# Ultrafast Carrier Relaxation and Second Harmonic Generation in a Higher-Fold
Weyl Fermionic System PtAl

Vikas Saini<EMAIL_ADDRESS>Tata Institute of Fundamental Research,
Mumbai 400005, India  Ajinkya Punjal  Tata Institute of Fundamental Research,
Mumbai 400005, India  Utkarsh Kumar Pandey  Tata Institute of Fundamental
Research, Mumbai 400005, India  Ruturaj Vikrant Puranik  Tata Institute of
Fundamental Research, Mumbai 400005, India  Vikash Sharma  Tata Institute of
Fundamental Research, Mumbai 400005, India  Vivek Dwij  Tata Institute of
Fundamental Research, Mumbai 400005, India  Kirtika Vijay  Accelerator Physics
and Synchrotrons Utilization Division, Raja Ramanna Centre for Advanced
Technology, Indore, 452013, India
Homi Bhabha National Institute, Training School Complex, Anushakti Nagar,
Mumbai, 400094, India  Ruta Kulkarni  Tata Institute of Fundamental Research,
Mumbai 400005, India  Soma Banik  Accelerator Physics and Synchrotrons
Utilization Division, Raja Ramanna Centre for Advanced Technology, Indore,
452013, India
Homi Bhabha National Institute, Training School Complex, Anushakti Nagar,
Mumbai, 400094, India  Aditya Dharmadhikari  Tata Institute of Fundamental
Research, Mumbai 400005, India  Bahadur Singh  Tata Institute of Fundamental
Research, Mumbai 400005, India  Shriganesh Prabhu<EMAIL_ADDRESS>Tata
Institute of Fundamental Research, Mumbai 400005, India  A. Thamizhavel
<EMAIL_ADDRESS>Tata Institute of Fundamental Research, Mumbai 400005,
India

###### Abstract

In topological materials, shielding of bulk and surface states by crystalline
symmetries has provided hitherto unknown access to electronic states in
condensed matter physics. Interestingly, photo-excited carriers relax on an
ultrafast timescale, demonstrating large transient mobility that could be
harnessed for the development of ultrafast optoelectronic devices. In
addition, these devices are much more effective than topologically trivial
systems because topological states are resilient to the corresponding
symmetry-invariant perturbations. By using optical pump probe measurements, we
systematically describe the relaxation dynamics of a topologically nontrivial
chiral single crystal, PtAl. Based on the experimental data on transient
reflectivity and electronic structures, it has been found that the carrier
relaxation process involves both acoustic and optical phonons with oscillation
frequencies of 0.06 and 2.94 THz, respectively, in picosecond time scale. PtAl
with a space group of $P$$2_{1}$3 allows only one non-zero susceptibility
element i.e. $d_{14}$, in second harmonic generation (SHG) with a large value
of 468(1) pm/V, which is significantly higher than that observed in standard
GaAs(111) and ZnTe(110) crystals. The intensity dependence of the SHG signal
in PtAl reveals a non-perturbative origin. The present study on PtAl provides
deeper insight into topological states which will be useful for ultrafast
optoelectronic devices.

##  I INTRODUCTION

Topological materials are enormously sought after, in condensed matter
research, for their novel symmetry protected electronic structures and unique
responses to electromagnetic radiations, which lead to numerous advanced
potential applications [1, 2, 3, 4, 5, 6, 7, 8, 9]. Topological phases are
distinguished by various parameters, such as the degeneracies of the valence
and conduction bands, the dimensionality of the crossing point, the chiral
charge, and the tilting directions of the bands. These topological phases are
the results of symmetry constraints present in the crystalline system combined
with the leading interactions and spin-orbit coupling (SOC). Depending on
symmorphic and non-symmorphic crystalline symmetries, we can distinguish two
categories for the generic and time reversal invariant point band crossings,
respectively. The non-symmorphic symmetry protection in electronic structure
leads to a higher-fold band crossing at high symmetry points and exotic
topology of bands. This enables the observation of novel emergent quasi-
particles in crystalline systems that are not observed as fundamental
particles [10, 11, 12].

Apart from their electrical transport properties, topological materials are
excellent platforms for studying the exotic physics of nonlinear optical
responses and possess application potential due to their novel electronic
structure and symmetry protections. Recent pump probe experiments on
topological insulators such as Bi2(Se, Te)3 have shown bulk and surface state
relaxations under the influence of terahertz radiation, making them good
terahertz emitters [13, 14]. In semimetals, the ultrafast carrier dynamics and
unconventional SHG of the topological Dirac semimetal Cd3As2 have also been
investigated, and distinctly Weyl semimetal TaAs manifests interesting
optically controlled chiral anomalies [15, 2, 7, 16, 17, 18, 19].

To be specific, PtAl crystallizes in the non-symmorphic space group $P2_{1}3$
that has a chiral crystal structure, similar to other chiral systems such as
RhSi, CoSi, and PdGa etc. The first-principles calculations including SOC and
symmetry analysis of this system unfold the existence of spin-3/2 exotic
emergent Rarita-Schwinger (RS) fermions in the vicinity of the center
($\Gamma$ point) of the Brillouin zone (BZ). The expected dispersion relations
of these quasiparticles have been experimentally observed recently [20].
Likewise, the corner point $R$ of the cubic BZ exhibits six-fold degenerate
band crossings, followed by two time-reversal copies of spin-1 excitations.
The chiral charges of these exotic Weyl points at the $\Gamma$ and $R$ points
are -4 and +4, respectively, which is significant and four times higher
compared to other Weyl semimetals such as Ta(As, P) and Mo(Te, Se)2 [21, 22,
23, 24, 25, 26, 27, 28, 29, 28, 30].

The predicted quantization value of the circular photogalvanic effect (CPGE)
for PtAl is noteworthy, being four times higher than that of achiral Weyl
semimetals due to the higher chiral charge (4) of its quasiparticles [8, 31,
22, 32]. This is crucial for the development of optoelectronic devices and
sensors. The exotic bulk topological states and chirality of the crystal
structure in PtAl leave curiosity and motivate the exploration of novel
electromagnetic responses.

We comprehend the ultrafast carrier relaxation mechanism of nontrivial
quasiparticles (RS Weyl fermions) through optical pump probe measurements. The
observation of susceptibility tensor $d_{14}$ in strong second harmonic
generation unequivocally proves the structural chirality in PtAl.

##  II METHODS

Single crystal growth– The single crystals of PtAl were prepared using the
Czochralski method and the phase purity of PtAl is confirmed by the powder
x-ray diffraction analysis, full details are given in reference [28].

XPS and RPES experiments – Synchrotron X-ray photoemission spectroscopy (SR-
XPS) and RPES measurements were performed at the undulator based Angle
Resolved Photoelectron Spectroscopy beamline (ARPES BL-10), Indus-2.
Atomically clean surface of the single crystal with similar bulk composition
was obtained by argon ion sputtering at 1.5 keV for 30 min. SR-XPS core levels
were recorded at h$\nu$= 700 eV with 0.3 eV energy resolution. RPES
measurements carried out by recording the valence band (VB) spectra across the
Pt $5p-5d$, Pt $4f-5d$ and Al $2p-3s$ transitions at the photon excitation
energies ranging from 41 eV to 88 eV with energy resolution of 20 meV to 30
meV. All the photoemission measurements were carried out at low temperature of
$\sim$20 K using SPECS Phoibos 150 electron energy analyzer. The base vacuum
during the measurement was $\sim 7~{}\times 10^{-11}$ mbar.

Optical pump probe measurement– For optical pump probe measurement, we used an
amplifier laser (Solstice Ace, 800 nm, 5.5 mJ, 1 kHz, 35 fs) which is split
into two parts. One of the parts goes to Optical Parametric Amplifier (OPA) to
generate 650 nm which is used to pump the sample and another part of the
amplifier is used to probe the dynamics. The pump beam is focused on the
sample using a 300 mm lens (Thorlabs LA1484) whereas the probe beam is focused
using a 200 mm (Thorlabs LA1708-B) lens. The spot sizes of these pulses were
measured using the beam profiler (Newport LBP2). The state of the polarization
of the wavelengths generated by the amplifier and OPA is linear. To probe the
dynamics in the system, the probe beam is scanned using a delay stage (Newport
UTS100PP) at various temporal delays with reference to the pump beam. We used
a balanced-photodetection (BPD) scheme and the signal is fed to a lock-in
amplifier (SR830) with a modulated pump beam (Thorlabs MC2000B) as reference.

Second harmonic generation– In the rotation anisotropy second harmonic
generation (SHG) polarimetry experiment, we used Ti:Sapphire amplifier laser
(Solstice Ace, 1 kHz, 35 fs) with a central wavelength of 800 nm. A clean-up
polarizer (CP) (Newport 10P109AR.16) was used to enhance the linear state of
polarisation of the amplifier beam. The beam was modulated using a chopper
(Thorlabs MC2000B-EC) for lock-in detection. The incident linear polarisation
was rotated using a Quarter Wave Plate (QWP) (Newport 10RP54-2B) with measured
ellipticity of 0.98 and a linear polarizer (LP) (Newport 10P109AR.16). A 400
mm lens (Newport) was used to focus the light onto the sample. The angle of
reflection and incidence is less than 3∘. The reflected fundamental and second
harmonic (SH) frequency was picked by a mirror and directed through a series
of spectral filters (EO Schott glass BG40, Thorlabs FESH0450) with a
theoretical contrast ratio greater than 1012 and a polarizer to an analyzer
(Newport 10GT04) the second harmonic signal. The SH light was focused using a
50 mm lens (Thorlabs LA1213) onto the photodiodes (Hamamatsu S1223). The
signal from the photodiode was amplified using a high-gain home-built current
preamp and detected using a lock-in amplifier (SR830). The polarizer and
analyzer were mounted on rotation stages (Newport PR50PP) to avoid angle
errors. The power was measured using an integrating sphere (Ophir) and the
spectra were measured using an Ocean Optics (FX series) spectrometer.

First principles calculations – Electronic structure calculations were
performed within the density functional theory (DFT) framework using the
Quantum Espresso package [33, 34]. A dense 21$\times$21$\times$21 $k$-mesh was
used for self-consistent calculations, using an energy cut-off of 60 Ry.
Optical properties were calculated using the full potential linearized
augmented plane-wave (FL-LAPW) method as implemented in WIEN2k package [35,
36, 37]. A $k$-mesh of 46$\times$46$\times$46 was used to obtain well-
converged results.

##  III RESULTS AND DISCUSSIONS

###  III.1 X-ray and Resonant Photoemission Spectroscopy

The PtAl single crystal has been grown by the Czochralski method [28]. The
single crystal was characterized using X-ray and resonant photoemission
spectroscopy. The details are given in the supplementary material (Figure S1).

Figure 1: Pump probe experiments were performed with both linearly polarized
pulses along the [110] direction. (a) The transient reflectivity is measured
as a function of probe delay for various pump fluences up to 1.75 mJ/cm2. Two
exponential fits with oscillating terms are used to model the transient
differential reflected signal, corresponding to oscillations frequencies of
approximately 0.06 and 2.94 THz after thermalization. (b) A contour plot of
the transient reflectivity ($\Delta R/R_{0}$) against various pump fluences
for probe time delays of up to 6 picoseconds. (c) A schematic of the pump and
probe polarization directions on the sample surface. (d) The background
subtracted optical phonon oscillations of the transient reflectivity
correspond to various pump fluences. (e) Schematic illustration of carrier
relaxation in the conduction band using optical and acoustic phonons. (f) The
phonon lifetimes ($\tau_{1}$, $\tau_{2}$) were estimated for both decay
channels and plotted against the pump fluence. (g) Fourier transform of
$\Delta R/R_{0}$ against the time delay at a pump fluence of 1.17 mJ/cm2. (h)
The proportionality weight coefficients (A1, A2) of the phonon relaxations are
plotted against the pump fluence. (i) The phonon oscillation frequencies are
extracted from the overlapped oscillating $\Delta R/R_{0}$ signal and plotted
against various pump fluences. (j) Experimentally observed Raman spectrum for
PtAl at room temperature.

###  III.2 Optical Pump Probe Spectroscopy

The carrier relaxation mechanism of the excited quasiparticles in PtAl is
investigated by the ultrafast pump probe technique. The pump and probe pulses
of a repetition rate of 1 kHz and energies of 1.9 eV and 1.55 eV,
respectively, are incident on the (110)-plane and are polarized along the same
direction, as depicted in Figure 1(c). In addition, the pump and probe pulses
are incident at the same position on the sample surface. The probe pulse
coincides with the pump pulse for uniform excitations, where the respective
diameters are 350 and 660 $\mu$m. Initially, the pump pulse injects charge
carriers from the valence band (VB) to the conduction band (CB) and the
relaxation mechanism of these excited carriers is tracked using a probe pulse,
which is incident on the sample after a short delay following the pump pulse.

Since PtAl is a semimetallic system with a relatively large density of states,
the reflection of carriers dominates over transmission in contrast to
semiconductors for infrared (IR) radiation. Experimentally the signal $\Delta
R$/$R_{0}$ $=$ ($R-R_{0}$)/$R_{0}$ is measured; where R and $R_{0}$ are the
transient reflections with and without of the pump pulse, respectively [18].
Carrier relaxation dynamics of PtAl is discussed in Figure 1. In negative time
delays, the probe pulse arrives before the pump pulse on the sample surface
and is completely reflected, resulting in zero differential reflectivity as
observed in Figure 1(a). When the time delay becomes positive, the probe pulse
is absorbed by the system leading to the sharp negative dip of $\Delta
R/R_{0}$ in the transient reflectivity. Beyond 0.4 ps, the system tries to
recover back to the equilibrium state therefore the magnitude of
$\Delta$R/$R_{0}$ decreases towards zero as time goes by.

The $\Delta$R/$R_{0}$ with various pump energies is depicted in the Figures
1(a) and 2(a). With increasing pump fluence the maxima of the
$\Delta$R/$R_{0}$ increases linearly which signify the carriers get injected
into the conduction band by a single photon absorption of the pump energy
nearly up to 1.17 mJ/cm2 [38, 39]. The linearity is shown in the inset of
Figure 1(a). As the pump fluence increases, more carriers are injected into
the conduction band, leading to an increase in the amplitude of the transient
reflectivity dip. This amplitude is related to the temperature and density of
hot electrons. Specifically, the electron temperature is highest during the
carrier injection phase, after which the hot electrons gradually cool down, as
this is observed from the color gradient in Figure 1(b). After carriers are
injected into the conduction band, the excited hot carriers try to come down
to the VB by lowering their energy through various mechanisms, such as
electron-electron, electron-phonon, phonon-phonon scatterings, and electron-
hole recombinations [40, 41, 42]. The electron-electron intraband scatterings
are faster than the electron-phonon and phonon-phonon scatterings which appear
in the time scale of 10 to a few hundred femtoseconds [43]. Furthermore,
electron-phonon scatterings occur on the picosecond timescale, whereas
interband electron-hole recombinations typically occur on a much slower
timescale in the range of 100 to 1000 ps [44, 45].

The electron temperature for a particular pump fluence is estimated using the
following expression [46, 47, 48]

$T_{e}=\left\langle\sqrt{T_{l}^{2}+\frac{2(1-R)F}{\gamma_{v}\delta}\exp{(-z/\delta)}}\right\rangle$
(1)

Where $T_{l}$ is the lattice temperature, in the present case the pump probe
measurements have been carried out at room temperature and hence it is
considered as 300 K. $R$ is the reflectivity of the pump pulse, which we
calculated from first-principles calculations as $\sim$0.535 at 650 nm. $F$
denotes the pump fluence. The skin depth ($\delta$) is also calculated and
found to be approximately 16.6 nm at 650 nm. $\gamma_{V}=\gamma\rho$, where
$\gamma$ is the Sommerfeld coefficient which can be estimated from the heat
capacity measurements. From the low-temperature heat capacity data we have
estimated $\gamma$ as $\sim$0.86 mJ/mole-K2 (see Figure S2 in the suppl.
material). The $\rho$ represents the molar density $\frac{1}{N_{A}V}$; $N_{A}$
represents the Avogadro’s constant, and $V$ is the unit cell volume. For PtAl,
the lattice constant $a$ = 4.864$\AA$, and hence the unit cell volume is
nearly 115$\AA$3. Here, $z$ represents the distance from the sample surface,
and that is taken $\delta/2$ as an average of the skin depth. The $T_{e}$
increases as the pump fluence increases, at 0.29 mJ/cm2 it is estimated to be
$2848$ K that increase up to $6944$ K for the fluence 1.75 mJ/cm2.

Figure 2: (a) $\Delta$R/R0 is plotted in the higher probe delay regime for
slow relaxation, where the black fitted line corresponds to a single
exponential term for carrier recombination. (b) The parameters $A_{3}$ and
$\tau_{3}$ for electron-hole recombination as a function of incident pump
fluence.

The oscillating transient reflectivity signal measured for PtAl against probe
delay exhibits two frequencies that overlap. Transient reflectivity
oscillations can arise for a variety of reasons, such as surface plasmons,
coherent optical phonons, strain waves, interference between the reflected
probe beams from the top and bottom layers of the sample, and coherent
acoustic phonons. These oscillations have been observed for systems ranging
from thin films to bulk materials [18, 49, 50, 51]. For PtAl, the optical
phonon frequency is nearly unchanged when the spot positions of the pump and
probe pulses are changed together on the sample surface, which eliminates the
possibility of oscillations caused by surface plasmons. The existence of
optical phonons in PtAl has been verified from the experimentally observed
Raman spectrum (Figure 1(j)), which shows an optical Raman peak around 3.2
THz, consistent with the higher frequency obtained in the oscillations (Figure
1(i)). The background subtracted oscillations corresponding to the coherent
optical phonons are shown in Figure 1(d) at various pump fluences, along with
the fitted corresponding oscillating term in Eq. 2. Furthermore, we have
calculated the skin depth ($\delta$) using first-principles calculations
($\delta$ $=$ $1/\alpha$), where $\alpha$ is the absorption coefficient and is
found to be 0.015 $\mu$m for $\lambda$ $\sim$ 800 nm. This is much smaller
than the sample thickness ($\sim$50 $\mu$m), so we can safely conclude that
the strain waves and interference of reflected beams are not considered.
Therefore, it is likely that the small frequency in the transient reflectivity
is a consequence of the coherent acoustic phonon oscillations, as observed for
Bi2Se3 [18].

Figure 3:  Bulk band structure of PtAl calculated using the GGA exchange
correlation functional in presence of SOC. Four pink and green color bands are
the valence bands whereas the other four bands crossed at the Fermi level
shown in the cyan and blue colors represent the conduction bands.

In PtAl, pump excitations take place in the 0.4 ps for the 0.29 mJ/cm2 pump
fluence and further, it increases slightly with higher pump energies as
observed from Figure 1(a) and consequently thermalization from the coulomb
scatterings appear approximately in 0.6 ps where the transient reflectivity
($-\Delta R/R_{0}$) decreases with the increasing time delay followed by less
absorption of the probe energy of the excited carriers. After the process of
thermalization, we observed that $-\Delta R/R_{0}$ does not decrease
monotonically towards zero rather it increases and later it starts to decrease
as observed in Figure 2(a). This behavior of the transient reflectivity in
PtAl is understood from the overlap of acoustic phonon oscillations carrying
0.06 THz frequency with another optical phonon frequency 2.94 THz on the
transient reflectivity, which is observed for approximately up to 15 ps time
delay (Figure 1(a)). The Fourier transform of transient reflectivity depicts
the oscillation frequencies as shown in Figure 1(g) in agreement with the
observed oscillation frequencies obtained using two exponent fitting (see
Figure 1(i)). The carrier relaxation process in PtAl is illustrated in Figure
1(e). After thermalization, hot electrons lose their energy through both
optical and acoustic phonons until they rapidly reach the bottom of the
conduction band [52]. After approximately 2 ps, the relaxation is understood
by the three exponent relaxation terms as described below [53]

$\normalsize\begin{split}\frac{\Delta
R}{R_{0}}=A_{1}exp{(-t/\tau_{1})}sin(2\pi f_{1}t+\phi_{1})+\\\
A_{2}exp{(-t/\tau_{2})}sin(2\pi
f_{2}t+\phi_{2})+A_{3}exp{(-t/\tau_{3})}\end{split}\normalsize$ (2)

Here $A_{1}$, $A_{2}$, and $A_{3}$ are the coefficients associated with the
respective decay channels, and $f_{1}$ and $f_{2}$ are the related frequencies
of optical and acoustic phonons. $\tau_{1}$, $\tau_{2}$, and $\tau_{3}$ are
the phonon lifetime for their respective decay channels. From the above
equation 2.94 THz electron-phonon relaxation is associated with the first term
$A_{1}$ and the other 0.06 THz relaxation is associated with the second term
$A_{2}$. Notably, the third term of the slow relaxation appears in large time
delay as fitted beyond 50 ps which is attributed to the recombination of hole
and electron carriers. The first two-terms fitted transient reflectivity
signal is depicted in Figure 1(a) for various pump fluences.

From the three exponents fitting we extracted the above mentioned parameters
which explain the process of carrier relaxation in PtAl. The obtained
parameters $A_{1}$ and $A_{2}$ from the fitting are plotted against pump
fluences and shown in Figure 1(b). The coefficients obtained from the optical
and acoustic phonon relaxation processes are primarily dominant at small time
delays between the pump and probe beams, typically up to 15 ps after
thermalization. The decay of acoustic phonon is prominent for all pump
fluences compared to the optical phonon as shown in Figure 1(h). More pump
energy implies more carriers are being injected into the CB. The optical
relaxation coefficient $|A_{1}|$ increases gradually as the pump fluence is
increased. On the other hand, the coefficient $|A_{2}|$ for acoustic phonon
relaxation initially increases with increasing pump fluence up to 1.17 mJ/cm2.
However, beyond 1.17 mJ/cm2, it decreases due to the increasing number of
excited carriers in the CB that suppress relaxation through this channel as
more carriers are injected into the CB. The lifetime of acoustic phonons is
roughly of the same order as that of optical phonons, on the order of a few
picoseconds as depicted in Figure 1(f), that is higher than that of in the
Bi2Se3 [18] and monolayer MoS2 [54]. The decrease in the relaxation time
against pump fluence is also observed in other systems like $\alpha$-In2Se3
nanoflake, WS2 monolayer, GaN/InGaN quantum well nanowires etc. [55, 56, 52,
57, 58] Both acoustic and optical phonon lifetimes decrease with increasing
pump fluence up to 1.17 mJ/cm2, indicating an increase in the strength of
electron-phonon coupling ($\lambda$), as the relation with relaxation rate is
discussed in the Refs. [48, 59]. The phonon frequencies of related phonon
oscillations remain nearly unchanged with increasing pump fluence as shown in
Figure 1(i).

For the slow relaxation, we have fitted a single exponential function for
probe delays above 50 ps, as shown in Figure 2(a). Relaxation time at the 0.58
mJ/cm2 pump fluence is around 1.9 ns which further decays with an increase in
the pump fluence resulting in relatively faster electron-hole recombination
[60, 61]. Alongside the proportionality coefficient $A_{3}$ also increases in
magnitude with increasing pump fluence, which reveals that more carriers are
recombined at higher pump energy as shown in Figure 2(b).

To understand the process of equilibrium of the injected carriers we look into
the electronic structure of PtAl. However, there are electronic bands along
all high symmetry paths near the Fermi level, therefore for the unpolarized
pump pulse all directional excitations are possible. Here, pump and probe
polarizations are along [110] crystallographic direction, which is equivalent
to the $\Gamma$ \- M direction in momentum space. Thus, only the optical
excitations of this direction are allowed for the valence electrons of mostly
green bands in Figure 3 by the 1.9 eV pump pulse to the conduction band of the
near M point, as shown in the blue colors in Figure 3. After excitations, hot
carriers distribute themselves based on the Fermi-Dirac statistics to lower
the electron temperature in the order of 0.6 ps time scale. This process of
thermalization takes place in the CB denoted in the blue color. The valleys
located at the X and M points are formed by the same blue color CB, which is
broad in momentum space. As a result, excited carriers can be easily scattered
towards the edges of these valleys of the M and X points (M $\leftrightarrow$
X) by emitting acoustic phonons of very low energy (see schematic in Figure
1(e)). This is consistent with our experimentally observed acoustic phonons of
$\sim$0.06 THz. The relaxations of the carriers via optical phonon emissions
take place in the same probe delay regime where oscillations from acoustic
phonons are observed as depicted in Figure 1(a). Later, once the excited
carriers are at the bottom of the CB they recombine with the hole carriers
present in the VB in the order of nanosecond timescale as discussed in Figure
2(b). Interestingly, PtAl exhibits structural chirality due to the absence of
rotation and inversion symmetry, which allows observation of second harmonic
generation through inversion asymmetry. Additionally, PtAl electronic bands
are rich in Berry curvature near the Fermi level. Therefore, we investigate
the role of Berry curvature of the electronic states in the second harmonic
generation.

###  III.3 Second Harmonic Generations

In this section, we will discuss the second order nonlinear optical response
of PtAl in the near infrared regime, specifically at 800 nm. Figure 4(a)
depicts the SHG by an 800 nm laser pulse at room temperature that shows a peak
around $\lambda$ = 400 nm. The incident beam profile is shown in the inset. We
have also performed SHG on a GaAs(111) sample, which is well known for
exhibiting second order optical response. When comparing the SHG signals of
PtAl with standard nonlinear materials such as GaAs and ZnTe, we observed that
PtAl generates a stronger SHG signal, as discussed later in this section.

Figure 4: Second order nonlinear optical response of PtAl. (a) The 800 nm
incident near IR radiation shows the second harmonic around 400 nm and the
left inset is a spot size profile of the incident beam where $x$ and $y$
dimensions are 184 and 200 $\mu$m, respectively. The right inset denotes the
polarization axes in the lab frame with respect to the crystallographic
directions. (b) The SHG power of PtAl is measured for several pump fluences,
with the inset showing the SHG of GaAs for comparison. A fluence-dependent
term $I$ $\propto$ $F^{n}$ is fitted, where $n$ is the fitting parameter.

The SHG signal of PtAl has been analyzed with different pump fluence, as shown
in Figure 4(b) up to 50 mJ/cm2. An increase in the fluence increases the SHG
signal at 400 nm. It has been observed that for fluences above $\sim$ 25
mJ/cm2, the relationship between the fluence and response deviates from the
expected quadratic behavior, which is governed by semiclassical perturbation
theory. The fitting exponent (n) for PtAl is 1.59(2). The SHG response was
also measured for the standard GaAs(111) material as shown in the inset of
Figure 4(b), the exponent for GaAs was obtained as 1.99(1), which is very
close to the expected value of 2. Therefore, the deviation from the expected
quadratic behavior has also been observed in other topologically nontrivial
materials such as Cd3As2, Ta(As, P), RhSi which is attributed to the finite
Berry curvature of the wavefunctions incorporating single and two-photon
interband transitions, as shown by calculations for the RhSi compound [2, 62,
63, 64].

Figure 5: The SHG was measured for the materials GaAs(111), ZnTe(110), and
PtAl(110). The normalized SHG power for GaAs is shown in (a) and (b), for ZnTe
in (c) and (d), and for PtAl in (e) and (f). The measurements were taken for
each parallel and perpendicular crossing of the polarizer and analyzer at
nearly perpendicular incidence on the sample for an 800 nm wavelength.

As mentioned earlier, PtAl is a chiral crystal with a space group of
$P2_{1}3$, which has two-fold screw rotation symmetry but lacks inversion,
rotational, and mirror plane symmetries. The point group $23(T)$ for PtAl
allows only one non-zero susceptibility element, $\chi_{xyz}$ $=$ $2d_{14}$.
For the cubic crystal structure point group $T$ suggests the coexistence of a
three fold and two-fold rotational symmetries thus the nonzero $d_{14}$
confirms the chiral crystal structure of PtAl. The polarization tensor for the
second-order response in a nonlinear medium can be expressed as follows

$\begin{bmatrix}P(x)\\\ P(y)\\\
P(z)\end{bmatrix}=\begin{bmatrix}d_{11}&d_{12}&d_{13}&d_{14}&d_{15}&d_{16}\\\
d_{21}&d_{22}&d_{23}&d_{24}&d_{25}&d_{26}\\\
d_{31}&d_{32}&d_{33}&d_{34}&d_{35}&d_{36}\end{bmatrix}\begin{bmatrix}E_{x}^{2}\\\
E_{y}^{2}\\\ E_{z}^{2}\\\ 2E_{y}E_{z}\\\ 2E_{x}E_{z}\\\ 2E_{x}E_{y}\\\
\end{bmatrix}$

Where Ex, Ey, and Ez are the electric field components of the incident
polarized light in the lab frame on the sample.

The SHG signal of PtAl is analyzed using linearly polarized light incident
normally on the (110) crystallographic plane of the sample as illustrated in
the right inset of Figure 4(a), this also depicts the in-plane
crystallographic directions. Before the beam is incident on the sample, it
passes through a polarizer to make linear polarization of the incident beam.
The reflected light then passes through an analyzer before being detected by a
photodiode. The incident light polarization makes an angle $\theta$, with the
PtAl crystal axis [110], so the in-plane components of the electric field,
$E_{x}$ and $E_{y}$, can be expressed as $E_{x}=E_{0}\cos(\theta)$ and
$E_{y}=E_{0}\sin(\theta)$ along [110] and [100] crystallographic directions,
where $E_{0}$ is the amplitude of the electric field and $E_{z}=0$. The
angular dependence of SHG has been measured for PtAl and for comparison we
have also measured the angular dependence of the standard samples GaAs and
ZnTe by rotating both the polarizer and analyzer simultaneously in two
configurations of parallel and perpendicular crossings.

The transformed $d$ matrix from the crystal frame to the lab frame is as
follows:

$d=\begin{bmatrix}0&0&0&0&0&-d_{14}\\\ -d_{14}&0&d_{14}&0&0&0\\\
0&0&0&d_{14}&0&0\end{bmatrix}$

The intensity components, $I_{\parallel}(\theta)$ and $I_{\perp}(\theta)$, are
measured using the equations
$I_{\parallel}(\theta)=|P(x)\cos(\theta)+P(y)\sin(\theta)|^{2}$ and
$I_{\perp}(\theta)=|P(x)\sin(\theta)-P(y)\cos(\theta)|^{2}$, respectively. To
analyze the angle dependence of the SHG, the SHAARP.$si$ package is used [65].
The code requires the refractive index at 800 nm and 400 nm. These values,
n($\omega$) = 4.58 + 3.91$i$ and n($2\omega$) = 2.89 + 2.71$i$, were obtained
from the first principles calculations.

The polarization dependence of the SHG for GaAs(111), ZnTe(110), and PtAl(110)
is analyzed for the parallel and perpendicular crossings as depicted in Figure
5. The obtained $d_{14}$ parameter for GaAs and ZnTe are $\sim$311(1) and
$\sim$97.4(1) pm/V, respectively which is in close agreement with the
previously reported values [66, 63].

The $d_{14}$ coefficients obtained for the parallel and perpendicular
crossings of polarization in PtAl are around $\sim$468(1) and $\sim$516(5)
pm/V, respectively. There are recent optical SHG measurements on the type-II
Weyl semimetal $\beta$-WP2, leading to a strong SHG signal in the bulk
materials [67]. The $d_{14}$ coefficient for PtAl is higher than those
measured for standard GaAs(111), ZnTe(110), and $\beta$-WP2 compounds,
suggesting that PtAl is a potential candidate for SHG.

## CONCLUSIONS

We prepared a single crystal of PtAl using the Czochralski method and carried
out optical measurements along with XPS measurements. The pump probe
experiment results showed the relaxation of the bulk topological states,
including a slow electron-hole pair recombination. The SHG in PtAl does not
follow a conventional square law dependence on incident intensity, as
predicted by semiclassical perturbation theory due to interband transitions of
carriers. The obtained $d_{14}$ coefficient for PtAl is significantly high as
compared to standard samples such as ZnTe and GaAs. The comprehensive analysis
of the experimental data enhances our understanding of the PtAl system and
could be useful for further studies and potential technological developments.

## Acknowledgements

We acknowledge Professor Jyotishman Dasgupta and Debojyoti Roy for their help
in Raman measurements. We acknowledge Professor V. Gopalan and Zu Rui for
their expert help in SHAARP program. We also acknowledge TIFR central
workshop, Atul Raut, Gajendra Mulay and Rodney Bernard for their support in
building experimental set-ups.

## Data Availability

The data supporting the findings of the study is available and can be
requested from the corresponding author.

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# Optical phased array neural probes for beam-steering in brain tissue

Wesley D. Sacher1,2,3,†,∗ Fu-Der Chen2,3,† Homeira Moradi-Chameh4 Xinyu Liu1
Ilan Felts Almog2 Thomas Lordello2 Michael Chang4 Azadeh Naderian4 Trevor M.
Fowler1 Eran Segev1 Tianyuan Xue2 Sara Mahallati4 Taufik A. Valiante4,5,6
Laurent C. Moreaux1 Joyce K. S. Poon2,3 Michael L. Roukes1 1Division of
Physics, Mathematics, and Astronomy, California Institute of Technology,
Pasadena, California 91125, USA  2Department of Electrical and Computer
Engineering, University of Toronto, 10 King’s College Rd., Toronto, Ontario
M5S 3G4, Canada  3Max Planck Institute of Microstructure Physics, Weinberg 2,
06120, Halle, Germany  4Krembil Research Institute, Division of Clinical and
Computational Neuroscience, University Health Network, Toronto, Ontario,
Canada  5Division of Neurosurgery, Department of Surgery, Toronto Western
Hospital, University of Toronto, Toronto, Ontario, Canada  6Institute of
Biomaterials and Biomedical Engineering, University of Toronto, Toronto,
Ontario, Canada  †Equal contribution  ∗Corresponding author:
<EMAIL_ADDRESS>
###### Abstract

Implantable silicon neural probes with integrated nanophotonic waveguides can
deliver patterned dynamic illumination into brain tissue at depth. Here, we
introduce neural probes with integrated optical phased arrays and demonstrate
optical beam steering _in vitro_. Beam formation in brain tissue was simulated
and characterized. The probes were used for optogenetic stimulation and
calcium imaging.

Genetically encoded optogenetic actuators and fluorescence indicators have
become powerful tools in the interrogation of brain activity, since they
enable the control and imaging of neurons with high cell-type specificity and
single-cell spatial resolution [1, 2, 3]. Today’s optical systems for
optogenetics and functional fluorescence imaging, such as multi-photon
microscopes and implantable fiber optics, are typically built from bulk off-
the-shelf components and are physically large and complex [4]. Yet, advances
in silicon (Si) integrated photonics have led to the dense integration of
nanoscale waveguides and devices into millimeter-scale circuits that achieve
complex functions [5, 6]. Thus, Si photonic technology can be leveraged to
create nanophotonic tools that miniaturize optical systems for neurobiology
and deliver light into brain tissues in ways that are not possible with bulk
optics. One approach is to realize implantable chip-scale photonic devices
that deliver and control patterned illumination in brain tissues at depths
inaccessible by free-space optics, i.e., beyond the optical attenuation
length. Along these lines, nanophotonic waveguides with grating coupler (GC)
light emitters [7, 8, 9, 10] and micro-light-emitting-diodes ($\mu$LEDs) [11]
have been integrated onto implantable Si probes. In brain tissues, since light
mostly scatters forward [12], low-divergence beams can be emitted from GCs
over distances of 200-300 $\mu$m [7, 8]. Compared to $\mu$LEDs, nanophotonic
waveguide-based probes do not generate excess heat beyond that caused by the
light itself, can more precisely tailor the optical emission profile, are
compatible with wafer-scale foundry manufacturing [13, 9], and can achieve a
high light source density. Furthermore, as evidenced by the recent
advancements in Si photonic beam-forming [5, 14, 15], sophisticated gratings
and photonic circuit designs can enable precisely patterned illumination with
high spatial resolution.

Here, we report the first implantable Si neural probes capable of optical
beam-steering in tissue. The probes use silicon nitride (SiN) optical phased
arrays (OPAs) as light emitters; the emitted beams were steered by wavelength
tuning. The OPAs were designed to operate at blue wavelengths for the
excitation of the opsin Channelrhodopsin-2 (ChR2) and the genetically encoded
calcium indicator GCaMP6. The probes were validated _in vitro_ in mouse brain
slices, demonstrating sufficient power for optogenetic stimulation and
functional imaging as well as spatial control of the beam on the neuron scale.
A preliminary report of this work appeared in [16].

Figure 1: OPA neural probes. (a) Schematic of the OPA neural probe connected
to the scanning system (inset) optical micrographs of an image fiber bundle
facet with cores addressed by the scanning system. (b) Scanning electron
micrograph (SEM) of one of the shanks of an OPA neural probe (inset) SEM of a
portion of the SiN gratings prior to top cladding deposition during
fabrication. (c) Photograph and micrographs of an OPA neural probe. (d)
Illustration of the experimental apparatus for testing the neural probes in
brain slices. Abbreviations: microelectrode array (MEA), artificial
cerebrospinal fluid (ACSF). (e, f) Photographs of the packaged OPA neural
probe emitting light in fluorescein; (e) has a smaller field of view and
external illumination applied for visibility of the shanks, (f) shows the
emitted beams (zoomed out, no illumination). (b, c, e, f) are from [16]; the
fiber bundle inset of (a) is from [9].

Figure 1 shows the OPA neural probes, which consisted of 4 shanks, each $\sim
18$ $\mu m$ thick, 3 mm long, and 50 $\mu m$ wide, on a 250 $\mu m$ pitch, and
a thicker base region. The SiN waveguides were 200 nm thick. The probes were
fabricated on 100 mm diameter silicon-on-insulator wafers as described in [7].
On each shank were 4 OPAs, with the design shown in Fig. 1(b). A star coupler
split the light in the input waveguide into 16 delay line waveguides. The
delay lines were routed for a differential path-length, and each terminated
with a light-emitting grating. As the input wavelength was tuned, the
differential phase-shift between the light-emitting gratings led to the
angular steering of the emission [17]. The delay lines consisted of waveguides
with an initial single-mode width of 240 nm following the star coupler for a
length of 12 $\mu$m that adiabatically widened to 400 nm to reduce phase
error. The differential length of the delay lines was 16 $\mu$m, chosen so the
free spectral range (FSR) ($\sim 6$ nm) matched the wavelength tuning range of
our external cavity diode laser of 484.3 to 491 nm. The pitch and width of the
arrayed gratings in the OPA were 700 nm and 300 nm, respectively. The period
of each grating was 440 nm; in water, the steering plane [Fig. 1(a)] was
angled at $\sim 25^{\circ}$ from the normal of the probe. The OPAs were
designed for low crosstalk between the arrayed waveguides. The array pitch was
significantly larger than the half-wavelength criterion for emission of a
single grating order, and typically 3 lobes were emitted from each OPA.
Optimization of the array pitch, increased SiN thickness for higher optical
confinement and lower crosstalk, and apodization [15] may suppress these
additional lobes. In the following, we focus on one of the OPA neural probes
that was packaged and studied in detail.

Figure 2: Characterization of the neural probe beam profiles in fluorescein.
(a) Top-down beam profiles at various wavelengths ($\lambda$). (b) Side
profile of the beam at $\lambda=484.3$ nm; the top surface of the shanks is
delineated by the dashed line. The scale bars are (a) 50 $\mu$m, (b) 100
$\mu$m. (c) Top-down measured (“Exp”) and simulated (“Sim” in water) FWHM beam
width versus propagation distance of the central lobe at $\lambda=491$ nm.

The probe was passive to reduce tissue heating, and the 16 OPAs on the probe
were independently addressed using the spatial addressing scheme in [18, 9].
As shown in Fig. 1(a), a micro-electro-mechanical system (MEMS) mirror
deflected a laser beam into individual cores of an image fiber bundle, which
was attached to the probe base. Each fiber core was aligned to an edge coupler
on the probe, which was connected to an OPA on the shank. The switching time
of the MEMS mirror was $\sim 5$ ms. About $\sim 10$ $\mu W$ was emitted from
each OPA.

Figure 3: OPA intensity top-down beam profiles in brain tissue. (a) Simulated
and (b) measured beam profiles at 4 wavelengths. In (b), the OPA neural probe
was inserted into a brain slice from a VGAT-ChR2-EYFP mouse [see Fig. 1(d)].
Left: top-down intensity beam profile images; right: intensity versus emission
angle ($\phi$) at a propagation distance of 100 $\mu$m (i.e., along arcs of
radius 100 $\mu$m centered on the emitting region of the OPA). (c) Measured
and simulated FWHM beam width versus propagation distance. (d) Measured and
simulated ratios of peak beam intensity to background intensity versus
propagation distance. The wavelength in (c,d) is 490 nm. The simulated results
in (c,d) are an average over 10 simulations with different phase masks (see
Supplementary Materials) and the bars represent the standard deviation of the
10 simulations; the beam profiles in (a) are from a single simulation.

Following the method in [9], to characterize the emitted beam profiles in non-
scattering media, the probe was immersed in a fluorescein solution and the
fluorescence was imaged. The setup in Fig. 1(d) was used, but with the chamber
replaced with a container of fluorescein; the probe was angled so the emitted
beams were parallel to the fluid surface. Top-down images of the emission
pattern from the probe at various wavelengths are shown in Fig. 2(a). Over a
wavelength tuning range from 484.3 to 491 nm, the beams were steered
continuously $\pm 16^{\mathrm{o}}$ with narrow beams formed within a distance
of 300 $\mu m$ (Fig. 2). The two side lobes were at angles of about $\pm
32^{\mathrm{o}}$ from the main beam. Figure 2(b) shows the beam profile imaged
from the side; the full-width-at-half-maximum (FWHM) thickness was $<19$ $\mu
m$ over a 300 $\mu m$ propagation distance. The peak intensity of the main
lobe was 7 to 17$\times$ larger than the background light intensity at
propagation distances of 50 to 300 $\mu$m, Fig. 2(a). A significant component
of the background was due to optical scattering from the photonic circuit.

OPA beam formation in brain tissue was verified and investigated in simulation
and experiment. The simulation method is described in Supplementary Materials;
the scattering coefficient ($\mu_{s}$) $=200$ cm-1, the absorption coefficient
($\mu_{a}$) $=0.62$ cm-1, and the anisotropy of tissue ($g$) $=0.83$. The
simulated beam profiles, Fig. 3(a), show that the optical scattering leads to
broadening of the emitted beams, a background generated between the lobes, and
a reduction in intensity with propagation distance. Over the majority of the
steering range, the FWHM beam width is $<17$ $\mu$m and the ratio of peak beam
intensity to background intensity is $>2.8$ for propagation distances of 50 to
150 $\mu$m, Figs. 3(c), 3(d), S1, and S2. Experimental validation of the OPAs
in brain tissue was performed by inserting the probe at shallow depths (OPA
$<100$ $\mu$m from the surface) into perfused _in vitro_ brain slices from
adult transgenic mice co-expressing Channelrhodopsin-2 and yellow fluorescent
protein (VGAT-ChR2-EYFP, [19]) and another strain of mice expressing the
genetically-encoded calcium indicator GCaMP6s (Thy1-GCaMP6s, [2]). The tissue
preparation is described in Supplementary Materials. All experimental
procedures described here were reviewed and approved by the animal care
committees of the University Health Network in accordance with the guidelines
of the Canadian Council on Animal Care.

Fluorescence images of the OPA beam profiles in cerebellar brain slices from
the VGAT-ChR2-EYFP mice were captured using the excitation of the YFP by the
OPA illumination and the setup in Fig. 1(d). Steerable beams were formed, as
shown in Figs. 3(b)-(d) and S2, with the FWHM beam width $<23$ $\mu$m and the
ratio of peak beam intensity to background intensity $>2.7$ for propagation
distances of 50 to 150 $\mu$m. Cerebellar slices were selected for their
relatively uniform YFP labeling; some non-uniformity was evident from the
intensity maxima in the Fig. 3(b) top-down images. As a simple test of
functional imaging, the probe was inserted into a hippocampal brain slice from
a Thy1-GCaMP6s mouse. The lobes of the OPA illuminated 3 neurons, or small
clusters thereof, and spontaneous time-dependent fluorescence was detected
with high contrast, Fig. 4. The rise and fall times of the calcium events
agreed with reported GCaMP6s dynamics [2].

Figure 4: Functional imaging test of the OPA neural probe inserted into a
brain slice from a Thy1-GCaMP6s mouse. (a) Top-down fluorescence images at
times t = 0 s and 22.7 s showing a calcium event in the central lobe; the OPA
emitter position is marked with “X”. (b) Change in fluorescence ($\Delta F/F$)
time traces of the regions of interest delineated in (a). Figure 5:
Optogenetic stimulation tests of the OPA neural probe (fixed wavelength)
inserted into brain slices on an MEA. (a,b) Illumination was applied from a
single OPA, and (c,d), in a different brain slice, illumination was applied
sequentially from 4 OPAs. The fluorescence images (a,c) show the relative
positions of the OPAs and the relevant MEA electrodes for (b,d); epi-
illumination from the top-down microscope was applied for visibility of the
shanks and the structure of the brain slice via the YFP labeling. The scale
bars are 500 $\mu$m. (b) Extracellular recording and examples of sorted spikes
from Channel (“Chn”) 42 of the MEA, as marked in (a), with illumination from
an OPA. (d) Extracellular recording showing the average number of spikes per
optical pulse from 4 of the OPAs on MEA Chn 53 and 51 as marked in (c). Each
point is from one stimulation trial consisting of 3 sets of 10 optical pulses;
the pulse width was 50 ms, the period was 200 ms, and the recovery period
between each set of 10 pulses was 10 s. The optical power was reduced across
the trials for each OPA. The error bars represent the standard error of the
mean spikes per pulse during a trial.

Optogenetic stimulation was tested by inserting the probe into VGAT-ChR2-EYFP
mouse cerebellar brain slices. Here, the probe orientation was modified
compared to Fig. 1(d) so that the probe emitted light nearly orthogonal to the
tissue surface (see Fig. S3, Supplementary Materials). Pulsed light was
applied, and extracellular electrophysiological signals were recorded by a
microelectrode array (MEA) beneath the brain slice. Robust spiking with
illumination from the neural probe was observed, Fig. 5(b), showing that the
optical intensity was sufficient for optogenetic stimulation. However, the
precise positions of the stimulated neurons relative to the OPA were unknown.
Spatial differences in the activity patterns across the MEA were not always
repeatable with the steering of the beam. We hypothesize this was due to one
or more of the following reasons: 1) the interconnectedness of the neurons, 2)
ChR2 expression in inhibitory rather than excitatory cells in VGAT-ChR2-EYFP
mice, and 3) the spacing between the OPA lobes and background between them.
Figure 5(d) supports the first 2 hypotheses. Figure 5(d) shows the correlation
in the spiking activity recorded at two microelectrodes in the same column
(Channels 53 and 51) in the MEA as a result of the excitation from 4 of the
OPAs on the probe. Here, illumination from one OPA on each shank was
sequentially applied (the OPAs belong to the same row), and a number of trials
with decreasing optical power were performed. The spike rates on Channels 53
and 51 indicated that lateral shifts of the illumination on the order of the
shank pitch (250 $\mu$m) were necessary for repeatable changes in the activity
patterns across the MEA (e.g., comparing the trends of OPAs 1 and 2).
Generally, the number of spikes per pulse increased with the optical power.
The experiments, data analysis, and additional data (Fig. S4) are detailed in
Supplementary Materials.

In summary, we have presented the first implantable Si neural probes with
integrated OPAs for generating steerable optical beams in brain tissue. Beam
formation was confirmed in simulation and _in vitro_ brain slices, and the
emitted intensity was sufficient for optogenetic stimulation and functional
imaging. The OPA feature sizes are compatible with photonic foundry processes
[13, 9]; OPAs at green/red wavelengths can be realized with larger feature
sizes for excitation of other opsins and fluorophores. These results show the
possibilities for delivering patterned, dynamic illumination at depth in brain
tissue for brain activity mapping [20].

Funding. National Institutes of Health (NS090596, NS099726); Caltech Kavli
Nanoscience Institute; Canadian Institutes of Health Research; Natural
Sciences and Engineering Research Council of Canada; Canadian Foundation for
Innovation.

Disclosures. The authors declare no conflicts of interest.

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Optical phased array neural probes for beam-steering in brain tissue:
Supplementary materials

##  I Optical Phased Array Beam Profile Simulations

We applied the beam propagation method (BPM) to simulate the optical
scattering in tissue [1]. The model simulates the forward propagation of a
beam in tissue with an iterative two-step process: 1) a two-dimensional phase
mask is applied to the propagating beam, the phase mask has a small phase
variance about the mean phase, which is equal to 0, and 2) beam propagation
between the phase masks is assumed to only diffract, and it is modeled with
the angular spectrum method [2]. The scalar electric field, $E$, is given by

$E(k_{x},k_{y},z+d)=E(k_{x},k_{y},z)\mathrm{e}^{in\sqrt{k^{2}-k_{x}^{2}+k_{y}^{2}}d},$
(S1)

where $d$ is the propagation distance, $n$ is the average refractive index of
the medium, and $k$ is the wavenumber ($k_{x}$ and $k_{y}$ are $x$ and $y$
components of the corresponding wavevector). The amplitude of any wave with
$k_{x}^{2}+k_{y}^{2}>k$ is set to 0 as it is evanescent. The model is
applicable to brain tissue since the beam is mostly forward scattered and its
simulation results have been validated with the analytical solutions from the
radiative transfer equation [1].

The patterns of the phase masks determine the scattering properties of the
medium. We followed the design strategy in [1] to create the phase mask
patterns. Each phase mask introduced a spatially varying random phase to the
fields with the statistical properties governed by $\sigma_{p}$ and
$\sigma_{x}$. $\sigma_{p}$ adjusted the variance of the phase introduced by
each phase mask, which affected the scattering coefficient. Each phase mask
was smoothened by a Gaussian filter with variance $\sigma_{x}$ to control the
phase correlation between pixels, which affected the anisotropy value. We also
multiplied the beam profile with the attenuation factor after each propagation
step. For the scattering simulation, we set the scattering coefficient
($\mu_{s}$) to 200 $cm^{-1}$, the anisotropy of the tissue ($g$) to 0.83, and
the attenuation coefficient ($\mu_{a}$) to 0.62 $cm^{-1}$ [3].

The field 3 $\mu m$ above the optical phased array (OPA) was calculated and
used as the launch field for the above propagation simulations. The SiO2
cladding thickness above the OPA was 1 $\mu m$. To calculate the launch field,
the emission field from a single grating emitter array element of the OPA was
first obtained (3 $\mu m$ above the grating) using finite difference time
domain (FDTD) simulations, with the simulations performed for transverse
magnetic (TM) polarized light in the waveguides. Then an array of single
grating emitter field profiles was generated via laterally shifting the
position of each subsequent emitter by the array pitch and applying phase
shifts to each field profile corresponding to the wavelength and delay line
parameters of the array element. Finally, the OPA field was the sum of the
arrayed field profiles. This process was repeated for each simulated
wavelength. The nominal OPA dimensions reported in the manuscript were used
for the simulations. In addition, we corrected for the amplitude distribution
across the output ports of the OPA star coupler by multiplying the emitter
field profiles by an envelope function. We set the simulation domain volume to
be $500\mu m$ x $500\mu m$ x $250\mu m$ to avoid any edge effects while
containing the entire simulation in the computer memory.

The same simulation model was used to study the OPA beam profiles in a non-
scattering medium (water) with all phase masks set to a uniform value of 0.
For verification, we compared cross-sections of beam profiles obtained from
the BPM simulations and the conventional diffraction integral method. No
significant differences were observed between the two methods at propagation
distances of up to 200 $\mu m$.

After the BPM simulations, we performed a series of steps to determine the 2D
beam profile that would be expected from a top-down microscope as in the
experimental apparatus in Fig. 1(d). First, we stacked the beam profile cross-
sections to form a 3D model of the beam in tissue. We then rotated the model
so that the beam propagation axis was parallel with the horizontal plane.
Bicubic spline interpolation was used to interpolate the pixel values on the
new grid of the rotated coordinate system. Lastly, a 2D beam profile was
obtained by filtering and adding together the transverse planes of the 3D beam
profile model, i.e., all planes parallel to the microscope focal plane. To
approximately emulate the microscope resolution limit, we applied a Gaussian
filter to each transverse plane with filter size equal to the Gaussian
propagation beam waist,

$w(z)=w_{0}\sqrt{1+\left(\frac{\lambda z}{\pi w_{0}^{2}}\right)^{2}},$ (S2)

where $w_{0}$ is the point spread function of the objective used in the
experimental apparatus [Fig. 1(d)], and $z$ is the distance of the transverse
plane from the focal plane. For each simulation, the transverse plane with the
highest intensity at the input to the scattering medium was selected as the
focal plane.

The simulated and measured top-down beam profile FWHM values and peak-to-
background ratios in Figs. 2, 3, and S2 were calculated along concentric arcs
centered on the OPA emitting region; the radius of each arc was equal to the
propagation distance. For FWHM beam width calculations, the maximum was simply
the maximum intensity along the arc, while for peak-to-background ratio
calculations, to reduce the impact of noise, the peak intensity was defined as
the average of the top 1% of intensity data points along the arc. The
background intensity for the peak-to-background ratio calculations was defined
as the intensity in the troughs between adjacent lobes. As the OPA beam
profiles typically had 3 lobes (Figs. 2 - 3), the background intensity was
calculated considering only the higher of the 2 troughs between the 3 lobes.
The trough intensity was calculated as the average of the lowest 1% of
intensity data points along the arc in the trough. The arcs spanned the
central lobe and the two adjacent troughs.

##  II Experimental apparatus

The scanning system in Fig. 1(a) is detailed in [4], with the exception that a
wavelength-tunable laser was used here rather than a fixed wavelength laser.
Briefly, light from the wavelength-tunable laser (TOPTICA Photonics Inc., DLC
DL pro tunable laser system with integrated optical isolator, fiber coupler,
motorized wavelength tuning, 484.3 - 491 nm wavelength tuning range) was
coupled into a single-mode fiber (460-HP, Nufern Inc.), which was connected to
an inline fiber polarization controller. The laser light was launched into
free space using a fiber collimator, and this free-space laser beam was gated
by a mechanical shutter, directed through a variable neutral density filter
(for control of optical power), and input into the scanning system, as shown
in Fig. 1(a). The scanning system included a 2-axis micro-electro-mechanical
system (MEMS) mirror (A7B2.1-3600AL, Mirrorcle Technologies Inc.), two
biconvex lenses with 35- and 150-mm focal lengths, and a 20$\times$ objective
lens (Plan Apochromat, 20-mm working distance, 0.42 numerical aperture,
Mitutoyo Corporation). Actuation of the MEMS mirror enabled addressing of
individual cores of the image fiber bundle (Fujikura FIGH-06-300S). The fiber
bundle was optically coupled to and packaged together with the OPA neural
probe using the method described in [4]. The packaged probe was attached to a
4-axis micro-manipulator (QUAD, Sutter Instrument Company) for immersing the
probe in the fluorescein solution (10 $\mu$M concentration, pH $>9$) and
inserting the probe into the brain slices. Since the OPA beam profiles were
polarization-dependent, the fiber bundle was fixed in position during the
experiments (to avoid polarization fluctuations due to movement of the fiber
bundle). The input light to the neural probe chip was TM-polarized.

The maximum optical power available at the input to the scanning system was
about 2 mW, and the loss of the scanning system (measured from the free-space
input of the scanning system to the distal facet of the fiber bundle) was
typically 40 - 60$\%$ (with the neutral density filter set to its minimum
loss). The transmission of the OPA neural probe chip (from the facet of an
optimally aligned single-mode fiber to the free-space OPA output) was
typically about -20 dB. As described in [4], the edge couplers accounted for
roughly 10 dB of this loss, and improved edge coupler designs may greatly
improve the optical transmission of OPA neural probes. In addition, deviations
of the fiber bundle core positions from a regular pitch and fiber misalignment
during the optical packaging procedure resulted in significant variations in
the coupling efficiency between the fiber bundle cores and the edge couplers
of the neural probe. As a result, the total transmission of the OPAs (from the
input to the scanning system to the free-space OPA output) varied from about
-23 dB to -40 dB, with the majority of the OPAs having transmissions between
about -23 to -33 dB.

The experimental apparatus used for OPA beam characterization and _in vitro_
testing of the neural probe [Figs. 1(d) and S3] included a Nikon Eclipse FN1
upright epifluorescence microscope with an sCMOS camera (Zyla 4.2 PLUS, Andor
Technology Ltd.) and a 10$\times$ objective lens (Plan Apochromat, 34-mm
working distance, 0.28 numerical aperture, Mitutoyo Corporation). The images
captured by the microscope were inverted (i.e., vertically mirrored). No image
processing to correct the image inversion was applied, and the beam profile
images [Figs. 2(a), 3(b), and 4(a)] and epifluorescence brain slice images
[Figs. 5(a), 5(c), and S4(a)] are inverted. For the fluorescein and
Thy1-GCaMP6s mouse brain slice imaging, an EGFP filter cube (49002, Chroma
Technology Corporation) was used in the epifluorescence microscope, and for
the VGAT-ChR2-EYFP mouse brain slice imaging, an EYFP filter cube (49003,
Chroma Technology Corporation) was used. The camera exposure time was: 50 ms
for the fluorescein beam profile images in Fig. 2(a), 500 ms for the _in
vitro_ brain slice beam profile images in Fig. 3(b), and 25 ms for the _in
vitro_ brain slice calcium imaging in Fig. 4. The microelectrode array (MEA)
was a perforated design with 60 titanium nitride electrodes, 30 $\mu m$
electrode diameter, and 100 $\mu m$ electrode pitch (60pMEA 100/30iR-Ti-pr-6
mm high plastic ring, Multi-Channel Systems). MEA electrical activity
recordings were performed using a MEA-1060-Up-BC amplifier and the MC Rack
software (Multi-Channel Systems). The sampling rate for the MEA recordings was
25 kHz.

##  III Brain slice preparation

All experimental procedures described here were reviewed and approved by the
animal care committees of the University Health Network in accordance with the
guidelines of the Canadian Council on Animal Care. Brain slices were prepared
from 40 - 80 days old VGAT-ChR2-EYFP (The Jackson Laboratory, stock number
014548) and Thy1-GCaMP6s (The Jackson Laboratory, stock number 025776) mice
for the _in vitro_ beam profile/optogenetic stimulation and the _in vitro_
calcium imaging experiments, respectively; the brain slice preparation is
detailed in [4]. 350 $\mu$m thick sagittal slices from the cerebellum were
used for the _in vitro_ beam profile and optogenetic stimulation experiments
(Figs. 3 and 5). A 300 - 450 $\mu m$ thick horizontal slice from hippocampus
was also tested during the beam profile experiments, but the labeling was
significantly more non-uniform compared to the slices from the cerebellum. The
calcium imaging experiment used a 350 - 450 $\mu m$ thick horizontal slice
from hippocampus. For the optogenetic stimulation and imaging experiments,
brain slices were transferred to the MEA chamber, Figs. 1(d) and S3, and
perfused with a constant flow of rodent artificial cerebrospinal fluid (ACSF)
[5], which was continuously aerated with carbogen. During imaging of the
Thy1-GCaMP6s mouse brain slice, KCl was added to the ACSF to increase the
excitability of the neurons and the amount of spontaneous neuronal activity;
the KCl concentration in the ACSF was 30 mM.

##  IV Optogenetic Stimulation Protocol

For the single-OPA optogenetic stimulation experiment shown in Fig. 5(b), 10
optical pulses with a pulse width of 30 ms and a period of 200 ms were applied
to the brain slice. A recovery period of 10 s was used after each stimulation
pulse train. We repeated the pulse train 10 times.

For the multi-OPA optogenetic stimulation experiments shown in Figs. 5(d) and
S4, multiple “stimulation trials” were performed, and for each trial,
illumination was applied to the brain slice from one of the 4 OPAs in Figs.
5(c) and S4(a). Each trial corresponds to a point in Figs. 5(d) or S4(b), and
the optical power was varied between trials. Each stimulation trial consisted
of 3 sets of 10 optical pulses; the optical pulse width was 50 ms, the period
was 200 ms, and the recovery period between each set of 10 optical pulses was
10 s. 7-8 trials with different optical power settings were performed for each
OPA by using the variable neutral density filter in the experimental apparatus
to reduce the input optical power to the scanning system in steps of
approximately 10$\%$ of the maximum power. The trials were performed in the
following order: 1) the optical power was set to the maximum value, 2) a trial
was performed for each OPA sequentially (from OPA 1 to 4), 3) the optical
power was reduced by a 10$\%$ increment, 4) the next set of OPA trials was
performed. This process was repeated until 7-8 trials were performed for each
OPA; at the lowest power setting, $<1$ spike per optical pulse (on average)
was observed. This procedure ensured that the stimulated electrical response
caused by different OPAs could not have been simply due to variations in
optical power between the OPAs. The recovery period between trials of the same
optical input power but different OPAs was typically 20-60 s. The recovery
period between trials where the input power was changed was 10-70 s and
limited by the time required to adjust the variable neutral density filter.

##  V Spike Sorting of Microelectrode Array Recordings

Spike sorting of the microelectrode array recordings was performed to analyze
the data from the optogenetic stimulation experiments (Figs. 5 and S4). The
full electrical traces from each experiment, spanning all optical pulse trains
and the recovery periods between them, were analyzed. We performed spike
sorting with the Spyking Circus package [6]. We selected electrode channels
where neuronal activity was detected in response to the optical stimulation. A
bandpass filter with a passband from 300 to 3000 Hz was applied to the signal
from each electrode channel. Then, any negative spike with amplitude larger
than 6 times the mean absolute deviation was selected as a valid spike. Each
spike waveform was extracted from a 3 ms time window centered at the spike
peak. Then, to extract spike templates, a subset of 10000 spikes was selected;
for data sets with $<10000$ spikes, all spikes were selected. The selected
spikes were projected to a lower dimension using Principal Component Analysis.
We selected the first 5 prominent components as the basis. Then a density-
based spike clustering algorithm was applied to cluster spikes with similar
waveforms [6]. The median of the spike waveform in the same cluster was
defined as the spike template of the cluster. Template matching was performed
to decompose all spikes as a linear combination of the templates, addressing
the problem of overlapping spikes [6]. Lastly, we performed a manual
inspection of the sorted spikes in the phy GUI interface [7]. We selected the
clusters that meet the following four criteria: 1) isolation distance $>10$,
2) likelihood ratio $<0.3$, 3) signal to noise ratio (SNR) $>2$ [8, 9, 10],
and 4) the percentage of spikes with interspike intervals $<2$ ms was less
than 2% when only considering the spikes in the optical stimulation windows.
Only sorted spikes within an optical stimulation pulse window were accounted
for in the spike rate calculations.

##  VI Supplementary Figures

Figure S1: Additional data for the OPA top-down beam profile simulations in
brain tissue shown in Fig. 3(a). Here, the beam profiles from Fig. 3(a) have
been cropped by 30 $\mu m$ on the left side (closest to the OPA). The
visibility of the beam profiles is improved since the large beam intensity at
the OPA emitter is removed and each intensity color scale is normalized to the
maximum of the lobes after they have separated. Figure S2: Additional data for
the OPA top-down beam profile simulations and measurements shown in Fig. 3.
Simulated and measured intensity beam profile characteristics are shown at
wavelengths of 486, 487 and 488 nm. (a) Measured and simulated FWHM beam width
versus propagation distance. (b) Measured and simulated ratios of peak beam
intensity to background intensity versus propagation distance. Each data point
for the simulated beam profiles from (a) and (b) is an average over 5
simulations with different random phase masks. The bars represent the standard
deviation of the 5 simulations at each propagation distance. The FWHM plot for
$\lambda=486$ nm shows 2 simulations: ”Sim 1” is the simulated FWHM of the
central lobe emitted by the OPA, and ”Sim 2” is the FWHM of a side lobe. The
inset shows the simulated intensity ($I$) profile from Fig. 3(a) (propagation
distance $=100$ $\mu$m, $\lambda=486$ nm) with arrows indicating the lobes
corresponding to ”Sim 1” and ”Sim 2”. The central lobe is less intense than
the side lobes at this wavelength, a result of the non-uniformity of the
emissions of the individual gratings in the OPA versus steering angle $\phi$,
i.e., the envelope of the emitters. Consequently, for propagation distances
beyond $\approx 120$ $\mu$m, the background intensity contributes more
significantly to the FWHM of the central lobe than the side lobes, leading to
a large FWHM for ”Sim 1” relative to ”Sim 2” and $\lambda=$ 487 and 488 nm.
Figure S3: Illustration of the experimental apparatus for testing optogenetic
stimulation of brain slices using the OPA neural probe. Here, the probe has a
different orientation compared to Fig. 1(d). This experimental apparatus was
used for the measurements in Figs. 5 and S4.

Figure S4: Additional optogenetic stimulation experiment showing the
stimulation effects of 4 of the neural probe OPAs on an _in vitro_ brain
slice. The experiment was performed on a 350 $\mu$m thick sagittal cerebellar
slice obtained from a VGAT-ChR2-EYFP mice; the same brain slice as in Figs.
5(c) and (d). The fluorescence image (a) shows the relative positions of the
OPAs with respect to the MEA channels of interest; epi-illumination from the
top-down microscope was applied for visibility of the shanks and the structure
of the brain slice. The scale bar is 500 $\mu$m. (b) shows the average number
of spikes per optical pulse from 4 of the OPAs on two different MEA channels
(“Chn”). As in Fig. 5(d), each point in (b) is from one stimulation trial
consisting of 3 sets of 10 optical pulses; the optical pulse width was 50 ms,
the period was 200 ms, and the recovery period between each set of 10 optical
pulses was 10 s. The optical power was reduced across the trials for each OPA.
The error bars represent the standard error of the mean number of spikes per
pulse in a trial.

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