A Nonlinear Coupling Method for Cascaded Difference Frequency Generation of Terahertz Waves

Abstract

The present invention discloses a non - linear coupling method for generating terahertz waves by cascaded difference frequency, which includes the steps of: (1) selecting three incident laser beams, where the three laser beams include a first pump light, a second pump light with different wavelengths, and a signal light; (2) analyzing the coupled wave equation for generating terahertz waves by cascaded difference frequency of the three laser beams; (3) selecting a coupling modulation function to modulate the coupling coefficient of the non - linear crystal to obtain a modulated adiabatic crystal, and this adiabatic crystal can meet the conditions for non - linear optical adiabatic frequency conversion from the signal light to terahertz waves; (4) through the adiabatic crystal obtained in step (3), realizing the non - linear optical adiabatic frequency conversion from the signal light to terahertz waves. The present invention can obtain a wide - tuning terahertz wave output while improving the conversion efficiency.

Description

Technical Field

[0001] The present invention relates to a method for processing light sources, and specifically refers to a non-linear coupling method for generating terahertz waves by cascaded difference frequency generation. Background Art

[0002] Terahertz waves refer to electromagnetic waves with frequencies in the range of 0.1 - 10 THz (wavelengths in the range of 0.03 - 3 mm). Due to their unique physical properties, they have important application prospects in fields such as medical imaging, non-destructive testing, security inspection systems, and wireless communication. The non-linear optical difference frequency method is an effective means of obtaining terahertz waves. The basic principle is that two pump beams with similar frequencies generate terahertz waves with a frequency equal to the difference between the pump beam frequencies through the second-order non-linear effect of a non-linear medium when the phase matching condition is satisfied.

[0003] In 1965, Zernike et al. first obtained terahertz waves with a frequency of 3 THz by difference frequency in a quartz crystal using near-infrared laser emitted by a neodymium glass laser. In 2010, Zhong Kai et al. obtained continuously tunable terahertz waves with a frequency range of 0.186 - 3.7 THz by difference frequency in a GaSe crystal using a signal beam and an idler beam with wavelengths of about 2.128 μm emitted by an OPO system. The peak power of the output terahertz waves was 11 W, and the corresponding energy conversion efficiency and quantum conversion efficiency were 5.4×10 -6 and 0.09% respectively. Wide-tunable terahertz waves can be obtained by the difference frequency method, but the conversion efficiency is relatively low.

[0004] To improve the conversion efficiency of terahertz wave generation by the difference frequency method, in 2013, Liu Pengxiang et al. proposed a method for generating terahertz waves by cascaded difference frequency generation. The basic principle is to use a low-frequency pump beam to generate a pump beam with a lower frequency by difference frequency with the generated terahertz waves. During this process, the photon energy of the terahertz waves is amplified, and the conversion efficiency of terahertz waves can be improved through multiple cascaded difference frequency processes of the generated low-frequency pump beam and the terahertz waves. A cascaded amplification process of terahertz wave power was realized using a Cherenkov-type quasi-phase matching waveguide structure. When the pump beam intensity was 400 MW / cm 2 the output terahertz wave power was increased by nearly 8 times compared with the non-cascaded difference frequency process. Limited by the phase matching condition, the cascaded difference frequency method can only obtain terahertz waves of a single frequency and does not have tunability.

[0005] In 2012, Porat et al. analogized the stimulated Raman adiabatic passage (STIRAP) technology of a three-level system and proposed a cascaded frequency conversion theory based on STIRAP technology. In the STIRAP technology of a three-level system, when the adiabatic condition is satisfied, particles can achieve an adiabatic population transfer process from the |1> energy level to the |3> energy level. During this process, there is almost no particle population on the |2> energy level, which can reduce the particle number loss caused by spontaneous emission. In the cascaded frequency conversion theory based on STIRAP technology, the input light can be converted into the output light under the condition of very low intensity of the generated intermediate light. This cascaded frequency conversion theory can effectively broaden the range of laser frequencies obtained. Summary of the Invention

[0006] The object of the present invention is to provide a nonlinear coupling method for generating terahertz waves by cascaded difference frequency, which can obtain a widely tunable terahertz wave output while improving the conversion efficiency.

[0007] The above object of the present invention is achieved by the following technical solution: A nonlinear coupling method for generating terahertz waves by cascaded difference frequency, characterized in that the method comprises the following steps:

[0008] (1) Select three incident lasers, including a first pump light, a second pump light, and a signal light with different wavelengths;

[0009] (2) Analyze the coupled wave equation for generating terahertz waves by cascaded difference frequency of the three lasers;

[0010] (3) Select a coupling modulation function to modulate the coupling coefficient of the nonlinear crystal to obtain a modulated adiabatic crystal, which can satisfy the conditions for nonlinear optical adiabatic frequency conversion from the signal light to the terahertz wave;

[0011] (4) Through the adiabatic crystal obtained in step (3), realize the nonlinear optical adiabatic frequency conversion from the signal light to the terahertz wave.

[0012] In the present invention, the specific process of step (1) is as follows:

[0013] To promote the conversion of the signal light to the terahertz wave during the cascaded difference frequency process, strong pump light is required to improve the coupling strength between different lasers. The three incident lasers are respectively:

[0014] The signal light source selects a nanosecond or femtosecond pulsed light source with an optical intensity of MW level,

[0015] The first pump light source selects a picosecond or femtosecond pulsed light source with an optical intensity of GW level,

[0016] The second pump light source selects a picosecond or femtosecond pulsed light source with an optical intensity of GW level.

[0017] The specific process of step (2) is as follows:

[0018] Terahertz wave generation by cascaded difference frequency involves two difference frequency processes. In the first difference frequency process, the signal light and the first pump light generate intermediate light through difference frequency. Subsequently, in the second difference frequency process, the generated intermediate light immediately generates terahertz wave by difference frequency with the second pump light. Under the approximation of no pump loss, the coupled wave equation for terahertz wave generation by cascaded difference frequency can be expressed as:

[0019]

[0020] Where represent the complex amplitudes of the signal light, intermediate light, and terahertz wave respectively, z represents the propagation distance, and i is the imaginary unit. Δk 1 and Δk 2 represent the phase mismatches of the two difference frequency processes, and the specific expressions are: Δk 1 =k 1 -k p1 -k 2 , Δk 2 =k 2 -k p2 -k 3 , where k j =n j ω j / c represents the wave number of the laser with frequency ω j , n j represents the refractive index, and c represents the speed of light. κ ij represents the coupling coefficient between the lasers with frequencies ω i and ω j , and the specific expression is:

[0021]

[0022]

[0023] κ ij =(ω i 2 k j / ω j 2 k i )κ ji *

[0024] Where A p1 and A p2 are the complex amplitude envelopes of the two pump lights respectively, ω i represents the frequencies of different lasers, and χ (2) is the second-order nonlinear coefficient of the nonlinear crystal.

[0025] The specific process of step (3) is as follows:

[0026] To achieve the nonlinear optical adiabatic frequency conversion from signal light to terahertz wave, it is necessary to modulate the coupling coefficient of the nonlinear crystal to meet the adiabatic condition required for adiabatic frequency conversion. At the same time, the crystal structure that satisfies both the phase matching condition and the adiabatic condition is also called an adiabatic crystal. Here, the commonly used Gaussian modulation is adopted, and the corresponding coupling modulation function is:

[0027]

[0028]

[0029] where s j and d j represent the delay parameter and the width parameter respectively. s j determines the position of the peak of the coupling modulation function inside the crystal, and d j determines the action range of the coupling modulation function. When s 1 > s 2 , the coupling order is the intuitive sequence, indicating that the coupling of the signal light and the first pump light is earlier than the coupling of the intermediate light and the second pump light. When s 1 < s 2 , the coupling order is the counter-intuitive sequence, indicating that the coupling of the intermediate light and the second pump light is earlier than the coupling of the signal light and the first pump light. To simultaneously meet the phase matching condition and the adiabatic condition, the phase reversal quasi-phase matching (PRQPM) technology is used to modulate the coupling coefficient of the crystal, and the duty cycle of the nonlinear crystal is continuously changed using the coupling modulation function.

[0030] The specific process of step (4) is as follows:

[0031] The first pump light, the second pump light, and the signal light are simultaneously incident perpendicularly into the adiabatic crystal obtained in step (3). The signal light and the first pump light generate intermediate light through difference frequency, and the generated intermediate light then generates terahertz wave through difference frequency with the second pump light. Due to the action of the coupled modulated nonlinear crystal, the two difference frequency processes occur almost simultaneously, and the intensity of the generated intermediate light will not show retention. The signal light can be converted into terahertz wave under the condition of very low intensity of the generated intermediate light.

[0032] In the nonlinear coupling method of the present invention, by modulating the coupling coefficient of the nonlinear crystal, the signal light can be converted into terahertz wave through two cascaded difference frequencies, and the intensity of the intermediate light generated in the whole process is very low. This method can obtain a wide-tuning terahertz wave output while improving the conversion efficiency.

[0033] The existing nonlinear optical difference frequency method for generating terahertz waves has the advantages of wide tuning, high power, operation at room temperature, and compact structure. However, the conversion efficiency of the current difference frequency method is relatively low. The cascaded difference frequency method can theoretically effectively improve the conversion efficiency of generating single-frequency terahertz waves, but it has the defect that it cannot obtain a wide-tuning terahertz wave output. Compared with the prior art, the nonlinear coupling method of the present invention can obtain a wide-tuning terahertz wave output while improving the conversion efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0035] Figure 1 It is a schematic diagram of coupling coefficient modulation in the present invention, where the abscissa is the crystal length and the ordinate is the normalized coupling coefficient;

[0036] Figure 2 It is a schematic structural diagram of an adiabatic crystal in the present invention, Λ i (i = 1, 2) represents two polarization periods of the crystal, and the black part represents the reversed domains in the polarization period, with a width of l i (i = 1, 2);

[0037] Figure 3 It is the variation of the intensities of the signal light, intermediate light, and terahertz wave with the crystal length in the present invention. The upper right inset is an enlarged view of the variation of the terahertz wave intensity;

[0038] Figure 4 It is the variation of the quantum conversion efficiency from the signal light to the terahertz wave with the output frequency in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0039] The nonlinear coupling method for generating terahertz waves by cascaded difference frequency in the present invention uses a lithium niobate (LN) crystal to generate terahertz waves by cascaded difference frequency. The specific steps are as follows:

[0040] Step 1: Select three laser beams incident on the LN crystal. The three laser beams include a first pump light, a second pump light, and a signal light with different wavelengths. The parameters of the three laser beams are as follows:

[0041] The wavelength of the signal light is λ 1 = 1.064 μm, and the intensity is 400 MW / cm 2 ;

[0042] The wavelength of the first pump light is λ p1 = 2.7 μm, and the intensity is 5 GW / cm 2 ;

[0043] The wavelength of the second pump light is λ p2 = 1.764 μm, and the intensity is 250 GW / cm2 ;

[0044] Step 2: Analyze the coupled wave equations for terahertz wave generation by cascaded difference frequency of three laser beams

[0045] Terahertz wave generation by cascaded difference frequency involves two difference frequency processes. In the first difference frequency process, the signal light and the first pump light generate an intermediate light through difference frequency. Subsequently, in the second difference frequency process, the generated intermediate light immediately generates a terahertz wave by difference frequency with the second pump light. Under the approximation of no pump loss, the coupled wave equations for terahertz wave generation by cascaded difference frequency can be expressed as:

[0046]

[0047] The phase mismatches of the cascaded difference frequency process are respectively:

[0048] Δk 1 = k 1 - k p1 - k 2

[0049] Δk 2 = k 2 - k p2 - k 3

[0050] k j = n j ω j / c

[0051] where, Δk 1 is the phase mismatch of the first difference frequency process, and Δk 2 is the phase mismatch of the second difference frequency process. k j is the wave number, where k p1 is the wave number of the first pump light, k p2 is the wave number of the second pump light, k λ1 is the wave number of the signal light, k λ2 is the wave number of the intermediate light, and k λ3 is the wave number of the terahertz wave. The nonlinear coefficient of the LN crystal is 168 pm / V, and the refractive indices of different wavelengths can be calculated at 24.5 °C through the Sellmeier equation. The Sellmeier equation of the LN crystal in the optical band is:

[0052]

[0053] f = (T - 24.5 °C)(T + 570.82)

[0054] where, a 1 = 5.756, a 2 = 0.0983, a3 = 0.2020, a 4 = 189.32, a 5 = 12.52, a 6 = 1.32×10 -2 , b 1 = 2.860×10 -6 , b 2 = 4.700×10 -8 , b 3 = 6.113×10 -8 , b 4 = 1.516×10 -4 . The unit of the wavelength λ is μm, f represents a function related to the temperature T, and the unit of T is °C.

[0055] The Sellmeier equation of the LN crystal in the terahertz band is:

[0056]

[0057] f = (T - 24.5 °C)(T + 570.82)

[0058] where, a 0 = 24.326, a 1 = 31298, a 2 = 48.084, b 0 = 2.14×10 -5 , b 1 = 0.15824, b 2 = -3.097×10 -4 . The unit of the wavelength λ is μm, and the unit of the temperature T is °C.

[0059] Step 3: To achieve the nonlinear optical adiabatic frequency conversion from the signal light to the terahertz wave, the coupling coefficient of the crystal is modulated, and the corresponding coupling modulation function is:

[0060]

[0061]

[0062] The length of the LN crystal is 20 mm, and the delay parameters are set to s 1 = -10 mm, s 2 = 6 mm at the center of 10 mm, and the width parameter is set to d 1 2 = 50 mm 2 , d 2 2 = 100 mm 2 .

[0063] Figure 1 shows the variation of the modulated coupling coefficient along the crystal propagation direction, and the coupling coefficient κ 23 has a peak value before κ 12 , corresponding to a counterintuitive sequence coupling order.

[0064] Figure 2 is a schematic diagram of an adiabatic crystal structure designed using the PRQPM technique, where Λ 1 , Λ 2 represent two polarization periods of the crystal. The white part in the figure represents the positive domain of the crystal, and the black part represents the inverted domains in the two polarization periods, with widths of l 1 , l 2 . represents the duty cycle of the two polarization periods. The polarization period Λ 1 =Δk 1 is selected to compensate for the phase mismatch in the first difference frequency process, and Λ 2 =Δk 2 is used to compensate for the phase mismatch in the second difference frequency process. Under the condition of satisfying the phase matching condition, the coupling modulation function can be expressed as:

[0065]

[0066]

[0067] At this time, the amplitude of the coupling coefficient is related to the duty cycle in the polarization period. In order to make the amplitude change of the coupling coefficient be Figure 1 shown as a Gaussian type, the duty cycle D 1 , D 2 of each period can be continuously changed to achieve the modulation function of the coupling coefficient. The variation of the coupling coefficient of the LN crystal after modulation is as shown in Figure 1 .

[0068] Step 4: Simultaneously vertically incident the three laser beams in Step 1 into the coupled and modulated LN crystal. First, the signal light with a wavelength of 1.064 μm and the first pump light with a wavelength of 2.7 μm generate an intermediate light with a wavelength of 1.756 μm through difference frequency, and then the generated intermediate light and the second pump light with a wavelength of 1.764 μm generate a terahertz wave with a wavelength of 387.2 μm and a frequency of 0.77 THz through difference frequency. Due to satisfying the adiabatic condition, the two difference frequency processes occur almost simultaneously.

[0069] Figure 3 shows the variation of the intensities of the signal light, intermediate light, and terahertz wave with the crystal length in the cascaded difference frequency process. Finally, no signal light and intermediate light are output at the end of the crystal. The intensity of the terahertz wave output at the end of the crystal is 0.47 MW / cm 2, the quantum conversion efficiency from signal light to terahertz wave can reach 43.2%. By fixing the wavelengths of the two pump lights and tuning the wavelength of the incident signal light, terahertz wave outputs with different frequencies can be obtained.

[0070] Figure 4 The variation of the quantum conversion efficiency with the output frequency is given when the wavelength of the tuned signal light varies in the range of 1.044 - 1.065 μm. The terahertz wave tuning range corresponding to a quantum conversion efficiency above 30% is 0.48 - 5.00 THz.

[0071] The above embodiments of the present invention do not limit the protection scope of the present invention. The implementation manners of the present invention are not limited thereto. All kinds of modifications, substitutions or changes in other forms made to the above structure of the present invention according to the above content of the present invention, in accordance with the common general technical knowledge and customary means in the art, without departing from the above basic technical idea of the present invention, shall fall within the protection scope of the present invention.

Claims

1. A non - linear coupling method for terahertz wave generation by cascaded difference frequency, characterized in that, the method comprises the following steps: Step (1) Select three incident laser beams, which include a first pump beam, a second pump beam with different wavelengths and a signal beam; the three incident laser beams are respectively: The signal beam source selects a nanosecond or femtosecond pulsed light source with an optical intensity of MW level, The first pump beam source selects a picosecond or femtosecond pulsed light source with an optical intensity of GW level, The second pump beam source selects a picosecond or femtosecond pulsed light source with an optical intensity of GW level; Step (2) Analyze the coupled wave equation for terahertz wave generation by cascaded difference frequency of the three laser beams; The specific process of step (2) is as follows: Terahertz wave generation by cascaded difference frequency includes two difference - frequency processes. In the first difference - frequency process, the signal beam and the first pump beam generate an intermediate beam through difference frequency. Subsequently, in the second difference - frequency process, the generated intermediate beam immediately generates a terahertz wave through difference frequency with the second pump beam. Under the approximation of no pump loss, the coupled wave equation for terahertz wave generation by cascaded difference frequency is expressed as: wherein respectively represent the complex amplitudes of the signal light, the intermediate light, and the terahertz wave, z represents the propagation distance, and i is the imaginary unit; Δk 1 and Δk 2 represent the phase mismatches of two difference frequency processes, and the specific expressions are: Δk 1 = k 1 - k p1 - k 2 , Δk 2 = k 2 - k p2 - k 3 , k j = n j ω j / c represents the wave number of the laser with frequency ω j , n j represents the refractive index, and c represents the speed of light; k lj = (ω l 2 k j / ω j 2 k l )k jl * Among them, A p1 and A p2 are the complex amplitude envelopes of two pump light beams respectively, ω l and ω j represent the frequencies of different lasers, and χ (2) is the second-order nonlinear coefficient of the nonlinear crystal; Step (3) Select a coupling modulation function to modulate the coupling coefficient of the non - linear crystal to obtain a modulated adiabatic crystal, which can meet the conditions for non - linear optical adiabatic frequency conversion from the signal beam to the terahertz wave; The specific process of step (3) is as follows: To achieve non - linear optical adiabatic frequency conversion from the signal beam to the terahertz wave, it is necessary to modulate the coupling coefficient of the non - linear crystal to meet the adiabatic conditions required for adiabatic frequency conversion. At the same time, the crystal structure that satisfies both the phase - matching condition and the adiabatic condition is also called an adiabatic crystal. Adopt Gaussian - type modulation, and the corresponding coupling modulation function is: where s m and d m represent the delay parameter and the width parameter respectively, m takes the value of 1 or 2, s m determines the position of the peak of the coupling modulation function inside the crystal, and d m determines the action range of the coupling modulation function; when s 1 > s 2 , the coupling order is the intuitive sequence, indicating that the coupling of the signal light and the first pump light is earlier than the coupling of the intermediate light and the second pump light. When s 1 < s 2 , the coupling order is the counter-intuitive sequence, indicating that the coupling of the intermediate light and the second pump light is earlier than the coupling of the signal light and the first pump light; to simultaneously satisfy the phase matching condition and the adiabatic condition, the coupling coefficient of the crystal is modulated by using the phase inversion quasi-phase matching technique, and the duty cycle of the nonlinear crystal is continuously changed by using the coupling modulation function; Step (4) Through the adiabatic crystal obtained in step (3), achieve the non - linear optical adiabatic frequency conversion from the signal beam to the terahertz wave; The specific process of step (4) is as follows: The first pump beam, the second pump beam and the signal beam are simultaneously incident perpendicularly into the adiabatic crystal obtained in step (3). The signal beam and the first pump beam generate an intermediate beam through difference frequency, and the generated intermediate beam subsequently generates a terahertz wave through difference frequency with the second pump beam.

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