Coherent combining of multiple beams with multi-dithering technique: 100KHz closed-loop compensation demonstration

We demonstrate the coherent combining of three beams with a phase-locking controller using VLSI multidithering technique. Three …ber-coupled phase shifters are used to compensate phase distortions in the beam propagation path. The highest dither frequency in our system is 70MHz. The achieved closed-loop compensation bandwidth of three beamlets is up to 100KHz. Keywords: coherent beam combining, phase-locking, multi-dithering 1. Introduction Coherent beam combining is an important research area for laser communications and beam projection applications. The reported experimental demonstrations from other research groups are brie‡y described as follows. In [1–3], a phase-compensating 70-mm-diameter aperture transceiver with a hexagonal closely-packed array of seven 23-mm-diameter …ber collimator sub-apertures was demonstrated. The signal at the far …eld receiver was maximized by modulating each sub-aperture’s phase through adjusting the pump current to its ampli…er’s pump diode using multi-dithering control with lock-in ampli…er. The dither frequency is about 20KHz. The feedback signal was acquired from the photo detector at the target plane in the concave-mirrorconverted far …eld. In [4], the optical outputs from 48 polarization maintaining …bers in an 8 8 …ber array (only 48 were used) with 250 m pitch were collimated through an 8 8 lenslet array with the same pitch. The 48 collimated micro-beams were coherently combined through modulating individual in-line phase modulators (piezo stretchers) using stochastic parallel gradient descent method. The update rate of the controller is about 8KHz iterations per second. The feedback signal was acquired from the photo detector at the target plane in convex-lens-converted far …eld. In both systems, the compensation e¤ects for the phase distortions along the propagation path were demonstrated. However, the speed of the phase-locking controller are not very fast in these two systems. As a part of the research e¤orts for the conformal adaptive phase-locked …ber collimator array [5], the coherent beam combining using multi-dithering technique is demonstrated in this paper. The coherent beam combining using stochastic parallel gradient descent techniques for the conformal optical system is presented separately in [6]. 2. Experimental Setup The real far …eld distance is too large (up to a few kilometers) to do the experiments in the laboratory. A far …eld conversion lens is used to simulate the far …eld in our experiments. A picture of the experimental optical setup with a three-element conformal optical transmitter in the laboratory is given in …gure 1. The red arrowed lines show the propagation paths of the three beamlets. Figure 1: Experimental optical setup with three-element transmitter. The red arrowed lines show the propagation paths of the beamlets. Transmitter with three sub-apertures. Equivalent conformal aperture diameter D 71mm. Subaperture lens diameter d=25mm. Sub-aperture lens focal length f=107mm. Distance between lens centers l=40mm. Wavelength =1060nm. Whole conformal aperture …ll-factor is 0.37. Sub-aperture beamlet …ll-factor is 0.75. The hotplate (in white) between the tip-tilt mirror and the cubic beam splitter is used to generate phase distortions. A cooling fan is used to generate air‡ow. For convenience, the upper-right sub-aperture (beamlet) is identi…ed as #1, the upper-left sub-aperture (beamlet) is identi…ed as #2, and the bottom sub-aperture (beamlet) is identi…ed as #3. In order to coherently combine the three beamlets in the far …eld, we prepare the beamlets as follows. The three quasi-monochromatic beamlets are collimated at the transmitter pupil plane. The three collimated beamlets are aligned in parallel to each other so that they can be combined and focused in the same target focal plane in the far …eld. The three beamlets are generated by splitting a beam from a single seed laser into a few parts which are correlated in phase to each other. The length di¤erences of three …ber optical paths are controlled to be smaller than the coherence length of the laser source. The three beamlets are linearly polarized. Their polarization angles are matched. More speci…cations of the experimental setup are given in …gure 2. A …ber-coupled diode laser with wavelength 1060nm is used in the experiments. The laser output has a linewidth of 300KHz and a coherence length of 700m. The length di¤erences between the …ber optical paths ( 10m) for each beamlet are <0.5m which is much smaller than the coherence length of the seed laser. The three outgoing beamlets into the free space are correlated in phase after passing through the optical …ber paths. The output power grating of the used diode seed laser is 150mW. All the optical …bers used in the experiments are Panda type polarization-maintaining single-mode …bers with the design wavelength =1060nm. All the …ber connectors are FC/APC in order to reduce the back-re‡ections in the …ber-to-…ber couplings. The polarization-maintaining …ber beam splitter has built-in phase shifters and amplitude controls. Each phase shifter need a control voltage (denoted by U1, U2 and U3) 2.2V to generate a -radian phase shift. The active waveguide of the Mach-Zehnder interferometer for the amplitude control need a control voltage (denoted by A1, A2 and A3) 4.1V to tune the beamlet power from its maximum value to zero. The amplitude control voltages (U1, U2 and U3) are tuned to appropriate DC values (usually 0:5V) in order to balance the powers of the three beamlets. The phase shifts for the three beamlets are modulated by the control voltages generated by the multi-dithering phase-locking controller. There are three polarization-maintaining …ber-coupled beam collimators for the three beamlets, respectively. The three beam collimators are used to collimate the three beamlets, to align them in parallel to each other and to couple them into the free space. The three collimated beamlets in parallel pass the far …eld conversion lens, and are re‡ected by a large plane mirror and then are re‡ected again by a small plane mirror, to a polarization-independent cubic beam splitter. After the cubic beam splitter, part of the beam is transmitted to the target pinhole (diameter 50 m) and part of the beam is re‡ected through an attenuator wheel to the microscope-coupled CCD focused at the target focal plane. A photo detector (PDA-10CF, 150MHz bandwidth) and a wideband ampli…ter (DHPVA-100, 100MHz bandwidth, 10-60dB gain) are located immediately behind the target pinhole. The bandwidth of the combo of the given photo detector and the ampli…er is from DC to 100MHz for the used wavelenth = 1060nm. The collected power (denoted by J) by the pinhole is used as the feedback input signal by the multi-dithering phase-locking controller. This feedback signal is our system metric to be maximized. The three beamlets propagate in free space from the transmitter pupil to the target pinhole. In this propagation path, wavefront phase distortions can be introduced with the hotplate and the cooling fan as shown in …gure 1. 3. Multi-dithering controller for phase-locking Multi-dithering algorithm[7,8] is a commonly used technique for the phase-locking control in coherent beam combining[2,3,9]. In our system, phase-locking control is implemented with a mixed-signal VLSI multi-dithering controller[10] as shown in …gure 3. The multi-dithering algorithm implemented on this speci…c controller is described as follows. There are eight parallel control channels available in our multi-dithering controller. We have three beamlets in our experiments. In total, we need to use three control channels to apply three voltages (denoted by Ui (t), i = 1; 2; 3) to the three …ber phase shifters for phase-locking control. For convenience, we use the following convention in this section. f g represents the ensemble of variables with the general indicator enclosed by fg. For example, Ui (t) is a single control voltage, while fUi (t)g indicates the ensemble fU1 (t) , U2 (t) , U3 (t)g. The system metric J can be written as a function of the control voltages J J (fUi (t)g) (1) The phase-locking control using multi-dithering technique can be realized by updating the control voltages fUi (t)g continuously with estimating their gradients in the following manner. For a given i = 1; 2; 3 dUi(t) dt = hJ (fUj(t) + j cos (!jt)g) cos [!i (t+ T ) + i]iLPBW (2) where LPBW = min fj!i !j jg ; for 1 6 i 6= j 6 3 (3) is the cuto¤ frequency of the lowpass operation denoted by h iLPBW , is the update gain for all the control voltages fUi(t)g, f ig are the respective small amplitudes of the harmonic dithers f i cos (!it)g for the control voltages fUi(t)g, f!ig are the respective frequencies of the harmonic dithers f i cos (!it)g for the control voltages fUi(t)g, T is de…ned as the total time delay between the instant at which the dithers are applied to the control voltages fUi(t)g and the instant at which the metric J is picked up by the multi-dithering controller to do the above lowpass evaluation, fcos (!it+ i)g are phase-shifted harmonic signals, f ig are the relative phase shifts of the phase-shifted harmonic signals. L as er (1 0 6 0 n m )