Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

Michael T.
Quick‡
^{a},
Nina
Owschimikow
^{a},
Ali Hossain
Khan
^{bc},
Anatolii
Polovitsyn
^{bc},
Iwan
Moreels
^{bc},
Ulrike
Woggon
^{a} and
Alexander W.
Achtstein‡
^{a}
^{a}Institute of Optics and Atomic Physics, Technical University of Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany. E-mail: alexander.achtstein@tu-berlin.de
^{b}Instituto Italiano di Tecnologia, via morego 30, 16163 Genova, Italy
^{c}Department of Chemistry, Ghent University, krijgslaan 281-S3, 9000 Gent, Belgium

Received
19th July 2019
, Accepted 6th September 2019

First published on 6th September 2019

We investigate broadband two-photon absorption autocorrelators based on II–VI semiconductor nanoplatelets as an alternative to common second harmonic generation based techniques. As compared to bulk materials the exceptionally high enhancement of two-photon absorption in these 2D structures results in very efficient two-photon absorption based autocorrelation detected via PL emission. We compare the results with TPA autocorrelation in CdS bulk as well as SHG based autocorrelation in β-barium borate. We show that CdSe nanoplatelet based autocorrelation can exceed the efficiency of conventional methods by two orders in magnitude, especially for short interaction length, and allows a precise pulse-width determination. We demonstrate that very high two-photon absorption cross sections of the nanoplatelets are the basis for this effective TPA autocorrelation. Based on our results with II–VI nanoplatelets efficient broadband autocorrelation with more than ∼100 nm bandwidth and very high sensitivity seems feasible.

In the early 90s TPA based autocorrelation using bulk materials has been proposed as a replacement of the hitherto established nonlinear processes.^{30,31} In this context not the two-photon absorption itself or the TPA based re-emission fluorescence have been used, but the TPA induced e–h pairs creating a photocurrent, often measured directly in a photodiode, whose active region already acts as a two-photon absorber.^{32–38} This idea has been extended to commercial diodes operated as unbiased photodiodes.^{39,40} However, the sensitivity of these devices is limited by the rather small nonlinearities of the quasi bulk semiconductor materials used e.g. in the intrinsic layer of a PIN diode and the very limited absorption probability within typical intrinsic layer thicknesses.

Nonlinear semiconductor nano materials offer several advantages as compared to bulk transparent nonlinear optical crystals. In contrast to SHG performed e.g. in β-barium borate (BBO), TPA does not require phase matching between the fundamental waves and the SHG, as the detected signal is formed after two-photon absorption by spontaneously re-emitted photons with the semiconductor bandgap energy. Especially regarding conversion efficiency and sensitivity TPA can outpace SHG techniques by orders of magnitude.^{21,36,40} Most interesting, however, is the possibility of very large autocorrelation bandwidth. For broadband SHG autocorrelation in e.g. BBO, LBO, or similar materials, dispersion requires to use increasingly thin crystals for broadband pulses. As the conversion efficiency increases quadratically with the product of crystal length and χ^{(2)},^{41} (under the assumption of no pump depletion) short crystals have low efficiency so that materials with high nonlinearities are desired. TPA based autocorrelation with nanocrystals does not experience this problem as explained above. The need for highly stable ultra-broadband autocorrelation is further justified by the growing field of fs and attosecond physics, where fs and sub femtosecond pulse lengths^{42} demand e.g. ∼100 nm or even octave spanning autocorrelators.

Many commercial and non-commercial autocorrelation devices based on different principles are currently on the market, however, the usage of nano materials for TPA autocorrelation is less investigated.^{40} Moreover, apart from choosing usual co-propagating beam Michelson interferometer type setups, also non-collinear geometries allow to cross correlate two light pulses of different frequency, e.g. by TPA, satisfying the condition hν_{1} + hν_{2} ≥ E_{g}.^{21} Hence we demonstrate in the following as a proof of concept efficient TPA autocorrelation with 2D CdSe nanoplatelets (NPLs), detected via PL, using their exceptionally high TPA nonlinearity. In this paper we will at first target the autocorrelation and then discuss its high efficiency based on the determination of the TPA cross section of CdSe nanoplatelets.

By definition the second order correlation function G^{(2)}(t) in time is given by a temporal convolution of two pulse intensities I_{A}(t) and I_{B}(t).

(1) |

Fourier transformation () allows to express this convolution also as a product in frequency domain. For Gaussian temporal pulses it can be shown that the FWHM τ_{p} of the pulse, is related to its autocorrelation width τ_{ac}via.^{43}Fig. 3 shows the four resulting autocorrelation curves of our samples, which are listed in Table 1. We use a BBO crystal as an autocorrelation reference and define the relative deviation of the FWHM as Δ = |(τ − τ_{BBO})/τ_{BBO}|, an indicator for the agreement among the different studied autocorrelation techniques. The deviation for the CdSe platelets is below 4%, thus giving excellent agreement with the BBO reference, while for the CdS bulk sample it is 9%, expectedly bigger due to considerable pulse broadening in CdS. Pulse broadening within the NPL samples due to dispersion can be shown to have no relevant effect in the two samples.^{44} This is the case because group velocity dispersion around 800 nm is low in polystyrene, the embedding matrix of the dispersed NPLs.^{45} The pulse broadening of an incoming pulse is given by:

(2) |

Fig. 3 Normalized autocorrelation curves resulting from different methods and samples, respectively vs. relative pulse delay in fs. Data were fitted assuming a Gaussian pulse shape, characteristic for the Coherent Mira 900 HP fs laser, as clearly seen for the BBO data. Autocorrelations are performed via SHG in BBO (blue), TPA in CdS bulk (red) and TPA in two different CdSe NPL samples (green) of distinct size via delaying one 800 nm beam vs. the other. The autocorrelation's FWHM is connected to the pulse FWHM τ_{p} by .^{43} The measured pulse width τ_{p} are indicated. |

CdSe NPL | ||||
---|---|---|---|---|

174 nm^{2} |
288 nm^{2} |
CdS | BBO | |

τ
_{p,1} (fs) meas. |
174 | 164 | 187 | 171 |

τ
_{p,1} (fs) est. |
174 | 174 | 191 | 171 |

d
_{sample} (mm) |
0.95 | 0.90 | 0.50 | 0.50 |

(mm) | 0.49 | 0.57 | 0.50 | — |

C (cm^{4} GW^{−2}) |
41 | 76 | 4.2 × 10^{3} |
— |

Here, τ_{0} and τ_{1} give the Gaussian pulse FWHM before and after passing the sample, is an effective emission depth within the sample and a is the (linear) chirp parameter. a is related to the instantaneous frequency ω(t) by ω(t) = ω_{c} + dΦ/dt = ω_{c} + 2at/τ_{p,0}^{2} within our Gaussian pulse of central frequency ω_{c}. B is a proportionality constant, given by B = (λ_{0}^{3}2ln(2))/(πc_{0}^{2}). The chirp parameter a relates to a spectral phase of a Gaussian pulse (chirp) and alters its time-bandwidth product.^{46} The pulse impinging on the sample is linearly chirped, as common for Ti:Sa laser systems, which are not bandwidth limited. a can be estimated from the time-bandwidth product of the laser source via (with a = 1.7 for our laser system). Second, to calculate the effective emission depth , reabsorption during propagation of two-photon induced PL emission through the samples has to be considered. The effective emission depth due to reabsorption is calculated by:

(3) |

L gives the sample's thickness, I_{F} the emission intensity and α represents the linear absorption coefficient. The relation above holds, as the Rayleigh length (2.5 mm) of the used 15 cm focussing lens for excitation is greater than the sample thickness (0.5 mm). The TPA induced luminescence emission per unit length (∂I_{F}/∂z) and the incoming excitation wave's intensity I_{exc} (800 nm) are connected for TPA via:

(4) |

Fig. 4 PL signal vs. the beam temporal and spatial peak intensity in GW cm^{−2} for NPLs of two different areas 174 nm^{2} (a) and 288 nm^{2} (b) as well as for CdS bulk (c). The quadratic fit according to eqn (5) (shown as a dotted fit line on the logarithmic scale) yields a factor C, the conversion figure of merit. |

To understand why CdSe NPLs are suitable for efficient second order autocorrelation, we target their TPA nonlinearity quantitatively in the next section. We use our intensity dependent measurements for TPA cross section calculation, which will demonstrate their considerably higher nonlinearity as compared to bulk. The acquired signal can be understood as the total emission intensity I_{F,out} modified by an excitation and detection efficiency φ (a setup constant for each beam). Likewise, the signal S is proportional to the square of the incoming excitation wave's intensity I_{exc}.

S(I_{exc}) = φI_{F,out} = CI_{exc}^{2} | (5) |

The conversion figure of merit C is directly obtained from fitting the data (Fig. 4) and used to retrieve the TPA cross section. The total number of PL photons leaving the sample, and hence the intensity I_{F,out}, is diminished by reflection R (of the excitation) at the sample's front surface when entering and reflection of the emitted PL photons when exiting the sample.

(6) |

R = (n(λ) − 1)^{2}/(n(λ) + 1)^{2} stands for the intensity reflection coefficient for entering or leaving the sample. They depend on the excitation and emission wavelength. Again, the derivative is linked to the attenuated excitation wave by the former introduced eqn (4). As the sample is transparent for the laser at 800 nm, no linear absorption is taken into account and the derivative of I_{exc} can be solely related to the TPA coefficient β by (∂I_{exc}/∂z) = −βI_{exc}^{2}. Using the eqn (4) and eqn (6) yields:

(7) |

Considering ϕ a system constant, it is possible to find β for a sample under test (s), once a reference (r) is known.

(8) |

To apply eqn (8) for nanocrystalline materials, a relation between β and the particle TPA cross section σ^{(2)} has to be used:

(9) |

(10) |

Taking CdS bulk as a reference (β_{r} = 8.8 cm GW^{−1} (ref. 2)) and using eqn (10) with the results given in this work, TPA cross sections of 3.8 × 10^{6} GM (24 × 12 nm^{2} CdSe NPL) and 7.7 × 10^{5} GM (29 × 6 nm^{2} CdSe NPL) are obtained, considering the quantum yields η of the CdSe samples (both 15%) and reference (6.2%). We refer to ESI† for a detailed calculation. These results are in good agreement with the very high TPA cross sections obtained in z-scan and two-photon PLE in ref. 5 for platelets of comparable size. Hence the outcome substantiates that CdSe nanoplatelets with their extremely high nonlinearities are ideal to build high efficiency and low intensity pulse characterization autocorrelators. This will be addressed in the following.

For SHG to occur, e.g. in a BBO crystal, coherent interaction between the incoming photons is required as well as phase matching between the fundamental and generated second harmonic field. This requires critical angle or thermal phase matching (e.g. in birefringent media), periodically poled (pp)-crystals or very thin crystals, where walk off and phase lag are not limiting the performance. However, for broadband autocorrelation the crystals need to be thin due to group velocity dispersion and mismatch limiting the bandwidth. Hence materials with high nonlinearities are desired, as suggested in the introduction. Here TPA materials with high cross sections come into play, as they do not require phase matching of the fundamental and converted photons, since re-emission after two-photon excitation is spontaneous and incoherent so that there can be no back conversion of the generated radiation into the fundamental beam. As an example for the high efficiency we compare the efficiency of a very thin, dense 10 μm layer of nanoplatelets with 3.7 × 10^{6} GM (and assumed fill factor 100%) with a BBO of identical thickness at 10 GW cm^{−2} at 800 nm, typical power densities for a ∼100 MHz repetition rate, ∼100 fs Ti:Sa laser system, using ∼13 mW focused by a 0.2 NA objective. Due to the extremely thin crystal assumption the conversion efficiency is only ∼5 × 10^{−2} % for the BBO, calculated using ref. 49 and taking into account that the Rayleigh length of the beam (>10 micron) is not smaller than the sample thickness. Estimating the TPA efficiency^{21} by φ = 1 − 1/(1 + β_{Mat}LI_{exc}) up to 80% is feasible, given the parameters above. For the intrinsic TPA coefficient β_{Mat} of the NPLs itself, which allows comparison to bulk materials, we calculate β_{Mat} = 392 cm GW^{−1} for the larger 24 × 12 nm^{2} NPL and β_{Mat} = 122 cm GW^{−1} for the 29 × 6 nm^{2} NPL via β_{Mat} = β_{eff}/f_{V} from the obtained cross sections above viaeqn (9). Furthermore, using a luminescence quantum yield η of 15% for NPLs, the conversion total efficiency yields = φ × η = 12 %.

For our setup we were able to record autocorrelation traces down to <1 mW beam power. The sensitivity may be extended using a shorter focal length focusing lens, resulting in higher excitation power in the sample. However we did not use shorter lenses, to maintain our setup in a condition, where the sample length is smaller than the Rayleigh length of the lens, to be able to do quantitative referencing of TPA cross sections. The measurable range of input power is limited to below 200 GW cm^{−2} (60 W CW equivalent), the above mentioned TPA saturation intensity.

Contrasting the calculations for CdSe nanoplatelets and BBO we find, that the conversion efficiencies of such NPLs can exceed equivalent SHG in BBO by two orders of magnitude. In a similar manner, the efficiency of TPA autocorrelation in CdS bulk can be exceeded by about two orders, based of the enhancement of the two photon absorption coefficient in CdSe nanoplatelets relative to bulk (β_{r} = 8.8 cm GW^{−1} (ref. 2)). In addition, oriented CdSe NPLs show directional PL emission in the z-direction.^{50} Hence, e.g. oriented multilayers can allow for high collection efficiency, for instance ideally matching a 0.4 NA detection optics.

It can be seen from the discussion above that autocorrelation with 2D semiconductors has higher efficiency, once very short interaction length is considered. Therefore TPA based autocorrelators have a great application potential for the characterization of ultrashort pulses. As the two-photon absorption spectrum is broad,^{5}i.e. very high bandwidth (>100 nm), few fs pulses may be autocorrelated efficiently opening up great application perspectives. The performance of TPA autocorrelation with nanoplatelets in terms of efficiency for wavelength different than 800 nm or for large spectral bandwidth follows from the spectral course of TPA cross sections for CdSe nanoplatelets, measured in ref. 5.

Reasoned in the ultra strong electronic confinement, the very high TPA cross sections result in superiority of nanoplatelets over bulk semiconductor materials for autocorrelation, used in the past. Many of the discussed semiconductors were limited to a wavelength regime above 1 micron and were also quickly reaching intensity saturation limits for intense beams.^{40} All these obstacles are not present with nanoplatelets, yielding high sensitivity and no saturation effects. Instead of detecting the luminescence externally, our NPLs can possibly be used in on-chip photonics, combining the large nonlinearities and resulting high sensitivities with direct detection of the two photon induced luminescence. For example nanoplatelets can be deposited on a planar photodiode, which detects the autocorrelation related PL with high efficiency. Especially due to the fact, that this PL emission is directional,^{50} and mainly in the direction of the surface normal of nanoplatelets such a structure will provide high efficiency. Advances towards the processing and characterization of quantum confined CdSe particles in optoelectronics have already been made.^{51,52} We also remark that conventional (epitaxial) II–VI quantum wells will not be able to compete with these structures, as due to e.g. interface roughness scattering the exciton coherence areas (volumina) do not reach the platelet values, resulting presumably in considerably lower nonlinearities and hence autocorrelation efficiencies. Further, as in such epitaxial structures the dielectric mismatch between the CdSe quantum well and surrounding (e.g. Zn_{x}Cd_{1−x}Se) material is low, the excitonic correlation is considerably lower and therefore the exciton Bohr radius is higher. This results in lower transition dipole moments,^{21} concatenated for the two photon transition, and due to second order Fermi's Golden Rule in considerably smaller TPA rates. We remark that the efficiency of autocorrelation can be further enhanced considerably by using larger nanoplatelets as the ones used in this study. Their TPA cross sections can be with ∼10^{8} GM (ref. 5) even a hundred times higher, further enhancing the autocorrelation efficiency. Hence II–VI nanoplatelets are a favored system for TPA based autocorrelation.

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## Footnotes |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/C9NR06156H |

‡ These authors contributed equally to this work. |

This journal is © The Royal Society of Chemistry 2019 |