CN112269264B - Method for finely regulating and controlling second-order nonlinear optical process - Google Patents

Abstract

The invention discloses a method for finely regulating and controlling a second-order nonlinear optical process through artificial microstructure design. Conventional quasi-phase matching (QPM) theory provides phase matching to a nonlinear process by designing an optical superlattice whose period is determined by the wave-vector mismatch in the nonlinear process. Theoretical calculation shows that the method cannot strictly ensure the unidirectionality of energy and phase transformation in the nonlinear process, can generate obvious errors under the condition of high conversion efficiency, and is difficult to regulate and control the harmonic phase while matching the phase. The invention provides a parameter of relative phase difference angle introduced when designing a superlattice structure, and energy change and phase change of frequency doubling wave or fundamental wave in a nonlinear process can be finely regulated and controlled by selecting a proper relative phase difference angle, so that the invention has important application in improving conversion efficiency of the nonlinear process.

Description

Method for finely regulating and controlling second-order nonlinear optical process

Technical Field

The invention belongs to the field of nonlinear optics, and particularly relates to a nonlinear optical energy control and phase matching technology in an artificial microstructure material, wherein an optical superlattice used in the technology can be designed according to preset frequency doubling waves and base frequency waves.

Background

Nonlinear optics is an important area in modern optics and is a discipline for studying the interaction between intense light and media. Second-order nonlinear optical effects such as frequency doubling, sum frequency, difference frequency and the like are always the focus of attention in the field. The second-order nonlinear process such as frequency conversion can be realized by utilizing the second-order nonlinear coefficient of the natural nonlinear material. However, the conversion efficiency is reduced due to phase mismatch caused by dispersion of the material. Taking frequency-doubled light as an example, Δ k ═ k₂-2k₁And the phase mismatch in the frequency multiplication process is expressed, and the energy of the fundamental wave can be continuously converted into the second harmonic only when the delta k is 0, so that the effective conversion efficiency is realized.

In 1962, Armstrong and Bloembergen proposed a quasi-phase matching concept (QPM), and a reciprocal lattice vector was introduced to compensate for phase mismatch by artificially modulating microstructures, thereby realizing phase matching and obtaining an effective nonlinear optical effect. The nonlinear materials that achieve this phase matching approach are called optical superlattices. A conventional QPM condition is that the amount of phase mismatch Δ k ═ G, which is the reciprocal lattice vector provided by the optical superlattice. Under the condition of small signal approximation, the QPM method can obtain good phase matching effect. However, in the case that the conversion efficiency is high and the small signal approximation is not established, theoretical calculation indicates that the conventional QPM condition cannot strictly guarantee that the doubled wave energy is continuously increased. Fig. 1 calculates the frequency doubling evolution in a typical optical superlattice, wherein the conventional QPM condition is satisfied, from which it can be seen that as the propagation distance increases, the Fundamental (FW) energy is gradually transferred into the doubled wave (SHG), and when the doubled wave energy reaches a maximum, the energy flows back, the doubled wave starts to become smaller, and the fundamental wave becomes larger.

To solve this problem, the document sci. rep.6,27457(2016) proposes a new superlattice design method, called strict Quasi-Phase Matching theory (RQPM), which starts from the frequency multiplication coupled wave equation:

where K is the coupling coefficient, f (x) is the structural function of the optical superlattice, A₁And A₂Is the complex amplitude of the fundamental and the frequency multiplication.

The derivation of the RQPM condition is very simple. Four different phase matching conditions, referred to as Type-I, Type-II, Type-III, and Type-IV RQPM conditions, are available for different purposes.

The Type-I RQPM condition is similar to the traditional QPM condition, and the energy of the frequency doubling wave in the frequency doubling process can be increased monotonically. On the contrary, the Type-II RQPM condition can ensure that the frequency doubling wave energy is monotonically decreased, and the whole frequency doubling process only needs to meet the requirement

By designing the two different superlattice structures, the energy conversion direction can be controlled. This ability to control the direction of energy transfer is very useful for parametric down-conversion processes such as difference frequency processes and optical parametric amplification.

Another very important phenomenon in nonlinear optics is the nonlinear phase shift, and the Type-III and Type-IV RQPM conditions can control the direction of the phase shift for frequency doubling in the nonlinear process. However, the existing RQPM method can only control one of the energy or phase of the nonlinear process, and cannot continuously control and finely regulate the energy and phase of the frequency doubling wave at the same time.

Disclosure of Invention

In order to solve the problem that the traditional QPM and RQPM methods cannot continuously control and finely regulate energy and phase simultaneously in a nonlinear process, the invention provides an improved method, and the specific improved scheme is as follows:

under the condition of non-small signal approximation, relative phase difference angle parameters are introduced, and an optical superlattice structure with the following structure functions is designed to regulate and control a nonlinear process:

(x) is a superlattice domain structure function;

A₁、A₂complex amplitudes of fundamental and frequency-doubled waves, respectively;

Δ k is the wave vector mismatch in the frequency multiplication process, and Δ k ═ k₂-2k₁；

Phi is a relative phase difference angle representing the phase difference between the nonlinear polarized wave and the frequency doubled wave in the nonlinear optical process. Phi continuously takes a value of 0-2 pi, and corresponds to fine regulation and control of different types of energy and phases.

The invention has the beneficial effect. The invention realizes fine regulation and control of the energy and the phase of the frequency doubling wave at the same time by continuously changing the phase difference between the nonlinear polarized wave and the frequency doubling wave. Compared with the traditional QPM method and the RQPM method, the method has larger regulation freedom degree. The structure of the superlattice can be designed according to preset frequency doubling waves and base frequency waves. The resulting structure can satisfy RQPM matching conditions when the relative phase difference angle phi takes some special values (e.g., phi-0 corresponds to Type-I RQPM conditions), while the structure and properties of the two have significant differences when the relative phase difference angle phi takes a general value, so the method can be considered to be a generalization of the RQPM method under general circumstances.

Drawings

FIG. 1 illustrates the energy conversion of a frequency doubling process in an optical superlattice corresponding to a conventional QPM method.

Fig. 2 is a schematic representation of the variation of the exit-side frequency doubled wave and fundamental energy with phi for the superlattice structure of the invention.

Fig. 3 is a schematic illustration of the variation of the frequency doubling and fundamental phase with phi at the exit end for a superlattice structure of the invention.

FIG. 4 is a graph showing the variation of the energy and phase of the frequency doubling wave and the fundamental wave during transmission of the superlattice in different intervals as a function of φ.

Detailed Description

The technical scheme of the invention is further explained in detail by combining the drawings and the specific embodiments in the specification.

The specific parameters are set as follows: the length of the superlattice is 0.3cm, fundamental waves with the wavelength of 1064nm enter from the left end face of the superlattice, and frequency doubling waves with the wavelength of 532nm are generated through the superlattice.

FIG. 2 shows that when φ is greater than or equal to 0 and less than π/2, the conversion efficiency of the double frequency wave at the exit end of the superlattice decreases with the increase of φ; when phi is more than 3 pi/2 and less than or equal to 2 pi, the conversion efficiency of the frequency doubling wave at the emergent end of the superlattice is increased along with the increase of phi. In the two cases, the energy flow directions are both the fundamental wave and the frequency multiplication wave transfer, so that effective frequency multiplication wave output can be realized.

FIG. 3 shows that when φ is 0 ≦ π < π/2 and 3 π/2 ≦ 2 π, phase tuning can be achieved while achieving effective harmonic output by setting a suitable value of φ.

FIG. 4 shows that arbitrary φ is taken in four quadrants, each quadrant representing fine-tuning of energy and phase simultaneously. When phi is positioned in 1 st and 4 th boundaries, the energy of the frequency doubling wave is monotonically increased; when phi is positioned in the 2 nd and 3 rd boundaries, the energy of the frequency doubling wave is monotonically decreased; when phi is positioned in 1 st and 2 nd boundaries, the phase of the frequency multiplication wave is monotonically decreased; when phi is located in the 3 rd and 4 th boundaries, the phase of the frequency multiplication wave is monotonously increased. When phi is located on the positive and negative axes of the x axis and the positive and negative axes of the y axis, the 4-class RQPM condition can be just met.

Claims (1)

1. A phase matching improvement method capable of simultaneously realizing fine regulation and control of energy and phase is suitable for a frequency doubling nonlinear optical process and is characterized in that an important parameter is introduced in addition to consideration of wave vector mismatch when a superlattice structure is designed: the corresponding superlattice structure function of the method can be expressed as follows:

(x) is a superlattice domain structure function;

A₁、A₂complex amplitudes of fundamental and frequency-doubled waves, respectively;

Δ k is the wave vector mismatch in the frequency multiplication process, and Δ k ═ k₂-2k₁；

Phi is a relative phase difference angle representing a phase difference between a nonlinear polarized wave and a frequency-doubled wave in a nonlinear optical process,

phi continuously takes a value of 0-2 pi, and corresponds to fine regulation and control of different types of energy and phases.

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