JPH05210136A - Fiber type waveguide conversion element - Google Patents

Abstract

PURPOSE:To generate a second harmonic wave with high wavelength conversion efficiency by using a core material, basic incident wave, core radius and clad material satisfying a specific relation. CONSTITUTION:This wavelength conversion element consists of a fiber consisting of the core made of a nonlinear optical crystal and the clad enclosing this core and converts the basic wave of an LP01 of a wavelength lambda which is made incident and is propagated in the central axis direction of the core to the second harmonic wave of a wavelength lambda/2. The core and clad consist of the core material, core radius and clad material satisfying the relation expressed by equation. In the equation, a denotes the radius at the section of the core; nG<2omega> denotes the refractive index to the second harmonic wave of the core corresponding to the SHG tensor to be effectively utilized at the time of the wavelength conversion; N<omega> denotes the equiv. refractive index for the basic wave of the fiber, respectively.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optical wavelength conversion device,
In particular, it relates to an optical fiber type wavelength conversion element using Cherenkov radiation type phase matching.

[0002]

2. Description of the Related Art An optical wavelength conversion element has been developed in which an optical waveguide is formed by using a non-linear optical crystal, a light wave is guided to a minute region, and a second harmonic is efficiently generated. The light wavelength conversion element is roughly classified into two types according to the method of satisfying the phase matching. one,
It is a type that matches the phase velocity of the second harmonic with the nonlinear polarization wave excited by the incident light, and performs phase matching between the fundamental wave, that is, the guided mode of the incident light and the guided mode of the second harmonic. On the other hand, the other is a type using so-called Cherenkov radiation type phase matching, which performs phase matching between the guided mode of the fundamental wave and the radiation mode of the second harmonic.

An optical wavelength conversion element using Cherenkov radiation type phase matching is formed in the shape of an optical fiber consisting of a core of a non-linear optical crystal and a clad surrounding the core, and an optical fiber type second harmonic wave generating element (Second). Har
monics generator) (hereinafter also referred to as SHG). FIG. 1 is a conceptual diagram of such SHG3. This SHG is composed of a cylindrical core 10 and the core 1.
And a cylindrical clad layer 20 concentrically surrounding 0. In FIG. 1, when the fundamental wave propagates through the core 10 from left to right in the figure, a second harmonic is generated. Non-linear polarized waves propagating at the same phase velocity generate second harmonics in a direction forming a predetermined angle, and the second harmonics are reflected by the outer inner surface of the cladding layer 20 and propagate. Phase matching is performed between the guided mode of the fundamental wave in the core 10 and the radiation mode of the second harmonic wave to the cladding layer 20.

In this way, the second harmonic and its reflected wave are emitted from the end face of the fiber in a conical shape, as shown in FIG. Further, the equiphase surface of the emission wavefront of the second harmonic wave emitted in this way has a conical shape with the central axis of the SHG as an axis. As described above, the Cherenkov radiation system can generate the second harmonic wave in which the phase of the light is almost automatically generated, so that the SHG is applied to a short wavelength light source or the like. As an example of a short-wavelength light source, as shown in FIG. 3, a semiconductor laser 1, a coupling lens 2 for condensing light emitted from the semiconductor laser and injecting the light into the end surface of the SHG 3, and a core are nonlinear. SH composed of optical crystals
There is a G3 and an axicon 4 for shaping the wavefront of the second harmonic wave radiated after being converted by the wavelength conversion element to make the second harmonic wave into a parallel light flux.

[0005]

With such SHG,
Although it constitutes a short-wavelength light source module, a nonlinear optical crystal material with a sufficiently large nonlinear optical constant used for the core has not been found yet, and it is not easy to set a clad material having a refractive index suitable for surrounding the core. Absent. Therefore, the wavelength conversion efficiency of SHG (the power of the radiated second harmonic / the output of the semiconductor laser, that is, the power of the fundamental wave)
Has been achieved at most about 0.1%.

It is an object of the invention to provide a fiber type SHG having a high conversion efficiency, which makes full use of the performance of the nonlinear optical material of the core.

[0007]

Fiber type S according to the present invention
The HG is composed of a fiber composed of a core made of a nonlinear optical crystal and a clad surrounding the core, and the LP ₀₁ mode fundamental wave having a wavelength λ which is incident and propagates in the central axis direction of the core has a wavelength of λ / 2. A fiber-type wavelength conversion element for converting into two harmonics, wherein the core and the clad have a relationship represented by the following mathematical formula 1.

[0008]

[Equation 6]

The fiber has a core material, a core radius and a clad material which satisfy the above conditions. The equivalent refractive index of the fiber with respect to the fundamental wave is expressed by the following equation 4.

[0010]

[Equation 7]

It is characterized by being a root of. The fiber type SHG of the present invention satisfies the condition of the above mathematical expression 1, and

[0012]

[Equation 8]

(Where ω is the angular frequency of the fundamental wave, μ
₀ is the magnetic permeability of vacuum, ε ₀ is the dielectric constant of vacuum, d is the nonlinear optical constant of the core crystal, C is the constant based on the fundamental wave, and G is
(2β) is a coefficient that reflects the fact that there is a step in the refractive index at the boundary between the core and the clad with respect to the second harmonic, and is a factor just equivalent to the Fresnel transmission coefficient, and F (2β) is the nonlinear polarization distribution and the second The factor indicating the so-called weight integral with the electric field distribution of the harmonic, β is the propagation constant of the fundamental wave, L is the length of the core crystal, and the full width at half maximum including the multiple maximum values of G (2β) in Of these, the wavelength near the maximum value is preferably the wavelength λ of the fundamental wave, and the constant C based on the fundamental wave is expressed by the following mathematical formula 3.

[0014]

[Equation 9]

It is characterized by satisfying the above.

[0016]

[Function] By setting the core material, the wavelength of the incident fundamental wave, the core radius and the clad material that satisfy the above requirements,
The second harmonic can be easily generated with high conversion efficiency.

[0017]

Embodiments of the present invention will now be described in detail with reference to the drawings. The configuration of the SHG according to the present invention is the same as that shown in FIG. This SHG is a fiber formed by using a core made of a nonlinear optical crystal and a clad surrounding the core. The feature of such SHG is that the radius in the cross section of the core is a,

[0018]

[Equation 10]

It is to satisfy. This is because the equivalent refractive index of the fiber is determined by the refractive index of the core and the clad and the core radius as described later. The SHG tensor is a second-order nonlinear optical constant d _ijk expressed as, for example, a 3 × 6 matrix d _il as described below, and is a third-order tensor amount.

[0020]

[Equation 11]

The present inventor has used the fiber diameter as an actual SHG.
As a result of analyzing the electromagnetic field distribution considering the existence of the boundary between the clad and the core as described above, the fiber diameter and the SHG length are such that the second harmonic generated once from the core does not return to the core again. That is, if the length of the second harmonic is reflected at the boundary between the cladding and air at most once, the output of the SHG should match the output of the SHG when the cladding is infinitely large. I found out. In other words, it has been found that the output of the SHG can be sufficiently approximated by the SHG length such that the second harmonic is reflected only once at the boundary between the cladding and the air.

Therefore, an SHG composed of a clad and a core
The output of the second harmonic in the case where the fiber diameter in is infinitely large was analyzed by the following method. (Fundamental wave LP ₀ mode)

[0023]

[Equation 12]

Here, the waveguiding direction is the z-axis, ε ₀ is the permittivity of the vacuum, and d is the SHG effectively used in wavelength conversion.
The nonlinear optical constant of the core crystal corresponding to the tensor, C, is the constant based on the fundamental wave.

[0025]

[Equation 13]

[0026]

[Equation 14]

(Electric field of second harmonic)

[0028]

[Equation 15]

(Power of second harmonic)

[0030]

[Equation 16]

Here, G (κ) is a coefficient that reflects the fact that there is a refractive index step at the boundary between the core and the clad with respect to the second harmonic, and indicates a factor just equivalent to the Fresnel transmission coefficient, and F (κ) ) Indicates a factor indicating the weight integral of the so-called nonlinear polarization distribution and the electric field distribution of the second harmonic. G (κ)
Can be determined from boundary conditions. G (κ) and F (κ)
Can be expressed by Equations 9 and 10.

[0032]

[Equation 17]

When the SHG length is in the order of several mm as in the actual SHG in the formula 8, the sin in the formula 8
² [(2β-κ) L / 2] / (2β-κ) ² term can be approximated by the Dirac δ function, πLδ (2β-κ) / 2, and thus fiber type wavelength conversion element using Cherenkov phase matching The second harmonic output of can be expressed by the following formula 11.

[0034]

[Equation 18]

Therefore, the power of the second harmonic wave is influenced by G (2β) and F (2β) in the equation (11). (F (2β) of the power of the second harmonic) In particular, the power of the second harmonic is greatly affected by F (2β) in Formula 11, so in order to increase the conversion efficiency, first, F (2β) It is necessary to consider the value of). That is,

[0036]

[Formula 19]

It will be understood that the value of the integral of should be increased. Furthermore, in this integral, J ₀ (Ur) ² is a function representing the electric field distribution in the core of the guided fundamental wave, and J ₀ (Ur) ² changes gently with respect to r. To do. Therefore, when integrating with J ₀ (Ur) = 1, the following formula 13 is obtained.

[0038]

[Equation 20]

The shape of this integrated value with respect to aγ has a pattern similar to that of a diffraction image of a circular aperture, and forms a maximum fringe when γ = 0. If aγ <3.833, the integrated value will take the value of the first lobe, which is a larger value than in the case where it is not so. That is, γ ² is

[0040]

[Equation 21]

It is In other words, the power of the second harmonic is approximated by the following mathematical formula, with γ = k _G sin θ.

[0042]

[Equation 22]

However, θ represents the Cherenkov radiation angle in the core, and k _G is λ where λ is the wavelength of the fundamental wave.

[0044]

[Equation 23]

The standard frequency using the refractive index of the core for the second harmonic is shown. According to this approximate expression 14, the power of the second harmonic can be graphed as shown in FIG. 2, and among the diffracted light having the amplitude distribution J ₀ (Ur) ² , the diffracted light in the Cherenkov radiation direction is emitted. Its power is similar to the Airy pattern. Therefore,
As is clear from FIG. 2, the characteristic of the power of the second harmonic can obtain the main intensity in the first lobe up to the first valley (3.8327) of the axis of ak _G sin θ. That is, Cherenkov radiation angle θ is

[0046]

[Equation 24]

It suffices if the range is satisfied. Therefore, the equivalent refractive index of the core is

[0048]

[Equation 25]

Since it is expressed by

[0050]

[Equation 26]

It becomes Therefore, since the equivalent refractive index of the guided mode of the fundamental wave is determined from the refractive index of the optical glass of the clad, the refractive index of the core with respect to the fundamental wave, and the radius, the core material, the incident fundamental wave, By setting the core radius and the clad material, the second harmonic can be easily generated with high wavelength conversion efficiency. (G (2β) of the power of the second harmonic) In order to obtain higher conversion efficiency, SHG satisfies the condition of Formula 1 and further increases G (2β) which is another factor of Formula 11 Is desirable. The value of G (2β) is a function including γ and η that make a complicated change with respect to the refractive index of the core and the clad. I understand.

[0052]

[Equation 27]

In this graph, the values of G (2β) that are equal to each other on the plane formed by the vertical and horizontal axes are represented by a plurality of curves.
The direction in which the value of (2β) is high corresponds to the vertical direction in the drawing. From this graph, it is analytically shown that the value of G (2β) becomes G (2β) = 1 when the refractive index (and hence the dielectric constant) of the core and the cladding with respect to the second harmonic is equal ( Dashed line C) shown in FIG. It can be seen that G (2β) has a maximum value P in places along the horizontal axis and is also large at the ridgeline, and it is desirable to utilize this maximum value in the design of the fiber type wavelength conversion element.
That is, a large conversion efficiency can be obtained by selecting, as the fundamental wave, a wavelength within the full width at half maximum including the maximum value of G (2β), preferably in the vicinity of the maximum value.

FIG. 5 shows SHG (curve A) using DMNP as the core material and SF11 glass as the cladding material,
The fundamental wavelength dependence characteristics of the conversion efficiency with SHG (curve B) using DMNP as the core material and SF15 glass as the cladding material are shown. Using the wavelength λ of the fundamental wave as a parameter, the conversion efficiency of the second harmonic power / fundamental wave power was obtained from Equation 11 with the fundamental wave power set to 40 mW and the SHG length set to 1 mm.

As shown by the curve A in FIG. 5, the wavelength of the fundamental wave for converting the cladding glass into SF11 is about 960 nm.
It can be seen that a large conversion efficiency is obtained by selecting.
In the case of SHG in which the clad glass is SF11 and the wavelength of the fundamental wave to be converted is about 960 nm, G (2
It can be seen that one of the maxima of β) agrees with this.
In the case of SF15 glass, as shown by the curve B in FIG. 5, in the case of SHG in which the wavelength of the fundamental wave is selected to be about 893 nm, the maximum value of G (2β) shown in FIG. 4 coincides with this.

As described above, the refractive indexes of the core and the clad material change due to the wavelength dispersion of the injected fundamental wave. However, by sweeping the wavelength of the fundamental wave, a large clad material and a large wavelength can be selected. Conversion efficiency is obtained. Therefore,
In order to obtain high conversion efficiency, SHG satisfies at least the condition of Formula 1, and the factor of G (2β) of another factor of Formula 11 causes a maximum value and the cladding glass and the fundamental wave to be wavelength-converted. If the wavelength is selected, SHG with high conversion efficiency can be obtained.

[0057]

According to the present invention, the fundamental wave of wavelength λ propagating in the direction of the central axis of the core is composed of a core made of a nonlinear optical crystal and a clad surrounding the core, and the second harmonic of wavelength λ / 2 is used. A fiber type wavelength conversion element for converting into a wave, which is a wavelength conversion element composed of a core material, an incident fundamental wave, a core radius, and a clad material which satisfy the above-mentioned formula 1,
The second harmonic can be generated with high wavelength conversion efficiency. Further, SHG satisfies the condition of Expression 1 above, and further increases G (2β) which is another factor of Expression 11, that is, within the full width at half maximum including the maximum value of G (2β), preferably High conversion efficiency can be obtained by selecting a wavelength near the maximum value.

[Brief description of drawings]

FIG. 1 is an enlarged perspective view of a fiber type wavelength conversion element.

FIG. 2 is a graph showing the characteristics of the power of the second harmonic in the fiber type wavelength conversion element according to the embodiment of the present invention.

FIG. 3 is a schematic view of a short wavelength light source using a fiber type wavelength conversion element.

FIG. 4 is a graph showing wavelength characteristics of G (2β) of the fiber type wavelength conversion element.

FIG. 5 is a graph showing conversion efficiency of a fiber type wavelength conversion element with respect to an incident fundamental wave.

[Explanation of symbols for main parts]

 10 core 20 clad

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[Procedure amendment]

[Submission date] August 25, 1992

[Procedure Amendment 1]

[Document name to be corrected] Drawing

[Name of item to be corrected] Fig. 4

[Correction method] Change

[Correction content]

[Figure 4]

[Procedure Amendment 2]

[Document name to be corrected] Drawing

[Name of item to be corrected] Figure 5

[Correction method] Change

[Correction content]

[Figure 5]

Claims (5)

[Claims] 1. A fiber comprising a core made of a non-linear optical crystal and a clad surrounding the core, wherein a fundamental wave of LP ₀₁ mode having a wavelength λ which is incident and propagates in the direction of the central axis of the core has a wavelength λ / 2. A fiber-type wavelength conversion element for converting into a second harmonic wave of
The relationship expressed by the following formula 1 A fiber type wavelength conversion element comprising a core material, a core radius and a clad material which satisfy the above conditions. 2. The equivalent index of refraction of the fiber with respect to the fundamental wave is expressed by the following equation 4 The fiber-type wavelength conversion element according to claim 1, which is a root of 3. The equation 3 (Where ω is the angular frequency of the fundamental wave, μ ₀ is the magnetic permeability of vacuum, ε ₀ is the dielectric constant of vacuum, d is the nonlinear optical constant of the core crystal, and C is the constant based on the fundamental wave. , G (2β) is a factor reflecting that there is a refractive index step at the boundary between the core and the clad with respect to the second harmonic, and F (2β) is the weight of the nonlinear polarization distribution and the electric field distribution of the second harmonic. Where β is the propagation constant of the fundamental wave, L is the length of the core crystal, and L is the full width at half maximum including the multiple maxima of G (2β) in, and preferably near the maxima. The fiber type wavelength conversion element according to claim 2, wherein the wavelength is the wavelength of the fundamental wave. 4. The constant based on the fundamental wave is expressed by the following equation: The fiber type wavelength conversion element according to claim 3, which satisfies: 5. The Cherenkov radiation angle θ is given by The fiber type wavelength conversion element according to claim 1, wherein the fiber type wavelength conversion element is in a range satisfying a standard frequency indicated by