Self-aligning universal beam coupler
David A. B. Miller
Ginzton Laboratory, Stanford University, 348 Via Pueblo Mall, Stanford CA 94305-4088, USA
Abstract: We propose a device that can take an arbitrary monochromatic input beam and couple it into a
single-mode guide or beam. Simple feedback loops from detectors to modulator elements allow the device
to adapt automatically to any specific input beam form. Potential applications include automatic
compensation for misalignment and defocusing of an input beam, coupling of complex modes or multiple
beams from fibers or free space to single-mode guides, and retaining coupling to a moving source.
Straightforward extensions allow multiple different overlapping orthogonal input beams to be separated
simultaneously to different single-mode guides with no splitting loss in principle. The approach is suitable
for implementation in integrated optics platforms that offer elements such as phase shifters, Mach-Zehnder
interferometers, grating couplers, and integrated monitoring detectors, and the basic approach is applicable
in principle to other types of waves, such as microwaves or acoustics.
There has recently been growing interest in exploiting multiple modes, both in optical fibers  and free-space ,
for expanding communications bandwidth and capabilities. Selecting and coupling to complicated mode forms such
as higher fiber modes  or angular momentum beams  is challenging, however, especially if splitting losses are
to be avoided. Coupling to waveguides generally remains difficult in optics, especially if alignment or precise
focusing cannot be guaranteed. Simultaneous coupling of multiple overlapping input modes without splitting loss
has had few known solutions [3,4]. Here we propose a novel approach to coupling that both allows complicated
modes to be coupled, e.g., to single-mode waveguides, and can accommodate misalignments and movements, all
without moving parts. It can also couple multiple different overlapping modes simultaneously to different output
waveguides, without fundamental splitting loss. The approach can be implemented using standard integrated optical
components, detectors and simple local feedback loops, and is automatic, not requiring advance knowledge of the
beam form to be coupled. The approach could be applied in principle to other waves, such as radio waves,
microwaves or acoustics .
2. Device concept
Fig. 1 shows a conceptual schematic of the approach. For simplicity for the moment, we consider a beam varying
only in the lateral direction. For illustration we divide the arbitrary input beam into 4 pieces, each incident on a
different one of the 4 beam splitter blocks. Each block includes a variable reflector (except number 4, which is 100%
reflecting) and a phase shifter. (The phase shifter PS1 is optional, allowing the overall output phase of the beam to
be controlled.) We presume loss-less devices whose reflectivity and phase shift can be set independently, for
example, by applied voltages for electrooptic or thermal control. For the moment, we neglect diffraction inside the
optics and presume that the phase shifters, reflectors, and detectors operate equally on the whole beam going
through one beamsplitter.
We shine the input beam onto the beamsplitter blocks as shown. Initially, the phase shifter and reflectivity
settings can be arbitrary as long as the reflectivities are non-zero so that we start with non-zero powers on the
detectors. First, we adjust the phase shifter P4 to minimize the power on detector D3. Doing so ensures that the wave
reflected downwards from beamsplitter 3 is in antiphase with any wave transmitted from the top through
beamsplitter 3. Then we adjust the reflectivity R3 to minimize the power in detector D3 again, now completely
cancelling the transmitted and reflected beams coming out of the bottom of beamsplitter 3. (If there are small phase
changes associated with adjusting reflectivity, then we can iterate this process, adjusting the phase shifter again, then
the reflectivity, and so on, to minimize the D3 signal.)
We then repeat this procedure for the next beamsplitter block, adjusting first phase shifter P3 to minimize the
power in detector D2, and then reflectivity R2 to minimize the D2 signal again. We repeat this procedure along the
line of phase shifters, beamsplitters and detectors. Finally, all the power in the incident beam emerges from the
output port on the right. (This approach could also be used to combine multiple beams of unknown relative phases,
as in fiber laser systems , with each beam incident on a separate beamsplitter block.)
Fig. 1. Schematic illustration of the device structure. Diagonal grey rectangles represent controllable partial reflectors. Vertical clear
rectangles represent controllable phase shifters.. (a) Coupler for a single input beam with four beamsplitter blocks (numbered 1 – 4),
phase shifters P1 – P4 and reflectors R1 - R3. (b) Coupler for two simultaneous orthogonal input beams (connections from detectors to
feedback electronics omitted for clarity).
Unlike typical adaptive optical schemes (see, e.g., Refs.[5,6]), this method is progressive rather than iterative –
the process is complete once we have stepped once through setting the elements one by one – and only requires local
feedback for minimization on one variable at a time – no global calculation of a merit function or simultaneous
multiparameter optimization is required. Simple low-speed electronics could implement the feedback.
To optimize this beam coupling continually, we can leave this feedback system running as we use the device,
stepping cyclically through the minimizations as discussed. This would allow real-time tracking and adjustments for
misalignments or to retain coupling to moving sources. For static sources, we could use an alternate algorithm based
only on maximizing output beam power (see Appendix A).
3. Waveguide device
Fig. 2 shows a waveguide version based on Mach-Zehnder interferometers (MZIs) as the adjustable “reflectors” and
phase shifters, with Fig. 2 (a) corresponding to Fig. 1 (a). A MZI gives variable overall phase shift of both outputs
based on the common mode drive of the controllable phase elements in each arm and variable “reflectivity” (i.e.,
splitting between the output ports) based on the differential arm drive. Such a waveguide approach avoids
diffractions inside the apparatus and allows equal path lengths for all the beam segments. Equal path lengths are
important for operation over a broad wavelength range or bandwidth; otherwise the relative propagation phase
changes with wavelength in the different waveguide paths.
For further equality of beam paths and losses, we could add dummy MZIs in paths 1, 2, and 3, respectively, as
shown in Fig. 2 (b), to give the same number of MZIs in every beam path through the device; the dummy devices
would be set so as not to couple between the adjacent waveguides (i.e., the “bar” rather than the “cross” state), and
to give a standard phase shift. Note that as long as no power is lost from the system out of the “open” arms – here,
the top right ports of the top two dummy devices in Fig. 2 (b) – the settings of these dummy devices are not critical;
the subsequent setting of MZIs 1 – 4 can compensate for any such loss-less modification of the input waves. We
could add further detectors at those top right ports, adjusting the dummy MZI reflectivities to minimize the signals
in such detectors, ensuring loss-less operation. We note that systems with large numbers (e.g., 2048) of MZIs have
been demonstrated experimentally, with low overall loss , so the relatively large arrays that might be required for
complex beams could be feasible practically. An alternative scheme to that of Fig. 2(a) or 2(b) using a binary tree of
devices for coupling to a single input beam is presented in Appendix B.
Fig. 2. Mach-Zehnder implementation with detectors. Device numberings correspond to those of Fig. 1. (a) Coupler for a single input
beam. (b) Coupler as in (a) with dummy devices added to ensure equal path lengths and background losses. (c) Coupler for two
simultaneous modes. The greyed-out lower portions in the bottom row of Mach-Zehnder devices are optional arms for symmetry only;
simple controllable phase shifters could be substituted for these Mach-Zehnder devices.
To use the waveguide scheme with a spatially continuous input beam, we need to put the different portions of the
beam into the different waveguides. We could use one grating coupler  per waveguide as explored for angular
momentum beams  or phased-array antennas . For full 2D arrays, we need space to pass the waveguides
between the grating couplers . We could either allow an imperfect fill factor, shining the whole beam onto the top
of the grating coupler array (as in Fig. 3(a)), or we could use an array of lenslets focusing the beam portions onto the
grating couplers to improve the fraction of the beam that lands on the grating couplers (Fig. 3 (b)). Grating coupler
approaches are also known that can separate polarizations to two separate channels [9,11-13], allowing the input
mode of interest to have arbitrary polarization content at the necessary expense of twice as many channels in the
4. Separation of multiple orthogonal beam
We can extend this concept to detecting multiple orthogonal modes simultaneously. In this case, we would use
detectors that are mostly transparent, such as silicon defect-enhanced photodetectors in telecommunications
wavelength ranges [14-17], sampling only a small amount of the power and transmitting the rest. Now, (Figs. 1(b)
and 2(c)), we first set the “top” row of phase shifts and reflections (devices 11 – 14) as before while shining the first
beam on the device, which gives output beam 1. Then, if we shine a second, orthogonal beam on the device, it will
transmit completely through the “top” row of beamsplitters and photodetectors, becoming an input beam for the
To understand why this second orthogonal beam passes through the first row, note that, for any loss-less beam
coupler that couples all of one input mode (e.g., our first input beam shining into our device) into a single output
mode (here output beam 1), it is impossible to combine any power from any other orthogonal beam into the same
output mode ; since there is nowhere else for the power in some second orthogonal beam to go (nothing in our
optics reflects this second beam backwards), it will all pass through to the second row of beamsplitter blocks. The
beam form will certainly be changed as it passes through the first row, but since our process can adapt to an arbitrary
beam, we can simply use the same alignment process as before, now with the second row of phase shifters and
reflectors (devices 21 – 23), and the detectors D21 – D22, to direct all of this power to output beam 2.
Fig. 3. (a) Figurative top-view schematic of an array of grating couplers with a set of Mach-Zehnder devices to produce one beam at the
output waveguide, analogous to Fig. 2(a). For graphic simplicity, we omit here any additional lengths of waveguide and possible dummy
Mach-Zehnder devices to equalize path lengths and losses. (b) Illustration of the addition of a lenslet array to improve the fill factor. The
input beam is shone onto the grating coupler surface or onto the lenslet array.
We can repeat this process for further orthogonal beams using further rows, up to the point where the number of
rows of beamsplitters (and the number of output beams) equals the number of beamsplitter blocks in the first row.
(Generally, we can leave all the preceding beams on, if we wish, as we adjust for successive added orthogonal
beams.) We could analogously apply the same approach to the structure of Fig. 3, adding further “rows” as in Fig. 2
(c) to allow simultaneous detection of multiple orthogonal 2D beams shone on the grating couplers or lenslets.
We could also add some identifying coding to each orthogonal input beam, such as a small amplitude
modulation at a different frequency for each beam; then, we can have all beams on at once, with each detector row
looking only for one beam’s specific modulation frequency or coding signal. Such an approach, combined with
continuous cycling through the different rows as above, allows continuous tracking and alignment adjustment of all
the orthogonal beams while leaving all of them on.
The number of portions or subdivisions we need to use for a given beam depends on how complex a mode we want
to select or how complicated a correction we want to apply. Generally, this device corresponds to the approach to
complexity counting discussed in Ref. . If we want to be able to select one specific input mode form out of MI
orthogonal possibilities, we need at least MI beamsplitter blocks in the (first) row. Subsequent rows to select other
specific modes from this set need, progressively, one fewer beamsplitter block. The number of rows of beamsplitter
blocks is the mode coupling number MC in the notation of Ref. 
At radio or microwave frequencies, we could use antennas instead of grating couplers. Various microwave
splitters and phase shifters are routinely possible . Use of nanometallic or plasmonic antennas , waveguides
, modulators  and detectors [21,22] is also conceivable for subwavelength circuitry in optics, allowing
possibly very small and highly functional mode separation and detection schemes.
In conclusion, we have shown a general method for coupling an arbitrary input beam to one specific output beam,
such as a waveguide mode, with an automatic method for setting the necessary coefficients in the array of adjustable
reflectors and phase shifters based on signals from photodetectors, and with extensions to allow multiple orthogonal
input beams to be separated without fundamental splitting loss. This should open a broad range of flexible and
adaptable optical functions and components, with analogous possibilities for other forms of waves such as
microwaves and acoustics.
Appendix A - Alternate alignment algorithm
As an alternative to the use of multiple detectors when aligning a single beam with the device, we could use only a
detector in the output beam, with a different algorithm. We first set all the reflectors in the beam splitter blocks in
Fig. 1(a) to be 100% transmitting, except the last one – beamsplitter block 4, which is set permanently to 100%
reflection – and the second last one (block 3), which we set to some intermediate value of reflectivity. Then,
monitoring a detector in the output beam (port 1 on the right), we adjust the phase shifter P4 on the right of
beamsplitter block 4 to maximize the output power. We then adjust the reflectivity R3 in beamsplitter block 3 to
maximize the output power again (these two steps in sequence arrange that there is no power emerging from the
bottom of block 3). We then proceed along the beamsplitter blocks in a similar fashion, setting the next beamsplitter
reflectivity to some initial intermediate value, adjusting the phase shifter just to its left to maximize the output, then
adjusting the reflectivity in this block to maximize output again, and so on along the beamsplitter blocks. (In this
case, we would not be able to do continuous feedback on the settings while the system was running because we need
to set some of the reflectors temporarily to 100% transmission during the optimization steps.)
This approach can be extended to multiple orthogonal beams. Once we have set the first row, we leave those
settings fixed and then proceed with aligning the second orthogonal beam in a similar fashion, monitoring the power
now in the output beam in the second row.
Appendix B - Alternate configuration for single beam coupling
For coupling a single beam, an alternate configuration of phase shifters, MZ interferometers and detectors is shown
in Fig. 4. In this approach, phase shifter P1 is adjusted to minimize the signal in detector DA1, and then the split
ratio (“reflectivity”) of MZI MA1 is adjusted through differential drive of the arms to minimize the DA1 signal
again. Similar processes can be used simultaneously with P2, DA2 and MA2, with P3, DA3 and MA3, and with P4,
DA4 and MA4. Next, the overall phase is adjusted in MA1 to minimize signal in DB1, and then the split ratio
(“reflectivity”) of MB1 is adjusted to minimize the DB1 signal again. A similar process can be run simultaneously
with MA3, DB2 and MB2. Finally, in this example, the phase in MB1 is adjusted to minimize the DC1 signal, and
then the split ratio (“reflectivity”) of MC1 is adjusted to minimize the DC1 signal again. Dummy phase shifters can
be incorporated in the input paths for beams 2, 4, 6, and 8, as shown to help ensure equality of path lengths in the
This approach has the advantages of requiring no dummy interferometers and allowing simultaneous feedback
loop adjustments, first in the DA column of detectors, then in the DB column, and finally in the DC column. In
contrast to the approach of Fig. 2(a) of the main text, the MZI devices are arranged in a binary tree rather than a
linear sequence, so the device is shorter and a given beam travels through fewer MZI devices, possibly reducing
loss. We could extend this approach also for coupling multiple orthogonal beams (e.g., by using beams transmitted
through mostly transparent versions of the detectors into analogous, shorter trees of devices); but, unlike the
approaches of Fig. 2, we would require crossing waveguides and/or multiple stacked planar circuits if we used a
planar optical approach.
Fig. 4. Alternative binary approach for coupling one arbitrary input beam to a single output beam. P1 – P4 are controllable phase
shifters, MA1 – MC1 are controllable MZ interferometers, and DA1 – DC1 are detectors used to give the signals for feedback loops.
The dummy phase shifters are optional and could be included for equality of path lengths and/or loss.
This project was supported by funds from Duke University under an award from DARPA InPho program, and by
Multidisciplinary University Research Initiative grants (Air Force Office of Scientific Research, FA9550-10-1-0264 and
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