Nonlinear optics in gallium phosphide cavities: simultaneous second and third harmonic generation - arXiv
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
Nonlinear optics in gallium phosphide cavities: simultaneous second
and third harmonic generation
arXiv:2202.00130v1 [physics.optics] 31 Jan 2022
Blaine McLaughlin1 , David P. Lake2,1 , Matthew Mitchell3,1 , and Paul E. Barclay1,*
1
Department of Physics and Astronomy and Institute for Quantum Science and
Technology, University of Calgary, Calgary, AB, T2N 1N4, Canada
2
Department of Applied Physics & Materials Science, California Institute of Technology,
Pasadena, CA, 91125, United States
3
Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver,
BC, V6T 1Z4, Canada
*
Corresponding author: pbarclay@ucalgary.ca
February 2, 2022
Abstract linear optical effects into on-chip photonics platforms
[25]. The high degree of optical confinement provided
We demonstrate the simultaneous generation of sec- by whispering gallery mode microcavities allows for
ond and third harmonic signals from a telecom wave- integrated nonlinear devices with great efficiency and
length pump in a gallium phosphide (GaP) mi- a high degree of control over the nonlinear behavior.
crodisk. Using analysis of the power scaling of both For example, nonlinear phenomena such as second
the second and third harmonic outputs and calcu- harmonic generation (SHG), sum frequency genera-
lations of nonlinear cavity mode coupling factors, we tion (SFG), third harmonic generation (THG) and
study contributions to the third harmonic signal from Kerr frequency comb generation have been realized in
direct and cascaded sum frequency generation pro- lithium niobate (LN) [6, 35, 31, 27, 30, 9, 58, 11, 8, 7],
cesses. We find that despite the relatively high mate- SiN [23, 37, 41], AlN [40, 4, 16], GaN [46, 34], GaAs
rial absorption in gallium phosphide at the third har- [19], GaP [43, 44, 28, 22, 48, 55], and AlN/SiN com-
monic wavelength, both of these processes can be sig- posite [51] microcavities.
nificant, with relative magnitudes that depend closely Many nonlinear photonic devices are designed for
on the detuning between the second harmonic wave- the optimization of a specific nonlinear process. How-
length of the cavity modes. ever, nonlinear photonic materials often possess sig-
nificant optical nonlinearities in both the second and
third order. While unwanted nonlinear effects of
1 Introduction a given order can be minimized through device de-
sign, for sufficiently large nonlinearities, both second
In recent years, resonant cavity structures have been and third-order processes contribute to a device’s re-
used in a wide range of applications within integrated sponse. In particular, generation of the third har-
photonics. In particular, whispering gallery mode mi- monic may occur due to competing second- and third-
crocavities have allowed for the incorporation of non- order nonlinear processes [25]: the process of cas-
1
caded sum frequency generation (CSFG), a second-
order nonlinear process that can produce a third har-
monic, occurs independently of direct third harmonic
generation (DTHG). These competing processes and
their efficiencies will in general depend on the relative
strengths of the material’s nonlinear susceptibilities
and the device’s optical mode spectrum. A device
could be designed with parameters to optimize the
generation of one process over another following the Figure 1: (a) Energy level diagram of the SHG, CSFG
theory in reference [25]. However, in a non-optimized and THG processes. Solid lines indicate WGM reso-
device the contributions from each harmonic gener- nant modes, while dashed lines represent virtual en-
ation process may not be immediately obvious.It is ergy levels. (b) Image of FDTD simulated field mag-
therefore necessary to develop experimental method- nitude of the TE23,1 microdisk mode.
ology for discerning the contributions from each pro-
cess to the third harmonic signal.
Generation of simultaneous SH and TH signals has Section 4 we compare these results with theory, and
previously been observed in LN [27, 26], Mg:LN [47], discuss future improvements for enhancing SH and
and GaP [48] microcavities. However, in these cases TH processes in these devices.
the third harmonic generation process is assumed
to be either CSFG (in LN) or DTHG (in GaP). A
detailed study of the generation processes of third 2 Theory of harmonic genera-
harmonic signals in these devices has not yet been tion in microdisks
performed. Here we demonstrate the simultaneous
observation of SH and TH signals generated from a The GaP microdisk devices used in this experiment
telecom pump in a GaP microdisk cavity and mea- were fabricated following the process in Ref. [33]. The
sure their dependence on pump power and wave- device under study has a radius of 3.05 µm and a
length. These harmonic signals can be attributed, thickness of 250 nm, with a sidewall angle of 70◦ re-
respectively, to a quasi-phase matched (QPM) SHG, sulting from the fabrication process. Previous ex-
and both DTHG and a QPM CSFG processes. The periments using these devices include observation of
presence of CSFG is indicated by a saturation of optomechanical coupling [33] and SHG from telecom-
the SH signal at high input power. Through use munication to near-IR wavelengths [22]. During the
of coupled-mode theory, we predict that the third SHG experiments, an additional signal corresponding
harmonic output power from CSFG and DTHG will to a third harmonic was also observed, but not stud-
scale differently with the coupled first harmonic in- ied in detail. A similar TH signal was observed but
put power. Additional analysis was performed with not studied in detail in an independent experiment
FDTD simulations. Using the simulated whispering with GaP photonic crystals by Schneider et al. [48].
gallery modes (WGMs) of our microdisk devices, we The presence of simultaneous SH and TH generation
calculate the nonlinear mode coupling factors that indicates that despite higher loss due to material ab-
dictate the strength of the nonlinear mode interac- sorption in GaP at the green TH wavelength, wave-
tions, and find that they are consistent with experi- length conversion with sufficiently high efficiency is
mentally observed behaviour. still possible. However, we can not naively assume
We begin in Section 2 by theoretically analysing that one of CSFG or DTHG is the process primarily
the nonlinear harmonic generation processes in gal- responsible.
lium phosphide microdisks. In Section 3 we use this Figure 1a shows an example energy diagram of the
theory to analyse experimentally observed SH and possible harmonic generation processes. Light at fre-
TH signals from a gallium phosphide microdisk. In quency ω0 is coupled from a waveguide into a mi-
2
crodisk supporting a mode with frequency ω1 close the phase matching conditions of a nonlinear process
to ω0 . Efficient nonlinear wave mixing processes can can be expressed in terms of the azimuthal indices
occur when the cavity also supports higher frequency m [20]. Additional angular momentum quanta are
modes whose frequencies are near the harmonics of accumulated due to the Berry phase of the WGM
the fundamental mode at ω1 . We consider a device orbiting the cavity [53], whose amount depends on
with modes at frequencies ω2 ≈ 2ω1 and ω3 ≈ 3ω1 . the symmetry of the cavity material’s crystal lattice
While the excitation of photons from ω1 to ω2 will [29]. GaP possesses 43m symmetry, with the crys-
dominantly occur through SHG, excitation to ω3 can tal axis inverting with a π/2 rotation. The second-
occur through two processes. The direct third-order order susceptibility components will change sign un-
process, DTHG, occurs independently of the SHG der this transformation, while the third-order sus-
process assuming that we are operating with an un- ceptibility components remain unchanged. As such,
depleted pump. Conversely, excitation to ω3 through there is an additional factor of ∆m = ±2 added to
CSFG is an entirely second-order nonlinear process, all second-order phase matching requirements, while
where light from the first and SH modes undergoes the third-order phase matching requirements remain
sum frequency generation (SFG) to excite the TH unchanged. The quasi-phase matching conditions for
mode. In a material with a weak third-order non- SHG, CSFG and DTHG in GaP are therefore:
linear susceptibility, observed TH signals can be pre-
dominantly from CSFG [26]. In a material with both SHG : m2 = 2m1 ± 2, (1)
strong second- and third-order susceptibilities, both
CSFG : m3 = m1 + m2 ± 2, (2)
processes can contribute significantly.
DTHG : m3 = 3m1 . (3)
In a microcavity fabricated from a crystalline ma-
terial, harmonic generation processes between modes In principle, it is possible for a given set of modes
are restricted due to polarization and phase match- with azimuthal orders {m1 , m2 , m3 } to satisfy all
ing requirements. The electric field of a TE(TM)- three phase matching processes at once, leading to
like WGM mode is given by ETE(TM)m,n (r, ϕ, z) ∼ a TH signal generated both directly through phase
eTE(TM)n,m (r, z) exp (imϕ), where n and m are matched DTHG and indirectly through 4̄-quasi-phase
the radial and azimuthal mode orders respectively. matched CSFG.
eT E(T M ) is the two-dimensional cross section of the
field in the rz-plane. We assume that the WGM 2.1 Coupled Mode Theory
modes in our structure with higher-order vertical
index can be ignored, which is valid whenever the For nonlinear materials, the dependence of the non-
device is sufficiently thin [2]. The modes of a mi- linear polarization on the electric field leads to a self-
crodisk differ from the perfectly polarized TE or TM referencing wave equation [3], in which the electric
modes of a cylindrical cavity [14]; rather they contain field strength of the higher harmonic frequency modes
non-zero field components for all dimensions, with depends directly on the field strength at the input
the in-plane (i.e. r̂) component resembling a typi- fundamental frequency mode. This dependence can
cal TE field, and the out-of-plane component (i.e. be expressed as a set of steady-state equations giv-
ẑ) resembling a typical TM field. We use the polar- ing the field amplitudes of each optical mode in the
ization notation of Borselli [2], where a mode whose microdisk as functions of the other optical mode am-
largest components are in-plane are considered ’TE- plitudes, as well as the field of the input coupling
like’, and modes whose largest components are out- waveguide. The amplitude equation for a standing-
of-plane are ’TM-like’. Figure 1b shows the simulated wave mode in a waveguide coupled cavity of generic
cross-sectional profile of the absolute value |E| of the mode index k is [10, 45, 24, 32, 21]:
TE23,1 microdisk mode for the device studied here. r
d κk κk,ex
In the case of a cavity with cylindrical symmetry, ak = iωk − ak + s+ , (4)
dt 2 2
3
with the waveguide transmission given by while for third-order nonlinear processes, the cou-
r pling factors have dimensions of J−1 . The individual
κk,ex
s− = s+ − ak , (5) terms in these equations can be understood as cor-
2
responding to photon creation for each ak term and
where ak is the electric field mode amplitude of the photon annihilation for each a∗k term. We apply an
cavity, s+(−) is the incoming (outgoing) waveguide undepleted-pump approximation, where the loss in
field amplitude flux, ωk is the mode frequency and the first harmonic mode due to the harmonic genera-
κk is the mode energy decay rate. The quality factor tion processes is considered negligible. This assump-
of a mode is defined here as Qk ≡ ωk /κk . κk can be tion is valid for low input powers on the order of ˜1
separated into contributing components mW [24].
κk = κk,i+p + κk,ex . (6) Applying the rotating-wave approximation for each
equation and solving for the steady state gives the
Here κk,i+p is the intrinsic plus parasitic energy decay harmonic mode output powers:
rate of the cavity, understood as the rate of energy
loss into all channels other than the output mode of 2
ηSHG Pin
the waveguide, including radiation loss, optical ab- P2 = , (10)
(1 + ζPin )2
sorption, and coupling to lossy higher-order waveg-
3
uide modes [50]. κk,ex is the external energy decay 3 ηCSFG Pin
P3 = ηDTHG Pin + , (11)
rate due to the coupling between the cavity and the (1 + ζPin )2
fundamental waveguide mode, which is used as the
input and output mode. The field amplitudes are where ηSHG,CSFG,DTHG is the conversion efficiency of
normalized such that |ak |2 is the circulating mode en- each harmonic generation process, and ζ is a power
ergy and |s± |2 is the incoming (outgoing) power flow saturation term which arises due to the CSFG pro-
through the waveguide. From (2), the outgoing power cess. In the special case of a triple resonance, i.e.
output from the cavity mode k is Pk = (κk,ex /2)|ak |2 . ∆1 = ∆2 = ∆3 = 0 (where ∆k = ωk − kω0 is the
To model our microdisk system, we consider a set mode frequency detuning), the efficiencies and satu-
of nearly triply resonant modes at frequencies ω1,2,3 . ration parameter are given by:
The waveguide input s+ is set to be nearly resonant
with the fundamental mode: ω0 ≈ ω1 . Due to non- 2
κ2 κ
2 1,ex 2,ex
linear effects, it can couple to the SH and TH cavity η SHG = 32ω |β
1 SHG | , (12a)
κ41 κ22
modes. Following the analyses of Rodriguez et al. [45] κ31,ex κ3,ex
and Li et al. [24], we obtain a set of coupled mode ηDTHG = 144ω12 |βDTHG |2 , (12b)
equations, κ61 κ23
r κ31,ex κ3,ex
d κ1 κ1,ex ηCSFG = 2304ω14 |βSHG |2 |βCSFG |2 6 2 2 , (12c)
a1 = iω1 − a1 + s+ , (7) κ1 κ2 κ3
dt 2 2
2 2 κ1,ex
d κ2 ζ = 96ω1 |βCSFG | 2 , (12d)
a2 = iω2 − a2 − iω2 βCSFG a∗1 a3 + iω2 βSHG a21 , κ1 κ2 κ3
dt 2
(8)
where the β terms are mode coupling factors dis-
d κ3
a3 = iω3 − ∗
a3 + iω3 βCSFG a1 a2 + iω3 βDTHG a31 , cussed in detail below. For low powers, the SH and
dt 2 TH outputs scale approximately quadratically and
(9)
cubically respectively, consistent with the power scal-
where βSHG,CSFG,DTHG are the inter-modal coupling ing from pure SHG and THG. At higher input pow-
factors associated with each nonlinear frequency con- ers, the SFG process begins to deplete the SH mode
version process. For second-order nonlinear pro- energy, in a manner that scales quadratically with
cesses, the coupling factors have dimensions of J−1/2 , pump power.
42.2 Nonlinear Mode Coupling Factors
Here we provide an analysis of the nonlinear cou- R
d3 x
P(2) ∗
εχijk E1i ∗
E2j E1k + E1i ∗ ∗
E1j E2k
1 ijk
pling factors βSHG , βCSFG , βDTHG , their dependence βSHG = 1/2 ,
on the field profiles of the phase-matched modes, and 4 R
d3 xε|E1 |2
R
d3 xε|E2 |2
their effects on the overall harmonic generation pro- (14)
cesses. The magnitudes of the coupling factors are
R 3 P (2) ∗ ∗ ∗ ∗
1 d x ijk εχijk E2i E3j E1k + E2i E1j E3k
determined by the spatial overlap of the fields of each βCSFG = ,
4 R d3 xε|E1 |2 1/2 R d3 xε|E2 |2 1/2 R d3 xε|E3 |2 1/2
mode participating in a given process. Following the
analysis of Rodriquez et al. [45], we derive an expres- (15)
∗ ∗ ∗
R 3 (3)
sion for the small change in the frequency of a given 3 d xεχ (E1 · E1 ) (E1 · E3 )
βDTHG = .
microdisk mode due to nonlinear polarization. When 8 R d3 xε|E1 |2 1/2 R d3 xε|E3 |2 3/2
the perturbed mode frequencies are introduced into (16)
(4), we will obtain the coupled mode Eqs. (7-9) with where χ(2) and χ(3) are the second- and third-order
explicit expressions for the coupling factors. nonlinear electric susceptibilities respectively, and
We consider a perturbation of the microdisk’s di- {i, j, k} label the x̂, ŷ and ẑ components of E. The
electric constant δε resulting from a nonlinear optical coupling factors can be further simplified depending
polarization δP = δεE. The corresponding fractional on the symmetries of the device, as well as the sym-
change in the mode frequency is proportional to the metries of the nonlinear susceptibility tensors.
fraction of electric field energy in the perturbation
To estimate the values of the nonlinear coupling
[15]:
factors in the experiment, we have calculated the
1 ε E∗ · δPk d3 x
R
δωk
=− R , (13) coupling factors of several potential combinations of
ωk 2 ε|E|2 d3 x modes obtained from FDTD simulations (performed
where E is the unperturbed electric field. Substitut- using MEEP [38]) of WGMs in our microdisk. The
ing ωk → ωk + δωk into (4) for each mode k = 1, 2, 3 cylindrical symmetry of the microdisk allows us to
and rearranging for terms proportional to ak then re- specify the azimuthal mode number m in the simu-
produces Eqs. (7-9) with explicit expressions for each lations. We identify the TE23,1 mode to be closest
β term given in terms of the field integrals. In order fundamental mode to the target pump wavelength
to maintain the mode amplitude normalization where of 1557 nm (190 THz) used in the experiment pre-
|ak |2 is in units of energy, it is necessary to apply sented below. Figure 1b shows the normalized abso-
an additional normalization term
R
ε|Ek |2 d3 x
1/2
to lute field profile of this mode. For crystals such as
each β term for each Ek in the numerator. This gives GaP with 43m symmetry, a TE pump field under-
the nonlinear coupling factors: going harmonic generation processes must produce a
TM-like SH mode, and a TE-like TH mode [3]. Ad-
ditionally, SFG between a TE and a TM mode must
produce a TE mode. Several TM and TE modes near
the target SH and TH frequencies were simulated for
phase matched azimuthal mode numbers and several
radial mode numbers. Only the lowest vertical order
TE and TM microdisk modes were considered in our
calculations. Our simulations use a value of n = 3.01
for all modes. Since the refractive index of GaP is
dispersive in the visible regime [39], there is consid-
erable uncertainty in the simulated higher harmonic
mode frequencies. The resulting field profiles were
substituted into Eqs. (14), (15) and (16) to calculate
5the coupling factors. Note that in general, energy vided to highlight which mode combinations conserve
matching (ω2 = 2ω1 etc.) is not always satisfied for energy.
a given combination of modes due to dispersion of Although it can be difficult to precisely identify
the microdisk and GaP material. However, these cal- which mode coupling processes are responsible for
culations shed insight into relative strengths of the observed SH and TH signals, the magnitudes of the
various coupling processes. Energy conservation is nonlinear coupling factors provide useful informa-
taken into account below when identifying candidate tion on the relative efficiencies of the DTHG and
mode combinations. CSFG processes. This is most useful at low input
powers, where the contributions from DTHG and
CSFG processes cannot be determined from power
scaling. One can define a critical SH quality fac-
tor Q2,c = 12 |βDTHG |/(|βSHG ||βCSFG |) following the
method in Ref. [24], which dictates the condition for
which both processes are equally efficient. This is ob-
tained from setting the ratio of Eqs. (12b) and (12c)
to unity. DTHG typically dominates the THG pro-
cess for mode combinations with Q2 Q2,c , and
likewise CSFG dominates for Q2 Q2,c . From our
coupling factor calculations, values of Q2,c for mode
combinations that are phase matched for both DTHG
and CSFG vary between 1 ∼ 103 . Considering that
previous measurements of our devices show Q ∼ 104
close to the SH wavelength of 778 nm [22], these re-
sults suggest that CSFG is more likely to dominate
in our devices in the ideal scenario of zero detuning.
However, for non-zero ∆2 , Q2,c is reduced following
the Lorentzian lineshape of the SH mode, and as we
will find experimentally below, DTHG can become
more significant. Note that Q2,c is only well defined
Figure 2: Absolute values of second-order (outlined
in the case that the third harmonic mode satisfies
in red circles) and third-order (outlined in green
the phase matching conditions for both CSFG and
squares) nonlinear coupling factors with the TE23,1
DTHG. In the case where the third harmonic mode
first harmonic mode. Groups of phase matched mi-
is phase matched to only one of DTHG or CSFG,
crodisk modes are plotted by the frequency and az-
we expect that only the phase matched process may
imuthal number of the highest harmonic mode in the
occur.
wave mixing process.
Figure 2 shows the resulting calculated coupling 3 Experiment
factors for the TE23,1 first harmonic mode. The
mode combinations are grouped into coupling factors To observe SH and TH signals from GaP microdisks,
corresponding to second-order (highlighted in red) we used a similar setup as in our previous studies of
and third-order (highlighted in green) conversion pro- SHG in these devices [22]. A fiber taper waveguide
cesses. We obtain coupling factors on the order of is used to evanescently couple light into microdisk
1 ∼ 100 J−1/2 for βSHG,CSF G and 104 ∼ 106 J−1 for modes, and to collect the SH and TH output. A con-
βDTHG . Dashed lines corresponding to the SH and tinuous wave tunable laser (New Focus TLB-6700)
TH frequencies (around 380 and 570 THz) are pro- with a central wavelength around 1557 nm was in-
6put to high-Q microdisk resonances. Most high-Q measure the SH and TH mode spectra.
modes of the devices were found to exhibit SH signals, Figures 3b and 3c show the measured SH and TH
as in Ref. [22]. During these previous SHG studies, output powers from the fiber taper, respectively, as a
some modes were also observed to generate TH sig- function of varying pump wavelength for several in-
nal. Here we study a microdisk supporting a mode put powers. The corresponding wavelengths of the
whose TH output was largest among measured de- peak SH and TH signal are plotted on the top x-axis
vices. as a reference. From this we see that the SH and
In order to minimize heating and photothermal dis- TH signals are enhanced when the pump is resonant
persion of the microdisk mode wavelengths [5], the with the cavity mode, as expected. Here the input
pump field amplitude was modulated with an electro- power is defined by the power in the fiber taper im-
optic modulator (EOM) controlled by a waveform mediately before the coupling region. Each point in
generator (Stanford DG535) outputting a square the data set is extracted from the measured spectra
wave signal with a duty cycle of 0.5%. The pump of each harmonic at a given input power and finely
wavelength was independently measured using an tuned pump wavelength. A Gaussian lineshape was
optical spectrum analyzer (ANDO AQ6137B). The fit to the spectrometer resolution limited harmonic
pump was then sent through an erbium-doped fiber spectra, and the total number of spectrometer CCD
amplifier (PriTel LNHP-FA-27-IO-CP). A variable counts under each lineshape were converted to fiber
optical attenuator (EXFO FVA-3100) was used to set taper output power, taking into account the various
the power input to the fiber taper. A set of polar- efficiencies and losses of the experimental apparatus.
ization controllers were set to maximise coupling be- The fringed dependence of the SH power on pump
tween the fiber taper field and microdisk resonances wavelength is related to etaloning effects in the sys-
of interest. A 90:10 beamsplitter sent 10% of the tem, which are common in back illuminated CCD
fiber taper output to a power meter (Newport 1936- detectors at near-infrared wavelengths [13].
R) for measuring the pump transmission, and 90% to Figure 4 plots the peak SH (orange) and TH
a spectrometer (Princeton Instruments SP2750 and (green) output powers as a function of pump power.
Excelon PIXIS 100B CCD array). Because of the The solid lines are fits to the SH and TH outputs
difference in power outputs at the SH and TH wave- using Eqs. (10) and (11). This data shows that the
lengths, it was necessary to conduct the experiment peak SH output power scales sub-quadratically with
in two sets, one for each harmonic signal. The SH the input power, with the slope decreasing with in-
signal saturated the spectrometer CCD for the input creasing input power, indicating a saturation of the
powers used here. Therefore, a neutral density filter SH signal due to CSFG predicted by the denominator
was used at the spectrometer input to attenuate it. of (10). The peak TH signal is approximately cubic
No such attenuation of the TH signal was required. with respect to the input power over the measured
Figure 3a shows the transmission of the fiber ta- range.
per when the pump wavelength is scanned over the The lack of sub-cubic saturation behaviour in our
first harmonic resonance for a 8.7 mW input power. measured TH signal suggests that the DTHG term in
A Fano lineshape was observed due the fiber taper (11) is the main THG process in our measurements.
touching the edge of the microdisk. This positioning However, this disagrees with our earlier theoretical
stabilizes the fiber taper and maximizes coupling to prediction from Q2,c for ∆2 = 0 that CSFG should
the TH output, however, it also enhances coupling to dominate. Note that pump depletion would affect
higher-order modes of the fiber taper, resulting in a both the SHG and THG signals and does not explain
non-Lorentzian resonance lineshape [56]. From fits to the observed behavior [59]. A plausible explanation
the Fano lineshapes, we obtain the pump mode decay of the difference in saturation behavior of the SHG
rates κ1 = 2.0×1010 rad/s and κ1,ex = 3.5×109 rad/s, and THG signals is that our system possesses non-
corresponding to Q1 ∼ 6 × 104 . Due to a lack of zero ∆2 and small ∆3 . Setting ηDTHG = ηCSFG for
suitable tunable lasers, we were unable to directly the general case of non-zero ∆2 and ∆3 gives the
7Figure 4: On-resonance output power for second
(orange) and third harmonic (green) signals. Solid
lines are fits to the saturated resonance theory. The
dashed line corresponds to quadratic power scaling
predicted from zero depletion.
Figure 3: (a) Transmission spectrum of GaP mi-
crodisk pump mode around 1557 nm for a 8.7 mW tion parameters with standard errors of ηSHG =
pump power. The Fano-like lineshape of the observed 5.9 (1.6) × 10−2 % mW−1 , ζ = 28 (7) % mW−1 , and
resonance is attributed to a phase mismatch between ηT HG = 1.9 (0.1) × 10−6 % mW−2 . Our measured
the coupled fiber taper modes. (b) Second and (c) SHG external efficiency is of similar magnitude to
third harmonic output signal power for several pump what was achieved in previous SHG experiments with
wavelengths and input powers. Top axes show the different microdisks on the same chip [22]. Our SHG
observed peak harmonic wavelength measured in the and THG external efficiencies are comparable to or
spectrometer. exceed results from similar experiments in LN and
MgO:LN microdisk devices [27, 47], but are smaller
than current state of the art SHG-THG generation in
condition (Q2,c /Q2 )2 ((∆2 /κ2 )2 + 1) = 1. Assum- LN microdisks [26]. However, these LN devices pos-
ing coupling to modes with Q2,c ∼ 103 predicted by sess Q ∼ 105 − 106 , larger than our devices. As dis-
our coupling factor calculations, then for Q2 ∼ 104 , cussed below, more efficient SHG and THG in GaP
the ηDTHG /ηCSFG ∼ 1 condition is satisfied when devices could be realized by reducing their optical
|∆2 | ∼ 10κ2 . This value of |∆2 | is reduced for loss, optimizing mode detunings, and improving the
larger Q2,c or smaller Q2 . If we assume ∆3 ∼ 0, microdisk-waveguide output coupling efficiency.
then even with ∆2 ∼ 10κ2 the saturation parame-
ter ζ ∼ 10 − 20 % mW−1 depending on the values of
|βCSFG | and κ2 . As shown below, this is consistent 4 Discussion
with ζ inferred from the measured saturation of the
SHG signal. The GaP microdisks used in this experiment allow
From our fits, we obtain efficiency and satura- simultaneous observation of SHG and THG for rela-
8tively low powers. Our observed efficiencies and satu- lies within the transparency window of GaP. Addi-
ration are limited primarily by detuning from the SH tional resonance tuning may be achieved through the
mode, poor coupling between the SH and TH modes use of external temperature control [17, 28] or appli-
and the fundamental fiber taper mode, and material cation of external cladding [52]. The ideal predicted
absorption at the TH wavelength. The fiber taper value of ζ is lower than what was measured here,
diameter is on the order of 1 µm and provides good which can be attributed to undercoupling to the SH
coupling efficiency at the pump wavelength. How- and TH modes.
ever, at the SHG and THG wavelengths, the coupling In future experiments, both DTHG and CSFG
efficiency is reduced due to lower modal overlap of the in a GaP microcavity device could be enhanced in
fiber taper and microdisks fields, and the multi-mode several ways. In addition to the techniques men-
nature of the fiber taper at these wavelengths. The tioned above, optimizations in fabrication processes
TH wavelength of 519 nm lies just outside the trans- [12], reductions of sidewall roughness, improvements
parency window of GaP, leading to material absorp- to waveguide coupling efficiency, dispersion engineer-
tion. We therefore have a fundamental lower limit ing to ensure triple resonance and maximizing con-
on κ3,i (i.e. an upper limit on Q3 ) due to absorp- structive DTHG-CSFG interference [24], and gain-
tion. The upper limit of the intrinsic quality factor induced loss compensation with dopants [59] would
of a cavity at wavelength λ can be approximated as significantly improve the device performance. Alter-
Qi,max (λ) ≈ (2πn(λ))/(λα(λ)) [36]. Using an atten- natively, the use of photonic crystals [42] or topolog-
uation coefficient αGaP (519 nm) ≈ 252 cm−1 [1, 57], ical metamaterials [49, 54, 18] may yield improved
we obtain Q3,i,max ≈ 1700 or minimum decay rate performance due to lower mode volumes.
κ3,i,min ≈ 2.1 × 1012 rad/s. In summary, we have observed the simultaneous
Using the maximum value of Q3 predicted above, generation of SH and TH signals from a telecom
and assuming Q2 ∼ 1.0×104 , as previously measured pump in GaP microdisks. This work represents the
in our GaP microdisks [22], for ∆2 ∼ κ2 and ∆3 ∼ 0, first detailed experimental analysis of third harmonic
we predict from Eqs. (12) efficiency and saturation generation in GaP microcavities. For experiments
values on the same order as the measured values for in which simultaneous second and third generation
coupling factors of |βSHG | ∼ 10 J−1/2 , |βCSFG | ∼ is observed, the methods presented here will allow
systematic analysis of the third harmonic generation
400 − 500 J−1/2 and |βDTHG | ∼ 2 − 3 × 106 J−1 . These
processes. Future third harmonic generation experi-
coupling factors are on the upper limit of what was
ments in GaP microcavity devices should to be per-
calculated for |βDTHG | and |βCSFG |, and on the lower
formed in carefully designed integrated devices whose
limit for |βSHG |.
modes are optimized for the desired wavelength and
Under ideal conditions for this device, with triple power range [24].
resonance and critical coupling for all harmonic © 2022 Optica Publishing Group. One print or
modes, we estimate ideal conversion efficiencies of electronic copy may be made for personal use only.
ηSHG ∼ 1.1 × 10−1 % mW−1 , ηDTHG ∼ 3.2 × Systematic reproduction and distribution, duplica-
10−5 % mW−2 , ηCSFG ∼ 3.2 × 10−3 % mW−2 , and tion of any material in this paper for a fee or for
ζ ∼ 7.7 % mW−1 for the coupling factor values listed commercial purposes, or modifications of the content
above. These ideal values for ηSHG and ηCSFG are an of this paper are prohibited.
order of magnitude larger than observed in our ex-
periment, suggesting that the measured efficiencies
are primarily limited by imperfect mode detuning, as 5 Funding
well as undercoupling to the SH and TH modes. The
maximum predicted value of ηDTHG here is limited by This work was supported by the Natural Sciences
material absorption, and may be enhanced by oper- and Engineering Research Council of Canada (Dis-
ating with a pump whose third harmonic wavelength covery Grant and Research Tools and Instruments
9programs). [8] Zheng Gong, Xianwen Liu, Yuntao Xu, Min-
grui Xu, Joshua B Surya, Juanjuan Lu, Alexan-
der Bruch, Changling Zou, and Hong X Tang.
6 Acknowledgments Soliton microcomb generation at 2 µm in z-cut
lithium niobate microring resonators. Optics let-
The authors thank D. Sukachev for their input.
ters, 44(12):3182–3185, 2019.
[9] Zhenzhong Hao, Jie Wang, Shuqiong Ma, Wenbo
7 Disclosures Mao, Fang Bo, Feng Gao, Guoquan Zhang, and
Jingjun Xu. Sum-frequency generation in on-
The authors have no competing interests to declare.
chip lithium niobate microdisk resonators. Pho-
tonics Research, 5(6):623–628, 2017.
References [10] Hermann A. Haus. Waves and Fields in Opto-
[1] A Borghesi and G Guizzetti. Gallium phos- electronics. Prentice-Hall, Inc., 1984.
phide (gap). In Handbook of Optical Constants [11] Yang He, Qi-Fan Yang, Jingwei Ling, Rui Luo,
of Solids, pages 445–464. Elsevier, 1997. Hanxiao Liang, Mingxiao Li, Boqiang Shen,
[2] Matthew Gregory Borselli. High-Q microres- Heming Wang, Kerry Vahala, and Qiang Lin.
onators as lasing elements for silicon photonics. Self-starting bi-chromatic linbo3 soliton micro-
PhD thesis, California Institute of Technology, comb. Optica, 6(9):1138–1144, Sep 2019.
2006. [12] Simon Hönl, Herwig Hahn, Yannick Baumgart-
[3] Robert W. Boyd. Nonlinear optics. Academic ner, Lukas Czornomaz, and Paul Seidler. Highly
Press, 3 edition, 2008. selective dry etching of gap in the presence of
alxga1–xp with a sicl4/sf6 plasma. Journal
[4] Alexander W Bruch, Xianwen Liu, Xiang Guo, of Physics D: Applied Physics, 51(18):185203,
Joshua B Surya, Zheng Gong, Liang Zhang, 2018.
Junxi Wang, Jianchang Yan, and Hong X
Tang. 17 000%/w second-harmonic conver- [13] Bin-Lin Hu, Jing Zhang, Kai-Qin Cao, Shi-Jing
sion efficiency in single-crystalline aluminum ni- Hao, De-Xin Sun, and Yin-Nian Liu. Research
tride microresonators. Applied Physics Letters, on the etalon effect in dispersive hyperspectral
113(13):131102, 2018. vnir imagers using back-illuminated ccds. IEEE
Transactions on Geoscience and Remote Sens-
[5] Tal Carmon, Lan Yang, and Kerry J. Va- ing, 56(9):5481–5494, 2018.
hala. Dynamical thermal behavior and ther-
mal self-stability of microcavities. Opt. Express, [14] John David Jackson. Classical Electrodynamics.
12(20):4742–4750, Oct 2004. Wiley, 3 edition, 2001.
[6] JU Fürst, DV Strekalov, Dominique Elser, [15] John D. Joannopoulos, Steven G. Johnson,
Mikael Lassen, Ulrik Lund Andersen, Christoph Joshua N. Winn, and Robert D. Meade. Pho-
Marquardt, and Gerd Leuchs. Naturally tonic Crystals: Molding the Flow of Light.
phase-matched second-harmonic generation in a Princeton University Press, 2 edition, 2008.
whispering-gallery-mode resonator. Physical re-
[16] Hojoong Jung, Chi Xiong, King Y Fong, Xufeng
view letters, 104(15):153901, 2010.
Zhang, and Hong X Tang. Optical frequency
[7] Zheng Gong, Xianwen Liu, Yuntao Xu, and comb generation from aluminum nitride micror-
Hong X Tang. Near-octave lithium niobate soli- ing resonator. Optics letters, 38(15):2810–2813,
ton microcomb. Optica, 7(10):1275–1278, 2020. 2013.
10[17] L Koehler, P Chevalier, E Shim, B Desia- [26] Jintian Lin, Ni Yao, Zhenzhong Hao, Jian-
tov, A Shams-Ansari, M Piccardo, Y Okawachi, hao Zhang, Wenbo Mao, Min Wang, Wei Chu,
M Yu, M Loncar, M Lipson, et al. Direct thermo- Rongbo Wu, Zhiwei Fang, Lingling Qiao, Wei
optical tuning of silicon microresonators for the Fang, Fang Bo, and Ya Cheng. Broadband
mid-infrared. Optics express, 26(26):34965– quasi-phase-matched harmonic generation in an
34976, 2018. on-chip monocrystalline lithium niobate mi-
crodisk resonator. Phys. Rev. Lett., 122:173903,
[18] Sergey Kruk, Alexander Poddubny, Daria
May 2019.
Smirnova, Lei Wang, Alexey Slobozhanyuk,
Alexander Shorokhov, Ivan Kravchenko, Barry [27] Shijie Liu, Yuanlin Zheng, and Xianfeng Chen.
Luther-Davies, and Yuri Kivshar. Nonlinear Cascading second-order nonlinear processes in a
light generation in topological nanostructures. lithium niobate-on-insulator microdisk. Optics
Nature nanotechnology, 14(2):126–130, 2019. letters, 42(18):3626–3629, 2017.
[19] Paulina S Kuo, Jorge Bravo-Abad, and Glenn S
[28] Alan D Logan, Michael Gould, Emma R
Solomon. Second-harmonic generation using-
Schmidgall, Karine Hestroffer, Zin Lin, Weiliang
quasi-phasematching in a gaas whispering-
Jin, Arka Majumdar, Fariba Hatami, Alejan-
gallery-mode microcavity. Nature communica-
dro W Rodriguez, and Kai-Mei C Fu. 400%/w
tions, 5(1):1–7, 2014.
second harmonic conversion efficiency in 14 µm-
[20] Paulina S Kuo and Glenn S Solomon. On- diameter gallium phosphide-on-oxide resonators.
and off-resonance second-harmonic generation in Optics express, 26(26):33687–33699, 2018.
gaas microdisks. Optics express, 19(18):16898–
16918, 2011. [29] Alejandro Lorenzo-Ruiz and Yoan Léger. Gen-
eralization of second-order quasi-phase match-
[21] David Lake. Multimode-optomechanics, spin- ing in whispering gallery mode resonators using
optomechanics, and nonlinear optics in photonic berry phase. ACS Photonics, 7(7):1617–1621,
devices, 2020. 2020.
[22] David P. Lake, Matthew Mitchell, Harishankar [30] Juanjuan Lu, Joshua B. Surya, Xianwen Liu,
Jayakumar, Laı́s Fujii dos Santos, Davor Curic, Alexander W. Bruch, Zheng Gong, Yuntao
and Paul E. Barclay. Efficient telecom to vis- Xu, and Hong X. Tang. Periodically poled
ible wavelength conversion in doubly resonant thin-film lithium niobate microring resonators
gallium phosphide microdisks. Applied Physics with a second-harmonic generation efficiency
Letters, 108(3):031109, 2016. of 250,000%/w. Optica, 6(12):1455–1460, Dec
[23] Jacob S Levy, Mark A Foster, Alexander L 2019.
Gaeta, and Michal Lipson. Harmonic generation
[31] Rui Luo, Haowei Jiang, Steven Rogers, Hanxiao
in silicon nitride ring resonators. Optics express,
Liang, Yang He, and Qiang Lin. On-chip second-
19(12):11415–11421, 2011.
harmonic generation and broadband parametric
[24] Ming Li, Chang-Ling Zou, Chun-Hua Dong, and down-conversion in a lithium niobate microres-
Dao-Xin Dai. Optimal third-harmonic genera- onator. Opt. Express, 25(20):24531–24539, Oct
tion in an optical microcavity with χ (2) and χ 2017.
(3) nonlinearities. Optics express, 26(21):27294–
27304, 2018. [32] Matthew Mitchell. Coherent cavity optomechan-
ics in wide-band gap materials, 2019.
[25] Yihang Li, Xuefeng Jiang, Guangming Zhao,
and Lan Yang. Whispering gallery mode mi- [33] Matthew Mitchell, Aaron C. Hryciw, and
croresonator for nonlinear optics, 2018. Paul E. Barclay. Cavity optomechanics in gal-
11lium phosphide microdisks. Applied Physics Let- [41] Martin H. P. Pfeiffer, Clemens Herkommer, Jun-
ters, 104(14):141104, 2014. qiu Liu, Hairun Guo, Maxim Karpov, Erwan
Lucas, Michael Zervas, and Tobias J. Kippen-
[34] Mohamed Sabry Mohamed, Angelica Simbula, berg. Octave-spanning dissipative kerr soliton
Jean-François Carlin, Momchil Minkov, Dario frequency combs in si3n4 microresonators. Op-
Gerace, Vincenzo Savona, Nicolas Grandjean, tica, 4(7):684–691, Jul 2017.
Matteo Galli, and Romuald Houdré. Efficient
continuous-wave nonlinear frequency conversion [42] Kelley Rivoire, Sonia Buckley, Fariba Hatami,
in high-q gallium nitride photonic crystal cav- and Jelena Vučković. Second harmonic genera-
ities on silicon. APL Photonics, 2(3):031301, tion in gap photonic crystal waveguides. Applied
2017. Physics Letters, 98(26):263113, 2011.
[43] Kelley Rivoire, Ziliang Lin, Fariba Hatami,
[35] Jeremy Moore, J Kenneth Douglas, Ian W
W. Ted Masselink, and Jelena Vučković. Sec-
Frank, Thomas A Friedmann, Ryan M Cama-
ond harmonic generation in gallium phosphide
cho, and Matt Eichenfield. Efficient second har-
photonic crystal nanocavities with ultralow con-
monic generation in lithium niobate on insula-
tinuous wave pump power. Opt. Express,
tor. In 2016 Conference on Lasers and Electro-
17(25):22609–22615, Dec 2009.
Optics (CLEO), pages 1–2. IEEE, 2016.
[44] Kelley Rivoire, Ziliang Lin, Fariba Hatami, and
[36] Jan Niehusmann, Andreas Vörckel, Peter Har- Jelena Vučković. Sum-frequency generation in
ing Bolivar, Thorsten Wahlbrink, Wolfgang Hen- doubly resonant gap photonic crystal nanocav-
schel, and Heinrich Kurz. Ultrahigh-quality- ities. Applied Physics Letters, 97(4):043103,
factor silicon-on-insulator microring resonator. 2010.
Opt. Lett., 29(24):2861–2863, Dec 2004.
[45] Alejandro Rodriguez, Marin Soljačić, J. D.
[37] Yoshitomo Okawachi, Kasturi Saha, Jacob S Joannopoulos, and Steven G. Johnson. χ(2) and
Levy, Y Henry Wen, Michal Lipson, and Alexan- χ(3) harmonic generation at a critical power in
der L Gaeta. Octave-spanning frequency comb inhomogeneous doubly resonant cavities. Opt.
generation in a silicon nitride chip. Optics let- Express, 15(12):7303–7318, Jun ts.
ters, 36(17):3398–3400, 2011.
[46] Iannis Roland, Maksym Gromovyi, Yijia Zeng,
Moustafa El Kurdi, Sebastien Sauvage, Chris-
[38] Ardavan F. Oskooi, David Roundy, Mihai
telle Brimont, Thierry Guillet, Bruno Gayral,
Ibanescu, Peter Bermel, J.D. Joannopoulos, and
Fabrice Semond, Jean-Yves Duboz, et al. Phase-
Steven G. Johnson. Meep: A flexible free-
matched second harmonic generation with on-
software package for electromagnetic simulations
chip gan-on-si microdisks. Scientific reports,
by the fdtd method. Computer Physics Commu-
6:34191, 2016.
nications, 181(3):687 – 702, 2010.
[47] Kiyotaka Sasagawa and Masahiro Tsuchiya.
[39] DF Parsons and PD Coleman. Far infrared opti- Highly efficient third harmonic generation in a
cal constants of gallium phosphide. Applied op- periodically poled mgo: Linbo3 disk resonator.
tics, 10(7):1683 1–1685, 1971. Applied Physics Express, 2(12):122401, 2009.
[40] WHP Pernice, C Xiong, C Schuck, and [48] Katharina Schneider, Pol Welter, Yannick
HX Tang. Second harmonic generation in Baumgartner, Herwig Hahn, Lukas Czornomaz,
phase matched aluminum nitride waveguides and Paul Seidler. Gallium phosphide-on-silicon
and micro-ring resonators. Applied Physics Let- dioxide photonic devices. Journal of Lightwave
ters, 100(22):223501, 2012. Technology, 36(14):2994–3002, Jul 2018.
12[49] Daria Smirnova, Sergey Kruk, Daniel Leykam, [57] Amnon Yariv and Pochi Yeh. Photonics: Optical
Elizaveta Melik-Gaykazyan, Duk-Yong Choi, Electronics in Modern Communications. Oxford
and Yuri Kivshar. Third-harmonic generation Univ. Press, 6 edition, 2007.
in photonic topological metasurfaces. Physical
review letters, 123(10):103901, 2019. [58] Xiaona Ye, Shijie Liu, Yuping Chen, Yuan-
lin Zheng, and Xianfeng Chen. Sum-frequency
[50] S. M. Spillane, T. J. Kippenberg, O. J. Painter, generation in lithium-niobate-on-insulator mi-
and K. J. Vahala. Ideality in a fiber-taper- crodisk via modal phase matching. Optics Let-
coupled microresonator system for application ters, 45(2):523–526, 2020.
to cavity quantum electrodynamics. Phys. Rev.
Lett., 91:043902, Jul 2003. [59] Rong Yu, Chunling Ding, Jiangpeng Wang, and
Duo Zhang. Enhanced visible light generation in
[51] Joshua B Surya, Xiang Guo, Chang-Ling Zou, an active microcavity via third-harmonic conver-
and Hong X Tang. Efficient third-harmonic gen- sion beyond the non-depletion approximation.
eration in composite aluminum nitride/silicon Journal of Applied Physics, 122(24):244303,
nitride microrings. Optica, 5(2):103–108, 2018. 2017.
[52] Lillian Thiel, Alan D. Logan, Srivatsa
Chakravarthi, Shivangee Shree, Karine He-
stroffer, Fariba Hatami, and Kai-Mei C. Fu.
Target-wavelength-trimmed second harmonic
generation with gallium phosphide-on-nitride
ring resonators, 2021.
[53] Akira Tomita and Raymond Y. Chiao. Obser-
vation of berry’s topological phase by use of an
optical fiber. Phys. Rev. Lett., 57:937–940, Aug
1986.
[54] You Wang, Li-Jun Lang, Ching Hua Lee, Baile
Zhang, and YD Chong. Topologically enhanced
harmonic generation in a nonlinear transmis-
sion line metamaterial. Nature communications,
10(1):1–7, 2019.
[55] Dalziel J. Wilson, Katharina Schneider, Simon
Hönl, Miles Anderson, Yannick Baumgartner,
Lukas Czornomaz, Tobias J. Kippenberg, and
Paul Seidler. Integrated gallium phosphide non-
linear photonics. Nature Photonics, 14(1):57–62,
Jan 2020.
[56] Marcelo Wu, Aaron C. Hryciw, Chris Healey,
David P. Lake, Harishankar Jayakumar,
Mark R. Freeman, John P. Davis, and Paul E.
Barclay. Dissipative and dispersive optome-
chanics in a nanocavity torque sensor. Phys.
Rev. X, 4:021052, Jun 2014.
13You can also read
