1. Introduction

To achieve the high brightness required for many laser applications it is necessary to phase lock multiple element optical arrays. Recently, IPG Photonics has reported 2.5-kW of power out of a single mode fiber with a near diffraction limited optical beam [1]. The intensity and hence the power available from a single-mode optical fiber is limited either by optical surface damage or nonlinear optical effects. These limitations can be overcome by coherent beam combining of the power from multiple optical fibers. We have demonstrated a novel coherent beam combining system that offers not only highly accurate and robust phase locking, but in addition, is readily scalable to more than 100 elements. Furthermore, this is the first phased array locking system that doesn’t require an external reference beam. The results of the first experimental demonstration for two new electronic coherent beam combining techniques, the self-referenced LOCSET and the self-synchronous LOCSET techniques are presented.

Accurate control of the optical phase is required for any phase locked multi-fiber approach. In a master oscillator power amplifier configuration, the optical paths of each of the fibers must be locked to within a fraction of the wavelength in order to coherently combine the individual outputs into a single, high-power beam. As a result of time varying thermal loads and other disturbances, active feedback is required in order to provide for stable coherent addition. There have been a number of experimental and theoretical research efforts addressing the need the for very high brightness fiber laser sources. The technical approaches that have been attempted include the optical self-organized approaches [2–8] and RF phase locking methods [9–11]. Electronic phase locking has demonstrated high fringe visibility for both passive [9–14] and amplified systems [10–12] and powers of 470 watts [12] have been phase locked using these methods. In the previous electronic phase locked fiber arrays, the reference beam was phase modulated at an RF frequency [9–12] and all of the previous systems required an external reference beam in their systems [9–14]. The light emerging from each element was then interfered with the light from a reference beam at the photodetector or an array of photodetectors. The light from each element must be sent to a spatially isolated photodetector, because the RF phase modulation was impressed solely upon the reference beam. Good fringe visibilities of >94% and hence very low phase errors have been consistently achieved using electronic phase locking methods.

Previously, we presented [13, 14] the first reports of a novel coherent beam combination system called Locking of Optical Coherence by Single-Detector Electronic-Frequency Tagging or LOCSET. The LOCSET technique preserved the strengths and simplicity of previous electronic phase locking while providing scaling to very large numbers of elements. In the LOCSET technique, each element of the amplifier array is phase modulated with a unique RF frequency, thus the phase shift for each element is tagged by that elements’ unique RF frequency.

In the self-referenced and self-synchronous LOCSET techniques [15] the array elements are phase modulated at unique RF frequencies exactly as was demonstrated in the first LOCSET technique [13, 14]. The optical phase shift between the optical wave in the unmodulated element (for self-referenced LOCSET) or the array mean phase (for self-synchronous LOCSET) are measured separately in the electronic domain and the phase error signal is fed back to the corresponding elements LiNbO₃ phase modulator to minimize the phase error for that element. The phase error signal for an individual phase modulated element originates from the RF beat note generated by the interference between the overlapping fields of the individual array element with the fields from the other array elements. Therefore, like our previous LOCSET technique [13, 14] the fields of all of the array elements must overlap on the photodetector to obtain the error signal. The theoretical model for both the self-referenced and self-synchronous LOCSET are summarized in the next section.

2. Summary of the Self-Synchronous and Self-Referenced LOCSET theory

In self-synchronous LOCSET all of the array elements are phase modulated, while in the self-referenced LOCSET configuration one array element is unmodulated while all of the remaining array elements are phase modulated. The results of the theoretical model for self-referenced LOCSET and self-synchronous LOCSET methods are summarized in the succeeding paragraphs.

Assuming that the unmodulated and phase modulated fields are plane waves and are identically polarized, then the unmodulated element optical field, E_u(t) and the i^th array element optical fields, E_i(t) are,

where E_u0 and E_i0 represent the field amplitudes for the unmodulated element and i^th phase modulated element, respectively. ω_L represents the laser frequency. ϕ_u and ϕ_i represent the optical phases of the unmodulated and the i^th array elements, respectively. β_i represents the phase modulation amplitude for the i^th array element. ω_i represents the RF modulation frequency for the i^th array element.

The optical fields from the unmodulated array element and all of the phase modulated array elements are superimposed on the photodetector so that the total field is,

where N is the number of phase modulated elements in the optical array.

The photodetector current is,

where l and j represent the summation indices for the phase modulated elements, μ_o and ε_o represent the magnetic and electric permeabilities of free space, R_PD represents the responsivity of the photodetector, and A represents the photodetector area.

The phase control signal is extracted from the photocurrent using coherent demodulation in the RF domain. The photodetector current is multiplied by sin(ω_i t) and integrated over a time, τ, where ω_i represents the phase modulation frequency of one of the phase modulated elements. The integration time, τ, is selected long enough to isolate the individual phase control signals of the phase modulated elements and short enough so that the phase control loop can effectively cancel the phase disturbances of the system. The phase control signals for the i^th array element of the self-referenced and the self-synchronous LOCSET systems are given by,

where S_Si represents the phase error control signal. In the self-referenced LOCSET configuration one array element is not phase modulated whereas, in the self-synchronous LOCSET configuration all of the array elements are phase modulated.

The phase error signal for a self-synchronous LOCSET system is obtained by evaluating Eq. (5), under the following conditions; ω_i is equal one of the array phase modulation frequencies and the integration time, τ≫2 π/|(ω_i–ω_j)| for all i and j when j≠i. Under those conditions, Eq. (5), the phase error signal, for the self-synchronous LOCSET system is given to an excellent approximation by,

where S_SSi represents the phase error control signal for the self-synchronous configuration of the system, J₀ represents a Bessel function of the first kind of zero order, J₁ represents a Bessel function of the first kind of order one, ϕ_i and ϕ_j represent the optical phases of the i^th and j^th array elements, respectively and finally, P_i and P_j represent the optical power incident upon the photodetector from the i^th and j^th elements, respectively. For these experiments, the i^th phase control loop operating point, ϕ_i–ϕ_j, is set to zero for all of the other array elements. Experimentally, this condition is achieved by adjusting the variable RF phase adjustors, which are shown in Fig. 2, to optimize the optical power on the photodetector. It is only necessary to make this adjustment once for any system set up. When a self-synchronous LOCSET system is adjusted to optimize the optical power on the photodetector, the control loop for each of the N elements strives to zero ϕ_i–ϕ_j, for all of the other array elements, thus locking the phases of the array elements even in the presence of disturbances.

If ω_i is one of the array phase modulation frequencies and if the integration time, τ≫2π/(ω_i–ω_j) for all i and j when j≠i then from Eq. (5), the phase error signal, for the selfreferenced LOCSET system is to an excellent approximation,

where S_SRi represents the phase error control signal for the self-referenced LOCSET configuration, ϕ_u presents the optical phase of the unmodulated array element and P_u represents the optical power incident upon the photodetector from the unmodulated array element. In Eq. (7) the first term in the bracket has the same form as the phase error signals used by previous phase locked arrays and the second term in the bracket is the self-synchronous term given in Equation (6). For these experiments, the i^th phase control loop operating point, ϕ_i–ϕ_u, is set to zero for all of the array elements. Experimentally, this condition is achieved by adjusting the variable RF phase adjustors, which are shown in Fig. 2, to optimize the optical power on the photodetector. When a self-referenced LOCSET system is adjusted to optimize the optical power on the photodetector, the control loops adjust the phases of the phase modulated array elements to track the phase of the unmodulated element, thus the phases of the array elements are locked in phase even in the presence of disturbances.

Assuming that the loop integrator time constant, τ≫1/|ω_i–ω_j| for any pair of phase modulation frequencies and that a portion of the central lobe of the far-field pattern of the array be imaged on the photodetector active area, then the phase error signal for the self-referenced LOCSET and self-synchronous LOCSET configurations are presented in Eqs. (6) and (7), respectively.

3. Experimental Systems for Self-Referenced and Self-Synchronous LOCSET

A block diagram of the experimental system is shown in Fig. 1. The master oscillator is a Lightwave Electronics series 122 Nonlinear Planar Ring Oscillator. The optical power from the master oscillator is coupled into the single mode polarization maintaining input fiber for the EOSpace 1×8 power splitter that has a separate phase modulator in each of the 8 legs. The outputs of the EOSpace power splitter/phase modulator are coupled into 8 single mode polarization maintaining optical fibers. The optical signals from the EOSpace power splitter/phase modulator legs are then directed either directly into the collimating optics or coupled through fiber amplifiers and then into the collimating optics. The collimated output beams from the array are sampled by a beam splitter and a small fraction of the output power from the array is sent to a focusing lens that images the central lobe of the far field onto a single photodetector. A small amplitude RF phase modulation is applied to each of the phase modulators at a unique RF frequency for each array element. Therefore, the photocurrent contains the RF phase modulation frequencies of each array element and the amplitudes of those RF frequency components contain the optical phase error signals for the array elements, as is shown in Eq. (5). Next, the RF phase modulation frequencies, corresponding to each array element, are isolated in the electronic domain and the optical phase error signals corresponding to each array element are separately extracted and fed back to the corresponding phase modulator for that array element and the phase of that array element is locked to the same phase as the other array elements. Each array element has a functionally identical phase control loop that operates simultaneously with the other array element control loops to lock all of the array phases together.

 

Fig. 1. LOCSET beam combining block diagram. PM represents phase modulators and PD represents the photodetector.

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The signal processing electronics for each array element is identical, with the exception of the difference between the RF phase modulation frequencies of each array element. A block diagram of the signal processing electronics for a 2 element system is shown in Fig. 2. Each array element is tagged by its unique RF phase modulation frequency. The amplified photocurrent is directed to a 1×2 RF power splitter and the output signals from the RF power splitter are each directed to two independent signal processing circuits, one signal processing circuit for fiber i, which is shown in Fig. 2 and a second signal processing circuit for fiber j, that is not shown in Fig. 2. The only difference between the signal processing circuits for fibers i and j are the phase modulation frequencies, ω_i and ω_j. The signal processing circuits perform 2 functions; first a small RF phase modulation is applied to the phase modulator for a single array element and second, the optical phase error signals for that element are extracted and fed back to the phase modulator to cancel phase variations in that array element. The phase error signals for a single element are extracted by coherently demodulating in the RF domain. Experimentally RF coherent demodulation is implemented using an RF mixer, M, to multiply the photodetector current times sin(ω_i t) and then integrating the output of the mixer over many cycles of the RF frequency for that array element. In this manner the phase error signal for each individual array element is isolated, extracted and fed back to lock the phase of each element to the same phase as the other array elements. The generalization from the 2 element array, shown in Fig. 2, to an N element array simply requires adding more fiber array elements, replacing the RF 1×2 power splitter with a RF 1×N power splitter and adding an additional signal processing circuit for each additional element. Finally, it is important to note that the phase control electronics is identical for both the self-synchronous and self-referenced LOCSET implementations.

 

Fig. 2. Block diagram of the electronics for a 2 element array. Where M represents an RF mixer and VP represents an electronically variable phase adjustment.

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4. Experimental Results

We present the results of phase locking experiments that demonstrate two novel phase locking architectures for both passive fiber arrays and amplified fiber arrays. A 3×3 array of passive optical fibers has been phase locked using the self-referenced LOCSET technique. To the best of the authors’ knowledge this represents the largest number of optical fiber elements that have been electronically phase locked as well as the first demonstration of the self-referenced LOCSET technique.

When the light from the unmodulated array element was blocked, the remaining 8 elements of the passive array were phase locked using the self-synchronous LOCSET technique. This is the first experimental demonstration of the self-synchronous LOCSET technique.

 

Fig. 3. Phase locking video (2.1 MB).

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In the next experiment an array of six 1/3-watt fiber amplifiers were phase locked using the self-referenced LOCSET technique, providing a total locked power of 2-W. There was no visibly perceptible degradation in the locked array performance between the passive fiber and amplified fiber array locking experiments. In another experiment, two 11-W fiber amplifiers were phase locked using the self-referenced LOCSET technique and again excellent results were achieved.

The phase lock performance was tested in 2 ways. First, in all of the experiments, the fibers were rigorously disturbed while the control loops were closed and the far-field array pattern was observed on a camera. Second, the root-mean-square phase error for a single element was determined from the measurements of the phase error signal, S_Sri. A separate photodetector and demodulator outside the control loop for measuring the root-mean-square phase error experiments.

 

Fig. 4. Measured root-mean-square phase error for one array element as a function of the number of array elements.

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Figure 3 is a video clip of a self-referenced LOCSET experiment where a sparse 3×3 array of optical fibers are electronically phase locked. The light is transmitted through the bundle of fibers that are being vigorously disturbed during the experiment. The phase lock electronics control loop is initially closed showing a stable far field-pattern and when the phase lock electronics control loop is opened the far-field pattern is not stable. Then the electronics is turned on again and the far field pattern snaps back into place. The self-synchronous LOCSET experiment produced identical results.

There was no observable degradation of the far-field pattern for either the self-referenced or the self-synchronous LOCSET techniques for either passive or amplified fiber arrays. The results of the measurement of the root-mean-square phase error versus the number of array elements for a self-referenced LOCSET passive fiber array locking is presented in Fig. 4. Clearly there was no significant variation in the root-mean-square phase error as the number of array elements was varied from 2 elements to 9 elements.

The root-mean-square phase error in the locked array was measured with an independent phase error measurement system that used a separate photodetector and demodulator to measure the phase error of an array leg. Figure 4 is a graph of the standard deviation of the measured phase error (in waves) for one channel versus the number of phase elements. Full scale on vertical axis of the graph is λ/4. The measured root-mean-square phase error is roughly λ/20 independent of the number of elements for more than 2 elements when the control loop was closed.

5. Conclusions

In conclusion, we have for the first time demonstrated optical phase locking by self-referenced LOCSET and self-synchronous LOCSET. We report what to our knowledge is the first electronically phase locked optical array without an external reference beam. We report the phase locking of a passive fiber 3×3 array and a 6 element fiber amplifier array. These optical phase locking techniques are simple and robust against mechanical vibrations and thermal variations. We also report the phase locking of 22-W of fiber amplifier power using these techniques. Excellent stability against environmental disturbances has been demonstrated in both passive and amplified fiber arrays using these techniques. We report a root-mean-square phase error of (λ/20) that is independent of the number of array elements. This approach is easily scalable to 100 elements because the phase error signals for each element are separated in the electronic domain versus the optical domain.