An all-optical timekeeping apparatus and method

Abstract

The invention relates to producing time information. Particularly, the invention relates to an optical apparatus and an optical method for producing time information. The optical apparatus comprises a pump pulse generator, a supercontinuum probe generator, a nonlinear element, wherein the nonlinear element is configured to produce a modulated supercontinuum caused by cross-phase modulation between the pump pulses and the supercontinuum probe, and a spectral analyser.

Description

[0001] An all-optical timekeeping apparatus and method

[0002] Technical field

[0003] The invention relates to producing time information. Particularly, the invention relates to an optical apparatus and an optical method for producing time information. The optical apparatus comprises a pump pulse generator, a supercontinuum probe generator, a nonlinear element, wherein the nonlinear element is configured to produce a modulated supercontinuum caused by cross-phase modulation between the pump pulses and the supercontinuum probe, and a spectral analyser.

[0004] Background

[0005] The rapid evolution of artificial intelligence, the expansion of complex and dense 5G / 6G communication networks, and the reliance on global navigation satellite systems (GNSS) all demand exceptionally accurate time measurements and precise synchronization at ultrafast speeds. Existing electronic devices struggle to meet these demands effectively.

[0006] The current electronic-based devices, such as time-interval meters (TIM) or time-to-digital converters (TDC), face limitations in accurately measuring time intervals beyond the scale of tens of picoseconds (10’12seconds). This constraint becomes increasingly problematic as technological advancements push the boundaries of speed and precision. The recent introduction of attosecond pulsed laser light, a breakthrough acknowledged by the Nobel Prize in Physics 2023, has opened up new avenues for applications such as capturing electronic transitions and chemical transformations in real-time. These applications are pivotal for tasks like data encoding, ultrafast communications, and advanced Al algorithms.

[0007] Quartz crystals are able to generate consistent clock signals because of their good piezoelectric properties. Depending upon how a quartz crystal is mechanically manipulated, it will have a well-defined natural frequency to which it will oscillate when an electrical pulse is passed through the crystal. Alternative timing sources that deviate from traditional quartz technology, including purely silicon based oscillators, are available. These new devices provide reliable timing to many electronic devices today. However, their application still needs to be improved for a number of reasons, primarily frequency ranges and frequency stability.

[0008] Atomic clocks also measure time using the vibrations of atoms. They use cesium atoms in a microwave cavity to keep time. Cesium atomic clocks are the most common and are used to define the international standard for time.

[0009] All these existing timing sources are critical for the reliable operation of expensive electronic devices. However, electronic devices always create time jitter, i.e. , deviation from true periodicity of a presumably periodic signal. To compensate for the jitter effect, stabilization and adjustment in the system is needed.

[0010] Furthermore, the accuracy of measurement is limited to several picoseconds. The challenge of accurately measuring time intervals smaller than several picoseconds, i.e., 10’12seconds, is widely recognized within the scientific and technological community. While this limitation has been acknowledged for some time, its significance has grown substantially in today's fast-paced world, where precision timing is essential for numerous advanced applications.

[0011] Thus, more precise methods for measuring extremely fast time intervals together with jitter reduction are needed.

[0012] Summary

[0013] An object of the present invention is to overcome the mentioned drawbacks in the prior art. More precisely, an object of the invention is to enable producing time information in the femtosecond and even shorter time scale.

[0014] A further object of the present invention is to provide an all-optical time-to- frequency converting system that can be used in the femtosecond and even in the sub-femtosecond time scales. This object is achieved by an optical apparatus and a method characterized by what is stated in the independent claims. Advantageous embodiments and variants of the invention are described in the dependent claims.

[0015] The features recited in the dependent claims and the embodiments in the description are mutually freely combinable unless otherwise explicitly stated.

[0016] The exemplary embodiments presented in this text and their advantages relate by applicable parts to all aspects of the invention, even though this is not always explicitly mentioned.

[0017] An optical apparatus for producing time information is presented. The apparatus comprises a pump pulse generator configured to produce pump pulses. The pump pulse generator may be a mode-locked laser. Ultrafast lasers producing pump pulses with a temporal pulse width of 50 to 150 fs (fullwidth at half maximum, FWHM) may be used.

[0018] The apparatus comprises a nonlinear element. The nonlinear element is configured to produce a modulated supercontinuum. The modulated supercontinuum contains modulations caused by cross-phase modulation (XPM) between the pump pulses and the supercontinuum probe due to interaction with the nonlinear element. Light-matter interaction between the probe pulses and the nonlinear element produces measurable nonlinear phase shifts, i.e., modulations, to the supercontinuum probe via the cross-phase modulation mechanism.

[0019] The apparatus comprises a spectral analyser. The spectral analyser is configured to measure optical spectra, such as a reference spectrum and an encoded spectrum of the supercontinuum. The reference spectrum comprises an optical spectrum of the supercontinuum probe without the cross-phase modulation, i.e., without the pump pulses. The encoded spectrum comprises an optical spectrum of the modulated supercontinuum, i.e., optical spectrum of the supercontinuum when the cross-phase modulation is activated through interaction between the pump pulses and the nonlinear element. A method for producing time information is presented. The method utilizes the apparatus presented herein.

[0020] The method comprises generating pump pulses using the pump pulse generator. The used pump pulse generator may be a mode-locked laser. The generated pump pulses may have a temporal pulse width in the range of 50 to 150 fs (full-width at half maximum, FWHM).

[0021] The method comprises generating a supercontinuum probe using the supercontinuum probe generator.

[0022] The method may comprise allowing the pump pulses to interact with the nonlinear element and producing a modulated supercontinuum containing modulations caused by cross-phase modulation between the pump pulses and the supercontinuum probe due to interaction with the nonlinear element. The interaction between the pump pulses and the nonlinear element enables the cross-phase modulation which then produces measurable nonlinear phase shifts, i.e., modulations, to the supercontinuum probe.

[0023] The method comprises measuring an encoded spectrum by the spectral analyser. The encoded spectrum comprises an optical spectrum of the modulated supercontinuum.

[0024] The measured optical spectra are processed to obtain time information. The method may comprise calculating a digital time signal from the encoded spectrum. The time signal contains time information corresponding to at least one modulation.

[0025] The present invention provides a major advantage over the prior art in that the limitation from electronics communication can be overcome in time interval measurements. With the presented system and method, it is possible to produce time information at an accuracy smaller than the current detection limit of electronic-based timekeeping methods. The presented system and method provide timekeeping in the femtosecond and even in the sub-femtosecond time scales, enabling ultrafast timekeeping in, inter alia, artificial intelligence (Al) systems, 5G and 6G networks, and global navigation satellite systems (GNSS). The ultrafast timekeeping provided by the present invention may also be utilizable in, e.g., detecting ultrafast chemical reactions (electron transitions and chemical transformation) in real time.

[0026] The present invention provides a method for producing time information utilizing materials having strong nonlinear optical properties. The precise temporal location of the modulations in the modulated supercontinuum may be accurately determined in the femtosecond or even in sub-femtosecond time scale.

[0027] The present invention is based on an all-optical approach, thus eliminating expensive electronics for precision timing, making it more reliable and faster in different conditions for extended periods of time. Also other drawbacks associated with electronics-based timing, such as jitter, may be eliminated or at least drastically reduced.

[0028] Brief description of the drawings

[0029] Figure 1 schematically presents an optical setup of a system according to the present invention;

[0030] Figures 2a-b schematically present optical setups of a system according to embodiments of the present invention;

[0031] Figures 3a-d schematically present signal processing according to a method of the present invention;

[0032] Figures 4a-d schematically present nonlinear elements according to embodiments of the present invention;

[0033] Figures 5a-5h schematically present nonlinear elements according to the present invention comprising antennae structures;

[0034] Figure 6 schematically presents a wavelength difference in a modulation measurable by the apparatus of the present invention; Figure 7 presents simulated and experimental linear transmission responses at a selection of incident angles;

[0035] Figure 8 presents simulated modulation spectra according to the present invention;

[0036] Figures 9a-9f present simulated and experimental modulation spectra according to the present invention at a selection of incident angles.

[0037] Detailed

[0038] Referring to Figure 1 , an optical apparatus 100 for producing time information TIME1 , TIME2 is presented. As illustrated in Figure 1 , the apparatus 100 may comprise a pump pulse generator LAS1. The pump pulse generator LAS1 is configured to produce pump pulses B0. The pump pulse generator may be a mode-locked laser. Ultrafast lasers producing pump pulses with a temporal pulse width of 50 to 150 fs (full-width at half maximum, FWHM) may be used. The presented method comprises generating pump pulses B0 using the pump pulse generator LAS1 , respectively.

[0039] Wavelength of the pump pulses B0 may be selected according to optical properties of other optical instruments of the apparatus 100. Particularly, wavelength of the pump pulses B0 may be selected to optimize the light-matter interaction at the nonlinear element to maximize the response, i.e. , the crossphase modulation. The pump pulses B0 may have a wavelength in the range of 600-2000 nm, preferably in the range of 700-800 nm or in the range of 1500-2000 nm, particularly preferably in the range of 1500-1800 nm. Extensive research has shown that long-range pump pulses, i.e., pump pulses in the wavelength range of 1500-2000 nm, may provide an improvement in the signal-to-noise ratio, especially when combined with epsilon-near-zero (ENZ) materials as the nonlinear element NL. Wavelength of the long range pump pulses falls outside of the predominant linear response range of the ENZ material. As a consequence, interference will be suppressed, leading to reduced noise and an improvement in the signal intensity.

[0040] Peak power of the pump pulses B0 should be sufficiently high to enable efficient interaction with the nonlinear element, such that the produced phase shifts, i.e., modulations are measurable. The peak power of the pump pulses BO may be in the range of 1-100 MW, corresponding to pulse energies of approx. 100 nJ to 100 pJ.

[0041] The apparatus 100 may comprise a supercontinuum probe generator WG1 configured to produce a supercontinuum probe B4. Correspondingly, the presented method comprises generating a supercontinuum probe B4 using the supercontinuum probe generator.

[0042] The supercontinuum probe B4 may have a wavelength range that at least partially overlaps an active wavelength region characteristic to the nonlinear element NL1. Particularly, the wavelength range of the supercontinuum probe B4 may be selected to optimize the light-matter interaction at the nonlinear element to maximize the response, i.e., the cross-phase modulation. The wavelength range of the supercontinuum probe may be in the range of 500- 2500 nm, preferably in the range of 800-1600 nm, more preferably in the range of 1000-1500 nm.

[0043] The supercontinuum probe B4 may be a steady-state, i.e., non-pulsed supercontinuum beam.

[0044] Alternatively, the supercontinuum probe B4 may originate from a pulsed light source. A pulsed supercontinuum probe may be, e.g., a dispersively stretched supercontinuum pulse originating from a pulsed laser source. The pulsed supercontinuum probe may have a temporal duration in the picosecond to nanosecond range, e.g., in the range of 1 ps to 1 ps. Ratio of the temporal width of the pulsed supercontinuum pulse to the temporal width of the pump pulses B0 may be, e.g., in the range of 106: 1 to 109:1 .

[0045] Referring to Figures 1 , 2a, 2b, and 4a-4d, the apparatus 100 comprises a nonlinear element NL1. As illustrated in Figure 4a, the nonlinear element may comprise at least a substrate SS1 and at least one active material ACT1 . The nonlinear element NL1 is configured to produce a modulated supercontinuum BMOD containing modulations MODI , MOD2 caused by cross-phase modulation (XPM) between the pump pulses B0 and the supercontinuum probe B4 due to interaction of the pump pulses B0 with the nonlinear element NL1 . The nonlinear element NL1 should have high a nonlinear response at an active wavelength region. The active wavelength region is determined by the material characteristics of the nonlinear element. The active wavelength region may be in the range of 400-2500 nm, such as in the visible region at 300-750 nm or in the infrared region in the range of 800-2000 nm, preferably in the range of 1000-1500 nm, more preferably in the range of 1200-1400 nm. Thickness of the active material ACT 1 of the nonlinear element NL1 may be in the range of 10 nm to 1 pm, such as 10 to 500 nm, preferably 30 to 200 nm.

[0046] The presented method correspondingly comprises producing a modulated supercontinuum BMOD containing modulations M0D1 , M0D2 caused by cross-phase modulation (XPM) between the pump pulses B0 and the supercontinuum probe B4 due to interaction with the nonlinear element NL1.

[0047] Referring to Figure 4b, the active material ACT1 may comprise an epsilon- near-zero material ENZ1. Thus, the nonlinear element NL1 may comprise an epsilon-near-zero material ENZ1. The epsilon-near-zero material preferably comprises a material that exhibits a real permittivity value approaching zero at an active wavelength region. Preferably, the epsilon-near-zero material is selected from the group comprising semi-transparent conductive oxides such as indium tin oxide (ITO), aluminium-doped zinc oxide (AZO), nitrides, nanomaterials, and any combination thereof. Said semi-transparent conductive oxides may have the active wavelength region in the infrared, i.e. , in the range of 1000-2500 nm, such as 1200-1600 nm, while nitrides may have the active wavelength region in the visible, i.e., in the range of 300-750 nm, such as 400-600 nm. Nanomaterial-based epsilon-near-zero materials may be designed according to need to have the active wavelength region in the visible or in the infrared, i.e., in the range of 300-2500 nm. Thickness of the epsilon-near-zero material ENZ1 may be in the range of 10 nm to 1 pm, such as 10 to 500 nm, preferably 30 to 200 nm.

[0048] The phase velocity of a wave, such as a light pulse, propagating through a medium is defined by:

[0049] 1 v„ p — ~i= , where 8 and p are permittivity and permeability of the medium, respectively. In an epsilon-near-zero material, the permittivity value approaches zero, whereby the phase velocity attains a very high value. This results in an extreme nonlinear behavior.

[0050] Such nonlinear behavior can be observed in several natural materials, for example in semi-transparent conductive oxides. For example, permittivity of a material containing electron gas can be described by a so-called Drude model using the following expression: where S^ is a correction parameter, Y is a damping factor and a)pis plasma frequency. In a situation where operating frequency (<w) is close to the plasma frequency, the real part of permittivity S'(o>p) can be expressed as:

[0051] Metals are a typical example where the electron gas model can be used to model the charge carrier behaviour. For typical metals, Soo = 1, Thus S'(o>p) ~ 0. The real part of permittivity thus approaches zero, and the material exhibits the extreme nonlinear behavior, i.e. , epsilon-near-zero behavior.

[0052] Referring to Figures 4c and 4d, the nonlinear element NL1 may further comprise at least one overlying layer OL1 . Preferably, the overlying layer OL1 is arranged on top of the active material ACT1 , such as the epsilon-near-zero material ENZ1 . Thickness of the overlaying layer OL1 may be in the range of 10-100 nm, preferably 20-50 nm.

[0053] Together, the active material ACT1 and the overlying layer OL1 form a metasurface MS1. Metasurfaces are an example of metamaterials, i.e., artificially engineered structures with a permittivity value approaching zero at certain frequencies. Thus, the metasurface MS1 formed of the active material ACT1 , such as the epsilon-near-zero material ENZ1 and the overlying layer OL1 as a whole exhibits an epsilon-near-zero behavior at a certain wavelength region. Due to the strong nonlinearities, these nonlinear metasurfaces demonstrate strong nonlinear effects like self-phase modulation (SPM) and cross-phase modulation (XPM). Self-phase modulation is a nonlinear optical effect where the phase of a light wave is modulated by its own intensity as it propagates through a nonlinear medium. Cross-phase modulation, on the other hand, is a nonlinear optical effect where the phase of a light wave is modulated by the intensity of another co-propagating light wave. In the present apparatus 100, the strong field enhancement within the active material ACT1 , such as the epsilon-near-zero material ENZ1 , and nonlinearities at the active wavelength region enable strong cross-phase modulation. When two light waves at different frequencies propagate through the nonlinear element NL1 , the refractive index experienced by each wave is affected by the intensity of the other light beam. This mutual intensity-dependent refractive index modulation leads to modulation in both propagating beams, producing the modulations MODI , MOD2 in the modulated supercontinuum BMOD.

[0054] The at least one overlying layer OL1 may be arranged as a plurality of antennae structures ANTI . Preferably, the antennae structures ANTI comprise metal or nitride materials. More preferably, the antennae structures ANTI are selected from the group comprising gold, silver aluminium, titanium nitride (TiN), zirconium nitride (ZrN), and any combination thereof. Thickness of each antennae structure of the plurality of antennae structures ANTI may be in the range of 10-100 nm, preferably 20-50 nm. The plurality of antennae structures ANTI exhibit enhanced electric fields and unusual light-matter interactions. Thus, the plurality of antennae structures ANTI enhance the nonlinear behavior of the active material ACT1 , such as the epsilon-near-zero material ENZ1 . The antennae structures may be cylindrical structures with a certain shape in their cross-section. Figures 5a-5h schematically present suitable antennae shapes in the Sx, Sy plane, i.e. , in a top view. Examples of shapes of the cross-section of the plurality of antennae structures ANTI include circles (Figure 5a), squares (Figure 5b), triangles (Figures 5c and 5d), crosses (Figures 5e and 5f), and rectangles (Figures 5g and 5h). Linear dimensions, i.e., the largest width and length of individual antennae in the plurality of antennae structures in the Sx, Sy plane, may be in the range of 50- 500 nm, preferably in the range of 150-300 nm. Mutual separation Dx, Dybetween individual antennae in the matrix of antennae structures, defined as an edge-to-edge distance, may be in the range of 100-1000 nm, preferably in the range of 300-800 nm.

[0055] Referring to Figures 1 , 2a and 2b, the apparatus 100 may comprise a means for periodically preventing and for allowing the pump pulses B0 to interact with the nonlinear element NL1 , such as a beam chopper BC or a beam blocker. Preferably, the means for periodically preventing and for allowing the pump pulses B0 to interact with the nonlinear element NL1 is placed in the optical path of the pump beam to prevent the interaction between the pump pulses B0 and the nonlinear element. The means for periodically preventing and for allowing the pump pulses B0 to interact with the nonlinear element NL1 enables measuring optical spectra of the supercontinuum probe B4 for references spectrum purposes when the interaction between the pump pulses B0 and the nonlinear element NL1 is prevented. On the other hand, the optical spectra of the modulated supercontinuum BMOD may be measured when allowing the pump pulses B0 to interact with the nonlinear element NL1 for obtaining the digital time signal SIG1 .

[0056] The term ‘periodically’ should be understood to mean that the interaction between the pump pulses B0 and the nonlinear element NL1 is prevented at each alternative pulse, and respectively allowed at each alternative pulse. In other words, the pump pulses will be chopped at half the repetition rate of the pump pulse generator LAS1 . In case of pulsed supercontinuum probe B4, the probe pulses have the pulse repetition rate of the supercontinuum probe pulse generator. In case the probe pulse generator LAS1 and the supercontinuum probe pulse generator are arranged as a single pulse generator, the supercontinuum probe B4 will have the pulse repetition rate the pulse generator, i.e., automatically twice that of the chopped pulse rate of the pump pulses. This allows repeatedly recording a reference signal at every second pulse to correct shot-to-shot fluctuations, leading to increased signal-to-noise ratio.

[0057] Correspondingly, the presented method may comprise preventing the pump pulses B0 from interacting with the nonlinear element NL1. When the interaction between the pump pulses B0 and the nonlinear element NL is prevented, optical spectrum of the supercontinuum probe B4 without the modulations produced by the pump pulses BO can be measured. The optical spectrum of the supercontinuum probe B4 may be used, e.g., as the reference spectrum REFI .

[0058] The presented method further comprises allowing the pump pulses BO to interact with the nonlinear element NL1 . This enables the interaction between the pump pulses BO and the nonlinear element NL1 .

[0059] Referring to Figures 1 , 2a and 2b, the apparatus 100 comprises a spectral analyser OSA1 . The optical analyser OSA1 is configured to measure optical spectra. Particularly, the optical analyser OSA is configured to measure an encoded spectrum ENC1 comprising an optical spectrum of the modulated supercontinuum BMOD. The optical analyser OSA1 may further be configured to measure a reference spectrum REF1 comprising an optical spectrum of the supercontinuum probe B4. The optical analyser OSA1 may be a typical optical spectrometer such as a CCD spectrometer, preferably suitable for fiber-optic systems. Spectral accuracy of the optical analyser OSA1 is may be in the range of 0.1-2 nm, preferably 0.1 -0-8 nm, determined as a full-width halfmaximum (FWHM) spectral accuracy. The spectral accuracy of the optical analyser OSA1 may be in the range of 1 / 10000 to 1 / 100 of the detection wavelength range of the optical analyser OSA1 (FWHM spectral accuracy). The presented method may correspondingly further comprise measuring a reference spectrum REF1 by the spectral analyser OSA1. The reference spectrum REF1 comprises an optical spectrum of the supercontinuum probe B4. The method further comprises measuring an encoded spectrum ENC1 by the spectral analyser OSA1. The encoded spectrum ENC1 comprises an optical spectrum of the modulated supercontinuum BMOD.

[0060] The spectral analyser OSA1 may be configured to record the reference spectrum REF1 and the encoded spectrum ENC1 using two adjacent pump pulses, allowing to correct shot-to-shot fluctuations and leading to increased signal-to-noise ratio. The spectral analyser OSA1 may be a single-channel spectral analyser or a multi-channel spectral analyser, such as a dual-channel spectral analyser. Referring to Figures 1 and 2a, the apparatus 100 may further comprise a control unit CTRL. The control unit CTRL may be configured to perform one or more tasks by executing a computer program code being stored on a memory MEM1 , MEM2, MEM3. The one or more tasks of the control unit CTRL may comprise the calculative steps of the method presented herein. The one or more tasks of the control unit CTRL may comprise at least calculating a difference spectrum DIFF1 by subtracting the reference spectrum REF1 from the encoded spectrum ENC1 whereby the difference spectrum DIFF1 contains said modulations MODI , MOD2. The one or more tasks of the control unit CTRL may further comprise converting the difference spectrum into a digital time signal SIG1 . The digital time signal SIG1 contains time information TIME1 , TIME2, corresponding to at least one modulation MODI , MOD2. The one or more tasks of the control unit CTRL may further comprise controlling operation of the apparatus 100.

[0061] Figures 3a-3d schematically present the formation of the modulations MODI , MOD2. Figure 3a presents an intensity profile of a supercontinuum probe B4. Figure 3b presents an intensity profile of a modulated supercontinuum BMOD together with a train of pump pulses B0. Figure 3c presents an encoded spectrum ENC1 , i.e., an optical spectrum of the modulated supercontinuum BMOD. Figure 3d presents a difference spectrum DIFF1 , i.e., an optical spectrum of the modulated supercontinuum with the reference spectrum subtracted from the encoded spectrum. The modulations MODI , MOD2 are easiest to determine and to process from the difference spectrum DIFF1 , because the spectral features of the supercontinuum B4 are removed.

[0062] The presented method may correspondingly comprise calculating a digital time signal SIG1 from the encoded spectrum ENC1. The digital time signal SIG1 contains time information TIME1 , TIME2 corresponding to at least one modulation MODI , MOD2. Calculating the digital time signal may utilize computational methods.

[0063] Calculating the time signal is illustrated in Figure 6. A spectrum S(A) as a function of wavelength A is presented. The spectrum S(A) may be, e.g., the encoded spectrum ENC1 or the difference spectrum DIFF1. Only one modulation MODI is illustrated in Figure 6 for clarity. The wavelength difference AA between the first and second spectral position depends on the magnitude of the temporal dislocation as a function of time. The wavelength difference AA can be converted into time through calibrated chirp of the supercontinuum probe. In other words, the control unit CTRL may be configured to convert the wavelength difference into time information TIME1 , TIME2 through calibrated chirp of the supercontinuum probe. Correspondingly, the method may comprise converting the wavelength difference AA into time information TIME1 , TIME2 through calibrated chirp of the supercontinuum probe.

[0064] The calibrated chirp of the supercontinuum probe should be in the course of this invention understood as a known change of frequency in the supercontinuum probe with time.

[0065] Figures 8 and 9a-9f present a temporal dislocation signal as a function of wavelength. As can be noted from the figure, the spectral position of the modulation shifts by several tens of nanometers upon slight variations in the time of arrival of the pump pulse at the nonlinear element NL1. The spectral shift is easily measurable, and the temporal dislocation may be determined from the wavelength difference, or in other words, spectral position of the modulation signal.

[0066] The presented method may further comprise calculating a difference spectrum DIFF1 by subtracting the reference spectrum REF1 from the encoded spectrum ENC1. The resulting difference spectrum DIFF1 contains said modulations M0D1 , M0D2. Said calculation of the digital time signal SIG1 may comprise calculating the difference spectrum DIFF1.

[0067] The modulations M0D1 , M0D2 induced by the interaction between the pump pulses BO with the nonlinear element NL1 are time-dependent. Slight deviations in the time of arrival of the pump pulses BO at the nonlinear element induce frequency shifts in the modulations MODI , MOD2. Thanks to the high nonlinear response of the epsilon-near-zero material ENZ1 , the frequency shifts in the modulations MODI , MOD2 are measurable and identifiable in the spectral domain in the encoded spectrum ENC1 and in the difference spectrum DIFF1. The cross-phase modulation in the epsilon-near-zero material ENZ1 is high enough to allow the separation the time information TIME1 , TIME2 even in a femtosecond time scale.

[0068] The cross-phase modulation is enhanced when using the at least one overlayer OL1 , especially when the overlayer OL1 is arranged as a plurality of antennae structures ANTI . The use of antennae structures ANTI may decrease the peak power of the pump pulses BO required to produce the modulations M0D1 , M0D2. A metasurface MS1 is formed of the active material ACT1 , such as the epsilon-near-zero material ENZ1 and the overlying layer OL1 , such as the antennae structures ANTI . The change in phase modulation of the supercontinuum probe as it passes through the nonlinear element NL1 comprising the metasurface MS1 is closely related to the change in the refractive index of the metasurface MS1. The relationship between the change of the phase ( ) and the change in the refractive index ( n) can be described as where d is the thickness of the medium through which the supercontinuum probe B4 passes, i.e. , thickness of the metasurface MS1 , ngis the group index in the nonlinear region of the metasurface, and is the wavelength of the supercontinuum probe B4. The group index ngmay slow down the velocity of the propagating waves by up to 0.005c, where c is the light velocity. Thickness of the metasurface MS1 is dictated by the thicknesses of the active material ACT1 and the overlying layer OL1 , and may thus be in the range of 20 nm to 1 pm, such as 20 to 500 nm, preferably 20 to 250 nm. The phase change is directly proportional to the change of the refractive index. Although the thickness is very small compared to the wavelength of the supercontinuum probe, the metasurface MS1 provides a remarkable cross-phase modulation due to i) the large nonlinear response of the metasurface MS1 , whereby the intensity of the pump pulses B0 induce a large change of refractive index, ii) enhancement and confinement of electric field within the active material ACT 1 , particularly the epsilon-near-zero material ENZ1 , and iii) strong coupling between the active material ACT1 , particularly the epsilon-near-zero material ENZ1 and the overlying layer OL1 , particularly the plurality of antennae structures ANTI , forming the metasurface MS1. Therefore, the cross-phase modulation provided by the metasurface MS1 , particularly, the epsilon-near- zero material ENZ1 combined with the antennae structures ANTI , is stronger than when using the epsilon-near-zero material alone, without the antennae structures ANTI . Hence, the temporal accuracy may increase to the femtosecond or even to the sub-femtosecond time scale, and the required peak pulse intensity is decreased.

[0069] Referring to Figures 1 and 2a, the apparatus 100 may further comprise a communication interface RXTX1 configured to receive a trigger signal SIG0 and / or to communicate time signals SIG1. The communication interface may further be configured to receive and / or to communicate any of the measured or calculated spectra, i.e., any of the reference spectrum REF1 , the encoded spectrum ENC1 , and the difference spectrum DIFF1. The communication interface RXTX is configured to perform digital communications for example over a wired or wireless connection. Examples of the connections comprise field bus technologies such as Profibus, Scanbus, Internet Protocol and Ethernet connections, radio networks, or personal area networking systems such as Bluetooth®.

[0070] The communication interface RXTX1 may be configured to receive trigger signals SIG0. The trigger signals SIG0 may be selected from, e.g., a digital time signal or a trigger light pulse. Start of a chemical transformation, e.g., due to an excitation light pulse, may also serve as the trigger signal SIG0. The communication interface RXTX1 may be configured to further communicate the trigger signal SIG0 to the control unit CTRL1 . The control unit CTRL1 may correspondingly be configured to control operation of the apparatus 100 based on the trigger signal SIG0, such as configured to initiate the presented method to produce time information TIME1 , TIME2 synchronized with the trigger signal SIG0. Thus, the presented apparatus and method may be used to synchronize time signals at an accuracy in the femtosecond or even in the sub-femtosecond time scale.

[0071] Correspondingly, the presented method may further comprise receiving the trigger signal SIG0 by the communication interface RXTX1. The method may further comprise communicating the trigger signal SIG0 by the communication interface RXTX1 to the control unit CTRL1 . The method may further comprise controlling the operation of the apparatus 100 by the control unit CTRL1 based on the trigger signal SIG0, such as initiating the presented method to produce time information TIME1 , TIME2 synchronized with the trigger signal SIG0.

[0072] The communication interface RXTX1 may further comprise one or more ports configured to receive trigger signals SIG0 and / or to communicate time signals SIG1. The one or more ports may comprise one or more digital input ports configured to receive trigger signals (SIG0), and / or one or more digital output ports configured to communicate any of the reference spectrum REF1 , the encoded spectrum ENC1 , the difference spectrum DIFF1 , and the time signals SIG1.

[0073] Referring to Figures 1 , 2a and 2b, the apparatus may comprise a supercontinuum probe generator WG1. The supercontinuum probe generator WG1 comprises all necessary means for generating the supercontinuum probe B4.

[0074] As illustrated in Figure 2a, the supercontinuum probe generator may comprise a pulsed laser LAS2 configured to produce first light pulses B1. The pulsed laser LAS2 may be arranged as an individual laser source, as illustrated in Figure 2a. Alternatively, the pump pulse generator LAS1 and the supercontinuum probe pulse generator may be arranged as a single pulse generator, as illustrated in Figure 2b. In the latter situation, the apparatus 100 further comprises a beam splitter BS configured to separate the first light pulses B1 from the pump pulses B0.

[0075] The supercontinuum probe generator WG1 may further comprise a second- harmonic generator SHG configured to produce second light pulses B2 from the first light pulses B1 . The second light pulses B2 may have a frequency two times that of the first light pulses B1. The second harmonic generator SHG may be a typical nonlinear crystal based on, e.g., beta-barium borate, lithium triborate, potassium dideuterium phosphate, potassium titanyl phosphate, and / or cesium lithium borate.

[0076] The supercontinuum probe generator WG1 may further comprise a supercontinuum generator SCG to produce supercontinuum pulses B3 from the second light pulses B2. Examples of suitable supercontinuum generators include transparent optical materials such as photonic crystal fibers, sapphire crystals, quartz crystals, calcium fluoride CaF2, and any combination thereof. The supercontinuum probe generator WG1 may further comprise a pulse stretcher PS configured to dispersively stretch the supercontinuum pulses B3 in the time domain to produce the supercontinuum probe B4. Polarizationmaintaining fibre spools, prisms, diffraction gratings and prisms, i.e., combinations of prisms and gratings, may be used as the pulse stretcher PS.

[0077] Generating the supercontinuum probe B4 in the presented method may correspondingly comprise

[0078] - producing first light pulses B1 by the pulsed laser LAS2,

[0079] - producing second light pulses B2 from the first light pulses B1 by the second-harmonic generator SHG, the second light pulses B2 having a frequency two times that of the first light pulses B1 ,

[0080] - producing supercontinuum pulses B3 from the second light pulses B2 by the supercontinuum generator SCG; and

[0081] - dispersively stretching the supercontinuum pulses B3 in the time domain by the pulse stretcher PS to produce the supercontinuum probe B4.

[0082] Referring to Figure 2b, the apparatus 100 may further comprise a translation stage TS. The translation stage TS is configured to adjust the temporal overlap between the pump pulses B0 and the supercontinuum probe B4 at the nonlinear element NL1. The one or more tasks of the control unit CTRL may thus further comprise controlling the translation stage TS to adjust the temporal overlap between the pump pulses B0 and the supercontinuum probe B4 at the nonlinear element NL1. The translation stage TS may be a pair of accurately transportable stages equipped with mirrors, with actuators or one or more motors configured to adjust the mutual distance between the transportable stages. The method may correspondingly comprise controlling the translation stage TS by the control unit CTRL to adjust the temporal overlap between the pump pulses B0 and the supercontinuum probe B4 at the nonlinear element NL1. The temporal overlap between the pulses may be adjusted, e.g., in the range of -500 to 500 fs, such as -200 to 200 fs, defined as the temporal difference between the arrival of the pump pulse BO and the supercontinuum probe at the nonlinear element NL1 .

[0083]

[0084] Linear transmission response of the samples used in Examples 2 and 3 (see below) were simulated and measured experimentally, respectively.

[0085] The experimental transmission response was measured at the visible range at 400-900 nm using a Flame spectrometer by Ocean Optics, Inc. and at the NIR range at 900-1600 nm using a Quest spectrometer by Ocean Optics, Inc.

[0086] The linear transmission spectra of the simulated and experimental samples are presented in Figure 7. The linear response was simulated with different incident angles at 0°, 20°, and 30°. The experimental response was measured with 0° incident angle. The linear transmission response has a local maximum at around 1200 nm, making this wavelength range interesting for the probing. As can be seen in the linear transmission spectra, the linear response is low at 600-800 nm and at 1500-1800 nm. Thus, the pump wavelengths for the modulation spectra are selected in these ranges.

[0087] Example 2: Simulated modulations

[0088] Spectral shift produced by the cross-phase modulation at a nonlinear element comprising an epsilon-near-zero material and antennae structures was simulated with a selection of pumping wavelengths and incident angles. 775 nm and 1600 nm were selected as the pump wavelengths. At 1600 nm, the modulations were simulated at incident angles of 0°, 20°, and 30°.

[0089] Indium tin oxide (ITO) was used as the epsilon-near-zero material in the simulation. Thickness of the ITO layer was selected to be 40 nm. Crossshaped gold (Au) structures were simulated as the antennae structures. The Au antennae structures have a thickness of 30 nm (Sz direction), length of 390 nm (Sy direction) and width of 140 nm (Sx direction). Periodicity, i.e., distance between respective edges between two adjacent nanostructures was 785 nm. The nonlinear element was simulated to be pumped by a mode-locked laser at 775 nm at an intensity of 16 GW / cm2, and at 1600 nm at an intensity of 4 GW / cm2.

[0090] Results of the simulation are presented in Figures 8 (775 nm pump) and 9a- 9c (1600 nm pump). The modulation signal was simulated over a range of delay times -160 fs to 240 fs, the delay time being defined as the difference between the time of arrival of the pump pulse compared to the time of arrival of the probe pulse at the nonlinear element. The modulated spectra S(A) were plotted as a function of wavelength A. The modulated spectra are separated from each other in the S(A) axis for clarity. The vertical dashed line in Figure 8 is placed at the maximum of the modulation spectrum at 0 fs delay between the pump and probe pulse, i.e. , at 1320 nm. The vertical line in Figures 9a-9c is placed at the maximum of the linear response, i.e., at 1220 nm.

[0091] The spectral shift in the modulation can be clearly seen in the simulated modulation spectra in Figures 8 and 9a-9c. The spectral shift swifts from the long-wavelength side to the short-wavelength side of the linear transmission maximum when shifting from negative time difference to positive time difference between the pump and probe pulses. modulations

[0092] Spectral shift produced by the cross-phase modulation at a nonlinear element comprising an epsilon-near-zero material and antennae structures was measured experimentally.

[0093] Similar sample characteristics were used for the experimental samples than for the simulations in Example 2. Indium tin oxide (ITO) was used as the epsilon-near-zero material. Thickness of the ITO layer was selected to be 40 nm. Cross-shaped gold (Au) structures were used as the antennae structures. The Au antennae structures have a thickness of 30 nm (Sz direction), length of 390 nm (Sy direction) and width of 140 nm (Sx direction). Periodicity, i.e., distance between respective edges between two adjacent nanostructures was 785 nm. The nonlinear element was pumped by a mode-locked laser at 1600 nm at an intensity of 4 GW / cm2

[0094] Results of the experiment, with a detection wavelength (probe) range of 1000- 1400 nm, i.e. , centered around 1200 nm, are presented in Figures 9d-9f. The modulation signal was simulated over a range of delay times -120 fs to 240 fs, the delay time being defined as the difference between the time of arrival of the pump pulse compared to the time of arrival of the probe pulse at the nonlinear element. The modulated spectra were plotted as a function of wavelength A. The modulated spectra are separated from each other in the vertical axis for clarity. The vertical dashed line in Figures 9d-9f is at the peak wavelength of the linear response, i.e., at 1220 nm.

[0095] The spectral shift in the modulation can be clearly seen in the experimental modulation spectra in Figures 8d-f. The spectral shift is less pronounced than in the simulations, but measurable and quantifiable, particularly at 0° incident angle (Fig. 9d).

Claims

Claims:

1. An optical apparatus (100) for producing time information (TIME1 , TIME2), comprising- a pump pulse generator (LAS1 ) configured to produce pump pulses (B0);- a supercontinuum probe generator (WG1 ) configured to produce a supercontinuum probe (B4);- a nonlinear element (NL1 ) comprising at least an active material (ACT1 ), wherein the nonlinear element (NL1 ) is configured to produce a modulated supercontinuum (BMOD) containing modulations (MODI , MOD2) caused by cross-phase modulation between the pump pulses (B0) and the supercontinuum probe (B4) due to interaction with the nonlinear element (NL1 );- a means for periodically preventing and for allowing the pump pulses (B0) to interact with the nonlinear element (NL1 ); and- a spectral analyser (OSA1 ) configured to measure at least an encoded spectrum (ENC1 ) comprising an optical spectrum of the modulated supercontinuum (BMOD).

2. The apparatus according to claim 1 , wherein the supercontinuum probe (B4) is a dispersively stretched supercontinuum pulse, and wherein the supercontinuum probe generator comprises- a pulsed laser (LAS2) configured to produce first light pulses (B1 ),- a second-harmonic generator (SHG) configured to produce second light pulses (B2) from the first light pulses (B1 ), the second light pulses (B2) having a frequency two times that of the first light pulses (B1 );- a supercontinuum generator (SCG) to produce supercontinuum pulses (B3) from the second light pulses (B2);- a pulse stretcher (PS) configured to dispersively stretch the supercontinuum pulses (B3) in the time domain to produce the supercontinuum probe (B4).

3. The apparatus (100) according to any of the preceding claims, wherein the apparatus (100) further comprises at least one of- a control unit (CTRL) configured to perform one or more tasks by executing a computer program code being stored on a memory (MEM1 , MEM2, MEM3), the one or more tasks comprising at least: calculating a difference spectrum (DIFF1 ) by subtracting a reference spectrum (REF1 ) from the encoded spectrum (ENC1 ), whereby the difference spectrum (DIFF1 ) contains said modulations (MODI , MOD2); converting the difference spectrum into a digital time signal (SIG1 ) containing time information (TIME1 , TIME2) corresponding to each modulation (MODI , MOD2); and controlling operation of the apparatus (100);- a communication interface (RXTX1 ) configured to receive trigger signals (SIG0) and / or to communicate time signals (SIG1 ); and / or- a translation stage (TS) configured to adjust the temporal overlap between the pump pulses (B0) and the supercontinuum probe (B4) at the nonlinear element (NL1 ); and / or wherein the one or more tasks of the control unit (CTRL) further comprise controlling the translation stage (TS) to adjust the temporal overlap between the pump pulses (B0) and the supercontinuum probe (B4) at the nonlinear element (NL1 ).

4. The apparatus (100) according to any of the preceding claims, wherein the communication interface (RXTX1 ) further comprises one or more ports configured to receive trigger signals (SIG0) and / or to communicate time signals (SIG1 ), wherein the one or more ports may comprise one or more digital input ports configured to receive trigger signals (SIG0), and / or one or more digital output ports configured to communicate any of the reference spectrum (REF1 ), the encoded spectrum (ENC1 ), the difference spectrum (DIFF1 ), and the time signals (SIG1 ).

5. The apparatus (100) according to any of the preceding claims 2 to 4, wherein the pump pulse generator (LAS1 ) and the supercontinuum probe pulse generator are arranged as a single pulse generator, whereby the apparatus (100) further comprises a beam splitter (BS) configured to separate the first light pulses (B1 ) from the pump pulses (B0).

6. The apparatus (100) according to any of the preceding claims, wherein the pump pulses (B0) have a wavelength in the range of 600-2000 nm, preferablyin the range of 700-800 nm or in the range of 1500-2000 nm, particularly preferably in the range of 1500-1800 nm.

7. The apparatus (100) according to any of the preceding claims, wherein the spectral analyser (0SA1 ) is a dual channel spectral analyser configured to record the encoded spectrum (ENC1 ), and configured to record the reference spectrum (REF1 ) at a probe reference channel.

8. An optical method for producing time information (TIME1 , TIME2) using the apparatus (100) according to any of the claims 1 to 6, comprising- generating pump pulses (B0) using the pump pulse generator (LAS1 );- generating a supercontinuum probe (B4) using the supercontinuum probe pulse generator (WG1 );- producing a modulated supercontinuum (BMOD) containing modulations (M0D1 , M0D2) caused by cross-phase modulation between the pump pulses (B0) and the supercontinuum probe (B4) due to interaction with the nonlinear element (NL1 );- measuring an encoded spectrum (ENC1 ) by the spectral analyser (OSA1 ), the encoded spectrum (ENC1 ) comprising an optical spectrum of the modulated supercontinuum (BMOD);- calculating a digital time signal (SIG1 ) from the encoded spectrum (ENC1 ), the time signal containing time information (TIME1 , TIME2) corresponding to at least one modulation (MODI , MOD2).

9. The method according to claim 8, wherein generating the supercontinuum probe (B4) comprises- producing first light pulses (B1 ) by the pulsed laser (LAS2),- producing second light pulses (B2) from the first light pulses (B1 ) by the second-harmonic generator (SHG), the second light pulses (B2) having a frequency two times that of the first light pulses (B1 ),- producing supercontinuum pulses (B3) from the second light pulses (B2) by the supercontinuum generator (SCG); and- dispersively stretching the supercontinuum pulses (B3) in the time domain by the pulse stretcher (PS) to produce the supercontinuum probe (B4).

10. The method according to claim 8 or 9, further comprising at least one of- receiving a trigger signal (SIGO) by a communication interface (RXTX1 );- measuring a reference spectrum (REF1 ) by the spectral analyser (OSA1 ), the reference spectrum (REF1 ) comprising an optical spectrum of the supercontinuum probe (B4) while preventing the pump pulses (BO) from interacting with a nonlinear element (NL1 ), wherein the nonlinear element (NL1 ) comprises at least an active material (ACT1 );- calculating a difference spectrum (DIFF1 ) by subtracting the reference spectrum (REF1 ) from the encoded spectrum (ENC1 ), whereby the difference spectrum (DIFF1 ) contains said modulations (MODI , MOD2); and- controlling a translation stage (TS) by the control unit (CTRL) to adjust the temporal overlap between the pump pulses (BO) and the supercontinuum probe (B4) at the nonlinear element (NL1 ).

11. The apparatus (100) according to any of claims 1 to 7 or the method according to any of claims 8 to 10, wherein the nonlinear element (NL1 ) further comprises a metasurface (MS1 ) arranged on top of active material (ACT1 ).

12. The apparatus (100) or the method according to claim 11 , wherein the metasurface (MS1 ) is arranged as a plurality of antennae structures (ANTI ), preferably wherein the antennae structures (ANTI ) comprise metal or nitride materials, more preferably wherein the antennae structures are selected from the group comprising gold, silver aluminium, titanium nitride (TiN), zirconium nitride (ZrN), and any combination thereof.

13. The apparatus (100) or the method according to any of the preceding claims, wherein the active material (ACT1 ) of the nonlinear element (NL1 ) comprises an epsilon-near-zero material (ENZ1 ).

14. The apparatus (100) or the method according to claim 13, wherein the epsilon-near-zero material (ENZ1 ) comprises a material that exhibits a real permittivity value approaching zero at an active wavelength region, preferably wherein the epsilon-near-zero material is selected from the group comprising semi-transparent conductive oxides such as indium tin oxide (ITO), aluminium- doped zinc oxide (AZO), nitrides, nanomaterials, and any combination thereof.

15. The apparatus (100) or the method according to claim 14, wherein the active wavelength region is in the range of 300-2500 nm, preferably in the range 400-2500 nm, more preferably in the visible region at 300-750 nm or in the infrared region at 750-2000 nm, even more preferably in the infrared region at 1000-1500 nm.

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