Nonlinear Optical Effects with Polariton Lasers in a GaAs Microcavity

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C: Physical Processes in Nanomaterials and Nanostructures

Nonlinear Optical Effects With Polariton Lasers in a GaAs Microcavity Ana Clara Sampaio Pimenta, Luana Costa Faria, Juan C González, Milena de Giorgi, Daniele Sanvitto, and Franklin Massami Matinaga J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02803 • Publication Date (Web): 13 Jul 2018 Downloaded from http://pubs.acs.org on July 19, 2018

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The Journal of Physical Chemistry

Nonlinear Optical Effects with Polariton Lasers in a GaAs Microcavity A. C. S. Pimenta1, L. C. Faria1, J. C. González2, M. de Giorgi3, D. Sanvitto3, F. M. Matinaga1* 1

Photonic Lab., Dep. de Física, Av. Antônio Carlos 6627, Pampulha, Belo Horizonte, Brazil. Molecular Beam Epitaxy Lab., Dep. de Física, Av. Antônio Carlos 6627, Pampulha, Belo Horizonte,

2

Brazil. 3

Nanotec - Istituto Nanotecnologia - CNR, via Monteroni 73100, Lecce, Italy.

Abstract: We report the nonlinear optical properties of polaritons in a single quantum well GaAs microcavity. Single and double resonance cavities have been used to enhance the nonlinear effect of a nonlinear medium in high-Q quality factor cavities due to the cavity field amplification. On the other hand, such a cavity can generate polaritons, which condense (BEC) for determined conditions, such as cavity detuning and polariton density. Here, we present experimental observations of the second harmonic generation (SHG) from polaritons in a GaAs microcavity, which exihibit a two-order higher efficiency than those from the usual method. Furthermore, the efficiency is particularly high when the polariton is a photon-like particle and in a condensed state.

Introduction: Nonlinear optics is one of the most promising phenomena for realizing coherent high energy optical sources as has been demonstrated in the past1,2 and with improvements in recent works with microcavities.3 Particularly in a microcavity, the light is confined in a Fabry-Pérot-type cavity, and restricted to a small mode volume (V) for long time (a high-Q cavity), so nonlinear effects are enhanced due to the increased light & matter interaction.4,5,6,7 Moreover, the double resonance cavity has been studied as a device for the enhancement of χ(2) and χ(3) nonlinear material indices.8,9,10 Those nonlinear processes in the resonant cavity seed a dynamical behavior on the cavity light transmission or emission, which also results in effects such as bistability,11,12 squeezing13,14 or self-pulsation.15,16,17 On the other side, the enhanced interaction of the exciton – light generates a polariton, a new particle present in the cavity mode. Some groups have been working on the nonlinear properties of polaritons, e.g. using polaritons to generate 2p exciton states,18 and also to generate the second harmonic (SHG) in the cavity gain medium

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experimentally.4 These nonlinear effects have been predicted by theory even in a low-Q, non-resonant excitation cavity.19 Therefore, besides the coherent high-energy sources, this cavity enhancement of nonlinear effects with polaritons is also attractive for low-power frequency-conversion devices,4 bistability, squeezed states and dynamical self-pulsation systems.11-17 In this work, we show the second harmonic generation (SHG) from polaritons in a single quantum well (SQW) GaAs microcavity by resonant excitation with a continuous wave (CW) Ti:sapphire (Ti:Sa) laser. The SHG could not be measured directly due to the cavity mirror (distributed Bragg reflector - DBR) absorption, so we collected the DBR photoluminescence (PL) excited by the polariton SHG. From the DBR PL intensity measurement, we observed the usual second-order curve as functions of the pump power and the GaAs zincblend (ZB) 43m SHG symmetry dependence with excitation polarization angle (90° periodicity). Additionally, when the cavity resonance was detuned during the SHG measurements, higher SHG efficiency was observed, which is in agreement with photon-like polariton and when it is in a condensed state.

Experimental: We used a λ microcavity with a 100 Å GaAs single quantum well (SQW) in the center, with a lower/upper DBR mirror formed by 26.5/24 pairs of AlAs/Al0.2Ga0.8As layers (fig. 1a), the system was cooled down to 10 K in a cold finger cryostat. This cavity showed a strong coupling with a normal mode splitting energy of 3.7 meV.20 The lower polariton was resonantly excited with a linearly polarized Ti:Sa CW laser at an incident angle of 12° in relation to the cavity normal direction Z (fig. 1a). We used lenses (L) and mirrors (M) to focus the pump light and collect the scattered light from the microcavity, one attenuator (A) to set the pump power, a bandpass filter (F) to clean the scattered pump light and a polarizer (P) to measure the vertical linear polarization component. The polariton normal emission was measured in the usual PL setup with a 1800 l/mm grazing spectrometer coupled to a charge coupled detector (CCD) as sketched on fig. 1b. Since the SHG light (~ 400nm) intensity was absorbed by the upper DBR layers (I/I0 < 10-13), we measured the Ga0.2Al0.8As/AlAs DBR PL (a band gap wavelength of approximately 686 nm) with a proper pump filtering set. The GaAs ZB


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crystal symmetry dependence was observed by measuring the DBR PL as a function of the Ti:Sa laser linear polarization (LP) angle, θ (fig. 1a), by setting a λ/2 wave plate in the excitation pump beam path in order to rotate the laser electric field € in the X-Y plane.

Results: The strong coupling in our microcavity is assured by the off-resonantly excited (pump at 760nm) cavity dispersion curve and is illustrated in fig. 2, which shows the excitation pump power emission dispersion for a) 4 mW, b) 16 mW and c) 80 mW. These lower polariton branch emissions have longer wavelengths at low pump power, and a blueshift occurs for higher pump power, until the polariton starts to condense at approximately 800 nm (fig. 2c).

a)

b)

Fig. 1: a) microcavity with a GaAs SQW and the DBR energy band diagram, b) Experimental setup.



Fig. 2: Polariton emission dispersion curves: wavelength (nm) & vector k (arbitrary units) for different pump power. a) 4mW, b) 16mW and c) 80mW (the dashed yellow line is a reference guide indicating the polariton blueshift before condensation). Apart from the known polariton optical properties of this cavity,20 we show here the linear emission and pump relation above the pump power threshold (see fig. 3a). The red solid line shows a linear relation for the pump below 400 mW, and an emission intensity saturation appears for higher pump powers. Fig. 3b shows the measurement of the polariton LP angle as a function of the pump LP angle. Again, an approximately linear relation is observed between both emission and pump LP angles, with the rate: ∆(polariton LP angle) / ∆

(pump LP angle)

= 1, indicating the polarization coherence between the

pump light and polariton emission. This LP angle correlation between the polariton and the excitation laser comes from the momentum conservation in the polariton-polariton scattering, which means, without a pump LP memory loss. Therefore, the polariton LP angle can be determined by the pump LP angle, i.e. we can tune the polariton polarization angle simply by tuning the Ti:Sa pump laser LP angle.

Fig. 3: a) Emission intensity as a function of pump power, b) polariton polarization angle as a function of pump laser polarization angle. The red solid line serves as a guide to the eye. To study the polariton SHG emission in the cavity, we had to measure the DBR PL i.e. an indirect measurement, since the polariton SHG scattering at approximately 400 nm was absorbed by DBR layers, as indicated in the cavity band gap diagram (fig. 1a). The Ga0.8Al0.2As layer energy level (1.8 eV at 10K) is the DBR PL emission channel. The observed photoluminescence spectrum is presented on fig. 4a, which was excited by the polariton SHG light emission. To confirm the PL interpretation, a similar


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DBR PL spectrum was also observed when we used a He-Ne laser (632.8 nm) to excite the DBR at 10K. Considering the DBR PL integrated spectrum was proportional to the polariton – SHG intensity (ISHG-DBR), we used this intensity proportionality to characterize the polariton SHG light emission (fig. 4b). We assumed the ISHG-DBR spectrum for each excitation pump power to obtain the nonlinear order (β) curve intensity relation β = 1.9 for a 409 mW pump power at 798nm.

Fig. 4: a) PL spectrum collected from the DBR layers for the 403 mW pump excitation and the polariton at 798.5nm. b) The integrated SHG-DBR PL as a function of the excitation pump power. In fig. 5a we show the plot of the ISHG-DBR dependence on the pump LP angle. Here we simply used the ISHG-DBR spectrum for each pump LP angle, applying bandpass filter to cut the pump light. Fig. 5b shows the relation in a radial plot, illustrating the GaAs 4 3m symmetry behavior for the SHG angular dependence. Fig. 5c shows the polariton emission intensity as a function of the pump LP angle measured with the same procedure, and from this data, the polariton LP degree (ρ = (Imax-Imin)/(Imax+Imin) is 0.12. Such a value shows that the SHG angular dependence (fig. 5a) is also directly related to that of the polariton, ρ (ρpo). The DBR PL intensity (fig. 5a) as a function of the pump polarization angle, shows a 90° periodically modulated intensity, which is twice the periodicity of the polariton intensity modulation (fig. 5c) and merely represents the polariton LP axis rotation. This 90° comes from the GaAs ZB 43m symmetry structure orientation. This dependence was confirmed by adjusting our data with the previews dependence for the ZB SHG scattering, parallel to the (011) plane:16,18,21



∝ sin cos

(1)

where χ is the second-order nonlinear elements of the ZB optical susceptibility tensor, IL is the pump laser intensity and θ is the excitation LP angle (fig. 1a). This dependence is represented by the fitted data (solid line) in fig. 5a) and 5b).

Fig. 5: a) SHG-DBR PL intensity as a function of the pump laser linear polarization angle. b) A radial plot of the SHG-DBR PL; the solid line is the fitted data obtained by eq.(1). c) The polariton emission intensity as a function of the pump LP angle (the solid line is a sinusoidal guide to the eye). In addition to this ZB SHG scattering angle behavior, we should observe a second-order relation (β=2) between the ISHG-DBR and the polariton intensity. Since the Ipolariton / Ipump intensity rate proportionality is not 1, but approximately linear above the pump threshold and below saturation (fig. 3a), the SHG intensity as a function of the pump intensity will not be the usual second-order curve for a microcavity with polaritons. Regardless, we measured a close second-order relation for the ISHG-DBR (fig. 6a) near the cavity resonance (800nm), and we observed an exponential increase in the


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nonlinear order with the cavity detuning energy δ = δc - δx (cavity resonance minus the exciton energy). For cavity detuning, the investigated sample exhibites a 1.3 meV/mm gradient on δ when we moved the sample perpendicular to the cavity normal direction. Fig. 6b shows the ISHG-DBR analyses from the point of view of the polariton LP degree ρpo. We note an agreement in the SHG-DBR LP amplitude (ηSHG) compared to ρpo. The main behavior difference is the single increase in ηSHG near the cavity resonant energy (δ ≅ 0), which corresponds to the condensation condition for a high polariton density (fig. 2).

Additionally, both ηSHG and the polarization degree ρpo have an

opposite inclination from that of the nonlinear order behavior (fig. 6a). This behavior comes from the photon-like-polariton (δ < 0) higher electrical field characteristics, contrary to those of the exciton-like-polariton (δ > 0). That is, a higher SHG efficiency for photon-like-polariton, with the exception of δ ≥ 0, where there should be a condensation effect with higher coherence and LP degree polariton light.

Fig. 6: a) Polariton DBR PL intensity nonlinear order (β) as a function of δ. b) SHGDBR and polariton polarization degree (ρ) as a function of δ (the solid line is a guide to the eye).

Another important result of this SHG-DBR PL emission measurement, is the quantum conversion efficiency γ = P2w/(Pw)2 (the SHG power divided by the squared excitation pump power). For this purpose, we measured the DBR PL (in a similar way to fig. 4a result) using a He:Ne laser for excitation and a collection lens with a focusing length of 5 cm and a diameter of 5 cm (fig. 1b). The measured polariton normal emission intensity was 5mW for a 408 mW excitation pump laser (measured with a calibrated powermeter).



Moreover, we consider that the SHG light (∼ 400nm) is nearly totally absorbed by the Al0.2Ga0.8As, in the first DBR layer (α ≅ 4.0x104 cm-1).22 This layer emits as a homogeneous source at 686 nm, so the emitted light will pass by the DBR (with 24 pairs), being attenuated by a factor of α (1.5x104 cm-1) in each Al0.2Ga0.8As layer (57.9nm in thickness and a bandgap energy of 1.807eV), before going out for detection. The derivative of the loss (e-αx) represents an attenuation factor of 0.136 for the light coming out at 686 nm. Furthermore, if we consider the reflection indices of AlGaAs (3.662) and AlAs (3.064), we have a reflection loss of 69.4 % from the 23 AlAs layers. On the other hand, the ISHG-DBR was corrected by the calibrated ISHG-DBR spectrum measured with the He-Ne excitation, which gives a factor of 77280 counts/mW in our spectrometer. This correction, takes into account the light collection loss parameter (lens angular aperture, scattering, and spectrometer efficiency). Considering all these loses, the reversal calculus gives us a polariton SHG emission power of 1.2mW, i.e. γ = 7.5x10-3/W. This result is a rough estimation since at low temperature, the excitonic absorption can change that estimated loss. However for a continuous wave excitation regime in a bulk system (DBR well thickness > 30nm), the AlAs/AlGaAs multilayer absorption coefficient, (i.e. the exciton absorption peak) is equal to the area of a rectangle, whose base is the exciton binding energy and whose height is the height of the continuum absorption edge.23

Discussion: Our first worry was about the origin of the DBR luminescence. It could have been due to two photon absorption process (TPA) followed by carrier relaxation to the Al0.2Ga0.8As energy bottom band before recombination. This possibility is not treated in this work, due to the indirect DBR-PL measurement, so we could not separate the contribution from TPA process from the SHG as done by interferometric measurement.24 On the other hand, It could have been an SHG excited as a usual semiconductor diode laser;25 however, we did not observe any DBR PL when we excited the cavity with off resonant pumping up to 400 mW. Additionally, the DBR PL was not observed when the cavity was detuned out of the polariton excitation range. The polariton is a particle that occupies the cavity field mode, however, the exciton is localized in the GaAs SQW layer. Therefore, since the polariton is a particle formed by the exciton and photon, we infer that the nonlinear effect occurs in the GaAs SQW, and


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in this case with SHG nonlinear susceptibility of χ(2) for a resonant polariton light, and not that for the off-resonant laser case.19 A polariton will have photon-like behavior for negative δ values and excitoniclike for positive δ. From fig. 6a, we observe a decrease on the nonlinearity order, which means a higher interaction between the photon field with the exciton on GaAs SQW. For the cavity quantum efficiency γ = 7.5x10-3/W, we call that this measurement was done with a CW excitation laser. This means that the required power (~ 10-1 W in fig. 4b) was three orders less than the usual work with pulsed high peak power laser systems (~ 102 W).4 One other advantage of the SHG from a polariton in a cavity is that the cavity is an internal passivated SHG medium, that avoids surface oxidation due to pump heating, such as that observed in nanostructures such as GaAs nanowires. 26,27 Conclusion: Polariton nonlinear optical properties with a low-power (~mW) continuum wave laser excitation were studied in a 100 Ả GaAs SQW microcavity, where exciton polariton, i.e a strong light matter interaction where explored to get SHG light as has been shown for molecular crystal cavity.4 The high γ factor in our cavity comes in part due to high χ(2) factor of GaAs, however, it is much higher (2 order) than system like a GaAs nanowire structures.28 These advantage, apart from the passivation problem in such structures, can be observed without more complex cavity engineering to control the fundamental (w) and the SHG field (2w) phases in the cavity.8-10,29 The SHG-polariton process has a dynamic relationship with the polariton intensity emission, together with the Kerr effect or TPA,10 bistability,11,12,20 and squeezing.13,14 All or each one would be related to polariton laser self-oscillation effects.30,31 The estimated 2-order higher γ factor for the polariton SHG compared with a GaAs quantum wire, should be considered for the design of a microcavity with it`s mirrors (DBR) fabricated with a dielectric material transparent to ultraviolet light. On the other hand, a microscopic model for the exciton-polariton field influence on the SHG in the microcavity should be developed to confirm the efficiency compared to that of the usual dielectric crystal symmetry relation. Such a theory would not be a simple dipole approximation model as has been demonstrated for SHG in resonant excitons for ZnO nanowires. 32



Author information: *Corresponding author e-mail: [email protected] Notes: The author declares no competing financial interest. Acknowledgments: This work was supported by Fapemig, CNPq and CAPES.

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Nonlinear Optical Effects with Polariton Lasers in a GaAs Microcavity

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