A broadband terahertz electro-optic sampling quasi-phase matching structure and a design method thereof

Abstract

This invention discloses a broadband terahertz electro-optic sampling quasi-phase-matched structure, comprising at least two electro-optic crystals stacked sequentially, with a compensation crystal positioned between each pair of adjacent electro-optic crystals. The electro-optic crystals and the compensation crystals have opposite dispersion relations, facilitating the compensation crystals to compensate for the phase difference accumulated between the terahertz light and the probe light within the electro-optic crystals. This invention selects the type and thickness of the electro-optic crystals as needed, chooses a compensation crystal with an opposite dispersion relation to the electro-optic crystals, calculates its thickness based on the measurement bandwidth and phase-matching conditions, and then determines the number of electro-optic crystal layers according to the measurement bandwidth requirements. Compared with existing technologies, this invention can broaden the measurement bandwidth while maintaining signal strength. This invention does not involve precision micro / nano fabrication, is low-cost and easy to manufacture, does not involve destructive processing of the crystals, is reusable, and can be recombined and rearranged as needed, offering high flexibility.

Description

Technical Field

[0001] This invention relates to the field of terahertz electro-optic sampling technology, and in particular to a broadband terahertz electro-optic sampling quasi-phase-matching structure and its design method. Background Technology

[0002] Terahertz technology has broad application prospects in fields such as ultrafast molecular dynamics and condensed matter physics, and is also an important technological development direction for next-generation communication technology and medical imaging.

[0003] Terahertz electro-optic sampling is a technique developed in recent years for measuring terahertz pulses. Electro-optic sampling can be used to measure the time-domain distribution of the electric field intensity of a terahertz pulse, directly obtaining the amplitude and phase information of the measured signal at different frequencies. Electro-optic sampling utilizes the linear electro-optic effect, which is essentially a second-order nonlinear process. The linear electro-optic effect, also known as the Pockel effect, occurs when a low-frequency electric field acts on a non-centrosymmetric material, producing a refractive index change proportional to the applied electric field intensity. By measuring the change in refractive index, the electric field intensity can be calculated. Materials with this property are called electro-optic crystals. In the terahertz electro-optic sampling process, a visible or near-infrared pulse light (i.e., the probe light) is passed through the electro-optic crystal. Due to the change in the refractive index ellipsoid caused by the terahertz electric field, the polarization state of the probe light changes. By measuring this polarization change, the terahertz electric field intensity within the electro-optic crystal can be obtained.

[0004] Electro-optic sampling requires phase matching, meaning the group velocity of the probe pulse must match the phase velocity of the terahertz wave. Simultaneously, the electro-optic crystal must possess a large nonlinear coefficient and exhibit no absorption in the terahertz and probe wavelength ranges. This imposes certain limitations on the material selection for the electro-optic crystal; GaP and ZnTe are commonly used crystals for electro-optic sampling. However, for electro-optic crystals with a certain thickness, phase matching restricts their terahertz measurement spectral range (bandwidth). For example, a 1 mm thick GaP crystal with a probe center wavelength of 1030 nm has a measurement bandwidth of approximately 4 THz. In practical applications, while reducing the crystal thickness can increase the measurement bandwidth, the signal strength will also decrease accordingly.

[0005] Current solutions involve etching gratings on the surface of the electro-optic crystal or using waveguides to achieve phase matching. However, these methods require extremely high processing precision, typically on the order of tens of nanometers, leading to high costs. Furthermore, the electro-optic crystal cannot be restored to its original state after processing; if the measurement bandwidth is changed, a new electro-optic crystal needs to be reprocessed, significantly increasing both economic and time costs. Summary of the Invention

[0006] To address the issue that existing terahertz electro-optic sampling processes incur higher economic and time costs in balancing measurement bandwidth and signal strength, the present invention aims to provide a broadband terahertz electro-optic sampling quasi-phase-matched structure and its design method, thereby at least partially solving the aforementioned problems.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows:

[0008] In a first aspect, the present invention provides a broadband terahertz electro-optic sampling quasi-phase-matching structure, comprising at least two electro-optic crystals arranged in sequence, wherein a compensation crystal is disposed between each pair of adjacent electro-optic crystals; wherein the electro-optic crystals and the compensation crystals have opposite dispersion relations, so as to compensate for the phase difference accumulated between the terahertz light and the probe light in the electro-optic crystals by means of the compensation crystals.

[0009] In a preferred embodiment, the terahertz light and the probe light do not generate signals in the compensation crystal.

[0010] Secondly, the present invention also provides a design method for a broadband terahertz electro-optic sampling quasi-phase-matched structure, comprising the following steps:

[0011] S1. Obtain the frequency Ω of the terahertz light and the frequency ω of the probe light;

[0012] S2. Determine the type of the electro-optic crystal, and the terahertz refractive index n of the terahertz light and the probe light in the electro-optic crystal, respectively. THz,1 Detecting the refractive index n of the light group g,1 ;

[0013] S3. Determine the thickness of the electro-optic crystal according to (Equation 1) and (Equation 2);

[0014]

[0015]

[0016] Equation 1 is derived from the phase-matching condition of an electro-optic crystal, l c Let l1 be the coherence length at which the electro-optic crystal can superimpose and enhance the signal, c be the speed of light in vacuum, C be the magnitude of the signal generated by the electro-optic crystal, and l1 be the thickness of the electro-optic crystal, not exceeding the coherence length l. c 4 times, where i is the imaginary unit;

[0017] S4. Select the type of the compensation crystal, and the terahertz refractive index n of the terahertz light and the probe light in the compensation crystal, respectively. THz,2 Detecting the refractive index n of the light group g,2 ;

[0018] S5. Determine the thickness of the compensation crystal according to (Equation 3);

[0019] Δk=Ω / c(n g,1 l1-n g,2 l2-n THz,1 l1+n THz,2 l2) (Equation 3);

[0020] Where Δk is the wavenumber difference, which approaches 0, and l2 is the thickness of the compensation crystal.

[0021] In a preferred embodiment, the method further includes:

[0022] S6. Determine the upper limit of the number of electro-optic crystals in the structure according to (Equation 4) and (Equation 5);

[0023]

[0024] N[n g,1 l1-n g,2 l2-n THz,1 l1+n THz,2 l2] max <π (Equation 5)

[0025] Where C' represents the total signal magnitude generated by a structure comprising at least two electro-optic crystals, N represents the number of electro-optic crystals, and the subscript max indicates the range of signals within the target terahertz bandwidth [n]. g,1 l1-n g,2 l2-n THz,1 l1+n THz,2 The maximum value of l2].

[0026] By adopting the above technical solution, the beneficial effects of the present invention are as follows:

[0027] In this invention, since the electro-optic crystal and the compensation crystal in the structure have opposite dispersion relations, the phase difference accumulated between the terahertz light and the probe light in the electro-optic crystal can be compensated by the compensation crystal. Since the phase difference is compensated, the signal can continue to be enhanced in the next electro-optic crystal, thereby breaking through the limitation of a single electro-optic crystal and enabling the measurement of broadband terahertz signals to broaden the measurement bandwidth while maintaining the signal strength.

[0028] Compared with existing technologies that involve etching gratings on the surface of electro-optic crystals or using waveguides to achieve phase matching, the present invention has the advantages of simple structure, no involvement of precision micro-nano processing, low cost, and ease of fabrication. In addition, the present invention does not involve destructive processing of the electro-optic crystal, making it easy to restore the electro-optic crystal to its initial state, thus enabling it to be reused and recombined as needed, offering high flexibility. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the structure of Embodiment 1 of the present invention;

[0030] Figure 2 This is a schematic diagram of the cumulative phase difference of the electro-optic crystal, compensation crystal, and quasi-phase matching structure in the 0.5-6THz range according to an embodiment of the present invention;

[0031] Figure 3 This is a schematic diagram comparing the signal intensity of electro-optic crystals with different numbers of layers in an embodiment of the present invention;

[0032] Figure 4 This is a flowchart of the method in Embodiment 2 of the present invention;

[0033] Figure 5 This is a schematic diagram of the coherence length of the GaP crystal in Embodiment 2 of the present invention.

[0034] In the diagram: 1-Electro-optic crystal, 2-Compensation crystal. Detailed Implementation

[0035] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings. It should be noted that these descriptions are for the purpose of aiding understanding the present invention, but do not constitute a limitation thereof. Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0036] It should be noted that in the description of this invention, the terms "upper", "lower", "left", "right", "front", "rear", etc., indicate the orientation or positional relationship based on the description of the structure of this invention shown in the accompanying drawings. They are only for the convenience of describing this invention and do not indicate or imply that the structure or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0037] The terms "first" and "second" in this technical solution are merely designations for corresponding structures that are identical or similar, or that perform similar functions. They do not represent an arrangement of the importance of these structures, nor do they imply any ranking, comparison of size, or other meaning.

[0038] Furthermore, unless otherwise explicitly specified and limited, the terms "installation" and "connection" should be interpreted broadly. For example, a connection can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be a connection within two structures. Those skilled in the art can understand the specific meaning of the above terms in this invention by considering the overall concept of the invention and the specific context of the solution.

[0039] Example 1

[0040] A broadband terahertz electro-optic sampling quasi-phase-matched structure, such as Figure 1 As shown, the device includes at least two electro-optic crystals 1 arranged in sequence, with a compensation crystal 2 disposed between each pair of adjacent electro-optic crystals 1. The electro-optic crystals 1 and the compensation crystals 2 have opposite dispersion relations, so that the phase difference accumulated between the terahertz light and the probe light in the electro-optic crystals 1 can be compensated by the compensation crystal 2. Furthermore, neither the terahertz light nor the probe light generates a signal in the compensation crystal 2.

[0041] In this embodiment, the electro-optic crystal 1 is specifically set to GaP, and the compensation crystal 2 is set to Si crystal. GaP is a commonly used electro-optic crystal in the terahertz band. When the center wavelength of the probe light is 1030 nm, in the 4-10 THz low-frequency band, the refractive index of the terahertz wavelength is greater than the group refractive index of the probe light. On the other hand, Si is a common and easily fabricated crystal. Its refractive index in the terahertz band is less than the group refractive index of the probe light. Therefore, the Si crystal can compensate for the phase difference accumulated in the GaP crystal, such as... Figure 2 As shown. Furthermore, the refractive index of Si crystal in the terahertz band is similar to that of GaP, thus reducing losses due to interface reflections.

[0042] like Figure 3 As shown, each curve represents a signal magnitude comparison diagram of a GaP crystal with multiple layers and a single layer thickness of 300 micrometers. The three dashed lines represent technical solutions that all employ the heterostructure design provided in this invention (each having 2-4 layers of GaP crystal with a thickness of 300 micrometers). Figure 3 The signal from a 900-micrometer-thick GaP crystal was also shown as a reference. It can be seen that a single 300-micrometer GaP crystal exhibits higher signal strength over a wider bandwidth compared to a single 900-micrometer GaP crystal. Furthermore, the curve corresponding to the technical solution of this invention shows even higher signal strength over a wider bandwidth compared to the single 300-micrometer GaP crystal. That is, while maintaining signal strength, this invention can extend the terahertz measurement bandwidth from 0.5-4 THz to 0.5-6 THz, thereby effectively expanding the terahertz electro-optic sampling bandwidth.

[0043] Example 2

[0044] A design method for a broadband terahertz electro-optic sampling quasi-phase-matched structure is applied to the structure disclosed in Embodiment 1, such as... Figure 4 As shown, the method includes the following steps:

[0045] S1, Obtain the frequency Ω of the terahertz light and the frequency ω of the probe light.

[0046] This embodiment uses a detection light center wavelength of 1030nm and a terahertz frequency of 5THz as the optimization target for illustration.

[0047] S2. Determine the type of electro-optic crystal, and the terahertz refractive index n of the terahertz light and probe light in the electro-optic crystal. THz,1 Detecting the refractive index n of the light group g,1 .

[0048] In this embodiment, the electro-optic crystal is configured as a GaP crystal. As shown in Table 1, the terahertz refractive index n of the terahertz light in the electro-optic crystal is... THz,1 The refractive index n of the probe light group in the electro-optic crystal is 3.42. g,1 It is 3.34.

[0049] Table 1 - Details of the refractive index of GaP crystals

[0050]

[0051] S3. Determine the thickness of the electro-optic crystal according to (Equation 1) and (Equation 2);

[0052]

[0053]

[0054] In terahertz electro-optic sampling, the probe light and the terahertz light must be in phase. At this point, the group velocity of the probe light pulse matches the phase velocity of the terahertz light, a condition known as phase matching. When the phase matching condition is met, the signals generated by the probe light as it passes through the electro-optic crystal can be superimposed and enhanced. However, in broadband terahertz measurements, the phase matching condition cannot be strictly met in practice. Therefore, the crystal length corresponding to the superimposed enhancement is defined as the coherence length *l*. c Its calculation formula is (Equation 1), l c That is, the coherence length at which the electro-optic crystal can superimpose and enhance the signal, where c is the speed of light in vacuum.

[0055] In Equation 2, C is the magnitude of the signal generated by the electro-optic crystal, l1 is the thickness of the electro-optic crystal, and i is the imaginary unit.

[0056] Combining equations (1) and (2), it can be seen that when the thickness l1 of the electro-optic crystal reaches 2l... c As the thickness of the electro-optic crystal continues to increase, the signal strength no longer increases, and the signal reaches 4l at the thickness l1. c The time decreases to 0, so the thickness of the electro-optic crystal does not exceed four times the coherence length.

[0057] like Figure 5As shown, the coherence length of GaP crystals in the range of 0.5-6 THz is given. The thickness of a single GaP crystal should be less than four times the coherence length at 6 THz, i.e., less than 400 micrometers. In this embodiment, the thickness of the electro-optic crystal is selected to be 300 micrometers.

[0058] S4. Select the type of compensation crystal, and the terahertz refractive index n of the terahertz light and probe light in the compensation crystal, respectively. THz,2 Detecting the refractive index n of the light group g,2 .

[0059] In this embodiment, the compensation crystal is configured as a Si crystal. As shown in Table 2, the terahertz refractive index n of the compensation crystal is... THz,2 The refractive index n of the probe beam in the compensation crystal is 3.42. g,2 It is 3.87.

[0060] Table 2 - Details of the refractive index of Si crystals

[0061]

[0062] S5. Determine the thickness of the compensation crystal according to (Equation 3);

[0063] Δk=Ω / c(n g,1 l1-n g,2 l2-n THz,1 l1+n THz,2 l2) (Equation 3);

[0064] Where Δk is the wavenumber difference, which approaches 0, and l2 is the thickness of the compensation crystal.

[0065] According to Equation 3, the thickness l2 of the compensation crystal is 18% of the thickness l1 of the electro-optic crystal. When the thickness l1 of the electro-optic crystal is selected as 300 micrometers, 18% is 54 micrometers. In this embodiment, the thickness l2 of the compensation crystal is specifically selected as 50 micrometers.

[0066] It is understood that the method provided in this embodiment also includes:

[0067] S6. Determine the upper limit of the number of electro-optic crystals stacked according to (Equation 4) and (Equation 5);

[0068]

[0069] N[n g,1 l1-n g,2 l2-n THz,1 l1+n THz,2 l2] max <π (Equation 5)

[0070] Where C' represents the total signal magnitude generated by a structure comprising at least two electro-optic crystals, N represents the number of electro-optic crystal stacks, and the subscript max indicates the maximum signal magnitude within the target terahertz bandwidth [n g,1 l1-n g,2 l2-n THz,1 l1+n THz,2 The maximum value of l2].

[0071] Calculations show that, while maintaining signal strength, the maximum number of layers N in an electro-optic crystal should be less than or equal to 3 layers.

[0072] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. A method for designing a broadband terahertz electro-optic sampling quasi-phase matching structure, characterized in that: The structure comprises at least two electro-optic crystals arranged in sequence, and a compensation crystal is arranged between each two adjacent electro-optic crystals; wherein the electro-optic crystal and the compensation crystal have opposite dispersion relations, so as to compensate the phase difference accumulated by the terahertz light and the probe light in the electro-optic crystal through the compensation crystal. The method comprises the following steps: S1, obtaining the frequency Ω of the terahertz light and the frequency ω of the probe light; S2, determining the type of the electro-optic crystal, and the terahertz refractive index n of the terahertz light and the probe light in the electro-optic crystal respectively THz,1 , the probe light group refractive index n g,1 ; S3, determining the thickness of the electro-optic crystal according to (formula 1) and (formula 2); l c = (Equation 1); C (Formula 2); wherein (Formula 1) is obtained according to a phase matching condition of the electro-optic crystal, l c is a coherence length at which the electro-optic crystal is capable of superimposedly enhancing the signal, c is a speed of light in vacuum, C is a size of the signal generated by the electro-optic crystal, l1 is a thickness of the electro-optic crystal and is not more than 4 times the coherence length l c , and i is an imaginary unit; S4, selecting a type of the compensating crystal, and terahertz refractive index n of the terahertz light and the probe light in the compensating crystal respectively THz,2 , probe light group refractive index n g,2 ; S5, determining the thickness of the compensation crystal according to (formula 3); Δk = Ω / c(n g,1 l1-n g,2 l2-n THz,1 l1+n THz,2 l2) (Equation 3); Wherein, Δk is the wave number difference, which tends to be close to 0, and l2 is the thickness of the compensation crystal.

2. The method of claim 1, wherein: The terahertz light and the probe light do not generate signals in the compensation crystal.

3. The method of claim 1, wherein: The method further comprises: S6, determining the upper limit of the number of electro-optic crystals in the structure according to (formula 4) and (formula 5); C=C (Formula 4); N[n g,1 l1-n g,2 l2-n THz,1 l1+n THz,2 l2] max <π (Equation 5); where C' is the magnitude of the total signal produced by the structure comprising at least two electro-optic crystals, N is the number of electro-optic crystals, and the subscript max indicates the maximum value of [n g,1 l1-n g,2 l2-n THz,1 l1+n THz,2 l2] in the target terahertz bandwidth.

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