the loss of light at the beam splitters reduces the achievable light efficiency to 6.25%. The experimental setup proposed in this paper makes use of polarizing elements to reduce these losses for better efficiency. 457
P.Senthilkumaran
4.58
2. MICHELSON
INTERFEROMETERS SETUP
IN TANDEM
(MIT)
The schematic of the Michelson interferometers in tandem for array generation is given in Ref. 3. For the sake of completeness a brief account of that technique is given below. Two Michelson interferometers are arranged in tandem as shown in Fig. 1. A collimated beam from a laser is launched into the set-up which results in the interference of four beams at the output plane. With appropriate tilts given to one of the mirrors of each Michelson interferometer setup, the complex amplitudes of the four light beams which form array at the output plane are given by (a/16), (a/16) exp ( - j2rr pux), (a/16) exp ( - j2rvy), (a/16) exp ( - j2+ux + my)), where a is the amplitude of the incident beam, and ,!L and Y are the spatial frequencies which are related to the tilts & and & given to mirrors M2 and M4, respectively. ,X= (sin @#A and Y= (sin &)/A, where A is the wavelength of the light. The intensity distribution at the observation plane is given by2: II = (a2/64)[1 + COS(~~~XUX)] [l + cos(27rvy)l equation spots.
(1) represents
a two-dimensional
(1) array of equal intensity light
1
M4 Fig. 1.
MIT setup for array generation. Ml, M2, M3 and M4 are mirrors. beam splitters; O-output plane.
BSl and BS2 are
An interferometric array generator with polarizing elements
459
In the MIT setup, assuming 100% reflections at the mirrors Ml, M2, M3 and M4, the loss of light amplitude is mainly due to the beam splitters. Each time light encounters the beam splitter, 50% of the incident light is wasted, since it is not taking part in array formation. This results in a poor light efficiency of 6.25%.
3. MIT SETUP WITH POLARIZING
ELEMENTS
The following experimental setup shown in Fig. 2 results in higher efficiency. Here, the use of the polarizing elements reduces the loss of light. The complex amplitudes of the four beams in this new setup now become (a/2), (a/2) exp ( - j27.r +x), (a/2) exp ( - j2rvy), (u/2) exp ( - j2n(px + VY)), with ,u and Y as explained in Section 2. The incident light is assumed to be plane polarized with amplitude a. The intensity pattern at the output plane due to the interference of these four beams is now given by 12 = (a’ls)[l + cos (2 7r/Jux)][l + cos (2 ?Tvy)]
0
PLl hi3
(2)
P2
” PBs1
_P3
PL2
-
0 9 PBS2
Fig. 2. Experimental setup to improve the efficiency of the MIT setup for array generation. Ml, M2, M3 and M4 are mirrdrs; Pl, P2, P3 and P4 are quarter-wave plates. PLl and PL2 are polarizers. PBS1 and PBS2 are polarizing beam splitters; O-output plane.
460
P. Senthilkumaran
Equation (2) represents the same type of array pattern given by equation (1) but with higher intensity profile, i.e. Z, = 8 Z,. Let us now see how the loss of light is minimized in the present proposed setup. The plane polarized laser beam incident on the polarizing beam splitter PBS1 (Fig. 2) is split up equally in the two arms of the first Michelson setup. Note that, in the MIT setup3, ordinary beam splitters were used instead of polarizing beam splitters. In the present setup, in each of the arms of the MIT setup a quarter-wave plate is inserted. All these four h/4 plates Pl, P2, P3 and P4 are oriented in such a way that the optic axis of the plate makes 45” to the plane of vibration of the light from the beam splitter. Thus each quarter-wave plate and the mirror combination will rotate the plane of polarization of the incident light by 90” by the time the light reaches back to the PBS. The result is that the light from two arms of the Michelson interferometer will enter the second Michelson interferometer setup without any wastage. Polarizer PLl placed between the beam splitters picks up the components of vibrations from the two orthogonally polarized lights that arrive from the first Michelson interferometer setup, so that the light will be split into two equal amplitudes at the second polarizing beam splitter PBS2. The quarter-wave plate and the mirror combinations in the second Michelson interferometer eliminate the wastage of light at the beam splitter (PBS2) in a similar way to that explained earlier. The light reaching the output plane will have two types of vibrations which are at right angles with each other. To have interference, E-vector vibrations of the light should be brought to the same plane. This is done by using a polarizer PL2, which picks up the components of the two orthogonally polarized states. Both the polarizers PLl and PL2 are oriented in such a way as to enclose 45” with the two orthogonal light vibrations so as to pick equal amplitudes from them. Each traversal through the polarizer results in the reduction of the amplitude of the light beam by a factor (l/q2). It can be seen that the efficiency of this setup is 50%, which is eight times higher than that of the setup proposed in Ref. 3. It may be noted that the efficiency is calculated as the ratio of the intensity of light arriving at the output port to the intensity of the light incident on the MIT setup, assuming no tilt is given to any of the mirrors. 4. SUMMARY The interferometric method of array generation reported in Ref. 3 is briefly given. The reason for poor efficiency in that method is due to the loss of light at the beam splitters. In the present paper, the use of polarizing elements is proposed to reduce this loss. This results in improved efficiency.
An interferometric array generator with polarizing elements
461
REFERENCES 1. Streibl, N. Beam shaping with optical array generators. Optics, 36 (1989) 1559
Journal of Modern
2. Senthilkumaran,
generation
P., Sriram, K. V., Kothiyal, M. P and Sirohi, R. S. Array using double wedge plate interferometer. Journal of Modern
Optics, 41 (1994) 481 3. Senthilkumaran, P and Sirohi, R. S. Michelson interferometers array generation. Optics Communications, 105 (1994) 158
in tandem for