Research Article

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Giant nonlinear optical effects induced bynitrogen-vacancy centers in diamond crystals
M ARI M OTOJIMA , 1 TAKARA S UZUKI , 1 H IDEMI S HIGEKAWA , 1 Y UTAK AINUMA , 2 TOSHU A N , 2 AND M UNEAKI H ASE 1,*
1 Department of Applied Physics, Faculty of Pure and Applied Sciences, University of Tsukuba, 1-1-1

Tennodai, Tsukuba 305-8573, Japan
2 School of Materials Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa
923-1292, Japan* mhase@bk.tsukuba.ac.jp

Abstract: We investigate the effect of nitrogen-vacancy (NV) centers in single crystal diamondon nonlinear optical effects using 40 fs femtosecond laser pulses. The near-infrared femtosecond
pulses allow us to study purely nonlinear optical effects, such as optical Kerr effect (OKE) andtwo-photon absorption (TPA), related to unique optical transitions by electronic structures with
NV centers. It is found that both nonlinear optical effects are enhanced by the introduction of
NV centers in the N+ dose levels of 2.0×1011 and 1.0×1012 N+ /cm2 . In particular, our data
demonstrate that the OKE signal is strongly enhanced for the heavily implanted type-IIa diamond.
We suggest that the strong enhancement of the OKE is possibly originated from cascading OKE,
where the high-density NV centers effectively break the inversion symmetry near the surface
region of diamond.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1.

Introduction

The optical and magnetic properties of the negatively charged nitrogen-vacancy (NV) centerin diamond have been extensively investigated because of its potential application to quantum
sensing [1], such as magnetic and electric fields [2,3], local temperature in bio-systems [4], andto quantum information technologies [5]. In most cases, near-infrared luminescence upon the
excitation by green laser can be controlled by the irradiation of microwave, which tunes the
optical transition paths between the excited and ground states [6]. To extend the optical propertyof diamond over the current generation of linear optical regime, one requires ultrashort laser
pulses, which enables us to induce coherent lattice vibrations [7–10] as well as nonlinear opticaleffect, such as the nonlinear refraction and nonlinear absorption [11–13]. Almeida et al recently
reported on nonlinear optical spectra in high-purity diamond using femtosecond laser pulses withphoton energy from 0.83 to 4.77 eV and measured coefficients for the nonlinear refraction andnonlinear absorption [13]. Because of the absence of defect-related bands below the band-gap(Eg = 5.5 eV), the two nonlinear optical effects were enhanced for the photon energy of ~ω =Eg /2. Although there are several investigations on nonlinear optical effects in bulk diamond andnano-diamond [14,15], the effects of the NV center on the nonlinear optical phenomena have
not yet been examined. However, this issue is important to further study new functionality of
diamond photonics to advance nonlinear quantum sensing.
Here we explore the NV center induced nonlinear optical effects in pure diamond, specifically
optical Kerr effect (OKE) and two-photon absorption (TPA) in transparent region using 800 nm
light, at which NV related bands will be sensitive. It is found that both the nonlinear optical effects
are enhanced by the introduction of NV centers. Importantly, the signal enhancement is more
visible for the time-resolved reflectivity measurement than that in the case of the conventionaltransmission measurements. We attribute the several times larger signal enhancement in thereflectivity mode observed at the highest dose level to dominant contribution from the cascaded#373515
Journal © 2019https://doi.org/10.1364/OE.27.032217
Received 24 Jul 2019; revised 27 Sep 2019; accepted 7 Oct 2019; published 22 Oct 2019

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OKE due to breaking the inversion symmetry near the surface region and minor one from TPA
due to the NV center related bands in diamond.
2.

Experimental

We first carried out Z-scan measurement to examine nonlinear optical effects, such as OKE
and TPA [16]. The Z-scan measurements were performed using a closed aperture mode, tostudy the nonlinear refraction and nonlinear absorption, respectively. As shown in Fig. 1(a), thetransmittance of a diamond sample through an aperture (a diameter of ≈0.8 mm) in the far-field
was measured as a function of the sample position z with respect to the focal plane. The lightsource used was a femtosecond regenerative amplifier system (RegA9040, Coherent), which
produces ≈40 fs pulses at a central wavelength of λ ≈800 nm with an average power of ≥500
mW at 100 kHz repetition rate. The output of the amplifier was focused via a focal length f =50 mm lens into the samples. Z-scan measurement enables us to evaluate the nonlinear opticaleffects associated with the third-order nonlinear susceptibility χ(3) from its transmittance change.
The third-order nonlinear susceptibility can be expressed by:(3)(3)(2) (2)
χ(3) = χbulk
+ χNV
+ χNV
χNV ,

(1)

(3)
(3)
where the first term χbulk
describes bulk third-order susceptibility, the second term χNV
represents
NV-induced third-order susceptibility, and the last term suggests a possible contribution from the(2)
cascaded second-order susceptibility χNV[11,17,18], which may be detected by surface sensitive
optical methods, such as optical reflectivity. Note that the second-order susceptibility χ(2) isgenerally zero whenever the material has inversion symmetry, i.e., in the case for high purity
diamond. The inversion symmetry can be, however, broken when NV centers are introduced,
since the N atom and its adjacent vacancy break the inversion symmetry of the diamond crystal[19]. Equation (1) is expected to be affected by both the OKE and TPA via Re χ(3) = 2n20 0 cn2 andIm χ(3) = n20 0 cβ/k, respectively, where n2 is the nonlinear refraction, n0 is the linear refraction
coefficient, 0 is the vacuum permittivity, c is the speed of light in vacuum, β represents nonlinear
absorption (TPA) coefficient, and k denotes the wave vector [11,16].
To investigate the time-domain response from the OKE and TPA due to the NV centers near
the sample surface, reflection-type pump-probe measurements for the diamond samples werealso carried out using the same femtosecond regenerative amplifier system at room temperatureby employing the fast scanning time-delay method [Fig. 1(b)] [20]. The pump and probe beams
were focused via the focal length f = 100 mm lens onto the sample surface with a mutual angleof ≤5◦ . The pump power was varied from 20 to 80 mW, while the probe power was kept at ≤ 2
mW. Polarization of the two beams was linear with orthogonal each other.
The samples used were Element Six [100] type-IIa diamond crystal fabricated by CVD method,whose impurity (nitrogen: [N] and boron: [B]) levels were [N] < 1 ppm and [B] < 0.05 ppm,
respectively. The sample size was 3.0 mm×3.0 mm×0.3 mm (thickness). To introduce NV
centers 30 keV nitrogen ions (N+ ) were implanted into the diamond samples at the N+ doselevels of 2.0×1011 and 1.0×1012 ions/cm2 . The implanted depth deduced from the Monte Carlocalculation (TRIM) was about 30–40 nm [21,22] and the profile was close to a Gaussian function
with FWHM of ∼ 50 nm. After that, the samples were annealed at 900–1000 ◦ C in an argon
atmosphere for 1 hour to produce NV centers with a production efficiency of ≈ 1% (see Fig. 2)[23]. The production of NV centers was confirmed by optically-detected magnetic resonance(ODMR) technique using a 532 nm laser at ≈ 1 mW [22].

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Fig. 1. (a) The experimental set-up for Z-scan measurement using the closed aperturemode. (b) Schematics of femtosecond pump-probe experiment with the reflection mode.
The difference of the photocurrent of the two Si-pin detectors was amplified, and averaged
in a digital oscilloscope using the scanning time delay at 20 Hz.

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Fig. 2. Schematic for the production of NV centers by N+ ion implantation and subsequentannealing in diamond crystalline samples. The N+ ions implanted into diamond produce
vacancies (V), which are required to make nitrogen-vacancy (NV) centers. Annealing
the diamond sample induces diffusion of the vacancies, which can then be trapped by the
implanted nitrogen atoms.

3.

Results and discussion

Figure 3 shows the results of the closed-aperture Z-scan measurements obtained for different
N+ dose levels observed at the laser fluence of I0 ≈20 mJ/cm2 . Anti-symmetric line shape,
whose peak and valley have not the same amplitude, was observed for all the samples. The
anti-symmetric lineshape, with a valley greater than the peak, indicates an existence of two-photon
absorption [13]. The intensity of the transmittance change becomes larger when the NV centerswere introduced at 2.0×1011 and 1.0×1012 N+ /cm2 . In particular, the valley at z = – 0.2 mm
exhibits ≈ 1.3 times larger transmission change compared to the pure diamond (non-implanted),
indicating that absorption by NV centers plays a central role in the enhancement of the signals in
Figs. 3(b) and 3(c).
We applied the general model of the Z-scan technique for the transmittance change [16,24],T(z, ∆φ0 , ∆ψ0 ) = 1 +4x2(x2 + 3)
∆φ
−
∆ψ0 ,
0
(x2 + 9)(x2 + 1)
(x2 + 9)(x2 + 1)

(2)

where x = zz0 , z is the position, z0 = πw20 /λ is the Rayleigh length with w0 being the beam waist,∆φ0 is induced phase shift and ∆ψ0 is a loss parameter. The parameters obtained by the fitting
are listed in Table 1. The fitting parameter of z0 ∼ 0.2 mm corresponds to w0 ∼ 7 µm, a value
being well consistent with that calculated (∼ 8 µm) using w0 = 0.61λ/NA, where NA = 0.06 is
the numerical aperture of the lens used. As seen in Table 1, the phase shift ∆φ0 associated withnonlinear refraction n2 becomes larger by a factor of ≈1.3 when the NV centers were introduced,
while ∆ψ0 associated with nonlinear absorption β (e.g., two-photon absorption) is enhanced bya factor of ≈1.6. Thus, we can see the small but significant increases in the nonlinear optical(3)effects associated with the NV center on the Z-scan data, which corresponding to χNV
in Eq. (1).
To study further details, we used the relationships between the fitting parameters, ∆φ0 and ∆ψ0 ,and nonlinear optical effects, which are ∆φ0 = kn2 I0 Leff and ∆ψ0 = βI0 Leff /2 [16], where Leff isthe effective length of the sample defined by (1 − e−αL )/α with α (≈0.1 cm−1 ) [25] the linear
absorption coefficient and L (= 0.3 mm) the sample length. Using these relations, we obtain n2 =4.16×10−20 m2 /W for the non-implanted diamond and n2 = 5.50×10−20 m2 /W for the NV centerResearch Article

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Fig. 3. Closed-aperture Z-scan results at I0 ≈20 mJ/cm2 obtained for the pure diamond
crystal and NV center introduced diamond at different dose levels, (a) non-implanted, (b)2.0×1011 N+ /cm2 , and (c) 1.0×1012 N+ /cm2 . The black solid lines represent the fit to thedata using Eq. (2).

introduced diamond at 1.0×1012 N+ /cm2 . In the same way, we obtain β = 0.993×10−2 cm/GW for
the non-implanted diamond and β = 1.61×10−2 cm/GW for the NV center introduced diamond at
1.0×1012 N+ /cm2 . These values are the same order of those obtained for high purity diamond[13]. Although the NV introduced samples exhibit the small enhancement of the nonlinear(3)
optical effects, the transmission mode might dominantly detect the bulk contribution χbulk
, and
(3)
(2)
masked the precise signal from NV centers, χNV and χNV , which are buried in the sample surface.
(3)(2)
To examine the precise effect of χNVand χNV, we show the results on the transient reflectivity
measurements below.
Table 1. The fitting parameters obtained using Eq. (2). The standard deviation of coefficients wereobtained during the fitting procedure with Igor Pro.
Sample∆φ0∆ψ0z0 (mm)Diamond (non-implanted)

0.394±0.010

0.0596±0.0067

0.221±0.008

Diamond (2.0×1011 N+ /cm2 )0.528±0.017

0.0816±0.0106

0.221±0.009

Diamond (1.0×1012 N+ /cm2 )0.521±0.008

0.0967±0.0047

0.195±0.004

Figure 4 shows the results of the time-resolved transient reflectivity (∆R/R) obtained by thepump-probe technique. The ∆R/R signal consists of an instantaneous drop, where the widthof the negative peak (FWHM of ≈50 fs obtained by a Gaussian fit and deconvolution) nearlycorresponds to the pulse duration of the laser used. The effectively smaller FWHM of the ∆R/R
signal than that observed in a highly pure diamond [13] and that of the transient transmission(∆T/T) using UV excitation [26] suggests the fact that the pulse duration in the present study isshorter than those in the literatures and the origin of the signal is due to nonlinear optical effects,
such as OKE and TPA, which are governed by non-resonant intermediate states [11].
Although the transient negative peak signal is similar to the optical response reported byNakamura et al [8], oscillations due to the generation of coherent optical phonons were notobserved because of longer pulse width (≈ 40 fs) than that (≈ 10 fs) needed for the observationof the 40 THz coherent optical phonon [7]. Now the several times larger ∆R/R signal observedResearch Article

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Fig. 4. Pump-probe reflectivity results obtained for the different dose levels of CVD
diamond crystals at I0 ≈30 mJ/cm2 .

in the NV center introduced diamond indicates that the origin of the signal increase comesfrom the surface region rather than the bulk, since the signal enhancement was much smallerwhen we observed the transmittance by the Z-scan technique, in which we observe the nonlinear
optical effects dominated by the native [N] and [B] defects in the bulk region. Note that wehave also observed the ∆T/T signal using the pump-probe technique (data not shown). In thiscase, however, the factor of the signal enhancement was only less than several tens percent as in
the case of the Z-scan measurements. Thus, the largest signal enhancement was observed only
for the transient reflectivity signal, indicating that the signal enhancement is due to NV centers
localized in the surface region.
Under the assumption that the linear absorption (one-photon) for the near infrared light (λ ≈800 nm) can be neglected and the incident angle of the probe beam is the sample normal, thetransient reflectivity change induced by the nonlinear optical effects can be expressed by thechange in the real part of the refractive index ∆n [27],∆R4= 2∆n ≈ 0.84(∆nOKE + ∆nTPA ),R
n0 − 1(3)where n0 = 2.4 for diamond at λ ≈ 800 nm was taken [28]. Here, ∆n is modulated by OKE,
∆nOKE = n2 I0 [11], and free carrier contribution via TPA, ∆nTPA , whose intensity dependence canbe expressed as below based on the Drude model [27],∆nTPA = −βI02
2πe2 N2πe2=−= κ βI02 .
n 0 m∗ ω 2
n0 m∗ ω2 2~ωτp(4)

where e is the electron charge, N is the free carrier density, m∗ is the electron effective mass, ω isthe angular frequency of the laser used, τp is the pulse length, and κ = -2πe2 /(n0 m∗ ω2 · 2~ωτp ).
As the pump fluence increases, nonlinear increase in the |∆R/R| signal was observed for all

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the diamond samples, as shown in Fig. 5. By fitting the |∆R/R| signals using a function of
aI0 + bI02 , we obtained the fitting parameters a and b for different NV densities. Then, using therelationships from Eqs. (3) and (4), i.e. a = 0.84n2 and b = 0.84|κ| β, the values of n2 and β are
obtained as listed in Table 2. Although the value of β shows small increase as the N+ dose isincreased, the value of n2 associated with OKE increases more than an order of magnitude for thecase of the heavily implanted diamond, 1.0×1012 N+ /cm2 . Note that the observed n2 was negativein our study, which would be due to the contribution from cascading OKE as discussed in moredetails in the latter sections. Hereafter, we will discuss the value of |n2 | to examine the effect of
the NV center in diamond. The |n2 | in Table 2 obtained for the non-implanted and the lightly
implanted diamond (2.0×1011 N+ /cm2 ) are very small if we consider the standard deviations, but
are in good agreement with those obtained by Z-scan measurements by other groups [13,29].

Fig. 5. Pump fluence dependence of the |∆R/R| signal observed in diamond samples. The
solid curves are the fit using a function of aI0 + bI02 .
Table 2. The nonlinear refraction coefficient, n2 , and the nonlinear absorption coefficient, β,obtained for different N+ dose levels, by using the fitting parameters described in the main text. The
standard deviations of coefficients were obtained during the fitting procedure with Igor Pro.
Sample|n2 | (×10−20 m2 /W)

β (×10−1 cm/GW)

Diamond (non-implanted)

0.73±0.63

0.90±0.06

Diamond (2.0×1011 N+ /cm2 )1.20±0.90

1.75±0.09

Diamond (1.0×1012 N+ /cm2 )24.2±0.50

1.01±0.05

On the other hand, the quadratic dependence of the |∆R/R| signal observed in the present
study is surprisingly coincide with the signal from photo-carriers generated upon green laser(532 nm) illumination as the function of the green laser power [30]. Bourgeois et al. havedetected two-photon excited free electrons in the conduction band (CB) as the photocurrent(photo-carriers) both in type-Ib and -IIa CVD diamonds [30]. Since the quadratic dependence
was enhanced for the pure type-IIa diamond, they concluded that the linear dependence dominatedfor the type-Ib diamond came from one-photon absorption via N0S defect state [31]. In our case,Research Article

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i.e., type-IIa diamond, however, the N0S defects rarely exist and therefore the effect of N0S defectstates is negligible. Thus, the linear dependence on the |∆R/R| signal should be dominated by the
OKE. Thus, our data demonstrate that the OKE signal is enhanced much in the case of heavily
implanted type-IIa diamond (1.0×1012 N+ /cm2 ). A possible reason for the giant enhancement of
the OKE is the contribution from the cascading OKE [11,17,18], whose nonlinear susceptibility(2) (2)is expressed by χNVχNV as in Eq. (1); the high density NV centers can effectively break the
inversion symmetry near the sample surface region. Note that non-zero χ(2) would generatesecond-harmonic generation (SHG) and therefore the incident pump photon energy cannot
fully be supplied for the competing TPA [32]. In the case of the nonlinear refraction (e.g.,cascading OKE), the coherence length Lcoh might be important, which is ∼16 µm, obtained using
Lcoh = π/∆k, where ∆k = k2ω − kω is the wave vector mismatch during SHG [32]. In the case of
the nonlinear absorption (e.g., TPA) via Im χ(3) , the Rayleigh length (z0 ≈200 µm in the present
study) would play a major role. However, considering the signal enhancement occurred in theregion where NV centers exist and inversion symmetry was broken ( χ(2) , 0), our data indicatethat the NV center introduced surface region with LNV ∼ 60–70 nm thick in maximum play adominant role.
By contrast, the nonlinear absorption, β, shows a largest value for the lightly implanted
diamond (2.0×1011 N+ /cm2 ), indicating the stronger absorption of the probe light upon thephotoexcitation, which can be discussed based on the band model of NV centers [33,34]. Since
the band-gap energy (Eg = 5.5 eV) of diamond is much larger than the photon energy used (1.55
eV), and for high-purity diamond the two-photon absorption starts from ≈ Eg /2 [13], it is required
to consider the mid-gap states associated with the NV centers, which locates in between the
band-gap, as illustrated in Fig. 6 [35]. For the negatively charged NV− state, the two-photon
absorption (1.55 + 1.55 eV) would promote an electron from the 3 A2 ground state into the CB[36]. In this case, the two-photon absorption induces free carrier generation in the CB, and then
immediately transfers the NV− to NV0 states, i.e., the ionization [37](see Fig. 6). Therefore, theexistence of the NV centers will promote strong two-photon absorption as the pump action in
the initial NV− state and subsequent transient one-photon absorption of a 1.55 eV probe photonby free carriers, which would induce a few times larger ∆R/R signal observed in NV center
introduced diamond at 2.0×1011 N+ /cm2 (Fig. 4). Note that the ionization and/or recombinationfrom the NV− to NV0 states or vise versa have been discussed under the green laser (532 nm)
irradiation [36,38]. There, both the ionization (NV− → NV0 ) and recombination (NV0 → NV− )rates exhibited quadratic dependence on the green laser power for relatively low densities of NV
centers (type-IIa, [N] < 1 ppm) [38]. The laser wavelength used in the present study is, however,near infrared (800 nm), and it is not possible to induce the recombination with such a low photon
energy (see Fig. 6, right panel). It is to be also noted that the transient ∆R/R signal observedin the present study is dynamical phenomenon, originating dominantly from the initial NV−
state, and contribution from the NV0 state to the ∆R/R signal will be negligibly small, althoughfurther experiments using different photon energies and theoretical analysis are required to fully
understand the ultrafast nonlinear dynamics in diamond. In addition, for the heavily implanted
diamond, the energy loss due to the SHG will be largest for the highest dose of 1.0×1012 N+ /cm2 ,and thereby the probability of TPA would be decreased. This would explain why the β value
associated with the TPA decreases at 1.0×1012 N+ /cm2 in Table 2.

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Fig. 6. Energy diagram for the NV− and NV0 states in diamond. The NV introduced
samples have natively the mid-gap electronic state of the negatively charged nitrogen-vacancy,i.e., NV− state (Left panel). The energy levels of the NV− and NV0 states are definedby the binding energy of the NV center. The Fermi level of our sample in the NV− state(the nitrogen concentration of ∼1017 cm−3 ) would be ≈4 eV above the valence band (VB)[33], and thereby electrons are populated at the 3 A2 ground state in the equilibrium. The
lifetime of the 3 E state is generally nanosecond time scale [34], however, in the present
non-resonant case, intermediate state given by the dashed line should have very short lifetime(an order of the pulse length) and it does not significantly contribute to the TPA signal. The
pumping action promotes an electron from the 3 A2 ground state into the conduction band(CB) via TPA (transition À), resulting in generation of a free electron, which is immediately
followed by the formation of the neutrally charged NV0 state (Ionization; right panel). Since
femtosecond laser pulses can follow the ultrafast carrier dynamics in the CB, a part of thefree carriers can absorb a probe photon (free carrier absorption; transition Á ) when thepump and probe pulses overlap each other at t = 0, resulting in the negative peak signal on∆R/R. For the NV0 state, unlike in the case of irradiation of green laser, TPA (or one-phonon
excitation) from the 2 E ground state with a 1.55 eV probe photon (transition Â) is hardto occur because of the energy mismatch and therefore recombination process via further
excitation of electron from the VB into the 2 E ground state (transition Ã) is not available.

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4.

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Conclusion

We investigate the effect of nitrogen-vacancy (NV) centers in diamond on nonlinear optical effects
using 40 fs femtosecond laser pulses. The near infrared femtosecond pulses allow us to study
purely nonlinear optical effects, such as optical Kerr effect and two-photon absorption, relating tounique optical transitions by electronic structures involved with NV centers. It is found that boththe nonlinear optical effects are enhanced by the introduction of NV centers in the N+ dose levels of
2.0×1011 and 1.0×1012 N+ /cm2 . The signal enhancement was more visible for the time-resolved
reflectivity measurement (∆R/R) than that in the case of the conventional transmission (T)measurements by the Z-scan technique. We attribute the several times larger signal enhancementin the ∆R/R mode observed at N+ dose levels of 1.0×1012 N+ /cm2 to dominant contribution
from the cascading OKE originating from breaking the inversion symmetry near the surface
region, and minor one from TPA due to the NV− bands in diamond. Our results will open the
new window to develop all optical quantum sensing and computing based on nonlinear opticaleffects, such as a single-photon source using waveguide or nanopillar structures [39,40], anddiamond ring resonators operating at telecom wavelengths [41], which are useful for quantum
technologies in a wide range of spatial and frequency resolutions.
FundingCore Research for Evolutional Science and Technology (CREST) (JPMJCR1875); Japan Society
for the Promotion of Science (17H06088).
Acknowledgments
The authors acknowledge Richarj Mondal of University of Tsukuba for his helpful comments on
the Z-scan measurements.
Disclosures
The authors declare no conflicts of interest.
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