CN102620908A - Method for acquiring reflection type volume holographic grating parameters - Google Patents

Abstract

The invention relates to a method for acquiring reflection type volume holographic grating parameters. Grating periods and grating slant angles are acquired by means of the relation among Bragg matching conditions of different readout wavelengths through the formula of relations between incident angles and the grating slant angles and calculation formulas of Bragg angles and the grating periods under the Bragg matching conditions. The refractive index modulation degree and the effective thickness of the grating can be acquired by substituting the acquired two angles and the grating periods and grating slant angles which are acquired in the step into a diffraction efficiency formula respectively by means of incidence angles corresponding to two diffraction efficiency zero points on a diffraction efficiency curve acquired by certain selected readout wavelength.

Description

A kind of method of reflection-type volume holographic grating parameter acquiring

Technical field

The present invention relates to grating and detect applied technical field, particularly a kind of method of reflection-type volume holographic grating parameter acquiring.

Background technology

Grating is a kind of diffraction screen with periodic space structure or optical property (like transmissivity, refractive index).Volume hologram forms the inner refractive index generating period property Changing Pattern of photorefractive media through two-beam at the recording medium internal interference, so volume hologram is exactly a kind of grating.When two-beam during incident, just forms the reflection-type volume holographic grating from the recording medium both sides.

The reflection-type body grating is a kind of important optical element.Because of it has higher diffraction efficiency, the selectivity of good angular selectivity and wavelength.Be widely used in relevant or incoherent synthetic, fiber laser of reflective narrow band pass filter, light beam or the optimization of semiconductor laser output beam quality at present, and during light beam, field such as spatial domain shaping.When utilizing the reflection-type body grating to carry out the practical devices design, at first to accurately know its grating periods lambda, grating slope angle φ, grating refractive index degree of modulation n ₁With grating parameters such as net thickness δ.With reference to Fig. 1.

For confirming of grating periods lambda, grating slope angle φ, mainly be according to the grating Writing condition at present, utilize the light wave wave vector of writing light inlet and grating wave vector under the Bragg diffraction condition, satisfy that parallelogram law calculates.And when Writing condition was unknown, existing method can not draw grating cycle and grating slope angle.For grating refractive index degree of modulation n ₁With net thickness δ, utilizations such as race mountain are different from the light wave conduct that writes light wave and read the diffraction efficiency curve that light wave obtains volume holographic grating, and then utilize the diffraction efficiency condition that zero point, corresponding Prague deviation angle was satisfied, and obtain grating refractive index degree of modulation n ₁With net thickness δ (race mountain, Zou Lixiong, Jiang Lingzhen etc.; " a kind of settlement method of body phase holographic grating refractive index modulation degree " Harbin Institute of Technology's journal, 1992,24 (4) 38-42); But this method is in calculation process, has utilized the Bragg angle that writes under the light wave condition.And he has just discussed non-these special circumstances of inclination transmission-type volume holographic grating.And do not mention for the measurement of general reflective volume holographic grating parameter.

Grating medium for finishing writing also needs chemical treatments such as development, photographic fixing, causes recording medium thickness to produce the contraction or expansion of non-quantitative.Cause the isoparametric change of grating cycle and grating slope angle simultaneously.At this moment, utilize Writing condition to confirm that grating parameter lacks tightness, carry out Design Theory accurately with regard to being difficult to practical devices like this, brought very big difficulty for the practical application of reflective volume holographic grating.

Summary of the invention

The technical matters that solves

For fear of the weak point of prior art, the present invention proposes a kind of method of reflection-type volume holographic grating parameter acquiring,

Technical scheme

A kind of method of reflection-type volume holographic grating parameter acquiring is characterized in that step is following:

Step 1: with the two light beams λ of any wavelength ₁And λ ₂Shine concurrent the gaining interest of reflection-type volume holographic grating to be measured respectively and penetrate, measure wavelength X ₁And λ ₂Pairing angle Selection linearity curve obtains wavelength X respectively ₁And λ ₂Corresponding diffraction efficiency angle Selection linearity curve;

Step 2: according to λ ₁And λ ₂Corresponding diffraction efficiency angle Selection linearity curve obtains the incident angle under the matching condition of Prague, i.e. λ ₁The corresponding incident angle θ of diffraction efficiency maximum ₁And λ ₂The corresponding incident angle θ of diffraction efficiency maximum ₂

Step 3:, calculate the corresponding incident angle ψ of Prague matching condition reflection-type volume holographic grating according to refraction law _R1And ψ _R2:

sinθ ₁/sinψ _R1＝n ₀

sinθ ₂/sinψ _R2＝n ₀

N wherein ₀Be reflection-type volume holographic grating mean refractive index.

Step 4: the relational expression λ that utilizes under the matching condition of Prague incident angle and grating slope angle in the medium ₁/ λ ₂=cos (ψ _R1-φ)/cos (ψ _R2-φ), calculate the grating slope angle

φ＝ψ _R2-arctan{[cos(ψ _R1-ψ _R2)-λ ₁/λ ₂]/sin(ψ _R1-ψ _R2)}；

Step 5: calculate grating periods lambda=λ ₁/ 2n ₀Cos (φ-ψ _R1);

Step 6: with λ ₁(or λ ₂) as the reading optical beam that calculates grating refractive index degree of modulation and grating net thickness, with two diffraction efficiency corresponding incident angle θ at zero point that are close to the main peak value on this reading optical beam diffraction efficiency angle Selection linearity curve _-1With θ _-2, and utilize refraction law that above-mentioned incident angle is converted to pairing incident angle ψ in the grating medium _-1=arcsin (sin θ _-1/ n ₀), ψ _-2=arcsin (sin θ _-2/ n ₀);

Step 7: calculate grating thickness

wherein:

$n_1=\sqrt{({9b}_1^2-{4b}_2^2)/({9a}_1^2-{4a}_2^2)};$

b ₁＝[(2π/λ ₁)cos(φ-ψ _-1)-(πλ ₁/Λ ²n ₀]/[2(cosψ _-1-(λ ₁/Λn ₀)cosφ)]；

b ₂＝[(2π/λ ₁)cos(φ-ψ _-2)-(πλ ₁/Λ ²n ₀]/[2(cosψ _-2-(λ ₁/Λn ₀)cosφ)]；

$a_1=\mathrm{\π}/{\mathrm{\λ}}_1\sqrt{\cos {\mathrm{\ψ}}_{-1}(\cos {\mathrm{\ψ}}_{-1}-({\mathrm{\λ}}_1/\mathrm{\Λ}{n}_0)\cos \mathrm{\φ})};$

$a_2=\mathrm{\π}/{\mathrm{\λ}}_1\sqrt{\cos {\mathrm{\ψ}}_{-2}(\cos {\mathrm{\ψ}}_{-2}-({\mathrm{\λ}}_1/\mathrm{\Λ}{n}_0)\cos \mathrm{\φ})}.$

Step 5 is calculated grating periods lambda=λ ₂/ 2n ₀Cos (φ-ψ _R2).

Beneficial effect

A kind of acquisition methods of measuring reflection-type volume holographic grating parameter that the present invention proposes; Utilize difference to read the relation between Prague matching condition of wavelength; Under the matching condition of Prague; Relation formula between incident angle and the grating slope angle and Bragg angle and the computing formula in grating cycle obtain grating cycle and grating slope angle.Utilize selected a certain two corresponding incident angles in diffraction efficiencies place at zero point of reading on the diffraction efficiency curve that wavelength obtains; And the grating cycle and the grating slope angle that obtain in two angles that will obtain and the above-mentioned steps be updated to respectively in the diffraction efficiency formula, can obtain grating refractive index degree of modulation and net thickness.

The invention has the beneficial effects as follows: in the process of obtaining each parameter of reflection-type volume holographic grating, the derivation of carrying out according to the diffraction characteristic parameter of reading light wave is fully calculated.Owing in the derivation calculation process, avoided to writing the dependence of parameter.Thereby well got rid of because the grating parameter that chemical treatment and the grating of grating medium after writing caused by environment in the preservation process changes, obtain be under existing conditions each parameter of grating to be measured actual value.For the unknown reflection-type volume holographic grating of a Writing condition, can calculate through method of the present invention and derive its each actual parameter simultaneously.Thereby better utilization reflection-type volume holographic grating carries out the light wave modulation, also can it be applied in the high-precision optical device designs simultaneously and go.

Description of drawings

Fig. 1: be reflective body grating structural drawing;

Fig. 2: for reading the graph of a relation of light wave wave vector, diffraction light wave-wave arrow and grating wave vector under the Bragg diffraction condition;

Fig. 3: for different light waves are read Prague matching condition structural drawing under the condition;

Fig. 4: be process flow diagram of the present invention;

Fig. 5: point of irradiation corresponding wavelength λ ₁Diffraction efficiency and incident angle relation curve;

Fig. 6: point of irradiation corresponding wavelength λ ₂Diffraction efficiency and incident angle relation curve.

Embodiment

Combine embodiment, accompanying drawing that the present invention is further described at present:

See also Fig. 4, it is following that described a kind of reflection-type volume holographic grating parameter acquiring method comprises step: step 1: utilize wavelength to be λ respectively ₁=532nm and λ ₂The pointolite that the laser instrument of=514nm sends shines reflection-type volume holographic grating to be measured a bit, changes irradiating angle, obtains point of irradiation corresponding wavelength λ ₁And λ ₂Diffraction efficiency and incident angle relation curve, i.e. diffraction efficiency angle Selection linearity curve is like Fig. 5, shown in 6; Step 2: on the diffraction efficiency angle Selection linearity curve of said two wavelength, confirm the incident angle under the matching condition of Prague respectively, i.e. the incident angle θ of correspondence in the diffraction efficiency maximum vacuum ₁And θ ₂, both are respectively θ at size ₁=21.5 °, θ ₁=34.0 °; Step 3: according to refraction law sin θ ₁/ sin ψ _R1=n ₀With sin θ ₂/ sin ψ _R2=n ₀(n ₀Be reflection-type volume holographic grating mean refractive index), calculate the corresponding incident angle ψ of reflection-type volume holographic grating under the matching condition of Prague _R1=13.7441 ° and ψ _R2=21.2538 °; Step 4:. utilizes under the matching condition of Prague the relational expression λ of incident angle and grating slope angle in the medium ₁/ λ ₂=cos (ψ _R1-φ)/cos (ψ _R2-φ), calculate grating slope angle φ=2.8062 °; Step 5: by grating slope angle φ, the incident angle ψ of correspondence under the matching condition of Prague _R1And the relational expression cos (φ-ψ between the grating periods lambda _R)=λ/2n ₀Λ derives grating periods lambda=0.1756 μ m; Step 6: choose above-mentioned one of the light wave of reading and (choose λ in the present embodiment ₂), as the light wave of reading that calculates grating refractive index degree of modulation and grating net thickness; Step 7: at λ ₂On the diffraction efficiency angle Selection linearity curve of=532nm correspondence, confirm two diffraction efficiency corresponding incident angle θ at zero point with main peak value left side next-door neighbour _-1=20.625 ° and θ _-2=19.25 °, utilize refraction law ψ _-1=arcsin (sin θ _-1/ n ₀) and ψ _-2=arcsin (sin θ _-2/ n ₀) incident angle corresponding in the said vacuum is converted to pairing incident angle ψ in the reflection-type volume holographic grating _-1=13.1998 °, ψ _-2=12.3407 °; Step 8: with incident angle ψ _-1And ψ _-2And the grating slope angle of trying to achieve in the said process and grating cycle be updated to simultaneously in the diffraction efficiency computing formula, calculate grating thickness δ=34.4 μ m.

Said step 8 comprises following steps: a. is with incident angle ψ _-1And ψ _-2And try to achieve grating slope angle φ in the said step 4,5 and the grating periods lambda is updated in the diffraction efficiency computing formula, the computing formula that obtains refractive index modulation degree does $n_1=\sqrt{({9b}_1^2-{4b}_2^2)/({9a}_1^2-{4a}_2^2)},$ Wherein:

b ₁＝[(2π/λ ₁)cos(φ-ψ _-1)-(πλ ₁/Λ ²n ₀]/[2(cosψ _-1-(λ ₁/Λn ₀)cosφ)]；

b ₂＝[(2π/λ ₁)cos(φ-ψ _-2)-(πλ ₁/Λ ²n ₀]/[2(cosψ _-2-(λ ₁/Λn ₀)cosφ)]；

$a_1=\mathrm{\π}/{\mathrm{\λ}}_1\sqrt{\cos {\mathrm{\ψ}}_{-1}(\cos {\mathrm{\ψ}}_{-1}-({\mathrm{\λ}}_1/\mathrm{\Λ}{n}_0)\cos \mathrm{\φ})};$

$a_2=\mathrm{\π}/{\mathrm{\λ}}_1\sqrt{\cos {\mathrm{\ψ}}_{-2}(\cos {\mathrm{\ψ}}_{-2}-({\mathrm{\λ}}_1/\mathrm{\Λ}{n}_0)\cos \mathrm{\φ})}.$

Calculate refractive index modulation degree n ₁=0.0554; B. with said refractive index modulation degree n ₁In=0.0554 substitution diffraction efficiency computing formula, the computing formula that obtains grating thickness does

And then draw the thickness δ=34.4 μ m of reflection-type volume holographic grating.

Claims (2)

1. the method for a reflection-type volume holographic grating parameter acquiring is characterized in that step is following:

Step 1: with the two light beams λ of any wavelength ₁And λ ₂Shine concurrent the gaining interest of reflection-type volume holographic grating to be measured respectively and penetrate, measure wavelength X ₁And λ ₂Pairing angle Selection linearity curve obtains wavelength X respectively ₁And λ ₂Corresponding diffraction efficiency angle Selection linearity curve;

Step 2: according to λ ₁And λ ₂Corresponding diffraction efficiency angle Selection linearity curve obtains the incident angle under the matching condition of Prague, i.e. λ ₁The corresponding incident angle θ of diffraction efficiency maximum ₁And λ ₂The corresponding incident angle θ of diffraction efficiency maximum ₂

Step 3:, calculate the corresponding incident angle ψ of Prague matching condition reflection-type volume holographic grating according to refraction law _R1And ψ _R2:

sinθ ₁/sinψ _R1＝n ₀

sinθ ₂/sinψ _R2＝n ₀

N wherein ₀Be reflection-type volume holographic grating mean refractive index.

Step 4: the relational expression λ that utilizes under the matching condition of Prague incident angle and grating slope angle in the medium ₁/ λ ₂=cos (ψ _R1-φ)/cos (ψ _R2-φ), calculate the grating slope angle

φ＝ψ _R2-arctan{[cos(ψ _R1-ψ _R2)-λ ₁/λ ₂]/sin(ψ _R1-ψ _R2)}；

Step 5: calculate grating periods lambda=λ ₁/ 2n ₀Cos (φ-ψ _R1);

Step 6: with λ ₁(or λ ₂) as the reading optical beam that calculates grating refractive index degree of modulation and grating net thickness, with two diffraction efficiency corresponding incident angle θ at zero point that are close to the main peak value on this reading optical beam diffraction efficiency angle Selection linearity curve _-1With θ _-2, and utilize refraction law that above-mentioned incident angle is converted to pairing incident angle ψ in the grating medium _-1=arcsin (sin θ _-1/ n ₀), ψ _-2=arcsin (sin θ _-2/ n ₀);

Step 7: calculate grating thickness

wherein:

$n_1=\sqrt{({9b}_1^2-{4b}_2^2)/({9a}_1^2-{4a}_2^2)};$

b ₁＝[(2π/λ ₁)cos(φ-ψ _-1)-(πλ ₁/Λ ²n ₀]/[2(cosψ _-1-(λ ₁/Λn ₀)cosφ)]；

b ₂＝[(2π/λ ₁)cos(φ-ψ _-2)-(πλ ₁/Λ ²n ₀]/[2(cosψ _-2-(λ ₁/Λn ₀)cosφ)]；

$a_1=\mathrm{\π}/{\mathrm{\λ}}_1\sqrt{\cos {\mathrm{\ψ}}_{-1}(\cos {\mathrm{\ψ}}_{-1}-({\mathrm{\λ}}_1/\mathrm{\Λ}{n}_0)\cos \mathrm{\φ})};$

$a_2=\mathrm{\π}/{\mathrm{\λ}}_1\sqrt{\cos {\mathrm{\ψ}}_{-2}(\cos {\mathrm{\ψ}}_{-2}-({\mathrm{\λ}}_1/\mathrm{\Λ}{n}_0)\cos \mathrm{\φ})}.$

2. according to the method for the said reflection-type volume holographic grating of claim 1 parameter acquiring, it is characterized in that step 5 calculating grating periods lambda=λ ₂/ 2n ₀Cos (φ-ψ _R2).

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