DE102012021316A1 - Method for performing wavelength conversion of light in solar cell technology, involves displacing light reflection devices in transverse direction to direction of long wavelength of next input spectral wavelength distribution - Google Patents

Abstract

The method involves producing a longitudinal mode by light reflection devices (1a,1b) in the resonator, whose wavelength depends on the resonator length. The transverse modes are generated by the curvature of light reflection devices. The wavelength of photons in the resonator is interacted with the mechanical vibrations of the reflection units (2) for generating the reflections. The light reflection devices in the transverse direction are displaced to the direction of the long wavelength of the next input spectral wavelength distribution in the longitudinal mode. An independent claim is included for a light source.

Description

The invention relates to a method for performing a wavelength conversion and the generation of coherent light in which photons are coupled with a spectral input wavelength distribution in a resonator having at least two light reflection arrays, in particular mirrors, wherein at least one longitudinal mode is generated by the light reflection arrays in the resonator , whose wavelength depends on the resonator length and a curvature of at least one of the light reflection arrays generates a plurality of transverse modes. The invention further relates to a light source with an optical resonator of the aforementioned type.

Optical resonators are known in the art and are usually formed by mirrors, between which the light circulates several times and thereby produces at least longitudinal modes depending on the resonator structure whose wavelength is defined by the distance between the mirrors or the resonator length, as well as transversal modes, provided at least one of the mirrors or generally the light reflection arrangements is curved, in which case a curvature with respect to the optical axis of the resonator is essentially meant, which means that the surface normals of such a curved light reflection arrangement are not exclusively parallel to the optical axis, apart from a location exactly on the optical axis but at an angle thereto, for example if such light reflection arrangements or mirrors have a spherical or parabolic curvature.

Consequently, a spatially extended light distribution is formed around the optical axis in accordance with the transverse modes permitted by the resonator geometry.

In the prior art, methods for wavelength conversion or light sources using such optical resonators are essentially known, in which an optically active medium is used within the resonators, which is thus at least at the target wavelength, which is to be emitted from such an optical resonator , Having an excitable for emission electronic transition.

By the inventor is from the publication DE 10 2009 049 962 a method and apparatus is known, with which a wavelength conversion in thermal equilibrium to produce a preferred Bose-Einstein distributed spectrum. According to this known prior art, an optically pumpable medium is used in the resonator, such as a liquid dye whose lower, participating in the photon emission level is stable, for example, forms a ground state or at least metastable, therefore, only slowly depopulated and thus without the formation of a population inversion can form a thermal balance of the photons. By correspondingly short selection of the resonator length of n × lambda / 2 with n ≦ 40, it is achieved that with only one longitudinal mode within the fluorescence bandwidth of the selected optically pumped medium, a wavelength conversion to long wavelength can take place up to the defined longitudinal mode.

It is felt to be disadvantageous here that the dyes used bleach at high intensities or the dyes or else other optically active media can be destroyed within the resonator at too high intensities.

It is therefore the object of the invention to provide a method for carrying out a wavelength conversion or a light source for such a conversion, which does not have the aforementioned disadvantages, ie is therefore permanently usable and also withstands high intensities in the resonator without destruction, and thus is particularly suitable. To achieve intensities that are above normal damage thresholds of optical media. The task is also to overcome other limitations that are known by the laser, such. As low damage thresholds of active media, thermal lensing effects or other parasitic effects and thus to achieve higher performance.

This object is achieved according to the method in that in a plurality of reflections of the photons, the wavelengths of the photons in the resonator, which is initially given by the spectral input wavelength distribution of the irradiated photons in the resonator, in the resonator taking place in the Refelkektionen interaction with the mechanical vibrations of a Variety of reflection units, in particular, the at least one of the light reflection arrangements in the transverse direction comprises, is moved in the direction of the next long wavelength of the spectral input wavelength distribution lying longitudinal mode.

A light source for carrying out such a method is thus essentially characterized in that a multiplicity of reflection units are provided in the resonator, in particular those arranged in a direction perpendicular about the optical axis around them and which in each case at least thermally oscillate (in the direction of FIG optical axis) are excited or are excitable. For example, one of the light reflection arrangements, in particular a curved one, in the transverse direction, that is to say substantially perpendicular to the optical axis, may comprise or consist of a plurality of reflection units spaced from the optical axis. However, in principle, in addition to the light reflection arrangements, the reflection units may be provided in the resonator.

An essential core idea of the invention is based on the fact that in a resonator of the type according to the invention in addition to the longitudinal modes due to the selected geometry of the light reflection arrays also a plurality of transverse modes can occur, the photons of these transverse modes excited by mechanical interaction with the individual, to vibrate Reflection units, in particular the at least one light reflection arrangement are shifted in the wavelength, which can be explained in the classical picture with the principle of Doppler shift or as a photon-phonon collision process with the phonons of the excited to the vibration reflection units.

This results in an energetic redshift of the photons in the direction of the next longitudinal mode lying longwave from the input spectrum, which is allowed by the selected resonator spacing, so that the energy within the resonator through this conversion process within the next allowed by the resonator longitudinal Basic fashion energetic, especially spatially concentrated. Also, this may possibly. Non-coherent photons are converted into coherent.

In principle, the wavelength spacing between the input wavelength spectrum of the photons and the output wavelength spectrum, in particular the wavelength of the longitudinal target mode is irrelevant in the case of a resonator assumed to be ideal and, depending on the distance, only causes a greater or lesser number of reflections.

A correspondingly sufficient number of reflections between the light reflection arrangements and thus of circulations in the resonator can in principle be achieved by a suitable selection of these light reflection arrangements which require a sufficiently high reflectivity for this purpose which, for example, in mirror structures by appropriate dielectric coatings or else by optical structures, especially in the range of half the target wavelength or odd multiples of half the target wavelength can be achieved.

The wavelength conversion achieved according to the invention is therefore based solely on a mechanical interaction between the photons in the resonator and the reflection units, in particular photon-limiting light reflection arrangements, such as mirrors, so that within such a resonator on the use of optically active media in contrast to the aforementioned prior art can be omitted, so that in principle with such a structure or method according to the invention intensities within the resonator can be generated, which lie beyond the usual damage thresholds of optical media and are limited by the damage thresholds of the used light reflection arrays and / or Reklektionseinheiten. The damage thresholds of the light reflection arrangement and / or reflection units are essentially not usually limited due to transversally extended profiles.

A possible preferred embodiment may therefore provide that the resonator is operated on the target wavelength of the respective longitudinal mode without a photon-absorbing or photon-emitting medium.

Alternatively, however, it is also conceivable to use an optically active medium in the resonator and thus to produce, for example, the photons of the spectral input wavelength distribution by a medium arranged in the resonator. Here, however, in contrast to the aforementioned prior art by this medium not even the wavelength conversion, but only the generation of the photons with the spectral input wavelength distribution, whereas the conversion effect further on the described mechanical interaction between the oscillations of the reflection units, in particular the at least one Light reflection arrangement and the photons based.

The excitation of such a medium arranged within a resonator can be of any type, for example electronically or optically in accordance with conventional principles known in physics. However, if no photon-absorbing or photon-emitting medium is used at the target wavelength within the resonator, it is essentially provided according to the invention to couple the photons of the input wavelength spectrum by a separately operated light source into the light source according to the invention, in particular parallel to the optical axis of the resonator formed, preferably exactly on this.

Wavelength conversion can be carried out very effectively, in particular, when the individual reflection units, in particular at least one of the light reflection arrangements or separately, are excited or excited to oscillate, for example thermally excited or excited, which are resonant with the frequency spacing of the transverse modes of the resonator that are defined by the resonator geometry.

Particularly advantageous here is a vibration of the individual reflection units, in particular parallel to the optical axis of the resonator in a frequency range of 1 to 100 gigahertz. In particular, the individual reflection units oscillate with respect to one another in a possibly random phase position, for example by thermal excitation.

Preferably, the individual reflection units have a respective individual mass, which allow vibrations in this frequency range. Such masses are achieved, for example, if the individual reflection units have one-dimensional or preferably two-dimensional expansions in the range of odd multiples of half the target wavelength, essentially independent of the specific material.

A preferred embodiment of the method or a device according to the invention may provide that the length of the resonator is selected to be n × lambda / 2, where lambda is the target wavelength of the longitudinal target mode and n ≦ 40, preferably n ≦ 10, more preferably n = 1 is.

In this way it can be ensured in a further preferred embodiment that the target wavelength of the longitudinal mode lies outside the spectral input wavelength distribution of the photons, so that all the photons of this input wavelength distribution point to one and the same longer wavelength mode allowed by the resonator through a plurality of reflections be moved.

If, on the other hand, the spectral input wavelength distribution is so broad or so positioned that at least one longitudinal mode of the resonator lies within this input wavelength distribution, then a portion of the short wavelength of this longitudinal mode photons of the input wavelength distribution is shifted exactly to this longitudinal mode and the overlying portion of the photons the next longitudinal mode allowed by the long wave allowed the resonator to resonate so that, in such a case, the energy of the individual photons may be distributed among a plurality of allowed longitudinal modes.

Regardless of whether several or preferably only a single longitudinal mode with a selected target wavelength is generated by the method according to the invention or with such a device, it can preferably be provided that the resonator is operated in thermal equilibrium, which means that the photons in the Resonator, which form a so-called photon gas, with the thermal vibrations of the individual reflection units, in particular the at least one light reflection arrangement or separately in thermal equilibrium and therefore a spectral output distribution of these photons is formed, with a lying in the long wavelength range wavelength of said longitudinal mode and a plurality of transversal modes whose intensity decreases toward the short wavelength range.

Particularly preferably, a Bose-Einstein-distributed photon spectrum is generated below a critical number of photons in the resonator, and preferably a Bose-Einstein condensate above a critical number of photons, in which essentially all the photons on the wavelength of the one or possibly more are permitted by the resonator focus on longitudinal modes.

Accordingly, the method according to the invention or a light source according to the invention can preferably be used in any application in which the task is to shift photons of an input wavelength or wavelength distribution in the direction of the long wavelength thereof, preferably spectral input wavelength distributions to one compared to the original spectral half-width lower spectral width are converted.

Applications can be varied and be given, for example, in the field of solar cell technology, in which the photovoltaic materials usually have particularly high absorption at selected wavelengths in the near infrared range, so that here a conversion of the incident daylight spectrum with short wavelengths to the absorption wavelength wavelengths towards the each selected absorption wavelength of the photovoltaic material can be moved, which can significantly increase the efficiency of solar cells.

By way of example, one possible embodiment may provide that the reflection units, if these are at least one of the light reflection arrangements, are formed by a large number of dielectric coated mirror elements. Thus, if a light reflection arrangement is formed by a mirror which delimits the resonator, then such a mirror can accordingly comprise a plurality of mirror elements, so that such a mirror can be termed segmented insofar as it has a multiplicity of two-dimensionally arranged mirror elements which surround the optical mirror Axis of the resonator are arranged around and can each be excited to vibrations or are excited, for example, thermally excited due to the ambient temperature and thus in a preferred embodiment each form individual oscillators, which further preferably oscillate in the direction of the optical axis and thus to the previously described Doppler effect or contribute to the phonon scattering. The individual reflection units can z. B. also be coupled with each other and vibrate out of phase to each other in the statistical average.

Furthermore, light reflection arrangements can also be formed by photonic crystals, which are essentially to be described as a periodic or quasi-periodic arrangement of dielectric structures, eg. As dielectric rods, layer sequences (as in the known dielectric mirror), or even appropriately sized holes in a dielectric material. These photonic crystals are particularly advantageous for the realization of three-dimensional resonators.

A further embodiment may provide that a light reflection arrangement is formed by such a photonic crystal, i. H. alternating, at least two-dimensional structure of different optical properties, in particular refractive indices, alternately repeating, in particular in an odd multiple of half the target wavelength of the longitudinal mode. Accordingly, structures may have a light-reflecting effect whose different refractive indices caused by the structure follow one another at a distance of an odd multiple of half the target wavelength, namely at least in the direction of the optical axis in one dimension and perpendicular thereto in at least one further dimension, but preferably also three-dimensionally that results in a spatial structure in which the individual structural units as a distance have the aforementioned preferably odd multiples of half the target wavelength of the longitudinal mode.

It should be noted that the structure preferably can not be perfectly periodic, since in this case there is no curvature and thus a cancellation of the degeneracy for the transverse modes. In such a photonic crystal, so-called defect modes can be located by modifying the optical properties at a specific location, which correspond to the interior of the classical mirror resonator. In this interior, the thermalization of the light would preferably take place. A possible embodiment would therefore be a "defect" in the photonic crystal, surrounded by a (nearly) periodic structure, in particular whose structure width is of the order of magnitude of the wavelength.

Such a structure is thus arranged around the optical axis of the resonator and leads both to the reflection of the photons in the direction of the optical axis and the possibility of forming transverse modes perpendicular thereto, since a correspondingly large extent of said structure or a plurality of structural units perpendicular is provided to the optical axis. The individual structures such as, for example, refractive index differences or dielectric disturbances (eg holes or columns) arranged in the abovementioned spacing at least oscillate thermally relative to one another and already lead to the wavelength conversion effect described according to the invention due to these thermal oscillations.

Particularly in this embodiment, it can also be provided that the at least two-dimensional, if appropriate, also three-dimensional structure is formed in a matrix material which is suitable for emitting the input wavelength spectrum after appropriate excitation. The matrix material can thus form a light source for the input photons and also at least one light reflection arrangement, so that a uniform overall arrangement can be created.

Regardless of whether the matrix material is also excitable and emits an input wavelength spectrum or merely serves to form structures of different optical properties, it can be provided that two light reflection arrangements spaced apart from the desired resonator length are arranged in one and the same matrix material at least two-dimensional, preferably three-dimensional structure of different optical properties is formed.

Another embodiment may also provide that the reflection units are not given by elements of the light reflection arrangements, which limit the geometrical geometrically, but by elements in addition to the light reflection arrangements, in particular the mirrors in the resonator. Such reflection units can, for. B. particles within the resonator, such as beads, in particular, the thermally vibrate or are additionally excited to oscillate.

Such reflection units, in particular beads, may preferably be smaller in dimensioning than the wavelength, in particular the wavelength of the longitudinal target mode, preferably less than 1/10, more preferably less than 1/100 of the wavelength. For example, the beads may be formed of silicon oxide. In such a case, the reflection units are to be considered as optically deviating from the environment medium, in particular optically denser medium. The preferred resonator length mentioned at the outset is then the effective optical length, taking into account the media in the resonator with possibly different refractive indices.

Further general relationships as well as embodiments of the invention are described below:
It is proposed to thermalize a low-dimensional photon gas and to obtain a Bose-Einstein photon condensation by optomechanical interactions in a microscopic optical cavity, preferably with a single longitudinal mode and many transverse modes. The geometry of the short cavity is such as to provide low frequency confinement at a photon energy that is well above the thermal energy, thus suppressing the thermal emission of photons and maintaining the number of photons.

Although previous experiments with Bose-Einstein photon condensation used dye molecules for photon gas thermal treatment, thermalization is studied due to interactions with thermally fluctuating nanomechanical oscillators that form at least one of the cavity mirrors. In the quantum degenerate region, the nanomechanical cavity converts broadband optical radiation into tunable coherent radiation.

When a gas is cooled from particles or its density is increased to the point that the associated de Broglie wave packets overlap spatially, quantum statistical effects come into play. For bosons with a non-vanishing mass, the phenomenon of Bose-Einstein condensation in a macroscopically occupied ground state then minimizes the free energy. The Bose-Einstein condensation was first achieved in diluted atomic gases, and other experiments reported condensates in the (fast) equilibrium of exciton polarons and magnons, respectively. On the other hand, blackbody radiation - the most common Bose gas, does not show Bose-Einstein condensation because the number of photons is not maintained at temperature variations (vanishing chemical potential) and photons disappear at low temperatures in the cavity walls, rather than occupying the cavity bottom state. In a recent work, a Bose-Einstein condensation of a two-dimensional photon gas in an optical microvoid filled with a dye solution was observed. The photon gas is thermally coupled to the temperature of the dye solution through multiple absorption-emission cycles in the dye, which maintains the average number of photons.

The cavity mirrors provide both a non-vanishing effective photon mass and a limiting potential.

It has long been recognized that thermal motion can increase the linewidth of optical radiation within an optical resonator, and for optical cavities made from macroscopic optical mirrors, effective optical length fluctuations from thermodynamic temperature fluctuations in the mirrors are the largest contributors Nanomechanical mirrors on wavelength scale usually dominate direct thermal length fluctuations. The coupling strength of light and mechanical motion scales with the ratio of mechanical zero point movement and cavity length and can be enhanced by the use of thin optical cavities and small mirror masses. Recent experiments based on microstructured nanomechanical vibrations have shown mechanical vibration frequencies in the GHz range that approximate the transverse vibration frequency of photons captured in the micro cavity experiment.

Here, a number-maintaining thermalization of a photon gas is proposed by means of optomechanical interactions in a microscopic optical cavity. The design uses a thin optical cavity with a lower cutoff frequency well above the thermal energy and a variety of transverse modes. The thermal motion of the nanomechanical oscillators, which are coupled to the photon gas, leads to a thermalization of the optical spectrum in the direction of a Bose-Einstein distribution above the lower limit frequency. Above the BEC threshold, optomechanical phase space density interactions result in a redistribution of a broadband optical spectrum (or more generally an imbalance spectrum) into a Bose-Einstein condensed photon distribution, including a macroscopically occupied, coherent ground state mode.

A schematic diagram of the proposed structure is in 1a shown. Photons are confined in an optical microresonator with a vibrating mirror, the latter serving to provide coupling of the optical mode spectrum to the thermal environment. The curved mirror cavity has many transverse modes and the requisite optomechanical coupling between transverse modes dictates the use of a mechanically flexible or segmented mirror with a collection of microscopic springs attached to different mirror segments, as in FIG 1a indicated, near.

Because the transverse optical wave vector must be modified during thermalization, it is believed that the mirror segments can also be tilted. Of course, tilting of a mirror segment occurs when the adjacent springs make out-of-phase oscillations in the course of their thermal random motion.

The distance between the mirrors is the wavelength range. For the sake of simplicity, the mirror spacing d is almost one-half of an optical wavelength. The quantum number of the longitudinal modes is fixed at n = 1. The narrow longitudinal inclusion introduces a lower cut-off frequency at a frequency ω _cutoff = 2πc / λc _utoff , where the cut-off wavelength λ is _cutoff ≅ d / 2.

über der Hohlraumgrenze führt. Mit anderen Worten wird eine signifikante Population der TEM_nm-Moden mit hohen transversalen Quantenzahlen n und m bei hoher Temperatur erreicht, während die Verteilung auf die niedrigeren transversalen Moden bei niedriger Temperatur begrenzt ist. 1b shows the spectrum of transverse modes above the lower limit frequency, the latter corresponding to the natural frequency of the corresponding transverse mode TEM ₀₀ . The mirror curvature also causes a harmonic trap potential for the photons. Since the quantum number of the longitudinal modes is fixed, the two remaining degrees of freedom of the transverse modes effectively make the photon gas two-dimensional. A thermal balance of the trapped photon gas is obtained, resulting in a distribution of the width

over the cavity boundary leads. In other words, a significant population of TEM _nm modes with high transversal quantum numbers n and m at high temperature is achieved, while the distribution is limited to the lower transverse modes at low temperature.

A redistribution between transverse modes and a thermalization of the photon gas is investigated here via the optomechanical effect, i. H. by the Doppler effect during reflection of the thermally oscillating mirror elements. The Doppler shift per complete cavity cycle is relatively small, so it is clear that many reflections are required within a very fine cavity.

für einen plankonkaven Spiegelhohlraum, der um die Hälfte der Grenzwellenlänge beabstandet ist, und typische Werte für Ω/2π sind dutzende von GHz. Es scheint vorteilhaft zu sein, eine gewisse Spiegelkrümmung zu verwenden, um sowohl das Photonengas räumlich einzuschließen als auch ein BEC mit wahrem Gleichgewicht bei einer finiten Temperatur in dem zweidimensionalen System zu ermöglichen. Mechanische Schwingungsfrequenzen in der Größenordnung von typischen transversalen Einfangfrequenzen des Photons, die im GHz-Bereich liegen, können nicht mit einem einzelnen Spiegel mit ausreichend großem Durchmesser erreicht werden, um das thermalisierte Modenspektrum einzufangen. Stattdessen ist der Einsatz einer segmentierten Geometrie mit vielen nanomechanischen Spiegeln, wie in 1a angezeigt, eine Lösung. Für optische Infrarotstrahlung mit einer Wellenlänge von 1,2 μm oder darüber können siliziumbasierte Nanostrukturen verwendet werden, während für den sichtbaren (oder sogar den Ultraviolett-)Spektralbereich z. B. nanostrukturierte Glasmaterialien erforderlich sind.The coupling can be maximized by using mechanical vibration frequencies ω _{m of} the micromechanical oscillators that oscillate to the transverse distance Ω in the cavity, ie, we assume that ω _m ≈ Ω. The mode spacing is

for a plano-concave mirror cavity spaced at half the cut-off wavelength and typical values for Ω / 2π are dozens of GHz. It seems to be advantageous to use some mirror curvature to spatially confine the photon gas as well as to allow for a true equilibrium BEC at a finite temperature in the two-dimensional system. mechanical Vibrational frequencies on the order of typical transonic photoreceptor frequencies lying in the GHz range can not be achieved with a single mirror of sufficiently large diameter to capture the thermalized mode spectrum. Instead, the use of a segmented geometry with many nanomechanical mirrors, as in 1a displayed a solution. For optical infrared radiation having a wavelength of 1.2 μm or more, silicon-based nanostructures can be used, while for the visible (or even the ultraviolet) spectral range, for example. B. nanostructured glass materials are required.

unterdrückt, was ~exp(–40) für k_BT ≅ 1/40 eV (Raumtemperatur) und

bei 1,2 μm Grenzwellenlänge ist.During thermalization, it is essential to vary the quantum numbers of the transverse modes so as to block the destruction or generation of photons, unlike a blackbody radiator. We expect that this condition will be well met in the range of hω _cutoff << k _B T. The thermal emission of photons is then by a factor of the order of

suppressed what ~ exp (-40) for k _B T ≅ 1/40 eV (room temperature) and

at 1.2 μm cut-off wavelength.

The microscopic process of thermalization involves photon scattering processes involving the absorption or emission of phonons, as in 2a specified. After many reflections, when the thermalization is achieved, the transverse decoherence from coupling to the thermal environment blocks strong coupling effects to be relevant. The relevant particles are thus photons, ie no polaritons.

Subsequently, a derivation of the asymptotic distribution function of the photon gas using a detailed compensation treatment is sought. Furthermore, the multiple reflection of light between one of the movable mirror segments and the fixed rearview mirror is considered, as in FIG 2 B shown. A discretized version of a fully flexible mirror is assumed. The initial state of the photon is denoted as | 1>, and its final state after a number N of reflections, when it leaves this part of the cavity, as | 3>. The corresponding initial and final states of the movable mirror are | 2> and | 4>, respectively. Since no explicit Hamiltonian formulation of the optomechanical coupling between transverse modes in the cavity is known, a simple quantum-mechanical particle-particle interaction model is used for the optomechanical interaction. Assuming weak interactions, then for a Bose system the probabilities for a transfer 1,2 -> 3,4 and 3,4 -> 1,2 can be written in the following general form: P _{1,2-> 3,4} = | M _12,34 | ² n ₁ n ₂ (n ₃ + 1) (n ₄ + 1) P _{3,4-> 1,2} = | M _34,12 | ² n ₃ n ₄ (n ₁ + 1) (n ₂ + 1) (1)

geschrieben werden kann.At equilibrium, the transition probabilities are identical due to the detailed compensation. Furthermore, the amounts of the matrix elements M and M _{12,34 34,12} are identical, resulting in n ₁ / (n ₁ + 1) · n ₂ / (n ₂ + 1) = n ₃ / (n ₃ + 1) * n ₄ / (n ₄ + 1) follows. If one assumes energy conservation, E ₁ + E ₂ = E ₃ + E ₄ , and that the equilibrium distribution functions depend only on the energy, it can be easily shown that the distribution functions in thermal equilibrium with μ _ph as a constant, the chemical potential, as

can be written.

definiert ist und k_r und k_z Wellenzhlen der transversalen bzw. longitudinalen Moden des Photons bezeichnen. Das System ist formal äquivalent zu einem zweidimensionalen, harmonisch eingeschlossenen System von massiven Bosonen, für die ein Bose-Einstein-Kondensat bei einer endlichen Temperatur existiert. Falls wir die zweifältige optische Polarisationsentartung berücksichtigen, beträgt die Modenentartung bei Frequenzen gleich oder über der Grenze, d. h. für ω ≥ ω_cutoff, g(ω) = 2((ω – ω_cutoff)/Ω + 1), und wir erhalten eine frequenzabhängige Photonenanzahlverteilung

wobei eine energieverschobene Definition des chemischen Potentials mit

verwendet wird, um die übliche Konvention von μ -> 0 in dem fernen quantenentarteten Bereich zu erfüllen. Bei einer konstanten Temperatur wird ein Bose-Einstein-Kondensat erwartet, nachdem die Photonenanzahl eine kritische Partikelanzahl

übersteigt. Bei Raumtemperatur, T = 300 K, und unter der Annahme einer Fallenschwingungsfrequenz Ω/2π = 10 GHz erhalten wir N_c ≅ 1,3·10⁶, was einer kritischen optischen Leistung im Hohlraum von etwa 54 W entspricht, was durchaus machbar ist. Vorausgesetzt, die Thermalisierung wurde erreicht, wird ein breitbandiges optisches Spektrum über der in eine scharfe Kondensatspitze umzuwandelnden kritischen Photonenanzahl liegen mit einer makroskopischen Photonenpopulation an der Position der Grenze auf einer breiten thermischen Schulter (siehe 3). Diese bimodale Verteilung ist der Zustand mit der niedrigsten freien Energie.A Bose-Einstein distribution function is achieved. Unlike the interparticle collisions of an atomic gas, the thermalization is with respect to an external reservoir provided by the movable mirror oscillators. For the sake of simplicity, it is assumed that the mirrors together with their mechanical suspension have sufficiently high heat capacity that their temperature remains unchanged. For a finite heat capacity, depending on the wavelength of the incident pump radiation relative to that of the emitted optical spectrum, the suspension undergoes cooling or heating experience the optical radiation. The equilibrium distribution of the photon gas in the microresonator is examined and the following discussion follows earlier work on the dye filled system. In short, in the paraxial boundary and for negligible interactions, the photon energy can be written as E ≅ m _eff c ² + (hk _r ) ² / 2m _eff + _{½m eff} Ω ² r ² , with an effective photon mass

is defined and k _r and k _z denote waves of the transverse and longitudinal modes of the photon, respectively. The system is formally equivalent to a two-dimensional, harmonic-locked system of massive bosons for which a Bose-Einstein condensate exists at a finite temperature. If we consider the twofold optical polarization degeneracy, the mode degeneracy at frequencies is equal to or above the limit, ie, for ω ≥ ω _cutoff , g (ω) = 2 ((ω - ω _cutoff ) / Ω + 1), and we obtain a frequency dependent one photon number distribution

wherein an energy-shifted definition of the chemical potential with

is used to satisfy the usual convention of μ -> 0 in the remote quantum degenerate region. At a constant temperature, a Bose-Einstein condensate is expected after the number of photons reaches a critical particle count

exceeds. At room temperature, T = 300 K, and assuming a trap vibration frequency Ω / 2π = 10 GHz, we obtain N _c ≅ 1.3 × 10 ⁶ , which corresponds to a critical cavity optical power of about 54 W, which is quite feasible. Provided the thermalization has been achieved, a broadband optical spectrum will lie above the critical number of photons to be converted to a sharp condensate peak with a macroscopic photon population at the position of the boundary on a broad thermal shoulder (see 3 ). This bimodal distribution is the state with the lowest free energy.

finden. Die verschiedenen Spiegelsegmente des Hohlraums schwingen thermisch unabhängig. Die Anzahl solcher Segmente pro Spiegel in dem Profil der optischen Moden über dieser Verschiebung muss als N_seg gemittelt werden. Ein Mittelwert der unabhängig fluktuierenden Segmentverschiebung wird geschätzt als

wobei angenommen wird, dass beide Seiten des Hohlraums aus schwingenden Spiegelsegmenten bestehen. Die Winkelablenkung des Lichtstrahls nach N Reflexionen für den Fall eines einzelnen Segments aufgrund der Neigung dieses Segments liegt in der Größenordnung Δα = N·2z₀/D, wobei D den Durchmesser des Spiegelsegments bezeichnet. Der Wert muss wieder über der Anzahl von Segmenten in dem Profil der optischen Moden gemittelt werden, und wir schätzen eine mittlere Auslenkung

Für einen Durchmesser D der Segmente in der Größenordnung der Wellenlänge λ erreicht die Impulsspreizung somit die Breite der Winkelverteilung eines thermalisierten optischen Spektrums

so dass erwartet wird, dass eine Impulserhaltung im Verlauf der Thermalisierung und der Spiegelbewegung erfüllt wird, um die transversalen optischen Moden effizient zu koppeln.An estimate of the thermalization time of the photon gas is given below, using a classical model based on the generation of a minor optical band during the reflection of thermally oscillating mirror segments. For a light beam of frequency ω passing through one of the sub-cavities formed by a mirror segment and the rearview mirror, where z (t) = z ₀ sinω _m t denotes the longitudinal displacement of a periodically oscillating mirror segment (measured at its center). The spatial motion leads to a periodic phase shift Δφ (t) = 2πN * 2z (t) / λ of the optical wave after N reflections (the geometry is as in FIG 2 B ). The optical wave is modulated by a modulation index β = 4πNz ₀ | λ, and for β << 1 the relative intensity in the first minor bands (β / 2) is ² ≅ (2πτ ₀ / λ) ² N ² . The size of z ₀ for a thermally oscillating mirror segment, which is considered to be a harmonic oscillation in thermal equilibrium, can easily be considered as

Find. The different mirror segments of the cavity oscillate thermally independently. The number of such segments per mirror in the profile of the optical modes over this shift must be averaged as N _seg . An average of the independently fluctuating segment shift is estimated as

it being assumed that both sides of the cavity consist of oscillating mirror segments. The angular deflection of the light beam after N reflections in the case of a single segment due to the inclination of this segment is of the order Δα = N * 2z ₀ / D, where D denotes the diameter of the mirror segment. The value must again be averaged over the number of segments in the profile of the optical modes, and we estimate a mean displacement

For a diameter D of the segments in the order of the wavelength λ, the pulse spread thus reaches the width of the angular distribution of a thermalized optical spectrum

thus, it is expected that a conservation of momentum in the course of thermalization and mirror motion is accomplished to efficiently couple the transverse optical modes.

was als eine Schätzung für die erforderliche Anzahl an Reflexionen in dem Hohlraum dienen kann, die die Thermalisierungszeitskala bestimmt. Unter der Annahme einer Masse des nanomechanischen Oszillators pro Spiegelsegment von m ≅ 10^–16 kg entsprechend den schwingenden Massen der subwellenlängengroßen, siliziumbasierten Mikrochipstrukturen und T = 300 K wird

erhalten. Für eine zweidimensionale Photonengasgeometrie wird die Anzahl an Spiegelsegmenten in dem optischen Modus in der Größenordnung von 100 × 100 betragen und N_total ≅ 5,8·10¹⁰ für λ ≅ 1,2 μm sein. Eine Alternative wäre die Verwendung einer eindimensionalen Photonengasgeometrie, die für eine planare Hohlraumstruktur verwendet werden könnte, was unter Verwendung einer lithografischen Strukturierung von Silziummikrochipsubstraten leichter herzustellen erscheint. Die Anzahl an Spiegelsegmenten wird hier auf grob N_seg ≅ 100 reduziert, und es wird entsprechend geschätzt N_total ≅ 5,8·10⁹. In dieser eindimensionalen Geometrie muss das Fallenpotential (mindestens etwas) einschränkender sein als parabolisch, um die Ausbildung eines BEC bei endlichen Temperaturen zu gestatten. Dies führt zu einem nichtäquidistanten Abstand von transversalen Moden, so dass die Resonanzbedingung mit den schwingenden Spiegelsegmenten durch das Spektrum der transversalen Moden hinweg nicht präzise erfüllt werden kann. Eine mögliche Geometrie ist als eine Verallgemeinerung einer siliziumbasierten gekoppelten optischen nanomechanischen Oszillatorgeometrie in 4 gezeigt.If a mechanical oscillation frequency ω _m is chosen to oscillate with the distance of the transverse modes, ie, ω _m ≅ Ω (see the discussion above), we expect the transfer of an optical quantum of oscillation at approximately (2πz _{0, av} / λ) ² N ² ≅ 1 (which is the condition that the minor bands become as large as the carrier). The thermal energy is reached after a number of reflections

which may serve as an estimate of the required number of reflections in the cavity that determines the thermalization time scale. Assuming a mass of the nanomechanical oscillator per mirror segment of m ≅ 10 ^-16 kg corresponding to the oscillating masses of the sub-wavelength-sized, silicon-based microchip structures and T = 300 K.

receive. For a two-dimensional photonic gas geometry, the number of mirror segments in the optical mode will be on the order of 100 x 100 and N _total ≅ 5.8 x 10 ¹⁰ for λ ≅ 1.2 μm. An alternative would be to use a one-dimensional photonic gas geometry that could be used for a planar cavity structure, which appears easier to fabricate using lithographic patterning of silicon microchip substrates. The number of mirror segments is here reduced to roughly N _seg ≅ 100, and it is accordingly estimated N _total ≅ 5.8 × 10 ⁹ . In this one-dimensional geometry, the trapping potential must be (at least slightly) more restrictive than parabolic in order to allow the formation of a BEC at finite temperatures. This leads to a non-equidistant spacing of transverse modes, so that the resonance condition with the oscillating mirror segments can not be precisely fulfilled by the spectrum of the transverse modes. One possible geometry is as a generalization of a silicon-based coupled nanomechanical optical oscillator geometry in 4 shown.

Unlike a model for a dye filled microvoid BEC system where fluctuation of the large canon particle number may occur due to effective particle exchange with the dye molecules, in the empty cavity system discussed herein, the number of photons is strictly maintained in an idealized trial situation. Accordingly, it comes only to an energy exchange (but no numerical exchange) with the reservoirs, and the photon gas is well described by a canonical ensemble, resulting in an expected intensity correlation function g ^{( 2 )} (0) = 1 in the condensed state.

As an alternative to relying on thermal mechanical motion for redistribution between cavity modes, one can in principle also apply an external acoustic drive to the microcavity structure, e.g. From a series of high frequency transducers similar to those used in acousto-optic modulators driven by quasi-random radio frequency signals. This allows larger vibration amplitudes than the thermal motion and could increase the coupling between modes. While such a drive does not result in a thermal balance distribution of optical modes, it may still allow for macroscopic accumulation of the optical ground state mode. An alternative method of achieving thermalization of the photon gas in a microresonator by optomechanical means is the scattering of light from microscopic nanospheres placed in the resonator whose positions undergo thermal fluctuations, the well-known Brownian motion. Resonance coupling to the cavity transverse mode spacing requires the use of high frequency (~ GHz) Brownian fluctuations.

Finally, thermalization of a low-dimensional photon gas in a microvoid is achieved by optomechanical interactions with the thermal environment. The conversion of the broadband optical radiation into a Bose-Einstein condensed state with a coherent, macroscopically occupied optical ground state mode is presented by purely mechanical reflections of thermally oscillating mirror surfaces. Technical advantages of such a coherent light source would include the absence of a required match with an atomic, molecular or solid-state resonance line. Such an opto-mechanical light source adds a fundamentally new concept to the synthesis in the field of optics, based on a redistribution of optical frequencies rather than emission (and / or absorption) processes of radiation.

Figure legends:

1 (a) : Optical microvoid method consisting of a segmented movable mirror and a fixed rearview mirror. One of the mirrors is curved with a radius of curvature R. (b) Density of macrocavity states.

auf, was der Eigenenergie der longitudinalen n = 1 und transversalen TEM₀₀-Moden entspricht. Das Spektrum der höheren transversalen Moden der longitudinalen n = 1 Modenmannigfaltigkeit ergibt sich aus den erwähnten Energieniveaus bei höheren Frequenzen.The small mirror spacing imposes a low-frequency cutoff frequency

which corresponds to the intrinsic energy of the longitudinal n = 1 and transversal TEM ₀₀ modes. The spectrum of the higher transverse modes of the longitudinal n = 1 mode manifold results from the mentioned energy levels at higher frequencies.

2 (a) : Charts representing the scattering of a phonon, with the frequency of a mirror resonance frequency ω _m , of a photon. (b) Illustration of the light path of a photon undergoing multiple reflections between a mirror segment and the cavity rearview mirror. Two springs indicate that the mirrors may also tilt in addition to longitudinal motion to couple the transverse modes.

3 : The figure shows the redistribution of optical frequencies from a broadband optical spectrum to a Bose-Einstein condensed spectrum, with a macroscopically occupied coherent BEC peak at the lower limit frequency of the cavity on a thermal shoulder after thermalization of optomechanical interactions in the micro cavity.

4 : Schematic diagram of a proposed realization of a photonic crystal microbubble for optomechanical thermalization of a low-dimensional photon gas. The quantum number of the longitudinal (corresponding to an optical propagation along the z-axis) modes is frozen, and for a planar mechanical structure (as seen in the drawing plane), the photon gas is one-dimensional (the y-direction is also frozen). A two-dimensional photon gas can be realized with a three-dimensional mechanical structure for which a cylindrically symmetric distribution of the patterned structure about the cavity axis is assumed.

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Cited patent literature

• DE 102009049962 [0005]

Claims (11)

Method for carrying out a wavelength conversion of light in which photons having an input spectral wavelength distribution are coupled into a resonator comprising at least two light reflection arrangements ( 1a . 1b ), in particular mirrors, wherein by the light reflection arrangements ( 1a . 1b ) in the resonator at least one longitudinal mode is generated whose wavelength depends on the resonator length and by a curvature of at least one of the light reflection arrangements ( 1b ) generate a plurality of transverse modes, characterized in that in a plurality of reflections, the wavelength of the photons in the resonator by interaction with the mechanical vibrations of a plurality of reflection units ( 2 ), in particular the at least one of the light reflection arrangements ( 1a . 1b ) in the transverse direction, is shifted in the direction of the next long wavelength of the input spectral wavelength distribution longitudinal mode. Method according to Claim 1, characterized in that the photons, in particular in thermal equilibrium, have a spectral output wavelength distribution ( 3 ) form with a long-wave boundary frequency wavelength of the longitudinal mode and a plurality of transverse modes whose intensity decreases towards the short-wave region, in particular that above a critical number of photons, the photons a Bose-Einstein-distributed spectrum, preferably a Bose-Einstein Form condensate. Method according to one of the preceding claims, characterized in that the length, in particular effective length of the resonator is selected to be n × lambda / 2, wherein lambda is the target wavelength of the longitudinal mode and n <= 40, preferably n <= 10, more preferred n = 1. Method according to one of the preceding claims, characterized in that the target wavelength of the longitudinal mode is outside the spectral input wavelength distribution. Method according to one of the preceding claims, characterized in that the resonator is operated on the target wavelength of the longitudinal mode without photon-absorbing or photon-emitting medium. Method according to one of the preceding claims, characterized in that the photons of the spectral input distribution are generated by a medium arranged in the resonator. Method according to one of the preceding claims, characterized in that the reflection units ( 2 ), in particular at least one of the light reflection arrangements or separately therefrom, are or are excited to oscillate, in particular thermally, which are resonant with the frequency spacing of the transverse modes of the resonator, in particular excited with frequencies of 1 to 100 GHz. A light source comprising an optical resonator having at least two light reflection arrays spaced apart in the direction of an optical axis (US Pat. 1a . 1b ), in particular mirrors, wherein at least one of the light reflection arrangements ( 1b ) is curved to produce transverse modes and with which a resonator length-dependent target wavelength of a longitudinal mode can be generated, characterized in that in the resonator a plurality of reflection units ( 2 ) are arranged, in particular arranged around the optical axis around, in particular at least one of the light reflection arrangements, in particular a curved, in the transverse direction has a plurality of spaced apart from the optical axis reflection units, which are each at least thermally excited to vibrate. Light source according to claim 8, characterized in that the reflection units of at least one light reflection arrangement are formed by a. A plurality of dielectrically coated mirror elements b. an at least two-dimensional structure in / on a matrix material, in particular by a photonic crystal, in particular wherein in the crystal of the resonator at least partially, preferably completely formed and wherein the mechanical vibrations are phonons in this crystal. Light source according to claim 9, characterized in that the at least two-dimensional structure is formed in a matrix material which emits the input spectrum after excitation. Light source according to one of the preceding claims, characterized in that the reflection units are formed by particles moving in the resonator, in particular microscopic particles which are scattered / reflectable photons, in particular wherein the particles are formed by moving, in particular thermally moving beads.

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