Non-compressed and single-beam generation of carrier-envelope-phase-stable optical pulses

Abstract

The present invention specifically relates to a method and system for generating CEP-stable optical pulses from input optical pulses having an optical carrier frequency f i of the optical carrier frequency f p and a pulse duration T p . A birefringent medium, a non-nonlinear medium, a dispersive optical system, and a parametric device (DFG) are continuously used to achieve this generation.

Description

Technical Field

[0001] Embodiments of the present invention generally relate to the field of optical systems and methods for generating carrier-envelope phase-stable (CEP-stable) optical pulses. Background Art

[0002] Pulsed laser sources are characterized by the temporal confinement of optical emission. The electric fields of these pulses are typically described in terms of an envelope and a carrier. The electric field of these pulses is the product of an oscillatory field with a period denoted as T0 = λ0 / c (optical carrier) and a slowly varying function on the scale of T0 (envelope). For ultrafast laser sources, the duration of the envelope is typically on the order of a few tens of femtoseconds (1 femtosecond = 10 -15 seconds), which is generally greater than the duration of the optical cycle in the near-infrared and mid-infrared. For example, at 800 nm, the optical cycle is 2.7 femtoseconds.

[0003] For certain applications, a pulse duration on the order of a few optical cycles (hereinafter referred to as few-cycle pulses) is advantageous. The electric field then approaches a transient field, which is a condition that is favorable for applications such as, for example, high-harmonic generation in gases or solids. Such pulses can in particular effectively generate attosecond pulses with durations that can reach a few tens of attoseconds (1 attosecond = 10 -18 seconds). An example is given by K. Zhao et al. in "Tailoring a 67 attosecond pulse through advantageous phase-mismatch", Optics Letters 37, 3891-3893 (2012).

[0004] The carrier-envelope phase (CEP) refers to the relative phase between the envelope and the carrier. The shot-to-shot stability of the CEP is crucial for maintaining the characteristics of the electric field from one pulse to another. This stability is crucial in the case of high-harmonic generation, as described by A. et al. in "Attosecond control of electronic processes by intensive light field", Nature 421, 611 (2003).

[0005] CEP can be modified by dispersive elements characterized by non-equal group refractive index and phase refractive index, such as bulk media (glass, gas, ...) or pairs of angular dispersive elements (grating pairs, prism pairs, ...). The fluctuations of the beam path in such dispersive elements are the main source of CEP fluctuations or drifts in ultrafast laser systems.

[0006] Filamentation is a non-linear optical process that allows a beam to propagate through a medium without diffraction. This self-guiding phenomenon requires the laser peak power to be higher than a threshold power called the critical power, and approximately equal to 0.15 * λ0 2 / (8π * n0 * n2), where n0 and n2 are the linear and non-linear optical refractive indices of the propagation medium, respectively. Filamentation of sub-picosecond or picosecond pulses broadens the input pulse through self-phase modulation and other cascaded non-linear processes, potentially leading to the generation of a broadband spectral continuum. Under some conditions (single-filament regime), filamentation maintains CEP shot-to-shot stability. An example of a continuum generated by sub-picoseconds is given in "Femtosecond continuum generation in bulk laser host materials with sub-μJ pump pulse" by M. Bradler et al., Applied Physics B 97.3 (2009): 561.

[0007] The stabilization of CEP requires complex and expensive devices, and its implementation is usually complex. The so-called passive and active stabilization methods are usually distinguished according to the presence (active) or absence (passive) of a feedback mechanism to stabilize CEP.

[0008] As an example of an active feedback mechanism for stabilizing CEP, the literature "High-energy pulse synthesis with sub-cycle waveform control for strong-field physics" by S-W Huang et al., Nature Photonics 5, 475 - 479 (2011) describes a source concept that includes an ultrafast pulse generator with actively stabilized CEP phase, a device for expanding the spectrum of these pulses into the infrared, two pulse shapers, two optical parametric amplifiers pumped non-collinearly by two pump wavelengths, and a phase system controlled by a measurement device based on cross-correlation detection.

[0009] As an example of a passive feedback mechanism for stabilizing CEP, A. et al. in the 13th International Conference on Ultrafast Phenomena, 2002 OSA Technical Digest Series (Optical Society of America, 2002), the literature "All-optical self-stabilization of carrier-envelope phase offset in few-cycle pulses by optical parametric amplifiers" describes various passively stabilized optical schemes via second-order nonlinear processes such as difference frequency generation (DFG).

[0010] The literature describes the generation of ultrafast laser pulses by DFG. In a material with second-order nonlinear optical properties, a first optical pulse with a carrier frequency of f s (hereinafter referred to as the "signal" pulse) interacts with a second optical pulse with a carrier frequency of f p >f s (hereinafter referred to as the "pump" pulse). During the interaction, a part of the energy of the "pump" pulse is transferred to the amplified "signal" pulse. At the same time, a third optical pulse is generated and the third optical pulse is co-amplified. The carrier frequency of this third pulse, called the "idler" pulse, is equal to f p - f s . The CEP of the "idler" pulse is equal to the difference between the CEP of the "pump" signal and the CEP of the "signal" pulse within a constant. If this difference is constant in a repeatable manner (i.e., from one pulse to another), the CEP of the "idler" pulse is stable over time, even though neither the "pump" pulse nor the "signal" pulse shares this property. Since DFG is a local and instantaneous process, difference frequency generation is limited to wavelengths with approximately equal optical group delays on the DFG medium.

[0011] The generation of passively stabilized few-cycle optical pulses by DFG can be divided into two categories.

[0012] When the "signal" and "pump" waves originate from a single broadband beam, the first type is called intrapulse DFG. An example of intrapulse DFG is given in "Generation of intensity, carrier-envelope phase-locked less-cycle laser pulse through filamentation" by C.P. Hauri et al., Appl. Phys. B 79(6), 673–677 (2004).

[0013] When the "signal" and "pump" waves are two beams propagating along different optical paths, even if one beam is derived from the other, the second type is called interpulse DFG. A common implementation of this configuration is to generate the "signal" beam from the "pump" through filamentation in a bulk crystal. The literature "Carrier-envelope phase stable, few-optical-cycle pulses tunable from visible to near IR" by G. Cirmi, C. Manzoni, D. Brida, S. De Silvestri and G. Cerullo, J. Opt. Soc. Am. B 25, B62-B69 (2008) discloses Figure 1 the example of interpulse DFG shown.

[0014] In principle, the CEP stability of the optical pulses generated by intrapulse DFG is better than that of the optical pulses generated by interpulse DFG because the "pump" and "signal" share a common optical path also called a single beam. However, intrapulse DFG requires ultra-broadband compressed pulses, which are difficult to generate and manage, especially in the μJ-order. As an example, a bandwidth of more than 300 THz would be required to generate CEP-stable pulses of about 1 μm through DFG. Compressing this bandwidth, which is equal to the optical group delay of all frequency components, is a major technical challenge that requires complex and meter-scale technical setups. An example of such a setup is given in the literature "Synthesized light transients" by Wirth, Adrian et al., Science 334.6053 (2011): 195-200.

[0015] In addition, known systems for generating stable optical pulses via DFG require the use of mirrors that increase the overall size of such systems. In addition, the presence of a beam splitter means that the light takes different paths, resulting in instability in the relative path lengths of the "pump" and "signal" beams, and thus instability in the CEP of the "idler" beam.

[0016] Therefore, there is a need to improve the generation of CEP-stable optical pulses at a given optical carrier frequency from an input optical pulse by avoiding both beam splitting and pulse compression. SUMMARY OF THE INVENTION

[0017] According to a first aspect, the invention is implemented as a single-beam and non-compressive optical system for generating a carrier-envelope phase-stable (CEP-stable) optical pulse at an optical carrier frequency f i from an input optical pulse having an optical carrier frequency f p and a pulse duration T p . The optical system comprises:

[0018] - a birefringent medium (B) for receiving the input optical pulse at the input; and for providing pairs of linearly polarized pulses (PP) as output in such a way that each pair of linearly polarized pulses (PP) has orthogonal polarizations along a first direction and a second direction (E1, E2) and each pair of linearly polarized pulses (PP) has a relative optical group delay approximately equal to or greater than the pulse duration (T p ) of the input optical pulse;

[0019] - a non-linear medium (NL) for receiving the output of the birefringent medium (B) at the input; and for providing pairs of linearly polarized pulses (PP) as output in such a way that at least one of the two pulses of each pair of linearly polarized pulses (PP) is spectrally broadened;

[0020] - a transparent dispersive optical system (O) for receiving the output of the non-linear medium (NL) at the input; and for providing pairs of linearly polarized pulses (PP) as output in such a way that there is full or partial temporal overlap between the two pulses of each pair of linearly polarized pulses (PP);

[0021] - a parametric device (DFG) for receiving the output of the transparent dispersive optical system (O) at the input; and for providing as output a frequency difference between a frequency component polarized along the first direction (E1) and a frequency component polarized along the second direction (E2).

[0022] The optical system may further comprise:

[0023] - A filter (F) for receiving the output of the parametric device (DFG) in an input; and for providing extraction of the frequency difference of the output of the parametric device (DFG) as an output;

[0024] - The filter is a dichroic mirror;

[0025] - A waveplate for controlling the polarization state of the input optical pulse;

[0026] - An optical device placed between the optical system (O) and the parametric device (DFG), the optical device being adapted to receive the output of the dispersive optical system (O) in an input; and for focusing the output of the dispersive optical system (O) on the parametric device (DFG);

[0027] - The birefringent medium (B) has a thickness equal to or greater than 100 μm, and the birefringent medium includes at least one crystal selected from calcite crystal, quartz crystal, α-BBO crystal, YVO4 crystal, and TeO2 crystal;

[0028] - The dispersive optical system (O) includes at least one material selected from a glass window, YAG crystal, thick lens, calcite crystal, quartz crystal, α-BBO crystal, YVO4 crystal, and TeO2 crystal;

[0029] - The nonlinear medium (NL) includes at least one material selected from YAG crystal, sapphire crystal, calcium fluoride crystal, and fused silica window;

[0030] - The parametric device (DFG) is a second-order nonlinear crystal including at least one material selected from β-BBO, LBO, LiNbO3, LiIO3, KTA, LGS, and AGS;

[0031] - The parametric device (DFG) is a nonlinear crystal characterized by a second-order susceptibility;

[0032] According to another aspect, the present invention can be implemented as a method for generating a carrier-envelope phase-stable (CEP-stable) optical pulse having an optical carrier frequency f i from an input optical pulse, the input optical pulse having an optical carrier frequency f p and a pulse duration T p . The method includes:

[0033] - Providing the input optical pulse having an optical carrier frequency f p and a pulse duration T p ;

[0034] - Generating pairs of linearly polarized pulses (PP) from the provided input optical pulses through a birefringent medium (B), each pair of linearly polarized pulses (PP) having orthogonal polarizations along a first direction and a second direction (E1, E2) and each pair of linearly polarized pulses (PP) having a relative optical group delay approximately equal to or greater than the pulse duration (T p ) of the input optical pulse;

[0035] - Triggering filamentation of at least one of the two pulses of each pair of linearly polarized pulses (PP) through a nonlinear medium (NL), at least one of the two pulses of each pair of linearly polarized pulses (PP) being spectrally broadened due to filamentation;

[0036] - Temporally overlapping (40) the two pulses of each pair of linearly polarized pulses (PP) from the output of the nonlinear medium (NL) through a dispersive optical system (O); and

[0037] - Generating a frequency difference between a frequency component polarized along the first direction (E1) and a frequency component polarized along the second direction (E2) through a parametric device (DFG).

[0038] The method may further include

[0039] - Extracting (60) the generated frequency difference through a filter;

[0040] - Focusing (42) the output of the optical system (O) onto the parametric device (DFG) through an optical device;

[0041] - Adjusting (12) the energy distribution between the two pulses of the pulse pair generated by the birefringent medium through a wave plate.

[0042] According to another aspect, the present invention may be implemented as a light source unit for generating carrier - envelope - phase - stable (CEP - stable) optical pulses of an optical carrier frequency f i from input optical pulses. The light source unit includes a pulse generator for delivering the input optical pulses, the input optical pulses having an optical carrier frequency f p , a pulse duration T p and being linearly polarized, an optical system adapted to receive the input optical pulses, and an optical amplifier adapted to amplify the output of the optical system.

[0043] The systems, products, and methods embodying the present invention will now be described by way of non - limiting examples and with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Showing an example of an inter - pulse DFG scheme of the prior art;

[0045] Figure 2 An example showing the principle of the system of the present invention;

[0046] Figure 3 Another example showing the system of the present invention;

[0047] Figure 4 An example showing the temporal waveform of the optical pulse in the system;

[0048] Figure 5 A schematic block diagram showing an example of the method of the present invention.

[0049] Unless otherwise indicated, similar or functionally similar elements in the drawings have been assigned the same reference numerals. Detailed Description

[0050] Reference Figure 2 , an optical system for generating a carrier-envelope-phase-stable optical pulse from an input optical pulse with an optical carrier frequency f i is presented. The carrier-envelope phase will be referred to as CEP hereinafter. The optical system is adapted to generate a CEP-stable optical pulse from an input optical pulse having an optical carrier frequency f p and a pulse duration T p . Thus, the optical system is suitable (or adapted) to receive an input optical pulse at the input and generate a CEP-stable optical pulse, which is provided as the output of the optical system. Now, the optical system will be discussed.

[0051] The system includes a birefringent medium (B). Birefringence is an optical property of a material having refractive indices that depend on the polarization and propagation direction of light. The simplest type of birefringence is described as uniaxial, which means that there is a single direction that controls the optical anisotropy. Rotating the material around this axis (referred to as the optical axis) does not change its optical behavior. For simplicity, only uniaxial crystals will be considered below. However, it should be understood that biaxial crystals can also be used to produce the desired optical properties.

[0052] Light whose polarization is perpendicular to the optical axis of the birefringent medium (B) is controlled by the refractive index n o (for "ordinary"). Light whose polarization direction is along the optical axis direction of the birefringent medium (B) experiences an optical index n e (for "extraordinary"). The two polarizations (i.e., ordinary polarization and extraordinary polarization) are orthogonal along the first direction and the second direction (E1, E2) respectively; the first direction and the second direction are orthogonal. The ordinary group delay is also different from the extraordinary group delay; in other words, the time for an optical pulse with polarization perpendicular to the optical axis to pass through the birefringent medium (B) is different from the time for an optical pulse with polarization in the optical axis direction to pass through the birefringent medium (B). This delay is denoted as T hereinafter.

[0053] The delay T notably depends on the thickness of the birefringent medium (B). The delay T is given by the following equation (1):

[0054] T = |n g,e - n g,o | * L / c (1)

[0055] where n g,e represents the extraordinary group delay,

[0056] n g,o represents the ordinary group delay,

[0057] L is the thickness of the medium,

[0058] c is the speed of light in a vacuum.

[0059] The birefringent medium (B) is adapted to split an input optical pulse into two linearly polarized pulses. The two linearly polarized pulses at the output of the birefringent medium (B) are consecutive and separated by a time delay equal to T. Thus, the birefringent medium (B) generates a pair of orthogonally linearly polarized pulses for each input optical pulse: one polarized pulse is perpendicularly polarized in the direction of the optical axis (first direction) of the birefringent medium (B) - the ordinary polarized pulse, and one polarized pulse is polarized in the direction of the optical axis (second direction) of the birefringent medium (B) - the extraordinary polarized pulse. The pair of pulses can be consecutive pulses.

[0060] Thus, the birefringent medium (B) is adapted to provide a pair of linearly polarized pulses (PP) from an input optical pulse. The pair of pulses includes an ordinary polarized pulse and an extraordinary polarized pulse having orthogonal polarizations along the first direction and the second direction (E1, E2). The traversal of the input optical pulse through the birefringent medium (B) introduces a relative optical group delay between the pair of ordinary polarized pulse and extraordinary polarized pulse.

[0061] The delay between the pair of ordinary polarized pulse and extraordinary polarized pulse can be approximately equal to or greater than the pulse duration of the input optical pulse (T p ). This ensures that the pair of pulses do not significantly overlap in time; in other words, the extraordinary component and the ordinary component of the electric field do not significantly overlap in time.

[0062] The birefringent medium (B) avoids using a pulse separator for splitting an input optical pulse into two or more output pulses. Thus, the system is more compact because introducing a delay between at least two pulses does not require a delay line; contrary to Figure 1 the known prior art shown. Furthermore, no reflective optical devices are involved in generating at least two pulses from an input optical pulse; compared with known systems, this also improves the compactness of the system of the present invention.

[0063] In an example, the birefringent medium (B) can be a calcite (CaCO3) crystal, a quartz plate (SiO2), an α-BBO (α-BaB2O4) crystal, a YVO4 crystal, a TeO2 crystal, or the like.

[0064] In an example, the thickness of the birefringent medium (B) can be equal to or greater than 100 μm.

[0065] In an example, the thickness of the birefringent medium (B) can be included between 1.5 mm and 6 mm.

[0066] In an example, the birefringent medium (B) can be cut at 90° from the optical axis.

[0067] In an example, the birefringent medium (B) can be oriented such that the polarization direction of the input optical pulse is approximately 56° with respect to the optical axis of the birefringent medium (B).

[0068] In a specific example, the birefringent medium (B) is a calcite crystal with a thickness between 1.5 mm and 6 mm, cut at 90° from the optical axis, oriented such that the polarization direction of the input optical pulse is approximately 56° with respect to the optical axis of the birefringent medium (B), and wherein approximately 30% of the energy of the input optical pulse is ordinary polarized and approximately 70% of the energy of the input optical pulse is extraordinary polarized. At 1030 nm, the birefringence delay T introduced between the extraordinary polarization and the ordinary polarization of the birefringent medium (B) is approximately 900 femtoseconds. In this example, the birefringence delay T is greater than the pulse duration of the input optical pulse (P), the extraordinary and ordinary components of the electric field do not significantly overlap in time, and can be considered independent pulses.

[0069] Now refer to Figure 4 , which shows an example of the temporal waveform of an optical pulse at different points in a system according to the present invention. The temporal waveform represents the variation of the intensity of the pulse (expressed in W / m 2 ) with time (expressed in femtoseconds).

[0070] The generator (P) ( Figure 4 not shown in p ) delivers short optical pulses. The input optical pulse has an optical carrier frequency f p and a pulse duration T

[0071] The temporal waveform labeled 1a) represents the wavelength λ along the first polarization direction (E1) p , the pulse duration T pThe input optical pulse. The first polarization direction (E1) is parallel to the ordinary polarization direction of the birefringent medium (B). The time waveform labeled 1g) represents the time waveform of the input pulse (P) along the second polarization direction (E2). (E2) is parallel to the extraordinary polarization direction of the birefringent medium (B). Except that the input optical pulse (P) along the extraordinary polarization direction (E2) transmits more energy, the time waveform of 1g) is the same as the time waveform of 1a).

[0072] The time waveform labeled 1b) represents the time waveform of the input pulse of waveform 1a) at the output of the birefringent medium (B). The waveform of the ordinary polarization pulse remains unchanged at the output of the birefringent medium (B). Unchanged means that waveform 1b) is substantially the same as waveform 1a): as is known in the art, due to optical dispersion, slight modification of the pulse may occur.

[0073] The time waveform 1h) represents the time waveform at the output of the birefringent medium (B) along the second polarization direction (E2). The input to the birefringent medium (B) is the pulse of waveform 1g). The time waveform 1h) is time-shifted by the group delay T with respect to the time waveform 1b). The extraordinary polarization pulse of the time waveform 1h) does not significantly overlap in time with the ordinary polarization pulse of the time waveform 1b): the extraordinary polarization pulse and the ordinary polarization pulse can be considered independent pulses. This is possible because the delay T caused by the birefringent medium (B) is greater than the pulse duration T of the input optical pulse p 。

[0074] Returning to Figure 2 , the system further includes a nonlinear medium (NL). As is known in the art, a nonlinear medium (NL) is a medium in which the polarization density responds nonlinearly to the electric field E of the pulse.

[0075] The nonlinear medium (NL) is adapted to receive at the input the output of the birefringent medium (B): the nonlinear medium (NL) receives at the input a pair of linearly polarized pulses (PP). The nonlinear medium (NL) is suitable (adapted) for spectrally broadening at least one of the two pulses in each pair of pulses received at the input. The optical properties of the nonlinear medium (NL) allow the filamentation of ordinary polarization and / or extraordinary polarization pulses. Filamentation is carried out as is known in the art.

[0076] In the example, the extraordinary polarization pulse (the pulse polarized along the second direction (E2)) can be strong enough to trigger filamentation and can be spectrally broadened. When propagating in the nonlinear medium (NL), the intensity of the ordinary polarization pulse is not sufficient to trigger filamentation and remains substantially the same: the ordinary polarization pulse is substantially the same as the pulse at the output of the birefringent material (B). At the output of the nonlinear medium (NL), due to group delay dispersion, some wavelengths of the broadened extraordinary polarization pulse may have the same optical group delay as the extraordinary polarization pulse.

[0077] In an example, the nonlinear medium (NL) can partially or fully comprise one or more materials selected from YAG (yttrium aluminum garnet) crystals, sapphire crystals, calcium fluoride crystals, fused silica windows.

[0078] In an example, the nonlinear medium (NL) can comprise a YAG crystal and have a thickness between 4 mm and 15 mm.

[0079] In a specific example, the nonlinear medium (NL) can comprise a YAG crystal having a thickness between 4 mm and 15 mm and an overlapping wavelength of approximately 655 nm.

[0080] Returning to Figure 4 , the time waveform labeled 1c) represents the time waveform of the pulse of waveform 1b) provided at the input of the nonlinear medium (NL). At the output of the nonlinear medium (NL), the waveform of the ordinary polarization pulse remains unchanged. Similarly, unchanged means that waveform 1c) is substantially the same as waveform 1b): as is known in the art, due to optical dispersion, slight modifications of the pulse may occur.

[0081] The time waveform labeled 1i) is the time waveform along the second direction of polarization (E2) at the output of the nonlinear medium (NL). Under the combination of spectral broadening and group delay dispersion, the time waveform of 1i) is broadened. The wavelength λ s is generated by the spectral broadening produced by the nonlinear medium (NL).

[0082] Referring again to Figure 4 , the output of the nonlinear material (NL) serves as the input of the dispersive optical system (O). The dispersive optical system (O) is adapted (or suitable) to have ordinary polarization pulses and extraordinary polarization pulses that are partially overlapped in time. The first solution can be to broaden the pulses in time such that they are partially overlapped in time. The second solution can be to use a birefringent crystal similar to the birefringent medium (B) but with a different orientation to cause the pulses to be partially overlapped in time. It should be understood that both solutions can be combined. It should also be understood that the pairs of linearly polarized pulses (PP) provided as the output of the nonlinear material (NL) can be fully overlapped in time.

[0083] The dispersive optical system (O) can be a bulk dispersive optical system. For example, the dispersive optical system does not include mirrors and / or is a monolithic component.

[0084] Returning to Figure 4 , the time waveform labeled 1d) represents the time waveform of the pulse of waveform 1c) at the output of the optical system (O). Compared with the output of the nonlinear medium (NL), the waveform of the ordinary polarization pulse remains unchanged at the output of the optical system (O).

[0085] The time waveform labeled 1j) shows the time waveform at the output of the optical system (O) along the second polarization direction (E2). Compared with the group delay dispersion of the time waveform 1i) provided at the input of the optical system (O), the time waveform 1j) is stretched. Interestingly, the wavelength λ along the second direction (E2) s and the wavelength λ along the first direction (E1) p have equal or very close group delays.

[0086] In an example, the dispersive optical system (O) can include at least one material selected from a glass window, a YAG crystal, a calcite (CaCO3) crystal, a quartz crystal, an α-BBO (α-BaB2O4) crystal, a yttrium orthovanadate (YVO4) crystal, a tellurium dioxide (TeO2) crystal. It should be understood that any material having optical properties that allow for pulse broadening or pulse synchronization in time can be selected.

[0087] In an example, the dispersive optical system can be a thick lens.

[0088] In an example, the optical system (O) can be an SF11 (glass code 785258) glass window.

[0089] In a specific example, the optical system (O) can include an SF11 glass window with a thickness between 1 mm and 5 mm.

[0090] Returning to Figure 2 , the system further includes a parametric device (DFG) that is adapted to receive the output provided by the dispersive optical system (O). The DFG is adapted to generate a frequency difference between a frequency component polarized along the first direction (E1) and a frequency component polarized along the second direction (E2). The DFG performs a frequency difference known in the art, where the pulse polarized along the first direction (E1) is used as the "pump" pulse and the pulse polarized along the second direction (E2) is used as the "signal" pulse.

[0091] Difference frequency generation on the DFG medium is limited to wavelengths having equal optical group delays. Thus, the generated frequency difference is f p -f s where f p is the frequency of the normally polarized pulse and f p is the frequency of the abnormally polarized pulse.

[0092] In an example, the parametric device (DFG) is a second-order nonlinear crystal comprising at least one material selected from β-BBO (barium borate in the low-temperature β-phase), LBO (lithium triborate, denoted as LiB3O5), lithium niobate (LiNbO3), lithium iodate (LiIO3), LGS (lithium gallium sulfide, denoted as LiGaS2), AGS (silver gallium sulfide, denoted as AgGaS2), KTA (potassium titanyl arsenate).

[0093] In an example, the parametric device (DFG) is a nonlinear crystal characterized by a second-order nonlinear susceptibility.

[0094] In a specific example, the parametric device (DFG) is a 100-μm thick barium borate crystal in the low-temperature β-phase, cut at an angle of approximately 52.6° for type-I phase matching. An idler wave at approximately 1800 nm is generated by difference frequency generation between components at approximately 655 nm (the "pump" wave of the DFG crystal) and at 1030 nm (the "signal" wave of the DFG crystal).

[0095] Now refer to Figure 4 , the time waveform labeled 1e) shows the time waveform along the first direction (E1) at the output of the parametric device (DFG), including the time waveform of the ordinary polarization pulse plus the time waveform of a third optical pulse (also referred to as the "idler" pulse) having a wavelength λ i (also referred to as the "idler" pulse) generated by difference frequency generation.

[0096] The difference between the CEP of the "pump" pulse and the CEP of the "signal" pulse is constant pulse-to-pulse, and the CEP of the "idler" pulse is passively stabilized, in other words, reproducible from pulse to pulse.

[0097] The time waveform labeled 1k) is the time waveform along the second direction (E2) at the output of the parametric device (DFG). The waveform of the extraordinary polarization pulse is similar to the waveform previously obtained at the output of the optical system (O).

[0098] Examples of optical systems have been referred to Figure 2 for discussion. Compared with the inter-pulse DFG scheme, the present invention is single-beam (no beam splitting), inherently phase-stable, and not affected by optical path fluctuations. In fact, as Figure 1The prior art solution shown requires the use of a beam splitter to generate two beams from an input beam, a delay line to time-delay one of the two beams, and a mirror to recombine the two beams to generate DFG. Although the present invention allows for the generation and transmission of two beams (including a delayed beam) with a single path, i.e., without the need for a mirror and / or a delay line. Thus, the system according to the present invention is more compact and less subject to beam interference. In addition, the CEP is more stable over time because there is an optical path shared by the "pump" and "signal" beams. Compared with the intra-pulse DFG scheme, the present invention does not require an ultra-wideband input pulse and does not require a compressed pulse for the DFG stage.

[0099] In Figure 2 the example, the system may further include a filter (F) whose input is adapted to receive the output of the parametric device (DFG). The filter is adapted to extract the frequency difference of the output of the parametric device (DFG) such that the optical system only outputs a third optical pulse with a wavelength of λ i . Thus, the output of the system only produces a CEP-stable optical pulse with an optical carrier frequency of f i .

[0100] In the example, the mirror can be a dichroic mirror.

[0101] In a specific example, the filter can be a dichroic mirror that suppresses wavelength components at approximately 655 nm and 1030 nm.

[0102] Figure 3 is Figure 2 an example of an optical system with other optical elements. In this example, the system further includes a wave plate between the pulse generator and the birefringent medium (B) at the optical input. Thus, the wave plate is adapted to receive the input optical pulse generated by the generator (P). The wave plate is also adapted to adjust the energy ratio between the pulses of the pulse pair generated in the birefringent medium (B). The polarization state of the input optical pulse is controlled by the wave plate, e.g., the energy distribution is balanced between the two pulses of the pulse pair to be generated by the birefringent medium. This advantageously improves filamentation in the nonlinear medium (NL).

[0103] Still referring to Figure 3 , the optical system includes at least one optical device placed between the optical system (O) and the parametric device (DFG). "Placed between" means that the optical device is on the path of the light (pulse) between the optical system (O) and the parametric device (DFG). Thus, the optical device is adapted to receive the output of the dispersive optical system (O) and is adapted to focus the output of the dispersive optical system (O) on the parametric device (DFG). Focusing the light improves the generation of DFG by the frequency difference. In this example, the optical device can be a lens adapted to focus the incident beam at the output.

[0104] At least one additional optical device (e.g., a lens) may be placed between the birefringent medium (B) and the nonlinear medium (NL) to focus the output of the birefringent medium (B) onto the nonlinear medium (NL). Filamentation is improved.

[0105] At least one additional optical device (e.g., a lens) may be placed between the parametric device (DFG) and the filter (F) to focus the output of the parametric device (DFG) onto the filter (F). The filtering performed by the filter is improved.

[0106] The elements of the system are arranged such that the light generated by the pulse generator is continuously transmitted from one element to another. For example, in Figure 2 the input optical pulse is continuously transmitted to the birefringent medium (B), the nonlinear medium (NL), the dispersive optical system (O), and the parametric device (DFG). If the system includes a filter, the pulse is ultimately transmitted to the filter. For example, in Figure 3 the input optical pulse is continuously transmitted to the wave plate, the birefringent medium (B), the first optional optical device (lens), the nonlinear medium (NL), the dispersive optical system (O), the second optional optical device (lens), the parametric device (DFG), the third optional optical device (lens), and the filter (F).

[0107] Now, another aspect of the present invention is described, which relates to a method for generating carrier - envelope - phase - stabilized (CEP - stabilized) optical pulses having an optical carrier frequency f i from an input optical pulse, the input optical pulse having an optical carrier frequency f p and a pulse duration T p . Basically, the method performs the operations implemented by the successive elements forming the system or the examples of the system discussed above.

[0108] The above - described method allows for an improvement in the generation of CEP - stabilized optical pulses. The CEP - stabilized optical pulses generated by this method are inherently phase - stabilized and are not affected by beam - path fluctuations.

[0109] The method includes providing (10) an input optical pulse having an optical carrier frequency f p and a pulse duration T p . The input optical pulse is linearly polarized. This providing may be performed by the pulse generator discussed above.

[0110] The method further includes generating (20) pairs of linearly polarized pulses (PP) from the provided input optical pulse. Each pair of linearly polarized pulses (PP) has orthogonal polarizations along a first direction and a second direction (E1, E2), and each pair of linearly polarized pulses (PP) has a pulse duration approximately equal to or greater than that of the input optical pulse (T p) relative optical group delay. This generation is performed by the birefringent medium (B) discussed above.

[0111] Then, the method further includes triggering (30) filamentation of at least one of the two pulses in each pair of pulses, and at least one of the two pulses in a pair of pulses is spectrally broadened due to filamentation. Filamentation is performed by the nonlinear medium (NL) discussed above.

[0112] The method further includes temporally overlapping (40) the two pulses in each pair of pulses from the output of the nonlinear medium (NL). This is achieved by a dispersive optical system (O).

[0113] The method further includes generating (50) a frequency difference between a frequency component polarized along a first direction (E1) and a frequency component polarized along a second direction (E2). This generation is performed by a parametric device (DFG).

[0114] The method may further include extracting (60) the generated frequency difference. This is performed by a filter as discussed Figure 2 above.

[0115] The method may further include focusing (42) the output of the birefringent medium (B) on the nonlinear medium (NL), and / or focusing the output of the optical system (O) on the parametric device (DFG), and / or focusing the output of the parametric device (DFG) on the filter.

[0116] The method may further include adjusting (12) the energy distribution between the two pulses of the pulse pair generated by the birefringent medium. This adjustment may be performed by a wave plate.

[0117] Now, another aspect of the present invention is described, which relates to a light source unit for generating a carrier - envelope - phase - stable (CEP - stable) optical pulse from an input optical pulse with an optical carrier frequency f i The light source unit includes a generator having an optical pulse with an optical carrier frequency f p and a pulse duration T p and an optical system and an optical amplifier as described above. An optical pulse is provided at the input of the optical system according to the present invention, which in turn provides a carrier - envelope - phase - stable (CEP - stable) optical pulse at the output. A carrier - envelope - phase - stable (CEP - stable) optical pulse is provided at the input of the optical amplifier, and the optical amplifier provides an amplified carrier - envelope - phase - stable (CEP - stable) optical pulse as the output. Thus, the optical amplifier is suitable for amplifying the output of the optical system.

[0118] In an example, the pulse generator of the light source unit provides an optical pulse having an optical carrier frequency f p and a pulse duration T ppulses. The pulses generated by the generator are linearly polarized.

[0119] In an example, the pulse generator (P) can be a picker from a ytterbium laser that emits short optical pulses of 350 fs with a pulse energy of about 10 μJ and a wavelength of 1030 nm.

[0120] The optical amplifier directly amplifies the carrier-envelope phase-stable (CEP-stable) optical pulses generated by the optical system, i.e., without first converting them into electrical signals as known in the art. The optical amplifier can be of any type or technology.

[0121] More generally, although the invention has been described with reference to certain embodiments, those skilled in the art will understand that various changes can be made and equivalents can be substituted without departing from the scope of the invention. In addition, many modifications can be made to adapt a particular situation to the teachings of the invention without departing from the scope of the invention. Therefore, the invention is not limited to the specific embodiments disclosed, but the invention will include all embodiments falling within the scope of the appended claims.

Claims

1. A single-beam and non-compressive optical system for generating carrier-envelope-phase-stable optical pulses of a second optical carrier frequency from an input optical pulse having a first optical carrier frequency and a pulse duration (T p ), the optical system comprising: - Birefringent medium (B), -- for receiving the input optical pulse in the input; and -- for providing pairs of linearly polarized pulses (PP) as output in such a way that each pair of linearly polarized pulses (PP) has orthogonal polarizations along a first direction (E1) and a second direction (E2) and each pair of linearly polarized pulses (PP) has a relative optical group delay equal to or greater than the pulse duration (T p ) of the input optical pulse; - Nonlinear medium (NL), -- for receiving the output of the birefringent medium (B) in the input; and -- for providing a pair of linearly polarized pulses (PP) as an output in such a way that at least one of the two pulses of each pair of linearly polarized pulses (PP) is spectrally broadened; - Transparent dispersive optical system (O), -- for receiving the output of the nonlinear medium (NL) in the input; and -- for providing a pair of linearly polarized pulses (PP) as an output in such a way that there is full or partial temporal overlap between the two pulses of each pair of linearly polarized pulses (PP); - Parametric device (DFG), -- for receiving the output of the transparent dispersive optical system (O) in the input; and -- for providing the frequency difference between the frequency components polarized along the first direction (E1) and the frequency components polarized along the second direction (E2) as an output.

2. The optical system according to claim 1, further comprising: - Filter (F), - for receiving the output of the parametric device (DFG) in the input; and - for providing the extraction of the frequency difference of the output of the parametric device (DFG) as an output.

3. The optical system according to claim 2, wherein, The filter is a dichroic mirror.

4. The optical system according to any one of claims 1 to 3, further comprising a wave plate for controlling the polarization state of the input optical pulse.

5. The optical system according to any one of claims 1 to 3, further comprising an optical device disposed between the dispersive optical system (O) and the parametric device (DFG), the optical device: - for receiving the output of the dispersive optical system (O) in the input; and - for focusing the output of the dispersive optical system (O) on the parametric device (DFG).

6. The optical system according to any one of claims 1 to 3, wherein, The birefringent medium (B) has a thickness equal to or greater than 100 μm, and the birefringent medium includes at least one crystal selected from calcite crystal, quartz crystal, α-BBO crystal, YVO4 crystal, and TeO2 crystal.

7. The optical system according to any one of claims 1 to 3, wherein, The dispersive optical system (O) includes at least one material selected from glass window, YAG crystal, thick lens, calcite crystal, quartz crystal, α-BBO crystal, YVO4 crystal, and TeO2 crystal.

8. The optical system according to any one of claims 1 to 3, wherein, The nonlinear medium (NL) includes at least one material selected from YAG crystal, sapphire crystal, calcium fluoride crystal, and fused silica window.

9. The optical system according to any one of claims 1 to 3, wherein, The parametric device (DFG) is a second-order nonlinear crystal including at least one material selected from β-BBO, LBO, LiNbO3, LiIO3, KTA, LGS, and AGS.

10. The optical system according to any one of claims 1 to 3, wherein, The parametric device (DFG) is a nonlinear crystal characterized by a second-order susceptibility.

11. A method for generating a carrier - envelope - phase - stabilized optical pulse with a second optical carrier frequency from an input optical pulse, the input optical pulse having a first optical carrier frequency and a pulse duration (T p ), the method comprising: - Provide (10) the input optical pulse having a first optical carrier frequency and a pulse duration (T p ); - generating (20) pairs of linearly polarized pulses (PP) from the provided input optical pulses through a birefringent medium (B), each pair of linearly polarized pulses (PP) having orthogonal polarizations along a first direction (E1) and a second direction (E2) and each pair of linearly polarized pulses (PP) having a relative optical group delay equal to or greater than the pulse duration (T p ) of the input optical pulse; - Triggering (30) filamentation of at least one of the two pulses of each pair of linearly polarized pulses (PP) through the nonlinear medium (NL), and at least one of the two pulses of each pair of linearly polarized pulses (PP) is spectrally broadened due to filamentation; - temporally overlapping (40) two pulses of each pair of linearly polarized pulses of the output from the nonlinear medium (NL) by means of a dispersive optical system (O); and - generating (50) a frequency difference between a frequency component polarized along the first direction (E1) and a frequency component polarized along the second direction (E2) by means of a parametric device (DFG).

12. The method according to claim 11, further comprising: - extracting (60) the generated frequency difference by means of a filter.

13. The method according to any one of claims 11 or 12, further comprising: - focusing (42) the output of the dispersive optical system (O) onto the parametric device (DFG) by means of an optical device.

14. The method according to any one of claims 11 or 12, further comprising: - adjusting (12) the energy distribution between two pulses of a pulse pair generated by the birefringent medium by means of a wave plate.

15. A light source unit for generating carrier-envelope-phase-stable light pulses of a second optical carrier frequency from input optical pulses, comprising: - A pulse generator for delivering the input optical pulse, the input optical pulse having a first optical carrier frequency, a pulse duration (T p ) and being linearly polarized; an optical system according to any one of claims 1 to 10, adapted to receive the input optical pulses; - an optical amplifier adapted to amplify the output of the optical system.

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