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An optimum analysis for Cassegrain optical antenna
Optik 126 (2015) 1171–1174
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
An optimum analysis for Cassegrain optical antenna Xiaojun Ma, Huajun Yang ∗ , Bing Wang, Ping Jiang, Mingyin Yu, Yuchun Huang, Shasha Ke School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China
a r t i c l e
a b s t r a c t
i n f o
Article history: Received 18 February 2014 Accepted 2 March 2015
In this paper, the energy loss caused by the secondary mirror of Cassegrain antenna has been discussed numerically. As the diameter of the secondary mirror is one-fifth of the primary mirror, the loss goes beyond 18.5%. Because of the alignment of the optical system being the significant factor, it influences the transmission quality of the optical antenna system. We analyze and numerically simulate how power attenuation ratio and gain of Cassegrain antenna vary with the antenna deflection, and measure the distance such that the central axis of the receiving antenna deviates from the z-axis in case of occurrence of off-axis space in the system. Finally, an optimum structure is proposed by trepanning the secondary mirror. Crown Copyright © 2015 Published by Elsevier GmbH. All rights reserved.
Keywords: Cassegrain antenna Optimum structure Simulation analysis Energy loss
1. Introduction
where
The role of transmitting an optical system in optical communication is to confirm that the beam from the light source is reshaped and then emitted at certain airspace in a straight line [1]. An optical transmission system contains a laser system, a collimation system, and an optical antenna. An optical antenna is a key device in optical communication system. As a result, great care is taken in designing the optical antenna system with accuracy [2,3]. In this paper, we discuss the energy loss of the secondary mirror of Cassegrain antenna system numerically, analyze how power attenuation ratio and gain of Cassegrain antenna vary with the antenna deflection, and measure the distance such that the central axis of the receiving antenna deviates from the z-axis in case of occurrence of off-axis space in the system. Finally, an optimum structure is proposed.
C ; A= ω(z)
2. Analysis of Cassegrain optical antenna 2.1. Numerical analysis of beam shading by secondary mirror By theoretical analysis [4,5], the electric field distribution of the Gaussian beam can be described as
E(r) = A exp
r2 − 2 ω (z)
exp
r2 jk 2R
2 ; k=
R = z 1+
ω02
ω(z) = ω0
2
1+
z 2 ω0 2
;
z
here, A is a constant coefficient, ω(z) is the radius of the Gaussian beam, ω0 is the beam waist, and is the wavelength of the laser beam. In Cassegrain optical system, the beam emitted by the Cassegrain antenna is a parallel beam with a tiny beam divergence; the beam is first reflected by the secondary mirror and then reflected by the primary mirror, which is shown in Fig. 1. In Fig. 1, the dotted line part is the beam obscured by the secondary mirror, and this part of the beam cannot be emitted by the optical antenna and loses the energy. According to the analysis of the antenna gain factor [6], we know that
gT (˛, ˇ, , X) = 2˛2 ×
2 1
2 1/2
exp(jˇu) exp(−˛ u)J (Xu )du 0
2
where ∗ Corresponding author. Tel.: +86 13880880789. E-mail address: [email protected] (H. Yang). http://dx.doi.org/10.1016/j.ijleo.2015.03.001 0030-4026/Crown Copyright © 2015 Published by Elsevier GmbH. All rights reserved.
˛=
a ; ω
=
b ; a
= ka sin ;
ˇ = (ka2 )
1 r
+
1 R
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X. Ma et al. / Optik 126 (2015) 1171–1174
Fig. 1. Transmitting antenna.
In the axial point, X = ka sin 0 = 0, so we can get the antenna principal axis gain factor as
gT (˛, ˇ, , 0) =
2˛2 ˇ2 + ˛4
Fig. 3. The relationship between a, b, and the antenna efficiency .
× ...
exp(−2˛2 ) + exp(−2˛2 2 ) − 2 exp[−˛2 ( 2 + 1)] ∗ ...
cos[ˇ( 2 − 1)] When the receiver is kept away from the transmitting antenna, ˇ ≈ 0, the formula can be described as gT (˛, 0, , 0) =
2 −2˛2 2 2 2 2 [e + e−2˛ − 2e−˛ ( +1) ] ˛2
The relationship between antenna gain factor and is shown in Fig. 2. We can see that the antenna gain factor becomes optimum when = 0.2. The efficiency of Cassegrain optical antenna can be described as
pout = = p
2 b 0
a
[|E2 |2 ]rdrdϕ
2 a
E1 (r) 2 rdrdϕ 0
0
where E1 is the electric field of the laser beam 1, p is the power of the signal beam, E2 is the electric field of the laser beam 2, and pout is the emission power of the optical antenna. Considering a and b as variables, the relationship between a, b, and the antenna efficiency is shown in Fig. 3. Obviously, when the primary diameter a = 150 mm and the secondary mirror diameter b = 30 mm, the maximum energy efficiency is achieved at 81.5%. 2.2. Analysis of Cassegrain optical antenna off-axis As Cassegrain optical antenna is plays an important role in the optical communication system, a precise optical axis alignment is necessary. However, in practical applications, if the optical antenna
Fig. 2. The relationship between antenna gain factor and .
Fig. 4. Laser power distribution in the case of alignment situation.
is off-axis and has a small beam divergence angle, the antenna transmission efficiency and the coupling efficiency of the whole system will be affected. When the Cassegrain optical antenna is exactly aligned, we obtain maximum transmission efficiency and the desired laser beam quality, as shown in Fig. 4. In practical applications, when the optical antenna off-axis occurs, the laser beam power distribution inevitably changes, as shown in Figs. 5 and 6. We get the coupling efficiency of the two Cassegrain antennas on the condition that a = 150 mm and b = 30 mm, which is shown in Fig. 7. The calculation results show that with an increase in the deflection angle, the coupling efficiency decreases quickly, and if the
Fig. 5. Laser power distribution with slight off-axis.
X. Ma et al. / Optik 126 (2015) 1171–1174
1173
Fig. 9. The relationship between and l and M. Fig. 6. Laser power distribution with severed off-axis.
we obtain from the small Galileo-type optical antenna are as follows: l = f +
ω =
(l − f )f 2 2
(l − f ) + (ω02 /) ω02 f 2
2
2
(f − l) + (ω02 /) 0
=
(f2 /f1 )
1+
deflection angle is >0.3 rad, the coupling efficiency quickly reduces to zero.
2
l (ω2 ) 0
l
Fig. 7. Coupling efficiency versus deflection angle.
2
2 = M
0 1+
l (ω2 )
2
0
ω is
where is the position of the light waist, the light waist, and is the divergence angle of the part of the light. The relationship between and l, and the beam expander ratio M is shown in Fig. 9. As M = f2 /f1 , we can modulate the distance of l and the focus lengths of the two lens to make sure the divergence angle is the same as the reflection system. 4. Conclusion
3. Optimum structure of Cassegrain antenna Although a Cassegrain configuration is widely used for expanding the beam in a reflecting mirror system, the loss caused by the secondary mirror is considered critical, and it would affect the effect of transmission. Therefore, we have proposed a method to improve the efficiency of Cassegrain antenna, which is made up of a reflection optical system and a small lens system, which is, in turn, composed of one long focus lens and one short focus lens, and this is shown in Fig. 8. The lens system is a small Galileo-type optical antenna. Let us assume that the distance of the beam is L. The various parameters
Because of the Gaussian distribution of the laser beam and the peculiarity of the Cassegrain optical antenna, the loss caused by the secondary mirror is >18.5%, and the influence of off-axis cannot be ignored. We have proposed an optimum structure, that is, trepanning the secondary mirror, and added two lenses, one short focus length lens and one long focus length lens, behind the secondary mirror. In this way, the energy utilization efficiency has been enhanced, and the lens system has a similar ability for expanding the beam. Acknowledgments This work is supported by the National Natural Science Foundation of China under Grant Nos. 61271167 and 61307093. It is also supported by the Research Foundation of the General Armament Department of China under Grant No. 9140A07040913DZ02106, and the Fundamental Research Funds for the Central Universities under Grant No. ZYGX2013J051. References
Fig. 8. Optimum structure of Cassegrain antenna.
[1] L.C.N. Scaduto, J. Sasian, et al., Two-mirror telescope design with thirdorder coma insensitive to decenter misalignment, Opt. Express 21 (6) (2013) 6851–6865. [2] Y. Li, Y. Zhu, J. Wang, The theory of optical communication, China, Publ. Sci. (2006) 370–371.
1174
X. Ma et al. / Optik 126 (2015) 1171–1174
[3] X. Chu, G. Zhou, Power coupling of two-Cassegrain-telescopes system in turblent atmosphere in a slant path, Opt. Express 15 (12) (2007) 7697–7707. [4] R. Padman, J. Anthony Murphy, R. Hills, Gaussian mode analysis of Cassegrain antenna efficiency, IEEE Trans. Antennas Propag. 35 (10) (1987) 1093–1103.
[5] H. Wu, S. Sheng, Z. Huang, et al., Study on power coupling of annular vortex beam propagating through a two-Cassegrain-telescope optical system in turbulent atmosphere, Opt. Soc. Am. 21 (4) (2013) 4005–4016. [6] H. Yang, Y. Hu, C. Li, K. Xie, J. Fu, H. Wei, Optimum design for optical antenna of space laser communication systems, in: IEEE International Conference on Communications Circuits & System, vol. 3, 2006, pp. 2016–2019.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
An optimum analysis for Cassegrain optical antenna Xiaojun Ma, Huajun Yang ∗ , Bing Wang, Ping Jiang, Mingyin Yu, Yuchun Huang, Shasha Ke School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China
a r t i c l e
a b s t r a c t
i n f o
Article history: Received 18 February 2014 Accepted 2 March 2015
In this paper, the energy loss caused by the secondary mirror of Cassegrain antenna has been discussed numerically. As the diameter of the secondary mirror is one-fifth of the primary mirror, the loss goes beyond 18.5%. Because of the alignment of the optical system being the significant factor, it influences the transmission quality of the optical antenna system. We analyze and numerically simulate how power attenuation ratio and gain of Cassegrain antenna vary with the antenna deflection, and measure the distance such that the central axis of the receiving antenna deviates from the z-axis in case of occurrence of off-axis space in the system. Finally, an optimum structure is proposed by trepanning the secondary mirror. Crown Copyright © 2015 Published by Elsevier GmbH. All rights reserved.
Keywords: Cassegrain antenna Optimum structure Simulation analysis Energy loss
1. Introduction
where
The role of transmitting an optical system in optical communication is to confirm that the beam from the light source is reshaped and then emitted at certain airspace in a straight line [1]. An optical transmission system contains a laser system, a collimation system, and an optical antenna. An optical antenna is a key device in optical communication system. As a result, great care is taken in designing the optical antenna system with accuracy [2,3]. In this paper, we discuss the energy loss of the secondary mirror of Cassegrain antenna system numerically, analyze how power attenuation ratio and gain of Cassegrain antenna vary with the antenna deflection, and measure the distance such that the central axis of the receiving antenna deviates from the z-axis in case of occurrence of off-axis space in the system. Finally, an optimum structure is proposed.
C ; A= ω(z)
2. Analysis of Cassegrain optical antenna 2.1. Numerical analysis of beam shading by secondary mirror By theoretical analysis [4,5], the electric field distribution of the Gaussian beam can be described as
E(r) = A exp
r2 − 2 ω (z)
exp
r2 jk 2R
2 ; k=
R = z 1+
ω02
ω(z) = ω0
2
1+
z 2 ω0 2
;
z
here, A is a constant coefficient, ω(z) is the radius of the Gaussian beam, ω0 is the beam waist, and is the wavelength of the laser beam. In Cassegrain optical system, the beam emitted by the Cassegrain antenna is a parallel beam with a tiny beam divergence; the beam is first reflected by the secondary mirror and then reflected by the primary mirror, which is shown in Fig. 1. In Fig. 1, the dotted line part is the beam obscured by the secondary mirror, and this part of the beam cannot be emitted by the optical antenna and loses the energy. According to the analysis of the antenna gain factor [6], we know that
gT (˛, ˇ, , X) = 2˛2 ×
2 1
2 1/2
exp(jˇu) exp(−˛ u)J (Xu )du 0
2
where ∗ Corresponding author. Tel.: +86 13880880789. E-mail address: [email protected] (H. Yang). http://dx.doi.org/10.1016/j.ijleo.2015.03.001 0030-4026/Crown Copyright © 2015 Published by Elsevier GmbH. All rights reserved.
˛=
a ; ω
=
b ; a
= ka sin ;
ˇ = (ka2 )
1 r
+
1 R
1172
X. Ma et al. / Optik 126 (2015) 1171–1174
Fig. 1. Transmitting antenna.
In the axial point, X = ka sin 0 = 0, so we can get the antenna principal axis gain factor as
gT (˛, ˇ, , 0) =
2˛2 ˇ2 + ˛4
Fig. 3. The relationship between a, b, and the antenna efficiency .
× ...
exp(−2˛2 ) + exp(−2˛2 2 ) − 2 exp[−˛2 ( 2 + 1)] ∗ ...
cos[ˇ( 2 − 1)] When the receiver is kept away from the transmitting antenna, ˇ ≈ 0, the formula can be described as gT (˛, 0, , 0) =
2 −2˛2 2 2 2 2 [e + e−2˛ − 2e−˛ ( +1) ] ˛2
The relationship between antenna gain factor and is shown in Fig. 2. We can see that the antenna gain factor becomes optimum when = 0.2. The efficiency of Cassegrain optical antenna can be described as
pout = = p
2 b 0
a
[|E2 |2 ]rdrdϕ
2 a
E1 (r) 2 rdrdϕ 0
0
where E1 is the electric field of the laser beam 1, p is the power of the signal beam, E2 is the electric field of the laser beam 2, and pout is the emission power of the optical antenna. Considering a and b as variables, the relationship between a, b, and the antenna efficiency is shown in Fig. 3. Obviously, when the primary diameter a = 150 mm and the secondary mirror diameter b = 30 mm, the maximum energy efficiency is achieved at 81.5%. 2.2. Analysis of Cassegrain optical antenna off-axis As Cassegrain optical antenna is plays an important role in the optical communication system, a precise optical axis alignment is necessary. However, in practical applications, if the optical antenna
Fig. 2. The relationship between antenna gain factor and .
Fig. 4. Laser power distribution in the case of alignment situation.
is off-axis and has a small beam divergence angle, the antenna transmission efficiency and the coupling efficiency of the whole system will be affected. When the Cassegrain optical antenna is exactly aligned, we obtain maximum transmission efficiency and the desired laser beam quality, as shown in Fig. 4. In practical applications, when the optical antenna off-axis occurs, the laser beam power distribution inevitably changes, as shown in Figs. 5 and 6. We get the coupling efficiency of the two Cassegrain antennas on the condition that a = 150 mm and b = 30 mm, which is shown in Fig. 7. The calculation results show that with an increase in the deflection angle, the coupling efficiency decreases quickly, and if the
Fig. 5. Laser power distribution with slight off-axis.
X. Ma et al. / Optik 126 (2015) 1171–1174
1173
Fig. 9. The relationship between and l and M. Fig. 6. Laser power distribution with severed off-axis.
we obtain from the small Galileo-type optical antenna are as follows: l = f +
ω =
(l − f )f 2 2
(l − f ) + (ω02 /) ω02 f 2
2
2
(f − l) + (ω02 /) 0
=
(f2 /f1 )
1+
deflection angle is >0.3 rad, the coupling efficiency quickly reduces to zero.
2
l (ω2 ) 0
l
Fig. 7. Coupling efficiency versus deflection angle.
2
2 = M
0 1+
l (ω2 )
2
0
ω is
where is the position of the light waist, the light waist, and is the divergence angle of the part of the light. The relationship between and l, and the beam expander ratio M is shown in Fig. 9. As M = f2 /f1 , we can modulate the distance of l and the focus lengths of the two lens to make sure the divergence angle is the same as the reflection system. 4. Conclusion
3. Optimum structure of Cassegrain antenna Although a Cassegrain configuration is widely used for expanding the beam in a reflecting mirror system, the loss caused by the secondary mirror is considered critical, and it would affect the effect of transmission. Therefore, we have proposed a method to improve the efficiency of Cassegrain antenna, which is made up of a reflection optical system and a small lens system, which is, in turn, composed of one long focus lens and one short focus lens, and this is shown in Fig. 8. The lens system is a small Galileo-type optical antenna. Let us assume that the distance of the beam is L. The various parameters
Because of the Gaussian distribution of the laser beam and the peculiarity of the Cassegrain optical antenna, the loss caused by the secondary mirror is >18.5%, and the influence of off-axis cannot be ignored. We have proposed an optimum structure, that is, trepanning the secondary mirror, and added two lenses, one short focus length lens and one long focus length lens, behind the secondary mirror. In this way, the energy utilization efficiency has been enhanced, and the lens system has a similar ability for expanding the beam. Acknowledgments This work is supported by the National Natural Science Foundation of China under Grant Nos. 61271167 and 61307093. It is also supported by the Research Foundation of the General Armament Department of China under Grant No. 9140A07040913DZ02106, and the Fundamental Research Funds for the Central Universities under Grant No. ZYGX2013J051. References
Fig. 8. Optimum structure of Cassegrain antenna.
[1] L.C.N. Scaduto, J. Sasian, et al., Two-mirror telescope design with thirdorder coma insensitive to decenter misalignment, Opt. Express 21 (6) (2013) 6851–6865. [2] Y. Li, Y. Zhu, J. Wang, The theory of optical communication, China, Publ. Sci. (2006) 370–371.
1174
X. Ma et al. / Optik 126 (2015) 1171–1174
[3] X. Chu, G. Zhou, Power coupling of two-Cassegrain-telescopes system in turblent atmosphere in a slant path, Opt. Express 15 (12) (2007) 7697–7707. [4] R. Padman, J. Anthony Murphy, R. Hills, Gaussian mode analysis of Cassegrain antenna efficiency, IEEE Trans. Antennas Propag. 35 (10) (1987) 1093–1103.
[5] H. Wu, S. Sheng, Z. Huang, et al., Study on power coupling of annular vortex beam propagating through a two-Cassegrain-telescope optical system in turbulent atmosphere, Opt. Soc. Am. 21 (4) (2013) 4005–4016. [6] H. Yang, Y. Hu, C. Li, K. Xie, J. Fu, H. Wei, Optimum design for optical antenna of space laser communication systems, in: IEEE International Conference on Communications Circuits & System, vol. 3, 2006, pp. 2016–2019.