Zakaria Aldeneh1, Takuya Higuchi1, Jee-weon Jung2, Skyler Seto1,Tatiana
Likhomanenko1,
Stephen Shum1, Ahmed Hussen Abdelaziz1, Shinji Watanabe2, Barry-John Theobald1

# Can you Remove the Downstream Model for Speaker Recognition
with Self-Supervised Speech Features?

###### Abstract

Self-supervised features are typically used in place of filter-banks in
speaker verification models. However, these models were originally designed to
ingest filter-banks as inputs, and thus, training them on top of self-
supervised features assumes that both feature types require the same amount of
learning for the task. In this work, we observe that pre-trained self-
supervised speech features inherently include information required for
downstream speaker verification task, and therefore, we can simplify the
downstream model without sacrificing performance. To this end, we revisit the
design of the downstream model for speaker verification using self-supervised
features. We show that we can simplify the model to use $97.51\%$ fewer
parameters while achieving a $29.93\%$ average improvement in performance on
SUPERB. Consequently, we show that the simplified downstream model is more
data efficient compared to baseline—it achieves better performance with only
$60\%$ of the training data.

Index Terms: Self-supervised learning, representation learning, speaker
recognition, speaker verification

##  1 Introduction

Self-Supervised Learning (SSL) for speech (e.g., wav$2$vec $2.0$ [1], HuBERT
[2], w2v-BERT [3], BEST-RQ [4]) enables learning powerful representations
using a large amount of unlabeled data. Once trained on unlabeled data, SSL
models can be fine-tuned on labeled data to achieve remarkable performance on
target downstream tasks (e.g., automatic speech recognition, speaker
recognition, language identification, emotion recognition) [5, 6, 7, 8, 9,
10]. Fine-tuning a pre-trained SSL model for each downstream task, however,
can be impractical due to computation and memory constraints. A more appealing
setup is using an SSL model as a general-purpose feature extractor, where the
pre-trained model is frozen, and features extracted from this frozen model are
used with smaller, task-dependent downstream models [11]. In this work, we
study the role the downstream model plays when using general-purpose SSL
features for speaker verification.

Downstream speaker verification models (such as x-vector [12] and ECAPA-TDNN
[13]) used in prior works were originally designed to ingest filter-bank
features as inputs, whereas state-of-the-art SSL models operate on raw
waveforms and the features that the SSL models extract are learned in an end-
to-end manner using a Transformer architecture [14, 15, 16]. An important
difference here is that unlike features derived from filter-banks, features
from SSL models capture long-form contextual information in their
representation, and it has been shown that this information is useful for
predictive machine learning tasks [17, 18, 19]. In addition, SSL
representations capture speaker information as it was shown that explicitly
disentangling speaker information during SSL pre-training results in improved
performance on content related tasks [20]. These findings suggest that SSL
pre-training may have already done some of the learning required for
downstream speaker-related tasks, whereas models trained on top of filter-bank
features must still extract all of this information from the network inputs.

Given the contrast between filter-banks and SSL features, we explore the role
the downstream model plays in speaker verification with SSL features. We first
seek to understand the capability of several SSL models when conducting
speaker verification without a downstream model (i.e., zero-shot capability)
and use the findings from our analyses to revisit the design of the downstream
speaker verification model. Specifically, we show that we can reduce the
capacity of the downstream speaker verification model by $97.51\%$ and still
obtain a $29.93\%$ average improvement in performance on the SUPERB [11]
benchmark. Additionally, we show that the simplified downstream model is
especially effective in limited training data scenarios, outperforming its
baseline counterpart with only $60\%$ of the training data.

Table 1: Zero-shot (i.e., no downstream model) speaker verification
performance of SSL models. ``Params.'' denotes the number of parameters in the
model; ``Data'' denotes the data used for training the model; $\Delta$ denotes
the relative ($\%$) improvement that SSL features provide over using filter-
bank (FBank) features. The values for ``Params.'' and ``Data'' columns are
taken from [11].

Model | Params. | Data | LibriSpeech (in-domain) | VoxCeleb1 (out-of-domain)
---|---|---|---|---
EER ($\%$) $\downarrow$ |  $\Delta$ ($\%$) $\uparrow$ |  EER ($\%$) $\downarrow$ |  $\Delta$ ($\%$) $\uparrow$
FBank | $-$ | $-$ | $7.2$ | $0.0$ | $40.4$ | $0.0$
HuBERT (base) |  $94.68$M |  LS $960$ hr | $4.4$ | $38.9$ | $32.0$ | $20.8$
HuBERT (large) |  $316.61$M |  LL $60$k hr | $3.1$ | $56.9$ | $31.7$ | $21.5$
wav2vec 2.0 (base) |  $95.04$M |  LS $960$ hr | $5.5$ | $23.6$ | $33.2$ | $17.8$
wav2vec 2.0 (large) |  $317.38$M |  LS $960$ hr | $2.6$ | $63.9$ | $30.7$ | $24.0$
wav2vec 2.0 (large) |  $317.38$M |  LL $60$k hr | $2.8$ | $61.1$ | $27.2$ | $32.7$
wav2vec 2.0 (large) |  $317.38$M |  VoxPopuli $100$k hr | $3.1$ | $56.9$ | $32.7$ | $19.1$
WavLM (base) |  $94.70$M |  LS $960$ hr | $4.7$ | $34.7$ | $31.3$ | $22.5$
WavLM (base+) |  $94.70$M |  Mix $94$k hr | $4.0$ | $44.4$ | $31.3$ | $22.5$
WavLM (large) |  $316.62$M |  Mix $94$k hr | $2.5$ | $65.3$ | $23.0$ | $43.1$
wav2vec |  $32.54$M |  LS $960$ hr | $5.3$ | $26.4$ | $30.7$ | $24.0$
vq-wav2vec |  $34.15$M |  LS $960$ hr | $11.4$ | $-58.3$ | $37.8$ | $6.4$
Modified CPC |  $1.84$M |  LL $60$k hr | $3.5$ | $51.4$ | $27.9$ | $30.9$

##  2 Related Work

In this section, we discuss relevant prior works that looked at the
intersection of SSL and speaker recognition. Specifically, we focus on SSL
approaches that learn generic representations rather than approaches designed
to extract specialized representations for speaker verification (e.g., [21,
22, 23]). We refer the reader to [24] for a thorough review on SSL
representations.

Fan et al. [5] studied the effectiveness of a wav$2$vec $2.0$ model on speaker
verification and language identification. The authors visualized the features
extracted from the model to show that the features capture speaker and
language information. The authors then attached a fully-connected layer to the
top of the model and ran experiments (both with and without fine-tuning the
full model) to quantitatively demonstrate effectiveness of the pre-trained
model on the downstream tasks. In contrast to [5], our work presents a
comparative study that quantifies (not visualizes) the speaker information
captured by several state-of-the-art SSL models (not just wav$2$vec $2.0$). In
addition, our work presents a study into the role the downstream model plays
when performing speaker verification using SSL features.

Chen et al. [7] ran experiments to understand the components of pre-training
that affect the performance of SSL models when fine-tuned on the speaker
verification task. The authors used a weighted average of the hidden states,
which is then passed to a downstream model for learning the speaker
embeddings. Their results suggested that SSL models provide better features
for speaker verification compared to those extracted from a model trained on
the same dataset to perform automatic speech recognition. Chen et al. [8]
examined the impact of different pre-training methods, SSL model sizes, and
training datasets on the downstream performance. The results reaffirmed the
benefit of SSL features over filter-banks; and the importance of data
augmentation for achieving state-of-the-art performance when training the
downstream model. In contrast to [7] and [8], our experiments do not use a
fixed downstream architecture; instead, we focus on re-designing the
downstream model given the differences between filter-banks and SSL features.

Peng et al. [10] studied parameter-efficient fine-tuning to adapt pre-trained
SSL models for speaker verification. They showed that using adaptors is better
than fine-tuning the full SSL model in low-resource settings. Stafylakis et
al. [9] proposed correlation pooling, an approach for aggregating frame-level
SSL features across time to induce fixed-size utterance-level features. The
authors showed that replacing statistics pooling with correlation pooling
improved the performance of speaker verification when using SSL features. In
contrast to [10] and [9], our work does not study adaptors (i.e., the addition
of modules between the layers of the pre-trained SSL model)—we use SSL models
as generic feature extractors and focus on the design of the full downstream
model, not just the pooling mechanism.

Table 2: An unconstrained speaker verification setup yields a lower equal error rate (EER, $\%$) on VoxCeleb1 compared to SUPERB. We fine-tune both the WavLM and ECAPA-TDNN models for the unconstrained setup; we include the VoxCeleb2 during fine-tuning and apply training-time augmentations. Model |  SUPERB |  Unconstrained
---|---|---
WavLM+ECAPA-TDNN |  $2.03$ |  $0.39$

##  3 Experiments

This work explores the design of the downstream speaker verification
architecture given the contrasting nature of filter-banks and SSL features. We
begin with an investigation into the speaker information that is captured by
state-of-the-art SSL methods (Section 3.1). We then run an ablation on the
downstream architecture to understand the role different components play in
speaker verification using SSL features (Section 3.2).

Table 3: We can simplify the downstream model for speaker verification when
using SSL features. The ``base'' SSL models were trained on LibriSpeech $960$
hr, and the ``large'' SSL models were trained on Libri-Light $60$k hr. The
downstream models were trained on the development set of VoxCeleb$1$. The
equal error rates (EERs, $\%$) are reported on the verification set of
VoxCeleb$1$.

| Downstream | Params. |  | EER (%) $\downarrow$
---|---|---|---|---
| FBank | HuBERT | wav2vec 2.0 | WavLM |  | HuBERT | wav2vec 2.0 | WavLM
| base | base | base |  | large | large | large
A |  x-vector [11, 25] |  $5.7$M | $9.56$ | $5.11$ | $6.02$ | $4.69$ |  | $5.98$ | $5.65$ | $3.77$
B | x-vector (our setup) |  $5.7$M | $9.95$ | $4.41$ | $5.12$ | $4.97$ |  | $5.28$ | $6.04$ | $4.04$
C |  Stafylakis et al. [9] | $-$ | $-$ | $-$ | $-$ | $-$ |  | $4.8$ | $-$ | $3.8$
D.$0$ | ECAPA-TDNN |  $8$M | $8.78$ | $3.81$ | $4.63$ | $3.67$ |  | $3.14$ | $6.35$ | $2.03$
|  $\rightarrow$ w/o frame-level encoder |  |  |  |  |  |  |  |  |
D.$1$ |  $\rightarrow$ w/ channel & context stats. pooling |  $725$K | $8.75$ | $2.95$ | $3.41$ | $2.71$ |  | $2.46$ | $2.60$ | $1.55$
D.$2$ |  $\rightarrow$ w/ attentive stats. pooling |  $725$K | $9.26$ | $2.87$ | $3.09$ | $2.51$ |  | $2.37$ | $2.56$ | $1.70$
D.$3$ |  $\rightarrow$ w/ stats. pooling |  $199$K | $10.74$ | $3.11$ | $3.19$ | $2.83$ |  | $2.34$ | $2.63$ | $1.56$
|  $\Delta(\text{D.$0$},\text{D.$3$})$ ($\%$) $\uparrow$ | $97.51$ | $-22.32$ | $18.37$ | $31.10$ | $22.89$ |  | $25.48$ | $58.58$ | $23.15$

###  3.1 What Speaker Information is Captured by SSL?

Motivation. Results from SUPERB [11] suggest that SSL models capture speaker
information even though these models were trained with frame-level objectives
that resemble the objective of automatic speech recognition. The captured
speaker information can be undesirable if the goal is to learn models that
focus on content related tasks [20]. We identified two limitations in prior
analyses that we address in our work. First, prior analyses focused only on
reporting the speaker verification performances of SSL models on the VoxCeleb1
dataset [26]. However, VoxCeleb1 is an out-of-domain data for the SSL models
that are evaluated in the literature—the models are trained on audiobooks.
Thus it is unclear if the performance degradation comes from out-of-domain
data, or from the task itself. Second, prior analyses used SSL features along
with either x-vector or ECAPA-TDNN architectures for the verification task.
However, there is evidence suggesting that the performance and the ranking is
highly sensitive to the choice of the downstream model [27]. To this end, we
seek to understand the capability of SSL models to do speaker verification
without a downstream model (i.e., zero-shot capability) on both in-domain and
out-of-domain data.

Approach. We extract frame-level features,
$\textbf{H}^{l}=\\{\textbf{h}_{1}^{l},\textbf{h}_{2}^{l},\dots,\textbf{h}_{T}^{l}\\}$,
from layer $l\in\\{1,\dots,L\\}$, and then induce a fixed-dimensional
representation by aggregating all $T$ frame-level features by computing the
mean and standard deviation across time; where $L$ is the number of layers in
the SSL model and $T$ is the number of frames in the representation. We use
the cosine score to measure the similarity for trial pairs.

Setup. We assess the zero-shot speaker verification capability of SSL methods
on LibriSpeech (in-domain) and VoxCeleb1 (out-of-domain). We use the test set
of VoxCeleb1 and the test-clean and test-other sets of LibriSpeech. We create
a verification split for LibriSpeech by: (1) sampling all utterances that are
$8<x<12$ seconds; (2) creating a list of all possible pairs; and (3) down-
sampling the negative class samples such that we retain a $1$:$5$ positive-to-
negative ratio in the trial list. We follow above process separately for the
test-clean and test-other sets of LibriSpeech and then merge the two to obtain
a list with $73$ speakers and $1908$ pairs.

Results. The zero-shot speaker verification capability for several SSL models
is shown in Table 1. We use zero-shot performance on filter-banks as our
baseline and discuss our findings below.

Do SSL features highlight speaker characteristics beyond what filter-banks
highlight? Features from all pre-trained SSL models (except vq-wav2vec on in-
domain test set) provide improvements over filter-bank features. WavLM (large)
features improve the baseline performance by $65.3\%$ and $43.1\%$ on
LibriSpeech and VoxCeleb1, respectively. Even though vq-wav2vec features
degrade the baseline performance by $58.3\%$ on LibriSpeech, it outperforms
the baseline by $6.4\%$ on VoxCeleb1. This result shows that SSL features can
provide an improvement over filter-bank features in the zero-shot setting.
Furthermore, the results reaffirm that the augmentation strategy used in WavLM
training effectively incorporates more speaker information in the
representation.

Does the domain mis-match impact the relative improvements from SSL features
compared to filter-banks? SUPERB evaluates the quality of speaker verification
models on the VoxCeleb1 dataset. However, most of the SSL models are trained
on audiobook data. Our results show that we obtain higher relative
improvements on LibriSpeech compared to VoxCeleb1. We compute Spearman's
$\rho$ between the relative improvements on the two datasets and obtain $0.66$
($p=0.019$). It suggests that, while there is a strong correlation between in-
domain and out-of-domain relative improvements, the rankings of the SSL models
are not identical and they depend on the domain of the downstream data (even
for the same task).

Are bigger SSL models better at capturing speaker information compared to
smaller models? Increasing the capacity of wav$2$vec $2.0$ from $95.04$M to
$317.38$M while using the same $960$ hours of training data increases the
relative improvements from $23.6\%$ to $63.9\%$ and from $17.8\%$ to $24.0\%$
on LibriSpeech and VoxCeleb1, respectively. This finding is also true for
WavLM, where increasing the capacity from $94.70$M to $316.62$M while using
the same $94$k hours of data increases the relative improvements from $44.4\%$
to $65.3\%$ and from $22.5\%$ to $43.1\%$ on LibriSpeech and VoxCeleb1,
respectively. Our results suggest that increasing the model size provides the
model with capacity to capture more information, including speaker
information.

Is the prior from SSL model architecture adequate for capturing speaker
characteristics? In the vision domain, Ulyanov et al. [28] showed that the
structure of convolutional networks provides a strong prior for learning. We
ask whether or not SSL speech model architecture alone (i.e., no learning)
provides appropriate priors for capturing speaker information from raw
waveforms. We find that random SSL models, on average, drop the performance by
$131.6\%$ for in-domain setup compared to baseline and drop the performance by
$8.4\%$ for out-of-domain setup, suggesting that the architecture alone is
insufficient for capturing speaker characteristics.

###  3.2 Can we Simplify the Downstream Model?

Motivation. The results from Section 3.1 reaffirm that SSL models capture
speaker information beyond what is captured with filter-banks. This finding
suggests that we may need a different model for downstream task because the
original downstream models were designed for filter-banks. We re-visit the
ECAPA-TDNN architecture [13], noting the impact of its components on the
downstream speaker verification task when used with SSL features.

Downstream Model. The ECAPA-TDNN model introduced enhancements to the Time
Delay Neural Network (TDNN) architecture and the attentive statistics pooling
layer to address the local spatial modeling limitations of convolutional
networks. We study the utility of the frame-level encoder and the pooling
mechanism when used with SSL features.

Frame-level Encoder. The frame-level encoder includes Res2Net blocks, Squeeze-
Excitation (SE) blocks, and Multi-layer Feature Aggregation (MFA). The SE
blocks were introduced to the the ECAPA-TDNN architecture to ``rescale the
frame-level features given global properties of the recording'' [13]. MFA was
introduced so the model can exploit information from multiple layers before
pooling.

Channel- and Context-dependent Statistics Pooling. The ECAPA-TDNN architecture
extends the temporal attention statistics from [29] to also depend on the
channel dimension. This change allows the model to attend to different time
frames for different features. The attention module calculates a scalar score
for each frame given the channel: $z_{t,c}=f_{c}(\textbf{h}_{t})$, where
$\textbf{h}_{t}$ are the hidden states from the previous layer at time $t$;
and $f_{c}$ is the channel-dependent non-linear transformation. The scalar
scores are normalized across time per channel. The temporal context of
attentive pooling is also extended by concatenating the global context
features.

The architectural enhancements that were introduced in downstream models can
be unnecessary when these models are used with SSL features. State-of-the-art
SSL models use the transformer model in their architecture. The output at each
frame from a transformer captures the full context of the utterance and the
multi-head attention mechanism enables each head to focus on different aspects
of the utterance. To this end, we ablate the ECAPA-TDNN architecture's
structure to study the enhancements' impact on the overall performance when
using SSL features.

Setup. We follow the SUPERB setup for speaker verification using SSL features.
We pass an input waveform through a frozen SSL model and take the weighted sum
of the hidden states from each layer to produce the output sequence:
$\textbf{o}_{t}=\sum_{l=1}^{L}w^{l}\cdot\textbf{h}_{t}^{l}$, where
$\textbf{h}_{t}^{l}$ are the hidden states from layer $l$ at time $t$; and
$w^{l}$ is the normalized scalar weight for layer $l$. The output sequence is
then fed into a downstream ECAPA-TDNN model to produce the embeddings:
$\textbf{e}=\text{ECAPA-
TDNN}(\textbf{o}_{1},\textbf{o}_{2},\dots,\textbf{o}_{T})$. The summation
weights and the downstream model parameters are trained to classify speakers
with an additive angular margin softmax [30] loss, where a scale of $30$ and a
margin of $0.4$ are used. We use $512$ channels for the convolutional frame
layers in ECAPA-TDNN, train the models on $4$ GPUs, and use the following
hyper-parameters: $\text{optim}=\text{AdamW}$ [31]; $\text{lr}=5.0e^{-5}$;
$\text{batch size}=40$. We train the models for $100\,000$ steps and create a
checkpoint every $5000$ steps. We report the best performance from all
checkpoints in accordance with SUPERB.

Note. Our work aims to study how well SSL models capture speaker information
and how to extract this information effectively from frozen SSL models. Our
goal is _not_ to achieve the best possible speaker verification performance—a
goal achievable by fine-tuning the SSL model on the downstream task. We run an
experiment to highlight the difference in performance on VoxCeleb1 when fixing
the SSL model (WavLM) according to SUPERB and when jointly fine-tuning both
WavLM and downstream models. Table 2 shows that we can achieve an EER of
$0.39\%$ when the SSL and downstream models are fine-tuned simultaneously,
highlighting the performance differences due to the SUPERB setup. Despite this
difference in performance, we use the SUPERB setup because it is a widely used
setup for benchmarking the quality of SSL features, and our focus is on
limited training data scenarios for the downstream task.

Results. The results of our downstream ablation are reported in Table 3 and we
discuss our findings below.

First, we replicate the x-vector setups reported in prior works to ensure a
fair comparison. Our x-vector setups provide, on average, a $2.32\%$ relative
improvement in performance compared to x-vector performance reported in [11,
25]. This result establishes that our setup is competitive and reflects state-
of-the-art performance on SUPERB. Replacing the x-vector with the ECAPA-TDNN
model improves the performance by $11.76\%$ given the filter-bank features and
$22.41\%$ on average for the SSL setups, reaffirming the utility of the
structural enhancements employed in ECAPA-TDNN.

We remove the frame-level encoder from the architecture and evaluate three
different pooling mechanisms: channel- and context-dependent statistics
pooling proposed with ECAPA-TDNN model, attentive statistics pooling from
[29], and statistics pooling from [12]. Removing the frame-level encoder
reduces the model's capability to use features from multiple layers and some
of its capability to exploit contextual information. ECAPA-TDNN's channel-
attentive pooling mechanism without the frame-level encoder improves filter-
bank performance by $0.34\%$ but improves the average SSL performance by
$29.91\%$. This result suggests that SSL models do not require the same frame-
level processing that filter-banks require for extracting speaker information.

Replacing channel- and context-dependent statistics pooling with attentive
statistics pooling from [29] drops the performance by $5.83\%$ for the filter-
bank model but improves the average performance by $2.5\%$ for the SSL models.
This result suggests that channel-attention is important when using filter-
bank features but not when using SSL features. Finally, replacing the
attentive statistics pooling with non-weighted statistics pooling reduces
filter-bank performance by $15.98\%$ and reduces the average SSL performance
by $2.93\%$, suggesting that the attention mechanism is less important for SSL
models compared to filter-banks for speaker verification.

Figure 1: The simplified downstream model (D.3 from Table 3) performs better
with less data compared to full downstream model (D.0 from Table 3). The equal
error rate (EER, $\%$) on VoxCeleb1 is reported under three data conditions:
$20\%$, $60\%$, and $100\%$ of the training speakers.

Data Efficiency. We further create a random subset of the VoxCeleb$1$
containing only $20\%$ of the training speakers to study the data efficiency
of the simplified downstream model similar to [32]. Then, we gradually
increase the number of training speakers by adding randomly selected speakers
until we cover $100\%$ of the data. We evaluate the downstream models using
three features: filter-banks, HuBERT (base), and HuBERT (large). We focus on
HuBERT in our analysis because it is widely used and it is used for pre-
training WavLM. The results in Figure 1 show that the simplified downstream
model (D.3 from Table 3) is more data efficient; the model achieves better
performance when using only $60\%$ of the data for both HuBERT setups.

##  4 Conclusion

We observed that state-of-the-art SSL features were used in downstream speaker
verification models designed originally for filter-bank features. We
hypothesized that downstream models can be simplified because SSL models have
potentially done some of the learning required for the task. Our results
suggest that, although we can't completely remove the downstream model when
using SSL features, we can simplify the model to use $97.51\%$ fewer
parameters and obtain a $29.93\%$ average improvement in performance compared
to the original model on SUPERB. We also showed that the simplified downstream
models require less training data—the model uses $60\%$ of the original data
to achieve better performance compared to the full model.

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[1,2]Iman Taghavi [1,2,5]Sudip Shekhar [1,2,3]and Lukas Chrostowski

1]Department of Electrical and Computer Engineering, University of British
Columbia, 2332 Main Mall, Vancouver, V6T 1Z4, B.C., Canada

2]Dream Photonics, 2366 Main Mall, Vancouver, B.C., Canada

3]Quantum Matter Institute, University of British Columbia, 2355 E Mall,
Vancouver, V6T 1Z4, B.C., Canada

4]Polaris Electro-Optics, 3400 Industrial Ln, 3130 25th St, Broomfield, 80020,
CO, USA

5]Dream Photonics Inc., Woodinville, WA, USA

# GHz-rate optical phase shift in light matter interaction-engineered,
silicon-ferroelectric nematic liquid crystals

<EMAIL_ADDRESS>Omid Esmaeeli  Sheri Jahan Chowdhury  Matthew Mitchell
Donald Witt  Cory Pecinovsky  Jason Sickler  Nicolas A.F. Jaeger
<EMAIL_ADDRESS><EMAIL_ADDRESS>[  [  [  [  [

###### Abstract

Organic electro-optic (OEO) materials have demonstrated promising performance
in developing electro-optic phase shifters (EOPS) and modulators compared to
their inorganic counterparts. Integration with other devices in a silicon
photonic (SiP) process, simple nanofabrication, and temperature/aging
robustness remain to be developed for this class of hybrid material platforms.
In particular, electro-optic (EO) polymers need an electro-thermal poling
method, which has limited their potential and utilization in large-scale SiP.
Devices made of paraelectric nematic liquid crystals (PN-LC), another primary
type of OEO material, feature a very efficient but slow phase shift mechanism.
We present a general-purpose EOPS that applies to various modulator
embodiments to address these concerns. Based on that, we report a GHz-fast
phase shift in a newly discovered family of OEO, namely ferroelectric nematic
liquid crystals (FN-LC), which finally enables liquid crystals to have
significant second-order nonlinear optical coefficients and associated Pockels
effect. The new material avoids poling issues associated with EO polymers and
can pave the way for hybrid silicon-OEO systems with CMOS-foundry
compatibility. Furthermore, we propose a finger-loaded, non-slotted waveguide
that enhances light-matter interaction, allowing us to achieve DC and AC
modulation efficiencies of $\approx$ 0.25 V$\cdot$mm and 25.7 V$\cdot$mm,
respectively, an on-chip insertion loss of $\approx$ 4 dB, and an EO bandwidth
of $f_{\text{-6dB}}$ > 4.18 GHz. The remaining figures of merit for our
poling-free EOPS are equivalent to EO polymer-enabled devices with fewer
manufacturing difficulties. We demonstrate an electrically and photonically
packaged chip that contains >100 silicon-FN-LC modulators to evaluate the
large-scale integration of our poling-free phase shifters and modulators.

###### keywords:

Silicon organic hybrid material, electro optic polymer, liquid crystal, phase
shifter, modulator

Silicon and silicon nitride photonics have enabled several recent
technological advancements, and future roadmaps have been designed based on
their capabilities and integration with established CMOS foundries [1]. The
electro-optic phase shifter (EOPS) [2, 3, 4, 5] is one of the most fundamental
components upon which other essential building blocks in photonic integrated
circuits (PIC) are based, including electro-optic (EO) switches [6, 7, 8], EO
modulators [9], optical interconnects [10, 11, 12], and comb generators [13].
Traditional phase shift mechanisms often show poor overall performance, such
as limited EO bandwidth (BW) and high static energy consumption
($E_{\text{stat}}$) when leveraging the thermo-optic effect or free-carrier
dispersion effect with traveling wave modulators. Free carrier dispersion also
leads to doping-induced insertion loss (IL). Innovations in hybrid material
platforms promise novel solutions to traditional Si photonics (SiP)
shortcomings. However, they typically face significant challenges, such as
several complex nanofabrication stages, scaling, and interaction with current
CMOS foundries. Modulators based on indium tin oxide (ITO) have recently
experienced notable improvements [9, 14, 15, 16]. The additional operations
necessary for ITO/insulator thin-film deposition, demanding quality control
methods, and their low extinction ratio (ER) suggest further R&D needs [17].
Carrier-free phase shift processes, such as the Pockels effect, are among the
more appealing techniques, especially regarding EO BW and energy consumption.
These metrics and low IL can excel in LiNbO3 on silicon (LNOI) [18]. Due to
the low EO coefficient of LiNbO3, however, phase shifters based on LNOI
require either a large footprint or a high drive voltage ($V_{\uppi}$), where
$V_{\uppi}$ is the voltage necessary to produce the $\uppi$ shift. A material
system based on barium titanate (BTO) can simultaneously meet the requirements
of low IL and high EO BW [19, 20]. Despite having a significant EO
coefficient, BTO is unable to fully utilize the improved light-matter
interactions (LMI) provided by some waveguide topologies, such as slot
waveguides, failing to give the record-low modulation efficiencies
($V_{\uppi}L$), where $L$ is the EOPS effective length [21]. BTO also involves
more meticulous fabrication steps, loses its high EO efficiency at cryogenic
temperatures, and necessitates process controls for optimum domain development
[22].

Furthermore, the preceding approaches cannot meet the trade-offs between
various device metrics of a particular modulator, such as size, EO and optical
BW, IL, $V_{\uppi}$, $E_{\mathrm{stat}}$, and dynamic energy consumption
($E_{\mathrm{dyn}}$) [23, 24]. Hybrid integration of Si with organic electro-
optic (OEO) materials has been proposed to overcome this shortcoming. They
have advantages over their inorganic equivalents due to a combination of their
EO and physicochemical characteristics. The EO properties of OEO materials,
including the Pockels factor ($n^{3}r_{33}$) and optical loss, have
continuously progressed over the last two decades ($n^{3}r_{33}$ as large as
9000 pm/V and absorption coefficients as low as $1.8\times 10^{-5}$ have been
reported [25], where $n$ is the OEO refractive index and $r_{33}$ represents
the Pockels coefficient). Thanks to their liquid state, an OEO can infiltrate
nanostructures during the coating step and benefit from the enhanced LMI.
Along with the resultant high modulation efficiencies, the low dielectric
dispersion [26] of OEO promises better modulators. As a result, <1 V, sub-mm-
long Mach-Zehnder modulators (MZM) with IL < 1 dB, EO BW surpassing 100 GHz,
and $E_{\mathrm{dyn}}<$100 $f$J/bit have been enabled [27]. Such an all-
inclusive, miniaturized modulator can work in extreme temperatures (as high as
383 K (110${}^{\text{o}}$C) [28] and as low as 4 K [29, 30]), which encompass
the crucial requirements for a state-of-the-art modulator.

While EO polymers have attracted increased attention mainly because of their
remarkable EO characteristics, their application to photonic-integrated
circuits (PIC) has challenges. Multiple process steps and often hazardous
solvents are needed to prepare EO polymer thin films, necessitating equipment
for precise mixing, coating, and drying. In addition, to align chromophores in
an EO polymer material, an electro-thermal poling step is necessary. Depending
on the waveguide geometry and accompanying LMI, dedicated DC lines may be
required on a larger scale. Despite considerable breakthroughs in producing
thermally and temporally stable polymers, not all poled polymers are resilient
to high temperatures ([28]), aging ([31]), and poling-induced optical loss
([32]). For practical applications, the devices may still require a certain
level of hermetic sealing to become temperature- and humidity-resistant. EO
polymers are also recognized for their lower resistance at higher
temperatures, which coincides with detrimental leakage currents. It leads to
decreased EO efficiency, which has a direct impact on device performance.
Additional nanofabrication steps have been identified as advantageous to
resolving this issue, such as exploiting a thin charge-barrier layer comprised
of alumina or titania created by atomic layer deposition,[33, 34]. Poling also
limits high-temperature excursions typical of back end-of-line (BEOL)
processing since such excursions would destroy the poling-induced order. The
problems above could increase the overall cost, add complexity, and jeopardize
the integration of polymer-based hybrid platforms.

Another class of OEO material is PN-LC, which provides a variety of efficient
but slow phase shift processes, such as the birefringence effect [35, 36, 3,
37]. Ultra-high modulation efficiencies have been reported using strong-LMI
implementations, including infiltrated slot waveguides with the material [2].
Unlike polymers, preparing PN-LC devices do not involve a solvent that must be
evaporated during post-baking processes. It simplifies the spin coating
process and may allow for new coating approaches. The material, for example,
can be coated on photonic parts via microfluidic channels or fluid dispensing.
A PN-LC-based platform is attractive for realizing EO switches, phase
shifters, or shutters, but it is not desirable for high-speed applications.

A new state of matter, ferroelectric nematic liquid crystals (FN-LC), has
recently been discovered [38, 39]. In the landscape of organic EO materials,
FN-LCs are situated between poled polymers, organic nonlinear optic (NLO)
crystals, and PN-LCs, bringing the most desirable aspects of each (see table
I). Like poled polymers and organic NLO crystals, FN-LCs are non-
centrosymmetric and have nonzero second-order susceptibilities
($\upchi^{(2)}$). Like organic NLO crystals and PN-LCs, they organize
spontaneously–the ordered state is the thermodynamic minimum with significant
order parameters. Similar to PN-LCs, the alignment can be controlled over
large areas by applying alignment layers at the interface or small external
fields. They can also be switched like PN-LCs, with a reorientation of the
fast and slow axes in an external field. A unique feature of the FN-LC is that
the molecular long axis (slow axis) is highly polarizable and coincident with
the director and the polar axis (Fig. 1(a) inset). This creates the condition
for achieving very large spontaneous polarizations and large second order
nonlinearities, which have been observed by second harmonic generation
measurements [40]. These nonlinearities have been dramatically enhanced by
adding NLO dyes to the polar matrix of the FN-LC host material [41]. However,
what remains to be demonstrated is the EO effect (i.e., Pockels effect)
observed in other non-centrosymmetric organic materials. In this work, we show
that FN-LCs can be integrated with similar ease as PN-LCs onto a SiP platform,
that alignment of the polar axis can be easily achieved over the length of the
device, and that a significant EO response can be observed.

To enhance LMI, waveguides such as Si [42] and plasmonic [43] slotted, sub-
wavelength grating (SWG) [44], photonic-crystal [45], and thinned [28], would
traditionally be used as EOPS in modulators. However, they often add excessive
loss [46], limit optical BW, and need extra fabrication stages, some of which
are not quite CMOS-compatible. For instance, opening oxide cladding over
isolated Si islands of SWG or metallic slots of plasmonic waveguides may
violate design rules in wafer nanofabrication. Also, exploiting the benefits
of structures such as thinned waveguides necessitates escalators from complete
to partial etch Si, which are not readily available. Geometries required for
efficient and low-loss mode converters, such as strip-to-slot, are not always
accessible through nanofabrication runs or have integration challenges with
the rest of the PIC. On the other hand, a non-slotted waveguide does not have
these issues at the cost of offering a weak LMI [47], thus requiring a high
voltage for poling and driving. The device size and EO BW must then be
compromised to keep the voltage within the ranges supplied by CMOS drivers.

We propose a finger-loaded non-slotted (FNS) waveguide consisting of two
strip-to-finger-loaded mode converters to resolve this trade-off, as seen in
Fig. 1(a). In analogy to segmented slotted [48] and non-slotted [49]
topologies, this structure eliminates the misalignment problem seen in strip-
loaded slot waveguides by offering at least one fewer step for the
nanofabrication of the partially etched slab layers. The periodicity and duty
cycle of the subwavelength structure of the FNS waveguide are selected to
produce a better balance between electrical and optical loss penalties,
another prevalent difficulty in slot waveguides. The waveguide core,
sandwiched between fingers, is narrowed to $W_{\text{c}}=$ 300 nm to localize
light in the gap between them, as seen in Fig. 2. Compared to a nonslotted
structure, the overlap integral between optical ($\widehat{E}_{\text{x}}$) and
electrical ($\overrightarrow{E_{\text{e}}}$) modal fields ($\Gamma$) is
enhanced by a factor of $\approx 2$. At the same time, the effective electrode
separation is $\approx 10$ times smaller. Consequently, the essential figure
of merit evaluated by the modulation efficiency-loss product (i.e.,
$V_{\uppi}L\upalpha$) remains $\approx 5$ times better despite the excess loss
caused by the subwavelength structure of the FNS topology. Our simulations
revealed that strip-to-finger-loaded mode converters did not substantially
impact total EOPS loss. Due to its SWG structure, FNS topology utilizes
capillary force action to mitigate material infiltration, another ubiquitous
issue in slot waveguides that frequently calls for oxide undercutting [50].

The constructed devices must then be aligned with an electric field. Because
of its pre-ordered molecular orientation and sensitivity to an external field,
FN-LC was found to be fully aligned with $\approx 10$ times smaller
$\overrightarrow{E_{\text{e}}}$ than required for poling EO polymers [51], for
similar waveguide structures. The process was carried out at room temperature;
no precise temperature monitor was necessary. These relaxed voltage and
temperature conditions have additional advantages. First, an inert gas such as
N2 is not required around the chip during alignment to avoid oxidation. The
FN-LC alignment process is relatively safer because there is no off-gassing.
Within the scope of our characterization setup, the device’s performance
exhibited little temperature susceptibility thanks to the non-electro-thermal
alignment technique. To be more precise, no performance aging was discovered
for the FN-LC-coated devices over 150 hours of operation in the range of
$10\sim 50^{\circ}$C under full optical and electrical load. EO polymers lose
their poling efficiency beyond their glass transition temperature ($\approx
80\sim 100^{\circ}$C). To show that FN-LC is useful at these temperatures,
more accelerated aging tests must be done in the future. The lower voltage
required for alignment simplifies design concerns for the large-scale
integration of FN-LC-enabled photonic devices in which the same RF lines can
be utilized. Finally, a fully-aligned FN-LC MZM showed
$\approx\leavevmode\nobreak\ $2 to 3 dB less material absorption loss, which
we attribute to the formation of a monodomain over the length of the device
and reduced scattering loss.

Monitoring optical loss and leakage current throughout the alignment process
provides critical information. As seen in Fig. 3(a)-(b), changes in optical
loss followed by saturation indicate that domain formation has been completed.
In some cases, the change was permanent, indicating that the optic axis
continues to remain in a vertical posture. Following the alignment, we
performed DC characterization of the optical transmission, as shown in Fig.
3(c), achieving an optical ER of $\approx$ 26 dB and
$V_{\uppi,\text{DC}}\approx$ 0.5 V. The birefringence effect is responsible
for this considerable shift.

A more comprehensive figure of merit for a given EOPS is the pure phase
efficiency ($\eta_{\text{pps}}$). The metric is defined as $(\partial
n/\partial v)\leavevmode\nobreak\ /(\partial\upkappa/\partial v$), where $n$
and $\upkappa$ are the real and imaginary parts of the complex refractive
index ($n+i\upkappa$), respectively. $V_{\uppi}$ and loss can be correlated to
the estimated values for $\partial n/\partial v$ and
$\partial\upkappa/\partial v$. The optical ER, $V_{\uppi}L\upalpha$,
$\eta_{\text{pps}}$ comprise a comprehensive assessment of EOPS
appropriateness as summarized in Table LABEL:FOMtable. For our proposed FNS
waveguide, significantly higher records up to $\eta_{\text{pps}}\approx$ 88.9
have been achieved. We believe the proposed EOPS’ improved phase shift
performance stems from combining our device design and the material.

Without a high-speed phase shift mechanism, FN-LC might not demonstrate any
significant benefit over traditional PN-LC, in which the slower mechanisms
mostly dominate the response. Various aspects of such a frequency response
characterization of the FN-LC-coated devices are shown in Fig. 4, and the
measurement details are covered in Methods. SWG-based grating couplers (GC)
were used for light injection into the devices for this step [52, 53, 54]. The
$S$-parameter collected by a Vector Network Analyzer (VNA) indicates that
$f_{\text{-6dB}}>$ 4.18 GHz. This achievement demonstrates a phase shift
mechanism with a rise/fall time in the nanosecond range, while PN-LC is
limited to functioning in the millisecond range [2]. Accordingly, we employed
$S_{21}$ data and an analytical approach (see Methods) to evaluate the EO
properties of the FN-LC material and the proposed EOPS. As a result, an EO
coefficient of $r_{33}\approx$ 24 pm/V and an AC modulation efficiency of
$V_{\uppi}L\approx$ 25.7 (V$\cdot$mm) were estimated. The metrics are still
significantly lower than the maximum record for EO polymers. This being the
first demonstration, promises further improvement in the future. The frequency
span of the response was confined to the equipment and electrical wire bonding
(EWB) used to drive the EOPS. Nonetheless, it appears that the FN-LC phase
shift mechanism switches from a strong birefringence effect at low frequencies
to a weaker but faster Pockels effect at higher frequencies. Complex phase
manipulation is frequently necessary to implement advanced modulation systems,
such as coherent transceivers [55]. Inefficient thermal heaters are commonly
employed to generate a slow phase shift, as seen in Fig. 4(c). Including slow
and fast EOPS in a single material may be an attractive attribute of the FN-
LC-based platform.

To evaluate the large-scale capability of our EOPS structures, we created a
SiP chip with the designed MZM on an area of 0.5 mm2. The chip was
photonically wire-bonded (PWB) to an external laser source via a fiber array
(FA) block. The PWB routes were established using adiabatic surface tapers at
the chip edge, followed by selective patterning of FN-LC on active components
in a post-processing step. Because of its high viscosity, FN-LC can be applied
locally, allowing for more controlled integration with the rest of the chip’s
various components, as depicted in Fig. 5. Thanks to the reduced alignment
voltage enabled by utilizing FNS waveguides in our Si-FN-LC design, the step
can be paired with a $V_{\text{DC}}$, which is used to bias modulators at
their quadrature point. Regular EWB and a printed circuit board (PCB) were
used to conduct alignment and drive the modulators. A hypothetical EO
polymeric version of this chip might necessitate on-chip routing
considerations and a separate PCB with high-voltage handling capabilities for
poling. It is the only OEO-based SiP chip with >100 modulators that has been
reported to our knowledge, which we credit partly to overcoming the poling
difficulties by utilizing the poling-free materials described here.

For the first time, we demonstrated GHz-fast EO phase shift and modulation in
a novel class of OEO materials, namely ferroelectric nematic liquid crystal.
In contrast to EO polymers, we established that the material does not require
any electro-thermal poling processes for alignment. Indeed, the material can
be oriented during regular modulator RF operation. To simplify the
nanofabrication steps, we also engineered the light-matter interaction using a
finger-loaded, non-slotted waveguide infiltrated with the material. Using FNS
phase shifters as small as 500 $\upmu$m in a push-pull MZM, we achieved a DC
modulation efficiency of $V_{\uppi}L\approx$ 0.25 V$\cdot$mm, an optical ER of
$\approx$ 26 dB, and an insertion loss of $\approx$ 4 dB. An excellent phase
shift efficiency in the order of $\partial n/\partial\upkappa\approx$ 88.9 was
estimated, which we attribute to the material and the FNS waveguide employed
in this work. Most importantly, we discovered a high-speed phase shift
mechanism with an EO BW > 4.18 GHz that outperforms the stronger but slower
birefringence effect found in classic paraelectric-nematic liquid crystals.
The BW of our FN-LC-covered modulator is limited by the experiment setup, not
the suggested devices or the material. Also, an analytical approach was
introduced to estimate the Pockels coefficient of the material, where an AC
modulation efficiency of $V_{\uppi}L\approx$ 25.7 V$\cdot$mm was obtained
owing to a modest $r_{33}\approx$ 24 pm/V at $f=4.18$ MHz. As a sufficiently
reliable and stable material platform for practical applications that can
scale, the comparatively low modulation efficiency at higher speeds for this
first-ever prototype is still a breakthrough and a harbinger of further
improvements.

The two novelties we combined in this work (the FNS waveguide and the FN-LC
material) to create a poling-free Si-organic hybrid platform may lay the
foundations for new hybrid photonic integrated circuits with comparable device
metrics to those of EO polymers but less stringent post-fabrication steps. One
of the main benefits of this result, which has yet to be thoroughly validated,
is that no electro-thermal poling step is necessary for the alignment process.
Future research will investigate the performance of our proposed poling-free
Si-organic modulators based on FN-LC at cryogenic temperatures, which can
benefit from better material elasticity.

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## Acknowledgements

The Natural Sciences and Engineering Research Council of Canada (NSERC), the
SiEPICfab consortium, the B.C. Knowledge Development Fund (BCKDF), the Canada
Foundation for Innovation (CFI), MITACS, and the Schmidt Sciences funded this
research.

## Data availability

The supporting data for the conclusions of this investigation are available
upon reasonable request.

## Author contribution

This work was conceptualized by I.T., L.C., S.S. C.P., J.S., and N.J.
contributed materials and technical information, while S.J., D.W. and I.T.
built the organic Si modulator described in this paper. I.T. conducted
measurements while N.J. and O.E. helped with the modulator measurement setup.
The manuscript was written by I.T., L.C., and S.S., with assistance from all
authors.

## Methods

Device fabrication: The modulators were patterned on a standard 220 nm silicon
on an insulator wafer with a buried oxide layer of 3.5 $\upmu$m. An electron
beam lithography tool (JBX-8100FS) was used to design the waveguides via
positive tone resist (ZEP 520A-7) [53, 54]. After that, the devices were dry-
etched with an ICP plasma etcher tool (Oxford COBRA). Using maskless
lithography (Heidelberg MLA-150), metal electrodes (100 nm gold atop 5 nm
titanium as an adhesion layer) were deposited 4.85 $\upmu$m distant from the
core waveguide. A passive optical measurement was performed for reference
after completing the nanofabrication stages of photonic-only structures and
before metallization.

After metallization, both chips were cleaned gently using acetone, IPA, DI
water, and a N2 gun, followed by a $\approx$ 30 sec oxygen plasma cleaning for
surface passivation just before coating. For the OEO cladding, we used PM-158
(a proprietary FN-LC material optimized for enhanced $\chi^{(2)}$ obtained
from Polaris Electro-Optics, Inc.). According to our pre-coating viscosity
experiments, the cleaned chips benefitted from being warmed up (70-80∘C) to
reduce the viscosity of FN-LC during application to the chip. A glass
capillary tube was used to apply enough FN-LC to the desired areas. Finally,
the chips were cooled to 25∘C before characterization.

FN-LC alignment and DC characterization: While no significant relationship was
found between the timing of the alignment stage and the time passed after
coating FN-LC, the alignment step was performed on the same day. After
coating, the produced samples were mounted on an active EO probe station with
temperature control. A source meter unit (Keithley 2400) was employed to apply
step voltage. The light from a tunable CW laser (Agilent 8164A/81682A) is
coupled into grating couplers using an 8-degree polished angle FA. In this
phase, we tune the laser wavelength to the highest peak achievable by
overlapping the MZM spectrum with that of the GC or PWB. An InGaAs power
sensor (Agilent 81635A) detects light. Finally, the components of phase shift
efficiency (i.e., $\partial n/\partial v$ and $\partial\upkappa/\partial v$)
were extracted using the associated shifts in the vertical ($P_{\text{out}}$)
and horizontal ($\uplambda$) directions as a function of applied voltage.

AC characterization: An 18 GHz vector network analyzer (Keysigth FieldFox VNA)
was added for AC characterization, with port 1 amplified using a microwave
amplifier (SHF-s807). It is mixed with a proper amount of DC voltage for
optimum MZM performance and simultaneously for FN-LC alignment. A high-speed
photodetector (Thorlabs RXM40AF) was employed at the output, along with low-
noise amplifiers (picosecond 5828). The VNA data was utilized to evaluate the
device $S$-parameters. The devices were aged at a regulated temperature (25∘C)
for $\approx$ 150 hours with no humidity control or hermetic sealing applied,
with light ($P_{\text{opt,in}}$ = 8 dBm) and an RF electrical signal ($v$ =
1.59 V) applied.

The material EO coefficient of FN-LC (i.e., $r_{33}$) was post-processed using
the analytical formula [50]:

$S_{21}=20\times
log\Biggl{[}\upalpha_{\text{opt}}\times\frac{\partial(p_{\text{mod}})}{\partial(n)}\frac{\partial(n)}{\partial(v)}\frac{\partial(v_{\text{det}})}{\partial(p_{\text{det}})}\times\leavevmode\nobreak\
G_{\text{RF}}\Biggr{]}$ (1)

where $G_{\text{RF}}$ is the calibrated gain of the modulator link,
$\upalpha_{\text{opt}}$ is the total optical loss, $p_{\text{mod}}$ is the
optical output of the MZM, $p_{\text{det}}$ ($v_{\text{det}}$) is the optical
(electrical) input (output) of the detector, $n$ is the effective index of the
FNS waveguide covered with FN-LC, and $v$ is the MZM drive voltage,
respectively. Here, $\partial(v_{\text{det}})/\partial(p_{\text{det}})$ and
$\partial(n)/\partial(v)$ correspond to the detector and the MZM
sensitivities. The latter is related to $V_{\uppi}$ and, finally, to $r_{33}$
by:

$V_{\uppi}=\frac{\uplambda}{2L}\Biggl{[}\frac{\partial(n)}{\partial(v)}\Biggr{]}^{-1},$
(2)
$r_{33}=\frac{2d}{n^{3}\Gamma}\Biggl{[}\frac{\partial(n)}{\partial(v)}\Biggr{]}$
(3)

where $d$ denotes the distance between the tip of two encountering fingers and
$\Gamma$ is the overlap integral between optical ($\widehat{E}_{\text{x}}$)
and electrical ($\overrightarrow{E_{\text{e}}}$) modal fields [56] evaluated
by:

$\Gamma=\frac{1}{Z_{0}}\iiint_{V}n_{\text{eff}}\left(\overrightarrow{E_{\text{e}}}\right)\left|{\widehat{E}}_{x}\right|^{2}/\iint_{A}L\times
Re\left(\widehat{E}\times\widehat{H}^{\ast}\right)$ (4)

In Equation 4, n${}_{\text{eff}}$ is the field-dependent effective mode index
of FNS waveguide, A and V are the cross-section and volume of the gap between
fingers tip and core waveguide, Z0 is the free space impedance, and
$\widehat{H}$ is the magnetic field of the optical mode, respectively.

Figure 1: 3D representation of the modulator selectively covered by FN-LC. a
80-nm-wide fingers are used to carry the RF signals and alignment field
($\overrightarrow{E_{\text{align}}}$) to an area as close as $d_{\text{f-c}}=$
100 nm away from the $W_{\text{c}}=$ 300 nm-wide core. This design optimizes
the overlap integral between the optical and electrical fields ($\Gamma$)
while minimizing optical loss. An external light source, either through a
grating coupler or a photonic wirebond (PWB), feeds the optical signal. The
waveguides are identified by a $2\leavevmode\nobreak\ \upmu$m trench that
surrounds them. A positive-tone ebeam resist patterns the device. Inset: An
illustrative chemical structure and polar order of dipolar constituents of the
FN-LC phase, where $n$ denotes the molecular director, $P$ is the
polarization, and $D-\uppi-A$ is the donor-bridge-acceptor electronic
structure. b The layer stack-up of the MZM consists of two FNS waveguides in
each arm. c A zoomed-in diagram of the FNS waveguide with infiltrated FN-LC
ordered along $\overrightarrow{E_{\text{align}}}$. Figure 2: Waveguide design
simulation results. a The mode evolution in each arm of the MZM demonstrated
by a 10 $\upmu m$-long adiabatic strip-to-finger mode converter (section I)
coupled to a 3 $\upmu m$-long portion of the 500 $\upmu m$ FNS waveguide
(section II). Transverse electric optical field ($\widehat{E}_{\text{x}}$) in
x-slice (x = 0 nm) sampled b before and c after the converter, which
represents nonslotted and FNS geometries, respectively.
$\widehat{E}_{\text{x}}$ is further decentralized when the core section is
shrunk to $W_{\text{c}}=$ 300 nm because it is pushed to the two gaps
surrounding it, where normalized electrical field
($\overrightarrow{E_{\text{e}}}$) and FN-LC coexist. d
$\widehat{E}_{\text{x}}$ and e $\overrightarrow{E_{\text{e}}}$ in the y-slice
perspective (y = 110 nm). Compared to a non-slotted waveguide, the LMI-
engineered FNS waveguide acts like a double-slot waveguide to offer $\approx$
10 times improvement in $\overrightarrow{E_{\text{e}}}$ as a result of
improved electrode distance as well as $\approx$ 2 times higher $\Gamma$.
Figure 3: FN-LC alignment. a Polarization-originated leakage current and b
optical output in response to an external electric field
($\overrightarrow{E_{\text{align}}}\leavevmode\nobreak\
\propto\leavevmode\nobreak\ V_{\text{align}}/[d_{\text{f-c}}+W_{\text{c}}]$)
applied to the MZM arms. The measurement is repeated with increasing
$V_{\text{align}}$ until complete domain formation is achieved. c A
microscopic image of the MZM along with the dipolar order of FN-LC in a
section of its FNS waveguide in the cases of
$\overrightarrow{E_{\text{align}}}\neq 0$ and
$\overrightarrow{E_{\text{align}}}=0$ (other possibilities for dipolar order
could exist, since we don’t know what the ground state is with this topology).
d Optical output spectrum (normalized) versus applied voltage exhibiting
changes in the EOPS complex refractive index ($n+i\upkappa$ where $\triangle
n\gg\triangle\upkappa$ for an ideal EOPS). The data is summarized in Table
LABEL:FOMtable. Figure 4: Device characterizations. a Experimental setup using
a VNA and appropriate amplification to drive FN-LC MZM in push-pull
configuration. The DC voltage ($V_{\text{DC}}$) applied to bias the modulator
at its quadrature point can also be used to replace the alignment step (i.e.,
Fig. 3a-b). b MZM schematic showing two 500 $\upmu$m-long EOPS and low-loss
strip-to-finger-loaded mode converters equipped with GC and PWB optical I/O
channels. The alignment has been performed unipolarly, as evidenced by the
green arrows. However, the RF field is applied bipolarly to achieve push-pull
performance, as the dark blue arrows show. The proposed EOPS made of FN-LC
incorporates both slow and fast phase shift mechanisms compared to the
conventional approach, shown in c, in which an inefficient thermo-optic effect
is required in conjunction with a fast EOPS for advanced modulation schemes. d
Measured $S_{21}$ reveals the existence of a high-speed phase shift mechanism
with an EO BW of $f_{\text{-6dB}}>4.18\leavevmode\nobreak\ $GHz. Post-
processed AC values of $V_{\uppi}L$ based on extracted $r_{33}$ as a function
of frequency are also shown. e A false-colored scanning electron microscope
(SEM) image of the LMI-engineered FNS waveguide with a zoomed-in view of its
mode converter. Figure 5: FN-LC-enabled silicon photonic chip. a A close-up
picture of the chiplet incorporating 108 FN-LC MZMs, the majority of which
occupies a footprint of 0.4 $mm^{2}$. EWBs are used to carry RF signals at the
chip level. FN-LC has been selectively applied to a cluster of MZMs on the
left for demonstration purposes. Top-down GC and the PWB handle optical I/O
for tests at device and chip level, respectively. b A microscopic zoomed-in
view of the FN-LC-enabled modulators of various EOPS lengths. c An SEM picture
shows PWBs as extra optical I/O paths and their adiabatic surface tapers for
low-loss power coupling. A 3D laser printer tool (Vanguard Automation - Sonata
1000) uses the two-photon polymerization effect to create free-form optical
waveguides. The FN-LC needs to cover the EOPS sections on the SiP chip,
leaving adequate space for the polymer required for PWB construction. d A
magnified, false-colored SEM view of the PWB waveguide created between fibers
and the on-chip surface taper.

EO polymer Organic NLO1 PN-LC2 FN-LC3 Non-zero second-order susceptibility,
$\upchi^{(2)}$ $\CIRCLE$ $\CIRCLE$ $\CIRCLE$ Non-centro symmetric crystal
lattice $\CIRCLE$ $\CIRCLE$ $\CIRCLE$ Spontaneouse molecular organization
$\CIRCLE$ $\CIRCLE$ $\CIRCLE$ Alignments using interface layer or small
$\widehat{E}_{\text{x}}$ $\CIRCLE$ $\CIRCLE$ Reorientation of slow/fast axes
in response to external $\widehat{E}_{\text{x}}$ $\CIRCLE$ $\CIRCLE$ Large
spontaneous polarizations and second order nonlinearities $\CIRCLE$

Table 1: OEO material comparison

  * 1

Nonlinear optic

  * 2

Paraelectric nematic liquid crystal

  * 3

Ferroelectric nematic liquid crystal