Nonlinear Medium for Efficient Steady-State Directional White-Light Generation

From Left to Right: (top row) Nils W. Rosemann, Jens P. Eußner, Andreas Beyer, Stephan W. Koch; (bottom row) Kerstin Volz, Stefanie Dehnen, Sangam Chatterjee 
(credit for Sangam's picture: Tim van de Bovenkamp)

Authors: Nils W. Rosemann^1,2, Jens P. Eußner^2,3, Andreas Beyer^1,2, Stephan W. Koch^1,2, Kerstin Volz^1,2, Stefanie Dehnen^2,3, Sangam Chatterjee^1,2,4

Affiliations:
¹Fachbereich Physik, Philipps-Universität Marburg, Marburg, Germany.
²Wissenschaftliches Zentrum für Materialwissenschaften, Philipps-Universität Marburg, Marburg, Germany.
³Fachbereich Chemie, Philipps-Universität Marburg, Marburg, Germany.
⁴Institute of Experimental Physics I, Justus-Liebig-University, Giessen, Germany.

Tailored light sources have greatly advanced over the past decades. In particular, the development of light-emitting diodes[1] (LED) was the last milestone in the field of illumination. This includes the virtually omnipresent white LEDs where ultraviolet emitting gallium nitride (GaN) LEDs [2] excite light converting phosphors to cover the visible spectrum. They are reasonably priced and are starting to replace incandescent or compact fluorescent sources for lighting and display applications [3,4].

For many scientific uses, the development of the laser was a comparable milestone [5]. Lasers are light sources with well-defined and well-manageable properties, making them an ideal tool for scientific research. Nevertheless, at some points the inherent (quasi-)monochromaticity of lasers is a drawback. Using a convenient converting phosphor can produce a broad spectrum but also results in a loss of the desired laser properties, in particular the high degree of directionality. To generate true white light while retaining this directionality, one can resort to nonlinear effects like soliton formation [6]. Unfortunately, nonlinear effects usually require large field-strength, thus large-scale, expensive pulsed or high-power lasers. On the route towards a more favorable solution, we recently presented an amorphous cluster compound that converts the infrared (IR) light of a reasonably priced laser diode into a broad visible spectrum while retaining the desired laser properties [7].

The compound contains clusters with a tin-sulfur based core and four organic ligands per formula unit. The core is composed of an adamantane-like scaffold, [Sn₄S₆]. It has a tetrahedral shape and is thus lacking inversion symmetry. This is accompanied by a random orientation of the four ligands R = 4-(CH₂=CH)-C₆H₄ (Fig. 1a). The ligands consolidate the structure of the core [8,9] and prevent crystallization of the compound, hence prevent any long-range order. As a result, the compound is obtained as an amorphous white powder (Fig. 1b).

Figure 1: (a) Molecular structure of the adamantane-like cluster molecule, with tin and sulfur atoms drawn as blue and yellow spheres, respectively; carbon (grey) and hydrogen (white) atoms are given as wires. (b) Photograph of the as prepared powder.

Upon irradiation with infrared laser light, the compound emits a warm white-light (Fig. 2a). Its spectrum is virtually independent of the excitation wavelength in the range from 725 to 1050 nm. Variation of the laser intensity, however, results in a slight shift of the spectral weight towards higher energies for higher intensities (Fig. 2b). This common impression of a dimming tungsten-halogen light bulb could lead to the assumption that the novel light-emission is also thermal. However, the input-output characteristic of the white-light process scales highly nonlinear. Additionally, the emitted intensity depending on the color temperature of the observed spectra differs vastly from the Stefan-Boltzmann law. These two points exclude a thermal process to be the source of the observed white light. Furthermore, spontaneous emission can be ruled out: exciting the compound above the absorption edge, i.e., with photon energies above 3.0 eV, changes the emitted spectrum drastically.

Figure 2: (a) Photograph of the cluster compound embedded in a polymer and sandwiched between two glass slips. The compound is excited in the bright center spot, using 800nm laser. (b) White-light spectra for different pump intensities, from low (grey) to high intensity (black). For reference, the emission of a black-body emitter at 2856K is shown.

The largest advantage application-wise is found in its directionality, i.e., the angular emission characteristics. When the sample is excited in a transmission like geometry, the spatial distribution of the white-light is found to be very close to that of the driving laser. In combination with the very low threshold of the nonlinear process, this enables the use of this light source for many applications where a broad spectrum and low-etendue are required, e.g., in microscopes or optical coherence tomography systems.

To explain the white-light emitting process, we developed a semi-classical model. This model ascribes the white-light emission to the driven movement of an electron in the clusters ground state potential. During this process, the electron gets accelerated by the IR-laser and subsequent deceleration of the electron leads to the emission of radiation just like Bremsstrahlung. Implementing this process numerically leads to an excellent agreement of theory and experiment. While such anharmonic oscillator models are commonly applied for nonlinear optical phenomena, here, the shape of the simulated ground state potential is completely based on experimentally verified parameters and results from first-principle calculations. This model does not yield the observed directionality that only could be ascribed to a phased-array effect caused by the driving continuous wave-laser.

Finally, we find that the compound can be used to coat semiconductor substrates like gallium arsenide or silicon. This enables the possibility of functionalization of well established III/V semiconductor laser diodes.

References:
[1] H. J. Round, “A note on carborundum”,  Electrical World, 49.6, 309 (1907). Abstract.
[2] Shuji Nakamura, Takashi Mukai, Masayuki Senoh, “Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes”, Applied Physics Letters, 64, 1687 (1994). Abstract.
[3] Fred Schubert, Jong Kyu Kim, “Light-emitting diodes hit the centenary milestone”, Compound Semiconductor, pages 20-22 (October, 2007). Article.
[4] Siddha Pimputkar, James S. Speck, Steven P. DenBaars, Shuji Nakamura, “Prospects for LED lighting”, Nature Photonics, 3, 180–182 (2009). Abstract.
[5] T. H. Maiman, “Stimulated optical radiation in ruby”, Nature, 187, 493–494 (1960). Abstract.
[6] Robert R. Alfano, "The Supercontinuum Laser Source" (Springer, 2013).
[7] Nils W. Rosemann, Jens P. Eußner, Andreas Beyer, Stephan W. Koch, Kerstin Volz, Stefanie Dehnen, Sangam Chatterjee, “A highly efficient directional molecular white-light emitter driven by a continuous-wave laser diode”, Science, 352, 1301–1304, (2016). Abstract.
[8] Hermann Berwe, Alois Haas, “Thiastannacyclohexane (R₂SnS)₃ und -adamantane (RSn)₄S₆ Synthesen, Eigenschaften und Strukturen”, Chemische Berichte, 120, 1175–1182 (1987). Abstract.
[9] Jens P. Eußnera, Stefanie Dehnen, “Bronze, silver and gold: functionalized group 11 organotin sulfide clusters”, Chemical Communications, 50, 11385–8 (2014). Abstract.

Dropleton – The New Semiconductor Quasiparticle

From Left to Right: (top row) Andrew E. Almand-Hunter, Hebin Li, Steven T. Cundiff, (bottom row) Martin Mootz, Mackillo Kira, Stephan.W. Koch

Authors: Andrew E. Almand-Hunter^1,2, Hebin Li¹, Steven T. Cundiff^1,2, Martin Mootz³, Mackillo Kira³, Stephan.W. Koch³

Affiliation: 
¹JILA, University of Colorado & National Institute of Standards and Technology, Boulder, CO, USA
²Department of Physics, University of Colorado, Boulder, CO, USA
³Department of Physics, Philipps-University Marburg, Germany.

The description of many-particle systems becomes significantly simplified if stable configurations of subsets of the particles can be identified, particularly when the particles are interacting with one another. Examples of stable configurations range from solar systems and galaxies on an astronomical scale [1] to atoms and nuclei on a microscopic scale [2]. In solid-state systems [3], the stable configurations are referred to as “quasiparticles” that have several particle-like features, even though their physical properties are influenced by the interactions. The dropleton is the latest addition to the “periodic table” of quasiparticles in solids, as reported in our recent publication [4].

Extended crystalline solids typically contain more than 10²⁰ interacting electrons per cm³, which makes the quantum many-body problem unsolvable based on overwhelming dimensionality. Therefore, finding quasiparticles is not only extremely useful but also instrumental in order to describe and understand the physics of solids. The “crystal electron’’ – or “Bloch electron’’ – is the simplest quasiparticle of solids. One can attribute a varying mass to an electron inside a crystal, in the same way as a swimmer’s bodyweight seems to change in water. As a quantum feature, crystal electron's effective mass not only depends on the electron-crystal interaction but also on its velocity [3]. When a single electron is removed from an ensemble of many electrons, the missing electron is also a quasiparticle called the “hole’’. The hole simply has the properties of the missing electron, such as a positive elementary charge and a negative effective mass. Conceptually, a hole resembles a bubble, i.e. particle vacancy, in water; its motion is clearly much simpler to track than that of remaining particles.

The quantum mechanically allowed electron-energy regions in solids are commonly known as energy bands and they can be separated by forbidden regions, the band gaps [3]. Without any doping and at low temperatures, a semiconductor is an insulator where all energetically low-lying bands are fully occupied by electrons and all energetically higher bands are completely free. The absorption of light transfers semiconductor electrons from the energetically highest fully occupied band – the valence band – into the originally unoccupied conduction band. Due to their opposite charge, the optically excited conduction-band electron and the simultaneously generated valence-band hole experience an attractive Coulomb interaction which may bind them to a new quasiparticle known as an exciton [5,6]. An exciton is similar in many ways to a hydrogen atom; however, it has a relatively short lifetime since the electron can return from the conduction into the valence band. In this electron-hole recombination process, the excess energy can be emitted as light or it can be transferred to the host crystal as heat.

Under suitable conditions, two excitons can bind into a molecule referred to as biexciton[7,8] which has strong analogies to the hydrogen molecule. Generally, it is an interesting open question if and in which form electron-hole pairs can form even larger clusters with quasiparticle character and how these clusters can be identified spectroscopically. One may distinguish the presence of distinct quasiparticles by the different color resonance they absorb or emit light [9-15], in the same way as atoms and molecules have distinct resonances in the absorption spectrum as fingerprints that provide a positive identification of the “culprit”.

However, identification of semiconductor quasiparticles from light absorption is not as simple as it seems. In general, an ordinary laser pulse only induces electron-hole-pair excitations whereas the more complex quasiparticles are created by the quantum mechanical many-particle interactions, yielding several possible outcomes [16] that blur the quasiparticle resonances. Since the state and the characteristic features of the excited state are very complex and depend sensitively on the detailed excitation conditions, it is generally very difficult to identify the quasiparticle signatures in spectra as long as “only” classical spectroscopy is used.

Figure 1: Classical vs. quantum-optical spectroscopy. In classical spectroscopy (left), the photons (wave symbols) are uncorrelated and they create unbound pairs of electrons (spheres) and holes (open circles). In quantum spectroscopy (right), the photons are correlated (yellow ellipse) such that they directly excite a correlated electron-hole cluster (yellow circle).

To overcome this problem, we developed the concept of quantum-optical spectroscopy [16,17] based on fundamental quantum properties of light. In general, quantized light can be described in terms of photons, i.e. the energy quanta of light. Whereas classical laser light basically contains isolated photons, i.e. no specific photon clusters, such clusters are characteristic for quantum light sources. Most important for our quasiparticle search, the cluster characteristics of the exciting light is directly transferred to the optically generated electron-hole excitations. Consequently, suitable quantum-light sources can e.g. generate predominantly excitons, or biexcitons, or even larger clusters [16,17]. In other words, one can directly excite new quasiparticles with a quantum-light source whose photon clusters match the cluster characteristics of the desired quasiparticle state. Figure 1 illustrates this main difference of classical and quantum-optical laser spectroscopy.

Even though freely adjustable quantum-light sources do not yet exist, we have demonstrated [18] that a large set of classical pump-probe spectra can be robustly projected into the desired quantum-optical spectra. To collect the data, we used short pulses to generate electrons and holes faster than they can decay. In our quasiparticle-search experiments [4], we actually apply pulses of light, produced by a laser, that are only 100 femtoseconds (1fs=10^-15s) in duration. To study the types of quasiparticles that can occur in a semiconductor, beyond just electrons, holes and excitons, we use a strong pulse, known as the “pump” pulse to excite a desired number of electrons and holes. We then monitor how a weak subsequent pulse, known as the “probe” pulse, is absorbed. To observe different types of quasiparticles, we perform these measurements very carefully as we slowly increase the intensity of the pump pulse. Then each pump-pulse intensity labels a probe-absorption spectrum within the massive set of raw data that is the input to the projected quantum-optical spectrum.

When we did this experiment, we noticed already in the raw data that the light began to be absorbed at a new color as the intensity of the pump pulse increased. This new color was distinct from the color corresponding to the creation of an exciton, or of unbound pairs of electrons and holes. We initially ascribed this observation to the formation of a biexciton. However, increasing the intensity of the pump caused this new absorption feature to change color, but very surprisingly, it did so in the wrong direction, namely opposite to the shift of the absorption due to the exciton. This gave us the hint that the new quasiparticles could be dormant underneath the blurred and shifted “biexciton” resonance.

Figure 2: Revealing new energy resonances of Dropletons. Dropleton's binding energy is determined from the light absorption that is sensitive to three-photon correlations. The spectra are plotted as a function of pump pulse's photon number. The red color denotes regions with high absorption.

To reveal which quasiparticle explains this curious behavior, we projected the raw data to an absorption spectrum that is sensitive to three-photon clusters; the quantum-optical absorption spectra are shown Fig. 2 as function of pump power. The energy is expressed in terms of binding energy with respect to exciton resonance. For low photon numbers, we observed only a biexciton resonance that had a fixed binding energy around 2.2meV, as intuitively expected. By increasing the number of photons in the pump pulse, we surprisingly observed that the semiconductor starts to absorb light at completely new colors identified by the steps. We also performed measurements that could reject molecular electron-hole states as an explanation for energy quantization, and demonstrated that the new quasiparticle evolves coherently living up to 25 picoseconds (1ps=10^-12s) [4].

After discovering these new energy resonances, we proceeded to identify the exact form of the new quasiparticle that matches the measured “fingerprints”. Since the quasiparticle has a stronger binding than biexciton it must contain more electron-hole pairs than biexciton, i.e. two. However, there is no quantum theory that can exactly solve the corresponding many-body problem. Therefore, we had to develop a new approach[19] to identify the new quasiparticles. More specifically, we expressed the system energy exactly in terms of pairwise electron-hole correlation function, instead of electron and hole densities that is the basis of the density functional theory [20]. Since the correlations uniquely define complicated quasiparticles, we could precisely determine the energies of different possible electron-hole configurations.

Figure 3: Illustration of a dropleton. In a dropleton, the probability distribution of the electrons and holes forms a ring-like pattern; a representative pair-correlation function is shown as a function of the electron-hole separation. The shell defines the size of the dropleton; roughly one electron-hole pair resides within each ring.

After a thorough search, all experimental observations were explained [4] only by a configuration where electrons and holes are not bound into excitons, but they rather are loosely organized, much like particles in a liquid. However, the liquid was confined inside a small bubble, which directly explained the quantization as a confinement effect. Due to liquid characteristics, quantization, and small size, we called the new quasiparticle a dropleton. The jumps in the dropleton energy levels were shown [4] to correspond to adding a new electron-hole pair to the dropleton. In total, we could detect dropletons with four, five, six, and seven electron-hole pairs and conclude that the quantum droplet size was in the range of 200nm (1nm=10^-9m) in diameter.

The discovery of dropleton is the first tangible demonstration that the quantum-optical spectroscopy excites and controls quasiparticles with unprecedented accuracy. To make full use of this encouraging advancement, it will be an important future goal to develop ultrafast and strong light sources whose quantum fluctuations can be freely adjusted. Since the dropletons are brand new addition to the quasiparticle family, it is not predictable how and when they can be seen in practical use. However, all quasiparticles also influence the operation of optoelectronic devices such as laser diodes which are already used in DVD readers/writers and in optical communications. Thus, the improved control of quasiparticles will certainly enhance our ability to design these types of devices. In addition, dropletons couple strongly with quantum light, which should be extremely useful when designing lasers and devices capable of encoding and processing quantum information. This level of control of light-matter interaction will provide intriguing possibilities to test foundations of quantum mechanics as well as introduce new ways to utilize them to build devices with an incredible performance.

References:
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[3] Charles Kittel, "Introduction to solid state physics" (Wiley & Sons, 8th Ed., 2005). 
[4] A.E. Almand-Hunter, H. Li, S.T. Cundiff, M. Mootz, M. Kira, S.W. Koch, "Quantum droplets of electrons and holes". Nature, 506, 471 (2014). Abstract.
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[16] Mackillo Kira, Stephan W. Koch, "Semiconductor quantum optics" (Cambridge University Press, 2011).
[17] M. Kira and S.W. Koch, "Quantum-optical spectroscopy in semiconductors". Physical Review A, 73, 013813 (2006). Abstract.
[18] M. Kira, S.W. Koch, R.P. Smith, A.E. Hunter, S. T. Cundiff, "Quantum spectroscopy with Schrödinger-cat states". Nature Physics, 7, 799 (2011). Abstract.
[19] M. Mootz, M. Kira and S.W. Koch, "Pair-excitation energetics of highly correlated many-body states", New J. Phys. 15, 093040 (2013). Full Article.
[20] David Sholl and Janice A. Steckel, "Density Functional Theory: A Practical Introduction" (Wiley, 2009).