Spectrometer assembly

Abstract

A spectrometer assembly (1) for determining spectral information about incoming electromagnetic radiation (F) comprises a radiation conversion element (2) that comprises a non-centrosymmetric material to frequency-double at least a portion of the incoming electromagnetic radiation (F) as the incoming electromagnetic radiation (F) propagates through the radiation conversion element (2). The radiation conversion element (2) exhibits a spatially inhomogeneous structure such that the frequency-doubled electromagnetic radiation (SH) comprises components propagating in a plurality of different directions. The spectrometer assembly further comprises a detection unit (3) which is configured to record a spatial speckle image that is generated by spatial interference of the components of the frequency-doubled electromagnetic radiation (SH) with each other, and a computing unit (4) which is configured to retrieve spectral information about the electromagnetic radiation (F) based on said spatial speckle image.

Description

[0001] TITLE SPECTROMETER ASSEMBLY TECHNICAL FIELDThe present invention relates to a spectrometer assembly for determining spectralinformation about incoming electromagnetic radiation, a calibration method for saidspectrometer assembly and a method for determining spectral information about incomingelectromagnetic radiation using said spectrometer assembly. The present invention further relates to an optical setup comprises said spectrometer assembly and a method ofoperating said optical setup.PRIOR ART Spectrometers are one of the most essential tools in science and technology, as they enablethe measurement of the spectral content of electromagnetic radiation, i.e. the intensity ofthe electromagnetic radiation as a function of wavelength or frequency. Spectrometers thatare capable of providing "online" spectral information about incoming electromagneticradiation and that are thus suitable for monitoring dynamic processes, such as for instancewavelength tuning of an optical source, are often termed "fast" spectrometers. To enablethe necessary speed, fast spectrometers usually do not comprise any mechanical moving (i.e. scanning) elements, but instead often comprise a first part that converts the spectral information into spatial information, for example, by dispersing different wavelengths atdifferent angles using a prism or grating, and a second part in form of a pixel detector whichthen captures the intensity of the electromagnetic radiation as a function of the spatialdistribution. Using appropriate calibration methods, the spectral information can then beretrieved from the spatial distribution.However, components such as gratings and prims to convert spectral information intospatial information tend to be scarce and expensive in certain regions of the electromagneticspectrum, in particular for optical wavelengths in the mid-infrared and far-infrared range. SUMMARY OF THE INVENTION In a first aspect, it is thus an object of the present invention to provide a versatilespectrometer assembly that allows for fast determination of spectral information aboutincoming electromagnetic radiation. This object is achieved by a spectrometer assembly for determining spectral information about incoming electromagnetic radiation according to claim 1. Further embodiments of the invention are laid down in the dependent claims. A spectrometer assembly for determining spectral information about incoming electromagnetic radiation is thus provided, comprising: aradiation conversion element that comprises a non-centrosymmetric material tofrequency-double at least a portion of the incoming electromagnetic radiation as the incoming electromagnetic radiation propagates through the radiation conversion element, wherein the radiation conversion element exhibits a spatially inhomogeneous structure such that the frequency-doubled electromagnetic radiation comprises components propagating in a plurality of different directions; a detection unit arranged after the radiation conversion element with respect to a propagation direction defined by the incoming electromagnetic radiation, the detection unit being configured to record a spatial speckle image that is generated by spatial interference of the components of the frequency-doubled electromagnetic radiation with each other, and a computing unit configured to retrieve spectral information about the electromagnetic radiation based on said spatial speckle image. In the following, the term "wavelength" and "optical frequency" are used interchangeably,since a wavelength can always be converted into an optical (angular) frequency and viceversa by taking into consideration the propagation medium.The incoming electromagnetic radiation may in particular be optical radiation lying within afundamental wavelength band of between 100 nm and 1000 µm, preferably between 300 nm and 10 µm, more preferably between 700 nm and 5 µm. The interaction between electromagnetic radiation and a material depends on the so-called susceptibilities of the material, which are tensor quantities describing the response of the material to the electromagnetic radiation. The susceptibilities may be typically defined via a Taylor expansion of the dielectric polarization density in response to the electric field of the electromagnetic radiation. Non-centrosymmetric materials are materials for which the second-order susceptibility tensor of said Taylor expansion is non-zero. When interacting with a non-centrosymmetric material, a portion of the incoming electromagnetic radiation can be frequency-doubled, i.e. so-called second-harmonic generation can occur, wherein electromagnetic radiation at half of the wavelength of theincoming electromagnetic radiation is generated if the phase-matching conditions are met,i.e. if the wavevector ^^of the incoming electromagnetic radiation and the wavevector ^^ofthe frequency-doubled electromagnetic radiation satisfy the following condition within thenon-centrosymmetric material: Δ^ = ^^ − ^^ = 0,wherein the phase-mismatch Δ^ is generally caused by the chromatic dispersion of the non-centrosymmetric material.The radiation conversion element having a spatially inhomogeneous structure preferablyexhibits second-order susceptibility tensors that are spatially oriented in a random manner.The random orientation leads to so-called "random quasi-phase-matching" and providesthe benefit of allowing second-harmonic generation across a broader fundamental wavelength band than in an element in which the susceptibility tensor is homogeneously oriented, as would typically be the case in a single-crystal-element, or than in an element in which the susceptibility tensor is periodically reversed, as would typically be the case in a periodically-poled element. In addition, random quasi-phase-matching in a spatially inhomogeneous structure provides the advantage of enabling second-harmonic generationindependently of the polarization of the incoming electromagnetic radiation. Furthermore,other nonlinear processes such as sum-frequency generation and difference-frequencygeneration tend to be suppressed within such a structure.The spatially inhomogeneous structure of the radiation conversion element causes scattering of the incoming electromagnetic radiation and / or the frequency-doubledelectromagnetic radiation. The scattering may be understood as a process governed by thelinear response of the spatially inhomogeneous structure, in which the field components ofthe electromagnetic radiation get refracted and / or reflected multiple times, thereby arbitrarilychanging the propagation direction of these field component within the spatiallyinhomogeneous structure. Different types of spatially inhomogeneous structures may be conceivable to achieve suchscattering in combination with second-harmonic generation.For instance, the radiation conversion element may comprise a plurality of particles comprising or consisting of the non-centrosymmetric material, wherein the particles arerandomly oriented within the radiation conversion element. The phase-matching conditionsmay thus be different at each particle, since the susceptibility tensor of the material may be randomly oriented, leading to broadband second-harmonic generation. The particles may have different shapes, in particular, they may be spherical and / or cube- shaped.Typically, the spectral width of the fundamental wavelength band that can be frequency-doubled by the radiation conversion element scales with a diameter distribution of theparticles, i.e. a broader distribution of particle diameters leads to a broader spectral widthof the fundamental wavelength band for which second-harmonic generation may occur.In order to maximize scattering within the radiation conversion element, it may beadvantageous to choose particle diameters which are on the order of the wavelength of theincoming electromagnetic radiation divided by the refractive index of the material of theparticles. In particular, the particles may have a diameter that is between 100 nm and 2500 nm, preferably between 100 nm and 1000 nm. Alternatively, the radiation conversion element may comprise holes distributed within the non-centrosymmetric material, the holes being filled with a second medium exhibiting a different refractive index than the non-centrosymmetric material, preferably a lower refractive index than the non-centrosymmetric material. The second medium may be a gas, in particular air. The phase-matching conditions may be different at each hole. Thus, typically, the spectralwidth of the fundamental wavelength band that can be frequency-doubled by the radiationconversion element scales with a diameter distribution of the holes, i.e. a broaderdistribution of hole diameters leads to a broader spectral width of the fundamentalwavelength band for which second-harmonic generation may occur.In particular, the holes may have a diameter that is between 100 nm and 2500 nm,preferably between 100 nm and 1000 nm. In order to obtain strong scattering and thus distinctive spatial speckle images, the radiation conversion element preferably has a thickness in propagation direction which is at least as large as, preferably at least 10 times larger than, a transport mean free path length experienced by the electromagnetic radiation propagating within the radiation conversion element, the transport mean free path length being defined as an average distance that a photon travels in the radiation conversion element before its direction is completelyrandomized. In particular, the thickness of the radiation conversion element may bebetween 10 µm and 20 µm.The spectrometer assembly may further comprise a filter arranged between the radiationconversion element and the detection unit, the filter being configured to blockelectromagnetic radiation within the fundamental wavelength band while allowing thefrequency-doubled electromagnetic radiation to pass. The non-centrosymmetric material used in the radiation conversion element may be one of lithium niobate, barium titanate, gallium arsenide, aluminium gallium arsenide and zinc oxide. The radiation conversion element may also comprise a combination of theseelements to broaden the wavelength range that may be simultaneously frequency-doubled.Lithium niobate may be particularly suitable for incoming electromagnetic radiation in thefundamental wavelength band of 350 nm to 4.5 µm.Barium titanate may be particularly suitable for incoming electromagnetic radiation in the fundamental wavelength band of 387 nm to 6.7 µm. Gallium arsenide may be particularly suitable for incoming electromagnetic radiation in the fundamental wavelength band of 870 nm to 16 µm. Aluminium gallium arsenide may be particularly suitable for incoming electromagnetic radiation in the fundamental wavelength band of 900 nm to 17 µm. Zinc oxide may be particularly suitable for incoming electromagnetic radiation in the fundamental wavelength band of 250 nm to 800 nm. The detection unit may comprise a silicon (Si) detector and / or an indium gallium arsenide(InGaAs) detector and / or a germanium (Ge) detector and / or an indium antimonide detector(InSb) or a mercury cadmium telluride detector (HgCdTe) to record the spatial speckleimage.Preferably, a silicon detector (Si) may be used if the incoming electromagnetic radiation isin the fundamental wavelength band of 300 nm to 2.2 µm. Silicon-based detectors providethe advantage of having faster response times and being cheaper than most other types ofdetectors. An indium gallium arsenide detector (InGaAs) may be used if the incoming electromagneticradiation is in the fundamental wavelength band of 900 nm to 5 µm.A germanium detector (Ge) may be used if the incoming electromagnetic radiation is in thefundamental wavelength band of 800 nm to 3.6 µm.An indium antimonid detector (InSb) may be used if the incoming electromagnetic radiationis in the fundamental wavelength band of 1.5 µm nm to 11 µm.Independently of the type of detector material, the detector is preferably a camera, inparticular with at least 1000 x 1000 pixels. In general, the obtainable spectral resolutionincreases when increasing the number of pixels.In a second aspect, the present invention provides a calibration method for obtaining acalibration data set using a spectrometer assembly as described above is disclosed, themethod comprising:a) sending electromagnetic calibration radiation having a known spectrum throughthe radiation conversion element of the spectrometer assembly, wherein at least a portion of the electromagnetic calibration radiation is frequency-doubled within the radiation conversion element, and wherein the frequency-doubled electromagnetic calibration radiation comprises components propagating in a plurality of different directions; b) recording a spatial calibration speckle image that is generated by spatial interference of the components of the frequency-doubled electromagnetic calibration radiation with each other; c) repeating steps a) and b) multiple times for a plurality of different known optical spectra in order to obtain a calibration speckle image for each of the different optical spectra, the calibration speckle images forming the calibration data set.The known spectrum of the electromagnetic calibration radiation may have a spectral widthwhich is chosen depending on a desired spectral resolution to be achieved by thespectrometer assembly. In particular, the spectral width of the known spectrum of the electromagnetic calibration radiation may be less than 10 nm, ideally less than 1 nm. Preferably, the different known optical spectra are obtained from a calibration source emitting electromagnetic calibration radiation with a spectrum having a central wavelengththat can be tuned in steps, in particular in equidistant steps. The steps may be preferablylarger than the spectral width. In particular, the steps may be in the range of 0.1 nm to 1nm. The calibration source may in particular be a wavelength-tunable laser. In addition, the calibration method may also comprise recording a spatial calibration speckle image of the calibration electromagnetic radiation in the fundamental wavelength band, i.e. generated by the spatial interference of components of the non-frequency-doubledelectromagnetic calibration radiation that are scattered within the radiation conversionelement. For this, a suitable filter blocking the frequency-doubled electromagnetic radiationand allowing the electromagnetic radiation in the fundamental wavelength band to pass may be placed in front of the detection unit.In a third aspect, the present invention provides a method for determining spectralinformation about incoming electromagnetic radiation to be analyzed using a spectrometer assembly according to the first aspect of the present invention, the method comprising: a) sending the incoming electromagnetic radiation to be analyzed through the radiation conversion element of the spectrometer assembly, wherein at least a portion of the incoming electromagnetic radiation is frequency-doubled within the radiation conversion element, and wherein the frequency-doubled portion of the electromagnetic radiation comprises components propagating in a plurality of different directions; b) recording a spatial sample speckle image generated by spatial interference ofthe components of the frequency-doubled electromagnetic radiation with each other, and c) retrieving spectral information about the incoming electromagnetic radiationbased on said spatial sample speckle image. In addition, the method may also comprise recording a spatial sample speckleimage of the incoming electromagnetic radiation in the fundamental wavelength band, i.e.generated by the spatial interference of components of the non-frequency-doubled incoming electromagnetic radiation that are scattered within the radiation conversionelement. For this, a suitable filter blocking the frequency-doubled electromagnetic radiationand allowing the electromagnetic radiation in the fundamental wavelength band to pass may be placed in front of the detection unit. By recording both a spatial sample speckle imageof the incoming electromagnetic radiation in the fundamental wavelength band as well as aspatial sample speckle image of the frequency-doubled electromagnetic radiation, thespectral detection bandwidth that may be covered using a single detector material may beincreased. In some cases, the spectral width of the incoming electromagnetic radiation inthe fundamental wavelength band may partially overlap with a detector sensitivity range ofthe detection unit, the detector sensitivity range being defined as the spectral bandwidthover which the detector material is sensitive, i.e. capable of providing a measurable signalresponse. In such cases, the spatial sample speckle image of the incoming electromagneticradiation in the fundamental wavelength band may be used to retrieve spectral informationabout a first spectral portion of the incoming electromagnetic radiation in a spectral regionthat overlaps with the detector sensitivity range of the detection unit, while the spatialsample speckle image of the frequency-doubled electromagnetic radiation may be used toretrieve spectral information about a second spectral portion the incoming electromagneticradiation in a spectral region that lies outside of the detector sensitivity range, but thatoverlaps with the detector sensitivity range of the detection unit once it has been frequency-doubled. The spectral information about the first and second spectral portion may then becombined to provide full spectral information about the incoming electromagnetic radiation,in particular a complete spectrum of the incoming electromagnetic radiation.In particular, retrieving the spectral information may comprise:computing correlation values between the spatial sample speckle image and a calibration data set comprising spatial calibration speckle images. Preferably, the method comprises obtaining the calibration data set using the calibration method described above. Recording a spatial calibration image and / or a sample spatial speckle image may comprise setting a pre-determined integration time for the detection unit, the pre-determinedintegration time being in particular between 0.1 ms and 100 ms. Due to the absence of moving parts in the spectrometer assembly, the spectral information can be retrieved almost instantly, i.e. essentially only being limited by the integration timeof the detection unit.In a fourth aspect, the invention provides an optical setup comprising: an optical source, in particular an optical parametric oscillator, configured to emit electromagnetic radiation with a tunable optical spectrum; the spectrometer assembly of the first aspect of the present invention, a control unit, wherein the control unit is configured to receive spectral information from the spectrometer assembly and to tune the optical spectrum of the electromagnetic radiation emitted by the optical source based on said spectral information. The parametric oscillator may in particular emit electromagnetic radiation in the fundamentalwavelength band of 1 µm to 5 µm.In a fifth aspect, the present invention provides a method of operating an optical setup according to the fourth aspect of the present invention, the method comprising: determining spectral information about the electromagnetic radiation emitted bythe optical source using the method of the third aspect of the present invention;tuning the optical spectrum of the electromagnetic radiation based on said spectral information. Such tuning may in particular be done "online", i.e. while the optical source is emitting the electromagnetic radiation, which may be particularly useful when aligning mechanical parts of the optical source. In some cases, tuning the optical spectrum may be achieved by mechanically changing a path length of the electromagnetic radiation within the optical source. BRIEF DESCRIPTION OF THE DRAWINGS Preferred embodiments of the invention are described in the following with reference to the drawings, which are for the purpose of illustrating the present preferred embodiments of the invention and not for the purpose of limiting the same. In the drawings,Fig. 1 schematically shows a spectrometer assembly according to a first embodiment;Fig. 2 schematically shows a spectrometer assembly according to a first embodiment;Fig.3 schematically shows a radiation conversion element according to a first embodiment; Fig.4 schematically shows a radiation conversion element according to a second embodiment; Fig.5 schematically shows a radiation conversion element according to a third embodiment;Fig. 6 schematically shows an embodiment of a method for determining spectralinformation about incoming electromagnetic radiation according to the present invention;Fig. 7 shows a measured example of a spatial speckle image generated by frequency-doubled electromagnetic radiation;Fig. 8 shows spectral information having been retrieved from the speckle imageshown in Fig.7;Fig. 9 shows a measured example of a linear spatial speckle image generated by non-frequency-doubled electromagnetic radiation;Fig.10 shows spectral information having been retrieved from the speckle imageshown in Fig.9, and Fig.11 schematically shows an optical setup according to the fifth aspect of the present invention. DESCRIPTION OF PREFERRED EMBODIMENTS Fig. 1 shows a spectrometer assembly 1 according to a first embodiment together with asource 11 emitting electromagnetic radiation F to be analyzed, and with a calibration source13 emitting electromagnetic calibration radiation C. Fig. 1 shows the electromagneticradiation F,C of both the source to be analyzed and the calibration source in a single figure for illustrative purposes. However, temporally, only electromagnetic radiation from one ofthe sources 11, 13 is preferably coupled into the spectrometer assembly 1 at the time, whilethe other source is switched off or blocked or not present at the same time. Theelectromagnetic radiation F to be analyzed and the electromagnetic calibration radiation Clie within a fundamental wavelength band. Upon entering the spectrometer assembly 1, the electromagnetic radiation F to be analyzed and the calibration radiation C are being focused by a first focusing lens 6 into a radiation conversion element 2 that comprises a non-centrosymmetric material to frequency-double at least a portion of the electromagneticradiation F to be analyzed and at least a portion of the electromagnetic calibration radiation C. After passing through the radiation conversion element 2, the electromagnetic radiationF, C in the fundamental wavelength band and the frequency-doubled portions SH, CSH arecollimated by a collimation lens 7, and subsequently impinge on a filter 5. The filter 5 isconfigured to block the electromagnetic radiation F, C within the fundamental wavelength band, while allowing the frequency-doubled electromagnetic radiation SH, CSH to pass andreach a detector unit 3. As shown in Fig. 1, a second focusing lens 8 can be arrangedbetween the filter 5 and the detector unit 3 to focus the frequency-doubled electromagneticradiation SH, CSH onto the detector unit 3. The detector unit 3 is configured to record aspatial speckle image that is generated by spatial interference of the components of therespective frequency-doubled electromagnetic radiation SH, CSH with each other. Thespectrometer assembly 1 further comprises a computing unit 4, which is connected to the detector unit 3 and is configured to retrieve spectral information about the electromagnetic radiation F,C based on said spatial speckle image. The electromagnetic radiation F to be analyzed and / or the electromagnetic calibration radiation C may be coupled into the spectrometer assembly using free-space alignment, e.g. using one or more mirrors orbeamsplitters or other appropriate beam routing components (not shown). Some or all ofthe components of the spectrometer assembly 1 may be mounted on holders which are displaceable with respect to each other to enable optimization of the alignment of the spectrometer assembly 1.In some embodiments, some or all of the components of the spectrometer assembly 1 arepre-aligned and subsequently spatially fixed with respect to each other to preventunintentional misalignment. In a second embodiment shown in Fig. 2, the spectrometerassembly 1 comprises a fiber input port 15 into which an optical fiber 14 can be plugged, the optical fiber 14 guiding the electromagnetic radiation F to be analyzed and / or theelectromagnetic calibration radiation C towards the fiber input port 15. The source 11emitting the electromagnetic radiation F to be analyzed, and the calibration source 13emitting electromagnetic calibration radiation C are not shown in Fig.2 for simplicity.In a specific embodiment, the incoming electromagnetic radiation F is light in the fundamental wavelength band of 690 nm-1040 nm, and the light is guided towards the fiber input port 15 using a single-mode fiber suitable for said fundamental wavelength band. The fiber input port 15 comprises a fiber collimation lens (not shown in the drawings) with a focal length of 18 mm. The first focusing lens 6 and the collimation lens 7 are aspheric lenses with an effective focal length of 20 mm, and the second focusing lens 8 is an achromatic lens with an effective focal length of 200 mm. The radiation conversion sample 2 comprisesa slab made of lithium niobate (LiNbO3) nanoparticles arranged on a glass substrate, theslab having a slab thickness of 20 µm in propagation direction and the glass substratehaving a substrate thickness of 170 µm in propagation direction. The filter 5 is a coloredglass bandpass filter with a transmission window ranging from 315 nm to 725 nm. The detection unit 3 comprises a monochrome silicon-based CMOS camera with 1440 x 1080 pixels, wherein each pixel has a pixel size of 3.45 µm x 3.45 µm.In Figs. 1 and 2, the frequency-doubled electromagnetic radiation SH and frequency-doubled electromagnetic calibration radiation CSH are sketched using straight arrows toindicate the general propagation direction on a macroscopic level. However, on a microscopic level, the radiation conversion element 2 exhibits a spatially inhomogeneousstructure such that the frequency-doubled electromagnetic radiation SH, CSH is scatteredby the radiation conversion element 2, i.e. such that the frequency-doubled electromagneticradiation SH, CSH comprises components propagating in a plurality of different directions. Figs.3-5 show three different embodiments of the radiation conversion element 2. Any of these embodiments may be implemented in the spectrometer assemblies shown in Figs.1 and 2.Both the embodiments of the radiation conversion element 2 shown in Fig. 3 and Fig. 4comprise a plurality of particles 20, which are randomly oriented within the radiationconversion element 2, and which comprise or consist of the non-centrosymmetric materialthat causes the frequency-doubling. In Fig.3, the particles 20 are substantially spherical. InFig. 4, the particles 20 are substantially cube-shaped. In the embodiment of the radiationconversion element 2 shown in Fig.5, the scattering is caused by holes 21 being distributed within the non-centrosymmetric material, the holes 21 being filled with a second medium exhibiting a different refractive index than the non-centrosymmetric material (hatched area in Fig.5), e.g. with air. Fabrication of the radiation conversion elementIn the following, a fabrication procedure for a specific embodiment of the radiationconversion is described, which comprises crystalline lithium niobate (LiNbO3) particlesproduced via solvothermal synthesis. In a first step, precursors oxides Nb2O5 (H.C. Starck,99.2%) and LiOH (Aldrich, 98%) are dispersed in a mixture of ethylene glycol and distilledwater. In a second step, the suspension is subjected to ultrasonication. In a third step, thesuspension is poured into a PTFE coated stainless steel acid digestion bomb (e.g. modelPA4748, volume 120 ml, Parr Instrument Company) and hydrothermally treated at 250°Cfor 70 hours. In a fourth step, the reaction product is washed with water by centrifugation.This chemical synthesis enables precise control over the size distribution of the producedparticles. The particles produced using this fabrication procedure are nanocubes havingdiameters ranging from 100 nm to 400 nm, a linear refractive index of n ≈ 2.3, and negligibleabsorption at visible wavelengths. They have a non-centrosymmetric hexagonal R3c crystal structure that enables second-harmonic generation, i.e. frequency doubling. In a fifth step, the particles are assembled into a slab by drop deposition over a substrate and solventevaporation. For a fundamental wavelength being shorter than 5 µm, a substrate made ofsapphire is preferably used. For a fundamental wavelength being longer than 5 µm, thesubstrate may be made of silicon (Si) or gallium arsenide (GaAs) or other suitable material being transparent at the fundamental wavelength.Further details regarding the fabrication are disclosed in A. Morandi et al., "MultipleScattering and Random Quasi-Phase-Matching in Disordered Assemblies of LiNbO3Nanocubes," ACS Photonics, pp. 1882-1888, 2022, DOI: 10.1021 / acsphotonics.2c00210.Compared to the fabrication procedure described by A. Morandi et al., the followingmodifications have found to yield improved results:^ To achieve different slab thicknesses, an aqueous suspension containing 10 wt% to 30wt% of LiNbO3 nanocubes may be prepared. It has been found that 26 wt % of water suspension is the most favourable for achieving a thickness in the desired thickness range of between 10 µm and 200 µm. Moreover, it has been found that includingpolyvinyl alcohol is not necessary.^ The mixture may be dropped over a substrate that is framed by hydrophilic tape withoutprior plasma cleaning of the substrate.^ Instead of being kept at 0°C for 36 hours, the substrate with the mixture on it may beplaced onto a horizontal substrate holder and kept at room temperature for less than 36hours, in particular between 5 and 10 hours, leading to faster evaporation of the waterand thus fast settling of the nanocubes on the glass substrate.As described in the reference by A. Morandi et al., the LiNbO3 nanocubes fabricated asdescribed above may be further used in an emulsion-templated assembly technique toobtain substantially spherical particles. In particular, 10 μL of aqueous an aqueoussuspension containing 2 wt% of the LiNbO3 nanocubes may be mixed with 1 mL ofsurfactant-loaded (10 wt % SPAN 80) hexadecane, followed by an emulsification processobtained though mechanical shaking. This generates a polydispersed distribution of water-in-oil dropletsfilled with the nanocubes, which can then be collected and deposited on aglass substrate with a pipet. The water in the droplets diffuses into the oil, shrinking the sizeof the droplets and forcing the nanocubes to assemble into microspheres. During thisprocess, the Brownian motion of the nanocubes in the droplets ensures that each nanocubeis positioned and oriented randomly within the microsphere. The obtained microspherescan have diameters ranging from 2 to 40 μm.Other process to obtain nanocubes or spherical particles or nanowires made of metal- oxides may also be conceivable, such as hydrothermal processes, molten salt synthesis for lithium niobate since or flame pyrolysis. A radiation conversion element that comprises holes as shown in Fig.5 may be obtainedusing e.g. an inverse opal process to obtain a photonic crystal as described in A. Blanco etal. "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensionalbandgap near 1.5 micrometres," Nature 405, 437–440 (2000),https: / / doi.org / 10.1038 / 35013024. Alternatively, it is also conceivable to use a lithographicprocess as described in N. Muller et. al, "Silicon Hyperuniform Disordered PhotonicMaterials with a Pronounced Gap in the Shortwave Infrared," Advanced Optical Materials,2: 115-119(2014), https: / / doi.org / 10.1002 / adom.201300415.Measurement method and calibration Fig.6 schematically shows an embodiment of a method for determining spectral information 2000 about incoming electromagnetic radiation F to be analyzed using an embodiment of the spectrometer assembly 1 described above. In this embodiment, a calibration data set 100 is first obtained using a calibration method 1000, which comprises: a) sending electromagnetic calibration radiation C having a known spectrum through the radiation conversion element 2 of the spectrometer assembly 1, as shown in Fig.1 and Fig.2, wherein at least a portion of the electromagnetic calibration radiation C is frequency-doubled within the radiation conversion element 2, and wherein the frequency- doubled electromagnetic calibration radiation CSH comprises components propagating in a plurality of different directions; b) recording a spatial calibration speckle image 101 that is generated by spatial interference of the components of the frequency-doubled electromagnetic calibration radiation CSH with each other; c) repeating steps a) and b) multiple times for a plurality of different known opticalspectra in order to obtain a calibration speckle image 101 for each of the different opticalspectra, the calibration speckle images forming the calibration data set 100.In a specific embodiment of the calibration method, the electromagnetic calibration radiation C originates from a frequency-tunable laser, and spatial calibration speckle images 101 are recorded for different center frequencies ^^, wherein the spectral shape stays the samespectrum for any central wavelength ^^, i.e., tuning the center frequency only translates thespectrum: ^^(^ − ^^). The input power of the electromagnetic calibration radiation C beforeentering the radiation conversion element can be expressed as: The input electric field of the electromagnetic calibration radiation C in the time-domain canbe expressed as a Fourier integral, i.e. wherein the relation between the spectrum and amplitude ^(^) of the Fourier componentsis The input electric field of the electromagnetic calibration radiation C (fundamental field) asingle frequency ^ in the frequency-domain can be expressed as: where z is the propagation direction and x and y are transverse axes being perpendicularto the propagation direction. The second-harmonic field component generated at a singlepoint in space P^ = (u^, u^, z^) inside the radiation conversion element for a single inputfrequency component has a second-harmonic amplitude, which is proportional to theamplitude ^(^) squared of the fundamental field, and has the same phase ^^(P^) = ^^ thanthe fundamental beam at that point in space: where ^^ is a proportionality constant, u and v are the transverse axis inside the radiationconversion element. The phase generated at the n-th point can be considered random. Thepropagation through the radiation conversion element only affects the value ofproportionality constant and the phase. Since the phase is random to begin with, thecontribution to the phase of the propagation inside the radiation conversion element can be disregarded. The proportionality constant gets randomized by the multiple scattering, thusat the exit of the radiation conversion element, a factor ^^ related to the n−th point can beconsidered.The second-harmonic (i.e. frequency-doubled) field at a pixel in position (x, y) of thedetection unit is given by the sum of the fields of all components of the frequency-doubledelectromagnetic radiation SH that reach said point (x, y): where the factor d(x,y) is the result of the sum of random phasors Therefore, its power of the frequency-double electromagnetic radiation at position (x,y)^^^(^, ^, ^) is: The term ^(^, ^) = |^(^, ^)|^ is the normalized spatial speckle image, which is the result ofthe random walk (and random phase generation) of the components of the frequency-doubled electromagnetic calibration radiation at the single frequency ^ inside the radiationconversion element.This can then be generalized from the monochromatic to the polychromatic case byconsidering a resulting spatial speckle image ^^(^,^) = |^^(^, ^)|^which depends on theinput frequency ^. The resulting total electric field at the pixel at position (x, y) is given by and the total frequency-integrated power of the frequency-double electromagnetic radiationat position ^^^(^, ^) is In this derivation, only second-harmonic generation (SHG) is considered. Sum frequencygeneration (SFG) and difference frequency generation (DFG) are disregarded, because thedifferent components of the fundamental electromagnetic radiation travel along differentpaths inside the radiation conversion element, hence the probability of having a sufficientlyhigh intensity of components with different frequencies in a single spatial point within theradiation conversion element is negligible.The overall speckle power ^P^^^ recorded by a single pixel of the detection unit, i.e.integrated over its full pixel area, for electromagnetic calibration radiation C having aspectrum ^^(^ − ^^) centered around the central frequency ^^ can be expressed as: where ∗ stands for the convolution operation and the angular brackets stand for the spatialintegration over the area of the pixel. Therefore, a spatial speckle image as a function offrequency can be obtained by measuring the second harmonic power for different inputcentral frequencies ^^, and deconvolving the resulting function ^^^^,^(^^)^ with square ofthe power spectral density|^^(^)|^of the calibration source. To do so, the Fourier transformof ^^^^,^(^^)^ may be calculated and then divided by the Fourier transform of |^^(^)|^, the result then being transformed back using the inverse Fourier-transform to obtain theexpression ^^^ (^, ^)^.After recording a spatial calibration speckle image 101 for different central frequencies ν^to form a calibration data set 100, this calibration data set 100 can be used to retrievespectral information 300 of the unknown electromagnetic radiation F, i.e. an unknownspectrum ^^(^).To this aim, the speckle image (i.e. spatial power distribution) ^^^,^ generated by theunknown electromagnetic F is measured. Then, the correlation function ^(^^) is calculated:^^^^,^^^^,^(^^)^ ^^^^,^^^^^^,^(^^)^ is the calibration image previously recorded at the central frequency ^^ .The denominator is only a normalization factor, and the numerator can be expressed as: The function ^^(^^ − ^^) is the spectral correlation function of the speckle pattern, and it isdefined as In a case where the spectral decorrelation is much smaller than a targeted spectralresolution of the spectrometer, e.g. if the spectral decorrelation is on the order of tens ofpicometer while the spectral resolution of the spectrometer is on the order of thenanometers, the following approximation can be made:^^(^^ − ^^) = ^(^^ − ^^)In other cases, the spectral correlation function ^^ may be measured.By using said approximation on the equation above, the following is obtained:^ ^^^^,^^^^,^(^^)^  =   ^  ^^^  ^^^^^ and, using the properties of the δ-distribution: ^ ^^^^,^^^^,^(^^)^  = ^ |^^(^)|^|^^(^ − ^^)|^(^^^^)^^^ ^^which can be written as a convolution: Since ^^^^, and ^^(^) have been already determined during the calibration procedure and^^ ^^^,^ obtained by calculating the correlation function ^(^^) frommeasurements of the image ^^^,^generated by the unknown frequency-doubled radiationand the calibration image ^^^,^(^^) centered at frequency ^^, deconvolution can be used toextract ^^(^). Measurement examples Fig. 7 shows an example of a spatial speckle image showing the interference of thecomponents of the frequency-doubled electromagnetic radiation SH, centered around acenter wavelength of 430 nm, that have been scattered in a radiation conversion elementthat comprises cubic lithium niobate nanoparticles having diameters ranging from 100 nmto 400 nm, the nanoparticles forming a layer with a thickness of 20 μm on a glass substrate having a thickness of 170 μm, wherein the image contains 350 x 350 pixels.Fig. 8 shows the normalized correlation function Γ(^^) (plotted as a function of wavelengthinstead of central frequency ^^) exhibiting a peak centered around a wavelength of 860 nm.Instead of using a filter which is configured to block the electromagnetic radiation within thefundamental wavelength band, while allowing the frequency-doubled electromagnetic radiation to pass as described above, a filter which is configured to allow theelectromagnetic radiation within the fundamental wavelength band to pass while blockingthe frequency-doubled electromagnetic radiation may be arranged in front of the detection unit. In such a case, a spatial speckle image may be obtained from of the components of the electromagnetic radiation in the fundamental wavelength band, i.e. from the portion of the electromagnetic radiation that is scattered in the radiation conversion element, but that is not frequency-doubled. Such a linear spatial speckle image is shown in Fig.9, with thecorresponding normalized correlation function Γ(^^) of the narrow-band fundamentalelectromagnetic radiation F centered at 770 nm shown in Fig.10. Tunable optical setup Fig. 11 schematically shows an embodiment of an optical setup 10, which comprises an optical source 11 emitting electromagnetic radiation with a tunable optical spectrum. The optical source 11 can in particular be a tunable optical parametric oscillator (OPO). The optical setup 10 further comprises the spectrometer assembly 1 according to any embodiment described above, as well as a control unit 12. The control unit is configured to receive spectral information from the spectrometer assembly 1 and to tune the optical spectrum of the electromagnetic radiation F emitted by the optical source 11 based on said spectral information.

[0002] LIST OF REFERENCE SIGNSspectrometer assembly 14 optical fiberconversion element 15 fiber input portparticles 100 calibration data setholes 101 calibration speckle imagedetection unit 200 spatial speckle imagecomputing unit 300 spectral informationfilter F (fundamental)first focusing lenselectromagnetic radiationcollimation lens SH frequency-doubledsecond focusing lenselectromagnetic radiationoptical setup CSH frequency-doubledsourceelectromagnetic calibrationcontrol unitradiationcalibration source

Claims

CLAIMS 1. A spectrometer assembly (1) for determining spectral information aboutincoming electromagnetic radiation (F), comprising: aradiation conversion element (2) that comprises a non-centrosymmetric materialto frequency-double at least a portion of the incoming electromagnetic radiation (F) as theincoming electromagnetic radiation (F) propagates through the radiation conversionelement (2), wherein the radiation conversion element (2) exhibits a spatiallyinhomogeneous structure such that the frequency-doubled electromagnetic radiation (SH) comprises components propagating in a plurality of different directions; adetection unit (3) arranged after the radiation conversion element (2) with respectto a propagation direction defined by the incoming electromagnetic radiation (F), thedetection unit (3) being configured to record a spatial speckle image that is generated byspatial interference of the components of the frequency-doubled electromagnetic radiation(SH) with each other, anda computing unit (4) configured to retrieve spectral information about theelectromagnetic radiation (F) based on said spatial speckle image.

2. The spectrometer assembly (1) of claim 1, wherein the radiation conversionelement (2) comprises a plurality of particles (20) comprising or consisting of the non-centrosymmetric material, wherein the particles (20) are randomly oriented within the radiation conversion element (2).

3. The spectrometer assembly (1) of claim 2, wherein the particles (20) have adiameter that is between 100 nm and 2500 nm, preferably between 100 nm and 1000 nm.

4. The spectrometer assembly (1) of claim 1, wherein the radiation conversionelement comprises holes (21) distributed within the non-centrosymmetric material, the holes(21) being filled with a second medium exhibiting a different refractive index than the non-centrosymmetric material, preferably a lower refractive index than the non-centrosymmetricmaterial, and the holes preferably having a diameter that is between 100 nm and 2500 nm,more preferably between 100 nm and 1000 nm.

5. The spectrometer assembly (1) of claim 4, wherein the second medium is agas, in particular, air.

6. The spectrometer assembly (1) of any one of the preceding claims, whereinthe radiation conversion element (2) has a thickness in propagation direction which is atleast as large as, preferably at least 10 times larger than, a transport mean free path length experienced by the electromagnetic radiation (F) propagating within the radiation conversion element (2), the transport mean free path length being defined as an average distance that a photon travels in the radiation conversion element (2) before its direction is completely randomized.

7. The spectrometer assembly (1) of any one of the preceding claims, whereinthe non-centrosymmetric material is one of lithium niobate, barium titanate, galliumarsenide, aluminium gallium arsenide and zinc oxide.

8. The spectrometer assembly (1) of any one of the preceding claims, whereinthe incoming electromagnetic radiation (F) lies within a fundamental wavelength band andwherein the spectrometer assembly (1) further comprises a filter (5) arranged between theradiation conversion element (2) and the detection unit (3), the filter being configured toblock electromagnetic radiation within said fundamental wavelength band while allowing thefrequency-doubled electromagnetic radiation (SH) to pass.

9. The spectrometer assembly (1) of any one of the preceding claims, whereinthe detection unit (3) comprises a silicon (Si) detector and / or an indium gallium arsenide(InGaAs) detector and / or a germanium (Ge) detector and / or an indium antimonide (InSb)detector and / or a mercury cadmium telluride (HgCdTe) detector to record the spatialspeckle image.

10. A calibration method (1000) for obtaining a calibration data set (100) using aspectrometer assembly (1) according to any one of the preceding claims, comprising:a) sending electromagnetic calibration radiation (C) having a known spectrumthrough the radiation conversion element (2) of the spectrometer assembly (1), wherein atleast a portion of the electromagnetic calibration radiation (C) is frequency-doubled withinthe radiation conversion element (2), and wherein the frequency-doubled electromagneticcalibration radiation (CSH) comprises components propagating in a plurality of differentdirections; b) recording a spatial calibration speckle image (101) that is generated by spatialinterference of the components of the frequency-doubled electromagnetic calibrationradiation (CSH) with each other;c) repeating steps a) and b) multiple times for a plurality of different known opticalspectra in order to obtain a calibration speckle image (101) for each of the different opticalspectra, the calibration speckle images forming the calibration data set (100).

11. A method for determining spectral information (2000) about incomingelectromagnetic radiation (F) to be analyzed using a spectrometer assembly (1) accordingto any one of claims 1-9, the method comprising:a) sending the incoming electromagnetic radiation (F) to be analyzed through theradiation conversion element (2) of the spectrometer assembly (1), wherein at least aportion of the incoming electromagnetic radiation (F) is frequency-doubled within theradiation conversion element (2), and wherein the frequency-doubled portion of theelectromagnetic radiation (SH) comprises components propagating in a plurality of different directions; b) recording a spatial sample speckle image (200) generated by spatialinterference of the components of the frequency-doubled electromagnetic radiation (SH) with each other, and c) retrieving spectral information (300) about the incoming electromagneticradiation (F) based on said spatial sample speckle image (200).

12. The method of claim 11, wherein retrieving the spectral information (300)comprises: computing correlation values between the spatial sample speckle image (200) anda calibration data set (100) comprising spatial calibration speckle images (101).

13. The method of claim 12, further comprising:obtaining the calibration data set (100) using the calibration method of claim 10.

14. An optical setup (10) comprising:an optical source (11), in particular an optical parametric oscillator, configured toemit electromagnetic radiation (F) with a tunable optical spectrum;the spectrometer assembly (1) of any of claims 1-9,a control unit (12), wherein the control unit (12) is configured to receive spectralinformation from the spectrometer assembly (1) and to tune the optical spectrum of theelectromagnetic radiation (F) emitted by the optical source (11) based on said spectralinformation.

15. A method of operating an optical setup (10) according to claim 14, themethod comprising: determining spectral information about the electromagnetic radiation (F) emittedby the optical source (11) using the method of any one of claims 11-13;tuning the optical spectrum of the electromagnetic radiation (F) based on saidspectral information.

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