Wavelength selective mode division multiplexing
on a silicon chip
G. F. R. Chen,1 T. Wang,1 K. J. A. Ooi,1 A. K. L. Chee,2 L. K. Ang1 and D. T. H. Tan1,*
1
Singapore University of Technology and Design, 8 Somapah Rd., Singapore 487372, Singapore
2
Massachusetts Institute of Technology, 77 Massachusetts Ave. Cambridge MA 02139, USA
*
[email protected],
Abstract: Multiplexing of optical modes in waveguides is demonstrated
using coupled vertical gratings. The device utilizes sinusoidally corrugated
waveguides of different widths with a period designed to multiplex
information at 1.55µm. The design, fabrication and characterization of
devices is performed. Multiplexing of modes is demonstrated in optical
structures which support 3 and 5 quasi-TE modes. The design utilizes
counter-propagating modes in periodic structures, thus enabling the device
to combine its mode division multiplexing capabilities with wavelength
division multiplexing functionalities to further augment the multiplexing
capacity of the device.
©2015 Optical Society of America
OCIS codes: (130.2790) Guided waves; (130.3120) Integrated optics devices; (130.7408)
Wavelength filtering devices.
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Received 5 Jan 2015; revised 9 Mar 2015; accepted 11 Mar 2015; published 20 Mar 2015
23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.008095 | OPTICS EXPRESS 8095
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1. Introduction
Multiplexing of information is a commonly used technique to increase the data capacity of a
transmission medium. This may be done in the time domain [1,2], wavelength [3–5], mode
[6–9], polarization [10,11] and most recently, angular orbital momentum [12,13]. In optical
time division multiplexing, optical pulses are interleaved in time, and therefore the data
capacity scales inversely with the pulse width. Wavelength division multiplexing enables data
channels to be supported at different wavelengths. Modal division multiplexing however,
operates based on the orthogonality of waveguide modes. Different modes co-propagating in a
waveguide cannot couple to one another and therefore, a multi-mode waveguide may be used
to increase the amount of data carried by utilizing each mode as a separate channel. With the
increasing need for short reach interconnects to provide greater bandwidth and reduce power
consumption in microprocessors and data centers, the management of on-chip data is
important.
In this paper, we investigate the use of coupled gratings [14–18] for mode division
multiplexing on a chip. We have previously demonstrated the use of such coupled gratings for
use in dispersion engineering [14–16], pulse compression [17] and wavelength division
multiplexing [3,4]. Contrary to closely spaced adjacent waveguides where coupling occurs in
co-propagating modes, periodic perturbations introduced to two coupled waveguides provides
a mechanism for cross-coupling of modes to occur contra-directionally [20]. Consequently,
the fundamental mode of a single mode waveguide grating may be used to couple into an
adjacent multi-mode waveguide grating at the wavelength of interest, via proper selection of
the corrugation period. The use of waveguide gratings supporting three and four modes for
mode-division multiplexing on a chip is studied for operation at 1.55µm. The design,
fabrication and characterization of these devices are performed.
2. Design
Figure 1(a) shows the schematic of a MDM device based on coupled vertical gratings. The
left grating is based on a single mode waveguide, and has a modulation depth of 50nm. The
right grating is a multi-mode waveguide, with width, W1 = 450nm, W2 = 1250nm or 1850nm,
each supporting three and five modes respectively. An apodization filter is also applied to
eliminate unwanted side lobes in the spectra. The device length, L is fixed at 500µm and the
gap, G between the two coupled gratings is 80nm or 100nm. A larger value of G leads to a
smaller overlap integral between the modes in the two coupled gratings and a smaller
coupling coefficient overall [2,17]. The cross coupling Bragg condition governing the drop
wavelength is given by,
λc = Λ.(neff1 + neff2,m )
(Eq. 1)
Or equivalently,
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23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.008095 | OPTICS EXPRESS 8096
β1 + β 2 =
2π
Λ
(Eq. 2)
where neff1 and neff2,m are the effective indices of the modes in the right and left waveguide
gratings respectively. β1 and β2 are the propagation constants of the right and left waveguide
gratings respectively. In wavelength division multiplexing previously demonstrated, neff,1 and
neff2,m are simply that of the fundamental modes in each grating (m = 0). In this case, neff1
represents the effective index of right waveguide’s fundamental mode, and neff2,m represents
the effective index of the mth order in the multi-mode waveguide on the left. In this particular
device, the introduction of the periodic perturbation creates a wavelength selectivity which
can be combined with mode division multiplexing to achieve two different methods of
multiplexing simultaneously. Figure 1(c) shows a device schematic of how the wavelength
selectivity can be combined with mode division multiplexing to achieve this.
Fig. 1. (a) Device schematic for the mode division multiplexer. The MDM consists of two
coupled gratings with widths, W1 and W2 respectively and modulation depths of ∆W1 and ∆W2
respectively. The peak to peak separation between W1 and W2 is denoted by the gap width, G.
(b) SEM micrograph over two periods of a typical device showing a close up of the gap. (c)
Schematic of how the MDM device can be combined with wavelength division multiplexing
capabilities.
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23 Mar 2015 | Vol. 23, No. 6 | DOI:10.1364/OE.23.008095 | OPTICS EXPRESS 8097
Fig. 2. (a) Effective index vs. waveguide width for modes m = 0 to m = 5. It is seen that three
modes exist for W2 = 1250nm and five modes exist for W2 = 1850nm. (b) Sum of propagation
constants vs. wavelength for the various modes.
Fig. 3. Mode profiles for (a) – (c) W2 = 1250nm for m = 0 – 2 and (d) – (f) W2 = 1850nm
for m = 2 – 4.
Figure 2 (a) shows the effective index as a function of waveguide width for the first five
mode orders. It is observed that three mode orders exist for a waveguide with width W2 =
1250nm and five orders for W2 = 1850nm. For the MDM device to drop the selected mode at
1.55µm, the corrugation pitch needs to be adjusted according to Eq. (1). The sum of the
propagation constants, β1 + β2 as a function of wavelength is plotted in Fig. 2(b). It is
observed that within each waveguide width, β1 + β2 decreases as the mode order increases,
thus implying that a larger value of Λ is needed to fulfill the MDM drop at 1.55µm. In
addition, the modes for the first three mode orders for W2 = 1250nm and modes, m = 2, 3 and
4 for W2 = 1850 are calculated using a fully vectorial beam propagation method, and shown in
Fig. 3(a)-3(f) respectively. Each of the right and left waveguides also possess a self – Bragg
coupling effect, which results in a broad stop band located at λself = 2.Λ.neff1,2 . Operationally,
the self – Bragg coupling effect from the right waveguide will show up within the C – band
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for some of the MDM devices below and therefore, should be considered when designing the
devices.
3. Fabrication and characterization
Fabrication of the MDM devices with W2 = 1250nm and 1850nm was performed using
electron-beam lithography, reactive ion etching and plasma enhanced chemical vapor
deposition of the SiO2 overcladding. Devices with W2 = 1250nm support three optical modes
and devices with W2 = 1850nm support five optical modes. In order to demonstrate the device
design’s ability to perform mode division multiplexing, we fabricate devices with W2 =
1250nm and Λ = 290nm, 300nm and 330nm to multiplex the zeroth, first and second order
modes. The gap width between the coupled gratings in these devices was 80nm to allow for
stronger coupling. Figure 4(a) shows the MDM device designed to multiplex the zeroth order
mode. Device parameters are W1 = 450nm, W2 = 1250nm, Λ = 290nm. The zeroth order drop
port is observed to be centered at 1545nm. Figure 4 (b) shows the first order drop with device
parameters of W1 = 450nm, W2 = 1250nm, Λ = 300nm. Several features of interest are
observed in the measured spectra. The broad stop band centered at 1540nm corresponds to the
self-Bragg coupling of the fundamental mode in waveguide 1 (W1 = 450nm). The drop port of
the first order mode is centered at 1575nm followed by the zeroth order mode observed at
1610nm. Multiplexing of the second order mode is seen in Fig. 4(c), where the MDM device
parameters are W1 = 450nm, W2 = 1250nm, Λ = 335nm. The two spectral features of interest
in this measurement are the MDM drop port for the second order mode centered at 1550nm,
and the self-Bragg coupling from the fundamental mode in waveguide 1, centered at 1590nm.
Further, in each of Figs. 5(a)-5(c), the calculated value of β1 + β2 as well as the value of 2π/Λ
is plotted to show the corresponding wavelengths for each of the spectral features of interest
measured in Figs. 4(a)-4(c) respectively. The intersection between the β1 + β2 plot with the
plot of 2π/Λ shows the Bragg wavelength for the particular mode order. Good agreement
between the expected and measured MDM wavelengths is observed when comparing Fig. 4
and 5, though it is observed that the self-Bragg coupling and the first order drop are slightly
red shifted from their expected locations. This effect is likely due to waveguide 1 being
slightly larger than 450nm (closer to 480nm).). We deduce that the slightly wider width of the
first grating structure is the cause of the red shift because this shift is observed in all three
spectral features of interest. The Bragg conditions governing the cross coupling wavelength,
λc = Λ.(neff1 + neff2,m ) , and the self Bragg coupling wavelength, λself = 2.Λ.neff1 implies that a
larger neff1 arising from a wider first waveguide width will cause an increase in λc as well as
λself. A change in the period of just the adjacent grating structure would only cause a change in
λc for the zeroth and first order modes, but would not cause a corresponding red shift in λself.
Similarly, a slightly wider width of the second waveguide would only cause a red shift in λc
for the zeroth and first order modes, but would not cause a corresponding red shift in λself
because there is no dependence of λself on neff2,m. In addition, typical insertion losses of the
device loss less coupling losses is ~1-2dB.
A further observation of the MDM device may be inferred from the extinction and
bandwidth of each of the drop ports. The cross coupling bandwidth is observed to increase
from 2nm to 7nm and 15nm as the mode order increases from zero to two. This phenomenon
is due to the larger cross coupling strength as the mode order is increased. Higher mode orders
have larger mode sizes, and extend further into the cladding, as is also evidenced by their
smaller effective indices. The calculated 1/e widths of the modes are 0.97µm, 1.31µm and
1.45µm for m = 0, 1 and 2 respectively, confirming the increasing field width as the mode
order increases. This leads to a stronger interaction with the periodic perturbations on the
waveguide sidewalls. In addition, the stronger cross coupling is manifested by stronger
extinction ratios as the mode order increases. For the same device length, the extinction ratio
is observed to increase from 5dB to 15dB and >20dB as the mode order increases from zero
to two.
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Tailoring of the MDM channel bandwidth is an important feature which enables varying
amounts of data bandwidth to be accommodated in each channel. It is also worthwhile to note
that the weak extinction observed for m = 0 can by increasing the device length. Since the
extinction ratio is a function of both the cross coupling strength, κc and the device length
according to the formula, R = tanh2(κcL), a longer device length will lead to better extinction.
One method to vary the bandwidth of each multiplexed channel is to tailor the gap width, G
between the coupled gratings. Figure 4(d) shows the measured spectrum of an MDM device
with W1 = 450nm, W2 = 1250nm, Λ = 335nm, but with G = 100nm. It is observed that the 3dB
bandwidth of the channel decreases from 4nm to 3nm. This tailoring of the gap width can be
used to ensure that all multiplexed channels have the same channel bandwidth regardless of
the mode order. In addition, placement of the multiplexed channels can be performed by
varying the pitch of the coupled gratings. It is observed from Fig. 4(a) and 4(b) that the zeroth
order multiplexed mode is shifted from 1545nm to 1610nm increasing the pitch from 295nm
to 305nm. In this way, operation at desired wavelengths may be designed for and
accommodated to combine both wavelength division and mode division multiplexing
capabilities.
Fig. 4. MDM transmission spectrum for (a) zeroth, (b) first and (c) second order mode.
W1 = 450nm and W2 = 1250nm, G = 80nm for all three plots. (d) MDM transmission spectrum
for W1 = 450nm and W2 = 1250nm, G = 100nm showing the smaller channel bandwidth
compared to G = 80nm.
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Fig. 5. Sum of propagation constants vs. wavelength corresponding to the (a) zeroth, (b) first
and (c) second order modes for W2 = 1250nm. In each plot, the horizontal blue line shows the
value of 2π/Λ corresponding to the value of Λ used. The intersection point of (β1 + β2) and
2π/Λ represent the wavelength at which the Bragg condition (Eq. (1) is satisfied.
The augmentation in the amount of data capacity in a transmission medium is directly
related to the number of modes supported by the waveguide. In order to further demonstrate
our device’s ability to multiplex higher order modes, we design and fabricate a second device
with W1 = 450nm and W2 = 1850nm with Λ = 315nm and 340nm. These device pitches were
selected to multiplex the second, third and fourth order modes close to the 1.55µm
wavelength according to Eq. (1). As before, the waveguides are apodized to minimize out of
band ripple. Figure 6 shows the measured transmission spectra of two devices showing the
three higher order modes being multiplexed. In these two devices, G = 100nm. In Fig. 6(a), a
device with Λ = 315nm is shown. In this transmission spectrum, two higher order modes are
observed to be dropped from the device. The second order mode for the waveguide with W2 =
1850nm is observed to be dropped at close to 1600nm. The third order mode is dropped at
close to 1550nm. In this particular case, the effective index of the third order mode (2.43 at
1550nm) is very close to that of the fundamental mode for W1 = 450nm. Consequently, we see
that the two resonances overlap at a wavelength of around 1550nm. Even though the coupling
strength
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Fig. 6. (a) Transmission (blue) and drop port (red) spectra showing the multiplexing of the
second and third order modes. (b) Transmission (blue) and drop port (red) spectra showing
multiplexing of the third and fourth order modes.
Fig. 7. Sum of propagation constants vs. wavelength corresponding to the (a) second and third
order modes and (b) fourth order modes for W2 = 1850nm. In each plot, the horizontal blue line
shows the value of 2π/Λ corresponding to the value of Λ used. The intersection point of
(β1 + β2) and 2π/Λ represent the wavelength at which the Bragg condition (Eq. (1) is satisfied.
is expected to be larger as the mode order increases, the amount of power dropped in the third
order mode compared to the second order mode is smaller because of the co-location of the
self-Bragg coupling (W1 = 450nm) and the cross-coupling for the third order mode. The third
order mode is again seen in Fig. 6(b) when the pitch is increased to 340nm. The crosscoupling for the third order mode is now shifted to 1600nm, along with the self-Bragg
coupling of the waveguide with W1 = 450nm. The fourth order drop is now observed at
1540nm. Further, in Figs. 7(a) and 7(b), the calculated value of β1 + β2 as well as the value of
2π/Λ is plotted to show the corresponding Bragg wavelengths for each of the spectral features
of interest measured in Figs. 6(a) and 6(b) respectively. Good agreement is seen in the
measured and expected Bragg wavelengths for each of the spectral features of interest. It
should also be noted that the stop band from self-Bragg coupling can be designed to be
outside of the C – band by introducing phase shifts between the right and left waveguides [21]
or appropriately designing the input waveguide width to shift its stop band outside of the Cband.
One of the main benefits of mode division multiplexing using our device design pertains
to the wavelength selectivity conferred onto the structure due to the periodic corrugation.
Since the periodic corrugation creates a perturbation which couples light at wavelengths
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satisfying the Bragg condition in the counter-propagating direction, multiplexing using
different mode orders can be combined with wavelength division multiplexing as well. This
allows us to potentially have a device which combines both wavelength division multiplexing
and mode division multiplexing to generate even greater data capacity on a chip.
4. Conclusions
We have demonstrated mode division multiplexers utilizing coupled waveguides possessing
periodic corrugations on a silicon chip. MDM devices multiplexing the zeroth to second order
modes and the second to fourth order modes are fabricated and experimentally characterized.
Higher order modes are observed to have stronger extinction ratios and larger drop port
bandwidths, implying a stronger coupling coefficient. Tailoring of the drop port bandwidth is
also demonstrated by changing the gap width of the coupled device. This design feature
enables us to ensure that multiplexed modes have the same drop port bandwidth regardless of
mode order. Since the location of the drop port may also be tailored using the pitch of the
device corrugation, strategies combining both wavelength (up to 100 channels within the C –
band [4]) and mode division multiplexing (3 – 5 modes) may be employed to achieve
transmission capacities two orders of magnitude greater than that available to a single
transmission medium. Operation by way of counter-propagating modes in periodic structures
enables this device to combine its mode division multiplexing capabilities with wavelength
division multiplexing functionalities to further augment the multiplexing capacity of the
device.
Acknowledgments
Support from the MOE ACRF Tier 2 Research Grant, A*STAR Public Sector Funding,
SUTD-MIT International Design center and SUTD-ZJU Collaborative Research Grant is
gratefully acknowledged.
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