# Unveiling the origins of quasi-phase matching spectral imperfections in
thin-film lithium niobate frequency doublers

Jie Zhao  1,3,* Xiaoting Li  2,3 Ting-Chen Hu  1 Ayed Al Sayem  1 Haochuan Li
2 Al Tate  1 Kwangwoong Kim  1 Rose Kopf  1 Pouria Sanjari  1,4 Mark Earnshaw
1 Nicolas K. Fontaine  1 Cheng Wang  2 and Andrea Blanco-Redondo1,5  1 Nokia
Bell Labs, 600 Mountain Avenue, Murray Hill, NJ 07974, USA
2 Department of Electrical Engineering & State Key Laboratory of Terahertz and
Millimeter Waves, City University of Hong Kong, Hong Kong, China
3 These authors contributed equally to this work.
4 Department of Electrical & Systems Engineering, University of Pennsylvania,
Philadelphia, PA 19104, USA
5CREOL, The College of Optics and Photonics, University of Central Florida,
Orlando, FL 32816, USA<EMAIL_ADDRESS>
††journal: opticajournal††articletype: Research Article

Thin-film lithium niobate (TFLN) based frequency doublers have been widely
recognized as essential components for both classical and quantum optical
communications. Nonetheless, the efficiency of these devices is hindered by
imperfections present in the quasi-phase matching (QPM) spectrum. In this
study, we present a thorough analysis of the spectral imperfections in TFLN
frequency doublers with varying lengths, ranging from 5 mm to 15 mm. Employing
a non-destructive diagnostic method based on scattered light imaging, we
identify the sources and waveguide sections that contribute to the
imperfections in the QPM spectrum. Furthermore, by mapping the TFLN film
thickness across the entire waveguiding regions, we successfully reproduce the
QPM spectra numerically, thus confirming the prominent influence of film
thickness variations on the observed spectral imperfections. This
comprehensive investigation provides valuable insights into the identification
and mitigation of spectral imperfections in TFLN-based frequency doublers,
paving the way toward the realization of nonlinear optical devices with
enhanced efficiency and improved spectral fidelity.

##  1 Introduction

Thin-film periodically poled lithium niobate (PPLN) waveguides offer a
compelling platform for achieving highly efficient wavelength conversion
devices, leveraging their high second-order nonlinear coefficient
($\chi^{(2)}$) and tight confinement of optical modes. These waveguides have
found diverse applications in second-harmonic generation (SHG) [1, 2],
entangled photon-pair generation [3, 4], optical parametric amplification [5],
optical isolation [6], and all-optical switching [7]. However, compared to
their bulk counterparts, these waveguides exhibit an increased susceptibility
to fabrication inhomogeneities, presenting a significant challenge to their
overall performance [8, 9, 10]. These inhomogeneities can give rise to
unfavorable effects in the QPM spectrum, including broadened central peaks and
unwanted side lobes, resulting in reduced conversion efficiency. Furthermore,
as phase errors accumulate along the waveguide’s length, longer devices
experience more pronounced impacts from fabrication non-uniformity, hindering
the further enhancement of power conversion efficiency [11]. To date, the
demonstrated thin-film PPLN devices have typically had lengths ranging between
4 and 6 mm. As a result, the overall conversion efficiency of these devices
remains lower than what has been reported for their bulk counterparts [12].
Therefore, it is imperative to direct research efforts towards investigating
approaches that can enable the fabrication of longer thin-film PPLN devices,
while ensuring good spectral fidelity. This research is crucial to bridge the
performance gap with their bulk counterparts and fully unlock the potential of
thin-film PPLN technology.

Prominent studies have examined the impact of fabrication inhomogeneities on
the QPM spectrum from Ti-indiffused and diced Zinc-indiffused bulk lithium
niobate (LN) waveguides [13, 14, 15], with a specific focus on waveguide width
variation as the primary error source. In particular, in Ref. [13], 83 mm Ti-
indiffused PPLN waveguides were diced into shorter sections to analyze the
generated QPM spectra from different regions of the waveguides, thereby
revealing the evolution of the QPM spectrum along the waveguide’s length. In
the context of thin-film PPLN devices, numerical methods have been employed to
replicate the measured QPM spectra based on an estimated TFLN film thickness
profile [10, 16, 9]. However, comprehensive experimental investigations akin
to those described in Ref. [13], which would greatly enhance our understanding
of QPM spectral imperfections and benefit the development of longer devices,
are currently lacking for thin-film PPLN devices.

Here, we introduce a non-destructive optical diagnostic method that enables
the visualization of the QPM spectrum at any location along the thin-film PPLN
waveguide. To accomplish this, we utilize a monochrome camera positioned
perpendicular to the chip surface to capture the scattered second-harmonic
(SH) light across the entire PPLN waveguiding region. By acquiring multiple
images while sweeping the pump wavelengths, the local QPM spectra at different
locations on the waveguide can subsequently be calculated and obtained. This
innovative technique uncovers the contributions from different sections of the
waveguide to the final QPM spectrum, facilitating an in-depth understanding of
the imperfections observed in the measured spectra. To evaluate the efficacy
of our approach, we conducted investigations on thin-film PPLN waveguides with
lengths of 5 mm, 7.5 mm, 12.5 mm, and 15 mm. Our findings indicate that the
observed imperfections in the spectra primarily stem from variations in TFLN
film thickness. Subsequently, we performed a thorough mapping of the film
thickness across the entire waveguiding regions. This comprehensive mapping
allowed us to successfully numerically reproduce the measured QPM spectra,
further confirming the significant influence of film thickness variations on
the spectral imperfections.

Figure 1:  (a) Schematic of the experimental setup for SHG characterization.
(b) Images of the collected scattered SH light from a 5 mm long PPLN waveguide
with the pump wavelength at 1594.4 nm and 1599 nm respectively. (c) Cross-
section of the PPLN waveguides. (d) Second-harmonic microscope image of the
periodically poled lithium niobate thin film.

##  2 Methods

The thin-film PPLN waveguides were fabricated using 5 mol% MgO-doped 300 nm
x-cut lithium niobate on insulator (LNOI) wafers. In this report, all measured
waveguides have a targeted etching depth of 150 nm and a waveguide top width
of approximately 850 nm, as shown in Fig. 1(c). These waveguides were designed
for efficient SHG from telecommunication wavelengths to near-visible
wavelengths. The required poling period for QPM is about 2.46 $\mu$m, and all
the interacting waves are in the fundamental TE mode.

In the initial fabrication step, poling electrodes with lengths varying from 5
mm to 15 mm were formed on the surface of TFLN using photolithography, while
maintaining a fixed poling period of 2.46 $\mu$m for each electrode. High-
voltage pulses, as described in Ref. [17], were then applied to these
electrodes for periodic poling of the TFLN. Figure 1(d) presents a
representative second-harmonic (SH) microscope image of the poled area,
revealing domain structures with ideal uniformity and duty cycles, which are
crucial for efficient frequency conversion. Multiple SH microscope images were
generated at different locations along each waveguide. It is worth emphasizing
that achieving high-fidelity poling of TFLN with long lengths and small
periods has been challenging. As the poling periods decrease, adjacent domains
tend to merge, while longer waveguides introduce more variations in the duty
cycle. Despite these challenges, we have achieved remarkable results in our
devices. To the best of our knowledge, the 7.5 mm long PPLN waveguide we have
fabricated is currently the longest demonstrated on the x-cut TFLN platform.
Here, even for the 15 mm long poling electrodes, the calculated poling duty
cycle remains highly uniform, at 52.83% $\pm$ 2.28%. Therefore, contributions
from imperfect periodic poling of TFLN (as discussed in detail through
theoretical calculations in Ref. [18]) to the QPM spectra are not considered
in our subsequent discussions and numerical simulations. The waveguides were
fabricated in the poled areas through aligned electron beam lithography and
dry etching, followed by a wet etching process for sidewall deposition
cleaning. Finally, the chip edges were cleaved to ensure optimal edge
coupling.

The experimental setup for SHG characterization is depicted in Fig. 1(a). A
tunable laser operating at telecommunication wavelengths serves as the pump
source for the PPLN waveguides, with its polarization adjusted by a set of
polarization controllers to ensure TE mode injection at the waveguide’s input
facet. Light is coupled into and out of the chip using tapered lensed fibers
to optimize the coupling efficiency. While sweeping the pump wavelength, the
corresponding SH light is collected at the output waveguide facet using a
lensed fiber and detected by a Si photodetector, following the conventional
method for obtaining the QPM spectrum. Additionally, we developed and employed
a novel approach for SHG characterization, which not only provides QPM
spectrum information at any location along the waveguide but also facilitates
the identification of sources causing spectral imperfections. Specifically,
while sweeping the pump wavelengths, a monochrome camera (Allied Vision Alvium
1800 U-511) was used to image the scattered SH light along the waveguide
region. For example, Fig. 1(b) presents the measured scattered SH light images
from a 5 mm thin-film PPLN waveguide with pump wavelengths of 1594.4 nm and
1599 nm, respectively. As we can see in these images, SH light with different
wavelengths is scattered from distinct parts of the waveguide. In the case of
this waveguide, the 799.5 nm SH light forms an unwanted side lobe in the QPM
spectrum, and Fig. 1(b) indicates that it is primarily generated near the
initial section of the PPLN. Such information proves valuable for
comprehending and addressing QPM spectral imperfections, particularly in
longer waveguides, as further elaborated in the subsequent sections.

##  3 Results

We measured SHG from waveguides with lengths of 5 mm, 7.5 mm, 12.5 mm, and 15
mm. Note that these waveguides are located on the same chip, and their
relative positions are depicted in Fig. 3(a). The QPM spectra obtained by the
conventional method (as described in the previous paragraph) are shown as the
blue curves in Figs. 2(c), (f), (i), and (l). Upon comparing these plots, it
becomes evident that increasing the waveguide length leads to the generation
of more side lobes, thereby diminishing the spectrum fidelity and the overall
achievable conversion efficiency. The variations in the main peak wavelengths
can be attributed to a combination of slight differences in the designed
waveguide widths and the film thicknesses from one waveguide to another, as
illustrated in Fig. 3(b). The spectrum fidelity values, calculated using the
definition from Ref. [11], are 0.46, 0.24, 0.17, and 0.15 respectively for the
four lengths. To gain deeper insights into the origins of these side lobes, we
captured scattered SH light images for each waveguide while sweeping the pump
wavelengths, similar to the representative images shown in Fig. 1(b). By
integrating the pixel values in each column of these images (perpendicular to
the waveguide’s direction), we obtained mappings of the SH light in terms of
propagation length and pump wavelength, which are presented as color images in
Figs. 2(a), (d), (g), and (j). These visual representations conveniently
illustrate the evolution of the QPM spectrum along the waveguide. Moreover,
end-point QPM spectra, which refer to the QPM spectra obtained at the end of
the PPLN waveguides, can be generated by averaging the final column values of
the SH light mappings. They are depicted by the yellow curves in Figs. 2(c),
(f), (i), and (l). The close alignment between these curves and the QPM
spectra obtained through the conventional method provides compelling evidence
that valid QPM spectra can be obtained using the scattered light imaging
technique at any location along the PPLN waveguide. Therefore, we analyze the
imperfections in the QPM spectra based on the SH light mappings. Notably,
these mappings exhibit a consistent trend: side peaks with longer wavelengths
than the main peaks predominantly arise from the initial section of the
waveguides, while the SH light from the main peaks only begins to emerge at
approximately 2-3 mm away from the waveguides’ starting points. This
similarity suggests the presence of one or several waveguide geometry
parameters that consistently vary along the direction of light propagation
across the entire chip.

Figure 2:  Measured and simulated QPM spectrum mappings and end-point QPM
spectra from thin-film PPLN waveguides with different lengths of 5 mm (a)-(c),
7.5 mm (d)-(f), 12.5 mm (g)-(i), and 15 mm (j)-(l). (a), (d), (g), and (j):
Measured QPM spectrum mappings using scattered-light imaging. (b), (e), (h),
and (k): Calculated QPM spectrum mappings based on measured TFLN film
thickness profiles. (c), (f), (i), and (l): Measured end-point QPM spectra
using the conventional method (blue curves), as well as scattered-light
imaging (yellow curves), overlaid with calculated plots (dashed black curves)
based on TFLN film thickness profiles.

For uniform waveguides, the QPM spectrum ($\Phi$, normalized per unit length)
can be calculated as [10, 11]:

$\displaystyle\Phi=\text{sinc}(\frac{\Delta\beta
L}{2})\text{exp}(i\frac{\Delta\beta L}{2}),$ (1)
$\displaystyle\Delta\beta=\frac{2\pi}{\lambda_{\text{SH}}}n_{\text{SH}}-2\frac{2\pi}{\lambda_{\text{pump}}}n_{\text{pump}}-\frac{2\pi}{\Lambda},$

where $L$ is the length of the waveguide, $\lambda_{\text{pump, SH}}$ denotes
the pump and SH wavelengths, and $n_{\text{pump, SH}}$ indicates the effective
mode indices for the pump and SH light. To determine the type of fabrication
errors causing these spectrum imperfections, we calculated the partial
derivatives of the momentum mismatch ($\Delta\beta$, as defined in Eq. 1) with
respect to the waveguide top width $w$, etching depth $h_{\text{etch}}$, and
film thickness $t_{\text{LN}}$ as follows:

$\displaystyle(\frac{\partial\Delta\beta}{\partial
w})_{\\{h_{\text{etch}}=154~{}nm,~{}t_{\text{LN}}=303~{}nm,~{}\lambda_{\text{pump}}=1580~{}nm\\}}$
$\displaystyle=-0.485~{}\mu m^{-2},$ (2)
$\displaystyle(\frac{\partial\Delta\beta}{\partial
h_{\text{etch}}})_{\\{w=850~{}nm,~{}t_{\text{LN}}=303~{}nm,~{}\lambda_{\text{pump}}=1580~{}nm\\}}$
$\displaystyle=1.842~{}\mu m^{-2},$
$\displaystyle(\frac{\partial\Delta\beta}{\partial
t_{\text{LN}}})_{\\{w=850~{}nm,~{}h_{\text{etch}}=154~{}nm,~{}\lambda_{\text{pump}}=1580~{}nm\\}}$
$\displaystyle=-4.018~{}\mu m^{-2}.$

The calculations reveal that $\Delta\beta$ of the waveguide structure employed
in this study is most sensitive to variations in film thickness. In addition,
based on the general framework developed in Ref. [11], we further estimated
the contribution from each individual waveguide parameter to the QPM spectrum
infidelity for all four waveguides, and the results are summarized in Table 1.
This estimation assumes that the spectrum infidelity is primarily influenced
by a single waveguide parameter, which exhibits 1/f noise to account for the
long-range correlations arising from the fabrication processes [14]. The
similarity in the calculated variations for each parameter across all four
waveguides provides further evidence of the consistent nature of the
fabrication variations throughout the entire chip.

Table 1:  Estimated waveguide geometry variation for all four waveguides based on the measured QPM spectra. Waveguide length | $\Delta w$ | $\Delta h_{\text{etch}}$ | $\Delta t_{\text{LN}}$
---|---|---|---
5 mm | 13.16 nm | 3.47 nm | 1.59 nm
7.5 mm | 22.04 nm | 5.81 nm | 2.66 nm
12.5 mm | 20.70 nm | 5.46 nm | 2.50 nm
15 mm | 20.42 nm | 5.38 nm | 2.47 nm

We conducted precise measurements using atomic force microscopy (AFM) on a
twin chip to assess the variations in waveguide width and etching depth along
a 15 mm long waveguide. The calculated errors for both parameters were found
to be lower than the estimated values mentioned in Table 1. On the other hand,
the estimated variations in film thickness appear more plausible, as such
levels of long-range variation can often arise from the chemical-mechanical
polishing process and are consistent with the labeled thickness uniformity
value provided by the wafer vendor. In order to examine the film thickness
variations, we used Filmetrics to measure the thickness of TFLN across the
entire etched chip. The measurement was performed with a step size of 200
$\mu$m, and the resulting mapping is illustrated in Fig. 3(a). It is worth
noting that this measurement was conducted subsequent to the dry-etching
process of the waveguide. Therefore, the plotted thickness values in Fig. 3
represent the raw measured data, augmented by a constant etching depth of 154
nm. As depicted in Fig. 3(a), it is evident that the film thickness exhibits
consistent variations across the entire chip, which aligns with our hypothesis
based on the QPM spectrum mappings shown in Fig. 2. Specifically, the
thickness gradually increases from the left edge of the chip (the input port
of the PPLN) and subsequently decreases towards the right side (the output
port of the PPLN). In addition to the overall mapping, Fig. 3(b) provides a
detailed plot of the measured TFLN thickness along four specific waveguides
with lengths of 5 mm (blue), 7.5 mm (red), 12.5 mm (yellow), and 15 mm
(black). The dashed lines in the figure indicate the end of the PPLN regions.
It is important to note that the chip analyzed in this study was obtained from
an area near the edge of the wafer. The thickness profile, which exhibits a
high-order polynomial trend, observed in this specific chip was not present in
subsequent measurements conducted on chips extracted from regions in the
center of the wafer.

Figure 3:  (a) Measured TFLN film thickness mapping over the entire chip, with
the black lines showing the position of PPLN waveguides. (b) Measured TFLN
thickness along the waveguides with lengths of 5 mm (blue), 7.5 mm (red), 12.5
mm (yellow), and 15 mm (black). The black dashed lines indicate the end of the
PPLN region for each waveguide.

Utilizing these film thickness values, we numerically calculated the QPM
spectrum mapping for all four waveguides, based on the methods described in
Refs. [19, 14]. These mappings are presented in Figs. 2(b), (e), (h), and (k).
We also depicted the end-point QPM spectra in Figs. 2(c), (f), (i), and (l),
overlaid with the curves acquired experimentally. A thorough comparison of
these plots highlights the successful reproduction of the main side lobes
observed in the measured QPM spectra for all four waveguides. Moreover, the
simulations accurately captured the evolution trend evident in the measured
QPM spectrum mappings. Several factors may contribute to the observed
discrepancies between the measured and simulated mappings in this study. These
factors include local variations in waveguide widths and etching depth, which
are considered secondary factors here and thus are not included in the
numerical calculations. Furthermore, considering the high sensitivity of the
spectra to film thickness variations, even slight deviations from the true
values, such as the absence of fine features in the captured thickness profile
and errors resulting from imperfect measurement accuracy, can significantly
contribute to the observed disparities. Taking the 15 mm PPLN waveguide as an
example, in Fig. 4, we show that slight local variations in the film thickness
profile can provide better alignment to the measured QPM spectra. The
optimized film thickness profile, as shown in Fig. 4(a), was obtained using
the Particle Swarm Optimization algorithm, aiming to reproduce the QPM spectra
at various locations along the waveguide (Fig. 4(b)). Note that the difference
between the optimized thickness profile and the raw data can be introduced by
other waveguide parameters other than film thickness, such as waveguide width
and etching depth. As for the 12.5 mm long waveguide, we could achieve a
better matching with the measured QPM spectrum mapping (shown in Fig. 2(h)) by
adding 2 nm to the poling period, shifting the whole spectrum to longer
wavelengths, though the alignment with the end-point QPM spectrum would be
compromised. It is important to emphasize that the goal of this work is not to
perfectly replicate the measured QPM spectrum mapping, as achieving this level
of precision with a single parameter variation (in this case, film thickness)
is unrealistic. Nevertheless, the remarkable agreement observed between the
simulated and measured QPM spectra provides strong evidence supporting the
hypothesis that the observed imperfections primarily originate from variations
in the film thickness along the waveguiding region.

Figure 4:  (a) Comparison of the measured and optimized film thickness profile
for the 15 mm long waveguide. (b) Simulated QPM spectrum mapping using the
optimized thickness profile. (c) QPM spectra at different locations along the
waveguide obtained through the experiment (solid blue curve), simulations with
raw thickness profile (solid red curve), as well as simulations with optimized
thickness profile (dashed black curve).

##  4 Conclusion

In conclusion, our study presents a non-destructive optical diagnostic method
for assessing imperfections in QPM spectra from thin-film PPLN waveguides.
This method allows for the extraction of QPM spectra at any position along the
waveguide without the need for physically dicing the waveguides. By comparing
the measured spectrum mappings with ideal ones, we can identify specific
regions that contribute to unwanted distortions in the QPM spectra, providing
crucial insights into the sources of these spectral imperfections. We applied
this approach to investigate the QPM spectrum imperfections in four fabricated
thin-film PPLN waveguides with lengths of 5 mm, 7.5 mm, 12.5 mm, and 15 mm.
Our analysis revealed a consistent trend in the QPM spectrum mappings across
these waveguides. Combining our experimental results with numerical
simulations, we identified variations in TFLN thickness along the waveguide as
the primary source of the observed spectral imperfections. Moreover, we
successfully replicated the main features of the measured QPM mappings using
film thickness data obtained from Filmetrics measurements. The strong
alignment between the simulated and measured mappings serves to validate our
conclusions.

There are several potential avenues for improving the fidelity of QPM spectra.
One straightforward approach is to fabricate PPLN waveguides in an area close
to the center of the LNOI wafer, where the film thickness is expected to be
more uniform and exhibit a reduced variation trend observed in this study.
Another promising strategy involves designing waveguide structures that are
less sensitive to thickness variations, as explored in simulations detailed in
Ref. [9], which may come at the cost of reduced conversion efficiency.
Additionally, obtaining a detailed TFLN thickness mapping prior to waveguide
fabrication and compensating for thickness variations through adjustments in
other waveguide parameters such as poling period and waveguide width is
another viable option. It is also possible to design folded waveguides that
possess a smaller area with more uniform film thickness [20], although this
would require additional components to control the accumulated phase mismatch
in the curved waveguides.

Taken together, our research provides new insights to the understanding of
imperfections in QPM spectra originating from thin-film PPLN waveguides. The
integration of experimental findings with numerical simulations sheds light on
the path toward the development of long thin-film PPLN devices with enhanced
overall conversion efficiency. These insights hold great potential for
benefiting applications in both classical and quantum communication domains,
opening up new possibilities for enhanced performance and functionality.

Funding Research Grants Council, University Grants Committee (CityU 11204820,
N_CityU113/20)

Acknowledgments Jie Zhao would like to thank Haowen Ren, Yanqi Luo, and Yang
Li for their valuable discussions and assistance in the fabrication process.

Disclosures The authors declare no conflicts of interest.

Data Availability Statement Data underlying the results presented in this
paper are not publicly available at this time but may be obtained from the
authors upon reasonable request.

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