Angle amplifier based on multiplexed volume holographic gratings Liangcai Cao*, Yifei Zhao, Qingsheng He, Guofan Jin State Key Laboratory of Precision Measurement Technology and Instruments, Dept. of Precision Instruments, Tsinghua Univ., Beijing, 100084, P.R. China ABSTRACT Angle amplifier of laser beam scanner is a widely used device in optical systems. Volume holographic optical elements can be applied in the angle amplifier. Compared with the traditional angle amplifier, it has the advantages of high angle resolution, high diffraction efficiency, small size, and high angle magnification and flexible design. Bragg anglewavelength-compensating recording method is introduced. Because of the Bragg compensatory relation between angle and wavelength, this device could be recorded at another wavelength. The design of the angle amplifier recording at the wavelength of 514.2nm for the working wavelength of 632.8nm is described. An optical setup for recording the angle amplifier device is designed and discussed. Experimental results in the photorefractive crystal Fe:LiNbO3 demonstrate the feasibility of the angle amplifier scheme. Keywords: Angle amplifier, volume holographic grating, holographic optical element, beam scanner.
1. INTRODUCTION Volume Holographic Optical Elements (HOE) have been widely investigated in the last several decades for their attractive advantages including high diffraction efficiency, high resolution, light weight, low cost and ease of handling. High wavelength and angular selectivity of very thick volume hologram lead to various applications in different fields such as in spectrometers,1 filters,2 wavelength division multiplexer and demultiplexer,3 as well as optical neural networks4. The holographic materials including photopolymer, dichromate gelatin, photorefractive crystal and photochromic glass have provided high quality and stable performances for the HOEs. The volume holographic gratings can diffract the incident beams at arbitrary angles as desired, with a high wavelength resolution as well as angle resolution. Angle amplifier of laser beam scanner is a commonly used device in optical systems. Beam scanner, beam steerer and beam deflector can change the angle of the incident beam at a small angle range for several degrees. For instance, acousto-optic deflectors and liquid crystal beam steering devices can achieve thousands of the total resolvable angles of the output beam directions with a fast speed and high angle resolution.5, 6 The cascaded beam steering architecture is usually used to extend the angle range. However, the angle range can not cover the field of view yet. Thus, an angle amplifier is needed. Holographic grating plate is one of the useful devices for the wide angle beam scanning.6 In this paper, the applications of the volume holographic gratings for the angle amplifier are investigated. Multiple holographic gratings are recorded in a common volume of a thick photorefractive material. Each grating is designed independently according to the requirements for predetermined angle amplification. After the angle amplification is determined as needed, we can design the superimposed volume gratings angle by angle. Therefore, the angle distribution of the diffracted beams can be arbitrary and the device can acquire special angle amplification as well as linear angle amplification. Another problem for design the device is that the device usually works at the wavelength that is not the same as the wavelength for the recording of the grating. It can be solved by the mutual compensation relation between angle and wavelength in Bragg formula.7-9 Thus, the device can be designed for any wavelength at which the holographic material is valid. This method was successfully employed in the design of a spectral dispersion device and for the dualwavelength volume holographic data storage. The working principles and the model design are presented in Section 2. In Section 3, a three-grating angle amplifier device is demonstrated in the experiment.
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Holography and Diffractive Optics III, edited by Yunlong Sheng, Dahsiung Hsu, Chongxiu Yu Proc. of SPIE Vol. 6832, 683216, (2007) · 0277-786X/07/$18 · doi: 10.1117/12.760261
Proc. of SPIE Vol. 6832 683216-1 2008 SPIE Digital Library -- Subscriber Archive Copy
2. PRINCIPLE As is shown in Fig. 1, the multiplexed holographic gratings acted as an angle amplifier. It is usually used in a sandwich structure. The beam steerer has a small angle range and a high angle resolution. The holographic gratings are recorded with wide plane waves of the reference and object beams to achieve a large effective area (aperture) on the surface of the angle amplifier. A standard AR coating should be placed on both sides of the holographic plate to decrease the energy loss. Usually, the holographic gratings can enlarge the angle of the beams from the beam scanner one by one. Another beam scanner is placed after the holographic plate to achieve a higher angle resolution for the enlarged angle range. The number of the holographic gratings can be less than or equal to the number of the angles that the beam scanner can generate. The diffraction efficiency of individual gratings multiplexed with a device with M holograms in total depends on M as
η (M )
( M #) = M2
2
.
(1)
The quantity M# depends on the properties of the holographic material and the optical system. Thus, the number of the gratings is limited by the efficiency and the dynamic range of the material. The gratings, in this paper, are only used for one dimensional beam scanner, which is recorded by the angle multiplexing. The reference beam and the object beam are rotated in a plane. For a two dimensional beam scanner or beam steering, the gratings would be recorded with a complicated multiplexed method, e.g., the peristrophic multiplexing. The rotated reference beam and object beam are not in a plane anymore, but typically the axis of the rotation is chosen normal to the holographic medium. J/\JnJthJGxGq JJOJOELthJJTC
CJTJTJGL
CJTJTJGL
2TJJJJ
JTJJbJTUGL
2TJJJJ
Fig.1 Angle amplifier based on the multiplexed holographic gratings in a sandwich structure.
The working wavelength of the beam amplifier is arbitrary from infrared to ultraviolet for different applications. When the holographic gratings are recorded, the available wavelength of the laser source is limited. Thus the two-color technique is often adopted.7-9 It is because the volume holographic gratings can be recorded with different angles and wavelengths. To be specific, the grating recorded with signal beam ( λ1 , θσ 1 ) and reference beam ( λ1 , θ ρ 1 ) can be recorded with another certain wavelength
λ2
in different incident angles θσ 2 and θ ρ 2 . Fig. 2 demonstrates the 2-D K-
vector space in the Kx-Kz plane. The grating vector Kg is determined by signal-wave vector Kσ 1 and reference-wave vector K ρ1 ; Also it can be constructed by Kσ 2 and K ρ 2 . As a result, the same volume holographic grating can be recorded by different writing wavelengths that meet the Bragg condition. With different incident angles of the signal and reference beams, the holographic gratings can be recorded at another wavelength. For these two wavelengths the Bragg condition are both satisfied
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Λ=
λ1
2 ⋅ n0 ⋅ sin θb1
=
λ2
2 ⋅ n0 ⋅ sin θb 2
,
(2)
where Λ is the period of holographic grating, n0 is the refractive index of the crystal, θ b1 and
θb 2
are the incident
angles inside the crystal of the wavelength λ1 and λ2 , respectively. This method was successfully applied in the spectral dispersion devices and described in detail in our previous works.8
K
Fig. 2. Bragg matching of different wavelength in K-space vector plane. AOIf1TJJG
BG1ffl
pojoLthpTc
C1TJTJGL
ftU?cYLO
A
L'l:Ycw Fig. 3. Recording and readout geometry for the design of the ith grating
The recording and readout geometry for the design of the ith grating is shown in Fig. 3. The recording object beam (O, dashed line) and the reference beam (R, dashed line) with a certain wavelength λR are incident at the surface of holographic plate under the angle θOi and
θ Ri , respectively. The ith Bragg grating is formed at the Bragg angle θ BR and the tilted angle φm . A read beam (W, solid line) at the working wavelength λW and angle θWi is diffracted by the grating under the Bragg condition, whose Bragg angle is not θ BR but θ BW for λW . Thus the output beam is at the direction of the desired angle θ Mi , with the position of xi on the surface of the beam scanner. Under the paraxial approximation condition, for the right interface between material and air,
Proc. of SPIE Vol. 6832 683216-3
ϕ Mi = arcsin(sin θ Mi / nW ) .
(3)
For the left interface between material and air, the incident angle of working light
ϕWi
is given by
ϕWi = arcsin(sin θWi / nW ) .
(4)
Using the Bragg condition, for the ith Bragg grating K g , the Bragg angle θ Bi , direction determined by
ϕ Mi
and
ϕWi
φi
and period Λ i are
as follows,
θ Bi = (ϕ Mi − ϕWi ) / 2 ,
(5)
Λ i = λW / (2nW sin θ Bi ) ,
(6)
φi = π / 2 + (ϕ Mi + ϕWi ) / 2 .
(7)
Using the Bragg condition once more, since the Bragg grating is recorded with the recording wavelength λR , the incident recording angle of the object beam
θOi
and the incident recording angle of the reference θ Ri are
θ BR = arcsin ( λR /(2nR Λ i ) )
(8)
θOi = arcsin(nR sin ϕOi ) = arcsin ( nR sin(θ BR + ϕi − π / 2) )
(9)
θ Ri = arcsin(nR sin ϕ Ri ) = arcsin ( nR sin(−θ BR + ϕi − π / 2) )
(10)
Notice that the refractive index of the material is related to the wavelength.9 By using the formula in succession, we can figure out the recording parameters for all the angles that need to be amplified.
3. DESIGN AND EXPERIMENTS Table 1. Recording parameters of the target device.
Incident angle
Output angle
Recording object
Recording reference
Angle between incident
θWi (o)
θ Mi (o)
θOi (o)
θ Ri (o)
and output
1
-5
-4.48
0.40
6.00
2
-10
-8.94
0.80
12.00
3
-15
-13.40
1.20
18.00
4
-20
-17.83
1.61
24.00
5
-25
-22.24
2.04
30.00
6
-30
-26.60
2.48
36.00
7
-35
-30.91
2.93
42.00
8 -40 -35.15 3.40 48.00 To demonstrate the functions of the device, we record the grating at the wavelength of 514.2 nm with an Ar+ laser. And the amplifier works at the wavelength of 632.8nm. The incident angle is assumed to be 1, 2, 3, 4, 5, 6, 7, and 8 degree,
Proc. of SPIE Vol. 6832 683216-4
respectively. The output angle is assumed to be -5, -10, -15, -20, -25, -30, -35, and -40 degree. The parameters are shown in Table 1.
Incident laser beam
Holographic plate PBS
position stage
Rotating stage
Mirror Rotating stage Fig. 4. The structure of the recording system.
To realize the recording angles for the design of the angle amplifier, the recording system should change the recording angle as desired. The system scheme is shown in Fig. 4. A plane wave is split by the polarized beam splitter (PBS) into the reference beam and the object beam. The holographic plate is placed on a rotating stage and a linear stage, while the mirror is mounted on a rotating stage. The values of the three stages for all the angles are shown in Table 2. When we record a grating, the position of the linear stage and the rotation stage is set to the designed value. Then the mirror is rotated to make the plane reference wave overlapped with the object wave inside the crystal. Table 2. The values of three stages for the target device.
α
β
Incident angle θWi (o)
Output angle θ Mi (o)
1
-5
42.56
90.40
117.3
2
-10
40.13
90.80
58.2
3
-15
37.70
91.20
38.4
4
-20
35.27
91.62
28.3
5
-25
32.86
92.04
22.2
6
-30
30.46
92.48
18.0
7
-35
28.08
92.93
14.9
(o )
(o )
Linear stage x (cm)
8 -40 25.72 93.40 12.5 To verify the design, we multiplexed three gratings (for incident angle of 3, 4, and 5 degree) in the photorefractive crystal of Fe:LiNbO3 by using a Ar+ laser at the wavelength of 514.2 nm. The thickness of the crystal is 2.5 mm. In our system, the rotating stages have a resolution of 0.02o, and the travel range of the linear stage is 20 cm, with a step of 1 mm. A detector measures the diffracted light intensities behind the crystal. The diffraction efficiency is obtained by blocking one of the writing beams with a shutter controlled by the computer. A simple exposure time schedule is adopted since only three gratings are multiplexed. The results are shown in Table 3 when the device works at the wavelength of 632.8nm. The measured angles between the incident and output beam is near to the designed angles. When the incident angle is changed for one degree, the output angle would change for nearly 5 degrees. The device can act as an angle amplifier. The measured angle resolution of the holograms is less than 0.05 degree. There is a small error between the experimental and the designed angles due to the low optical quality on the surface of the crystal sample and the error of the stages.
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Table 3. the experimental results of the angel amplifier device.
Incident angle θWi ( ) o
Output angle θ Mi ( )
Angle between incident and output. (o)
o
Designed
Experimental
3
-15
18
18.1
4
-20
24
24.4
5
-25
30
30.9
4. CONCLUTION In this paper, an angle amplifier device with multiplexed volume holographic gratings is investigated. The basic principle based on the angle-and-wavelength multiplexing is introduced. And the recording can be realized with another wavelength according to the mutual compensation relation between Bragg angle and wavelength. Both the optical setup and the recording parameters are designed. A device of eight gratings is designed. And a device of three gratings is fabricated and works as an angle amplifier, the output angle is nearly 15, 20 and 25 degree when the incident angle is 3, 4, and 5 degree. It is shown that the design of such a device is very arbitrary and simple. This kind of amplifier can be used in types of beam scanning and beam steering systems. It has been proved that multiple-grating volume holographic angle amplifier has significant advantages and is promising to supply high-performance instrumentation for diverse fields of light beam control.
ACKNOWLEDGMENTS This work paper is sponsored by the National Natural Science Foundation of China (No. 60677037) and National Basic Research Program of China (No. G19990330).
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