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A new method based on an optical delay line structure is proposed for two-dimensional raster optical beam steering. For one-dimensional beam steering, the laser beam to be deflected is split into N co-directional sub-beams of equal intensity with the aid of a plane-parallel plate. These sub-beams experience a relative time delay, which translates into a phase difference, thus forming a phased array. When the laser wavelength is tuned, the relative phase varies and the far-field interference footprint can be steered across a receive plane. By employing two plane-parallel plates in series, the described scheme can be extended to produce a two-dimensional N × N array of sub-beams, allowing two-dimensional beam steering via wavelength tuning. In this case, wavelength tuning over a larger range leads to a linear deflection which repeats itself in a raster-like fashion. One direction of deflection repeats itself multiple times as wavelength is scanned over larger range, that is, a raster effect. In this paper, the principle is theoretically derived and formulated, and the preliminary experimental results with four sub-beams are presented.
©2006 Optical Society of America
1. Introduction
Optical free-space multiple access systems employing laser beams that connect optical transceivers offer new potential applications in laser communications [1–4]. It is expected that such a scheme will be used in satellite clusters, distributed satellite systems, and formation-flying satellites, or even in free-space optical switching applications [5–7]. Several methods of deflecting optical beams exist, and they are based on five techniques or devices: mechanical steering using mirrors, real-time re-writable holograms, liquid crystals, acousto-optic devices, or optical phased arrays [1, 8, 9]. The first three approaches are slow. Acousto-optic devices are fast, but they suffer from low efficiency and produce an unwanted zero-order diffraction beam. The “classical” optical phased array has a fast response but is quite complex, as it requires individual phase control of the optical sub-beams [10, 11].
We propose a new method based on an optical delay line structure. For one-dimensional beam steering, the laser beam to be deflected is split into N co-directional sub-beams of equal intensity with the aid of a plane-parallel plate. These sub-beams experience a relative time delay, which translates into a phase difference, thus forming a phased array. When the laser wavelength is tuned, the relative phases vary and, as a consequence, the far-field interference footprint is steered across the receive plane. Beam steering can be very fast, limited only by the rate of laser wavelength tuning. According to recent results, optical frequency modulation techniques [12, 13] can modulate laser wavelengths at rates of several gigahertz.
This paper presents preliminary experimental results for a plane-parallel plate, named the multiple beam generator (MBG), with four sub-beams. The next section describes the principle of the beam deflection, with the optical wavelength as the main independent variable. By employing two plane-parallel plates in series, the scheme can be extended to produce a two-dimensional N × N array of sub-beams, allowing two-dimensional beam steering via wavelength tuning. Section 3 describes the experimental setups for the two-dimensional beam scanning and presents the measurement results.
2. Principle of the beam deflection
2.1. Equal intensity multibeam generation
The MBG device basically consists of two optical surfaces, namely a beam splitter and a mirror. These two surfaces enable us to realize an optical delay line and generate parallel beams. The geometry of the optical delay line for the MBG is shown in Fig. 1 (In Fig. 1 the beam enters the device from the left through an anti-refection coating). The incident light passes through the beam splitter surface with reflectance R 1 so that an output beam becomes available at point A. The light reflected by the beam splitter is then reflected by the mirror surface, and a second output beam is transmitted parallel to the first one at point C. In a similar manner, the i-th beam is reflected by a beam splitter with reflectance R i. The reflectance R i on the beam splitter surface at the i-th beam is chosen as [14]
where N is the total number of beams on one axis. For example, when the number of sub-beams equals N=4, the reflectance on the first output window is R 1=3/4. The reflectances on the successive windows are R 2=2/3, R 3=1/2, and R 4=0.
Fig. 1. Beam splitting method to produce equal-intensity parallel beams. The device basically consists of a beam splitter and a mirror surface.
2.2. Optical phase difference
We refer to Fig. 1 to calculate the optical phase difference (OPD) between two consecutive output beams in an output plane normal to the output beam direction. For distances AB¯ and ADC¯, we obtain
where n 1 sin θ 1 = n 2 sin θ 2. With θ 1 and θ 2, we denote the incident and refractive angles of the beam, where n 1 and n 2 are the refractive indices of the media. The optical phases ΦB and ΦC at points B and C relative to that at point A are given by
where k 0 is the wave number (=2π/λ 0), λ 0 the vacuum wavelength, and d the thickness of the MBG. When the wavelength is changed to λ 1, the phase at points B and C change by
if we neglect any dispersion of n 1 and n 2. The OPD due to wavelength tuning between points B and C is
if n 1=1.
The total transmission efficiency of the proposed method is much higher than that achievable with a grating. For a mirror coating with R=0.96 (compare Fig. 1) corresponding to an aluminum mirror at λ = 1.5 μm, the transmission efficiency is calculated to be -0.26 dB. With higher reflectance, a higher efficiency can be realized: A reflectance of R=0.99 would reduce the transmission loss to -0.07 dB.
2.3. Beam deflection
In the far field, this phase difference manifests itself as a deflection of the superimposed beams by an angle given as
where a is the aperture spacing of the beams on the beam splitter surface and k 1 = 2π/λ 1 is the wave number after wavelength tuning. The aperture spacing between two consecutive beams is given by a = 2d tanθ 2. Substituting θ 2 = tan-1(a/2d) into Eq. (9) and using the relation n 1 sin θ 1 = n 2 sin θ 2, the deflection angle follows as
when the deflection angle is small, e.g. θ def ≪ π/2. Defining a sensitivity coefficient
the deflection angle can be written as
2.4. Two-dimensional beam scanning
To realize two-dimensional raster beam scanning, two MBGs are arranged orthogonally as shown in Fig. 2. The optical alignment for generating parallel beams is very simple even in the two-dimensional case. The first MBG generated N output beams of identical intensity; the second one was arranged orthogonally and again produces N times output beams. Thus, the output was a N × N beam array. Each MBG has a different optical delay in order to produce different deflection sensitivities in vertical and horizontal direction. The deflection angles for the x and y directions are given by
where λ 0 and λ 1 are the wavelengths before and after wavelength tuning, respectively. One can show that the deflection sensitivity coefficients for the x and y directions are given by
where γ=(2d/a) and the scaling factor m relates the thicknesses d' and d of the two MBG devices in the form d’ = md. When the deflection sensitivity for the y axis becomes N times larger than that for the x axis,
the far-field optical beam can be steered within a square area across the receive plane where N is the number of multiple beams for the x and y directions. Substituting Eqs. (15) and (16) into Eq. (17), we obtain the solution for the scaling factor m as
When n 2=1, the scaling factor m equals N, that is d’ = Nd.
Figure 3 shows a simulated angular trace as a function of wavelength for two-dimensional beam scanning. For this calculation, the parameters given in Table 1 were used. The movement along the y axis achieved with the first MBG of 2-mm thickness shows a higher deflection sensitivity as a function of wavelength than that along the x axis achieved with the second MBG of 1-mm thickness. One direction of beam deflection repeats itself multiple times as the wavelength is scanned over a larger range, resulting in a raster effect.
2.5. Maximum deflection angle
The beam divergence of a coherent beam of diameter D is given by ~λ/D. For a high filling factor, the beam divergence of an N-array beam becomes ~λ/((N-1)acosθ 1), where a is the aperture spacing of the beams. The side lobe is separated by λ/(acosθ 1) from the main lobe. Therefore, the maximum deflectable angle becomes θ max = ±λ/(2acosθ 1), which is the range within the main lobe can be steered. For example, the maximum deflection angles are calculated to be θ max,x = ±1.1 mrad and θ max,y = ±0.91 mrad when one uses the parameters given in Table 1. The resolution of beam scanning along one axis can be equal to the diffracted beam width of λ/(Nacosθ 1) when the condition in Eq. (18) is maintained, which is the same divergence angle of the beam. A more precise resolution of raster beam scanning can be realized if the thickness of the MBG for the y-axis deflection is larger than Nd.
Fig. 2. Method of generating two-dimensional multiple beams by introducing two different relative optical time delays.
Fig. 3. Simulated two-dimensional deflection characteristics of the 2 × 2 laser beams as a function of wavelength.
Table 1. Parameters used for two-dimensional beam deflection as shown in Fig. 3.
3. Experimental setup and results
3.1 Two-dimensional beam scanning
Two MGBs were fabricated with a thickness of d = 2 mm and 1 mm, respectively, and with reflective coatings according to Eq. (1). They were incorporated into the experimental setup shown in Fig. 4 for two-dimensional beam scanning. The first MBG generated two output beams of identical intensity; the second one was arranged orthogonally and again doubled the number of beams. Thus, the output was a 2 × 2 beam array. With the configuration shown in Fig. 4 the optical beam pattern was measured using a wavelength of 1550 nm (see Fig. 5). The beams differ in intensity because the incident angle was set to 45 deg in spite of the design value of 40.8 deg to arrive at an easier layout for the optical elements. For the following beam deflection measurement, only 2 × 2 laser beams were used; otherwise, the low resolution of the beam profiler available (i.e. 1 mrad) would not have been sufficient. (With a smaller total aperture, the deflection angle will be larger.)
The 2 × 2 laser beam array was focused with a lens and the intensity distribution was measured. Figure 6 shows the movie of the focused image of the array as a function of wavelength. Figures 7(a) and 7(b) show the beam pattern for x and y axes as a function of wavelength, demonstrating that the peak intensity is steered. The two-dimensional deflection characteristics as a function of the optical wavelength are shown in Fig. 8. The direction of the peak intensity is plotted as a function of the wavelength. Because of the low resolution of the measurement setup of 1 mrad, the discrete 3-level result was to be expected. The deflection characteristic along the y axis (MBG with 2-mm thickness) shows higher deflection sensitivity against the wavelength than that along the x axis (MBG with the 1-mm thickness). As the sensitivity coefficients are different for orthogonal directions, a two-dimensional raster scan is achieved.
The number of resolvable spots in the far field, i.e. the number of deflected positions, is governed by the number of sub-beams, just with a microwave array antenna. In our case, the number of sub-beams will eventually be limited by optical losses in the MBG device. The required wavelength tunability of the laser is given by Eqs. (13) and (14).
Fig. 6. Movie of the 2 × 2 beam array as obtained in the focal plane of a lens in normalized intensity. [Media 1]
Fig. 8. Two-dimensional deflection characteristics of the 2 × 2 laser beams as a function of wavelength. (Because of the low resolution of the measurement setup of 1 mrad, the discrete 3-level result was to be expected.).
4. Conclusion
A two-dimensional raster beam scanning method effectuated by only wavelength tuning was proposed. Devices with an optical delay line structure were manufactured and the beam deflection performance was tested. The principle for the two-dimensional beam deflection was experimentally confirmed. The extension of the device to a much larger number of an array can be possible for a further application. But the number of multiple reflections on glass substrates is limited because the minimum coating width of the surface reflection coating is limited to around 0.1 mm due to the accuracy of the mask process in the case used in this paper. The fast random beam steering is the other issue for two-dimensional operations in this method. The speed of beam deflection is limited by the rate of wavelength tuning of the laser source or optical modulator involved, but according to recent results, optical frequency modulation techniques [12, 13] at rates of several gigahertz will solve this issue. The rise and fall times of the optical signal are affected by the delay time within the array. The proposed method offers a very simple optical phased array concept and can be used for future free-space multicast optical communications in terrestrial and space applications.
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