JPH0352893A - Diffraction grating - Google Patents

Abstract

PURPOSE:To obtain diffraction grating consisting of a double diffraction grating specified in several dimension or relative configuration of each diffraction grating and carried out in coexistence of high efficiency and dispersing properties at low angle of wavelength by making angle disperse of wavelength small. CONSTITUTION:The diffraction grating consisting of a double diffraction grating set so as to satisfy the formula (K1 is lattice constant on input side; K2 is lattice constant on output side; theta' is angle formed by two diffraction gratings; thetai' is diffraction angle by diffraction grating on input side; thetao is diffraction angle by diffraction grating on output side). Specifically, for example, diffraction gratings 1 and 2 having each the above-mentioned lattice constant is integrally formed in the obverse and reverse of wedge-shaped same substrate 4 having spread of the angle theta'.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of Industrial Application The present invention relates to a diffraction grating used in various optical fields.

BACKGROUND OF THE INVENTION Diffraction gratings are one of the most common and important optical elements. Regarding such diffraction gratings, for example, "Principles of Optics UJ (written by M. Born and E. Wolf, translated by Toru Kusakawa and Hidetsugu Yokota)" published by Tokai University Press (1975.5.15 edition) 8.6.1 Diffraction grating J, and a diffraction grating is an element that separates light that is not of a single wavelength into single wavelengths.

A typical example of such a diffraction grating is a surface relief type diffraction grating. This has a very high efficiency, which in principle exceeds 90%.

Problem to be Solved by the Invention However, in order to achieve high efficiency in such a diffraction grating, the grating pitch must be made as small as the wavelength to achieve Bragg diffraction.

However, if the grating pitch is small, the angular dispersion becomes large. That is, assuming that the input angle to the diffraction grating is Ol1, the diffraction angle is Oo, the wavelength is λ, and the grating pitch is A, the formula showing the diffraction angle characteristic of the diffraction grating is sinOi + sin
θ0=λ/A. Therefore, for example, assuming that the input light is a semiconductor laser beam and its wavelength λ has a mode hop from 0.77 μm to 0.79 pn+, the diffraction angle Oo will also be 3 from the above equation.
Hop from 2.9' to 34.9° (however, A=0
．． 7. Oi is Bragg angle). Such a diffraction angle e
A large spread of o of as much as 2 degrees is extremely large depending on the application, and is often impractical.

Means for Solving the Problem Let the grating constant of the diffraction grating on the input side be K, the grating constant of the diffraction grating on the output side be K, and the angle between the two diffraction gratings be Δθ'.
When the diffraction angle by the input-side diffraction grating is Oi' and the diffraction angle by the output-side diffraction grating is l)o, the specifications or relative arrangement of each diffraction grating were set so as to satisfy the following formula. It was constructed with a double diffraction grating.

When the working diffraction grating is made double and its respective specifications such as the lattice constant or relative arrangement satisfy the above formula, the angular dispersion of wavelength becomes small, so high efficiency and low angular dispersion function are achieved. This means that both can be compatible, and it can be used without any problem even in applications where broadening of the diffraction angle is a problem.

Embodiment An embodiment of the present invention will be explained based on FIGS. 1 and 2. In this example, in order to achieve high efficiency and low angular dispersion,
Basically, it is a transmission type double diffraction grating 3 comprising a diffraction grating 1 placed on the input side and a diffraction grating 2 placed on the output side. Here, the grating pitches A,, A, of each of the diffraction gratings 1 and 2 are assumed to have high efficiency while maintaining the same wavelength, but the pitches A,, A, are shaped or shaped to have a predetermined relationship. has been done. This condition is expressed as 2 as shown in Figure 2.
This will be explained with reference to a diffraction diagram of the multiple diffraction grating 3.

Here, the lattice constant of the input side diffraction grating l is K (corresponding to grating bit A1), the lattice constant of the output side diffraction grating 2 is K,
(corresponding to grating bit A8), two diffraction gratings 1 and 2
The angle formed by ΔQ /, the angle of incidence on the input side diffraction grating l is Oi, the diffraction angle is Oi', the output side diffraction grating 2
Let the diffraction angle by Oo be Oo. Also, the propagation constant is κ. shall be. Then +c. sinOi + κ, sinOi'
=K, −−−−'−−−−−−−−=−−−−
(1) κ, sin (Oi'1△e') + κ, sin
(Qo+Δ0')=K,・・・・・・・・・・・・
...(2) The relationship will be established. These (1)
Solving equation (2) yields the following.

Therefore, if the angular dispersion due to wavelength change is Oi' Oo, then...
...(6). However, n. is the central refractive index of the diffraction grating. Also, the angles θi' and Oo are shown in (3) and (4) above.
It is determined by the formula.

Here, the fact that the double diffraction grating 3 has a lower angular dispersion than that of only l diffraction gratings means that Oi'〉Oo, so based on equations (5) and (6), the following relational expression is satisfied. Each diffraction grating 1. It is sufficient to set the dimensions K, , K, ie, the grating pitches A, , A, or the angle ΔO' between the two, which indicates the relative arrangement. In addition, the above-mentioned lattice pitch A
,, A, becomes A=2π/K, , A,=2π/K.

In this way, the double diffraction grating 3 of this embodiment achieves both high efficiency and low angular dispersion.

Note that the double diffraction grating structure may be one in which the diffraction gratings 1 and 2 are integrally formed on the front and back sides of the same wedge-shaped substrate 4 having a spread angle ΔO', as shown in FIG. 3, for example. . Furthermore, the structure is not limited to a transmission type double grating structure, but may also be a reflection type double diffraction grating structure as shown in FIG. 4, or a transmission type and reflection type double diffraction structure as shown in FIG. It may also be a structure.

Effects of the Invention As described above, the present invention has the following advantages: the grating constant of the input side diffraction grating is Kl%, the grating constant of the output side diffraction grating is K8, the angle between the two diffraction gratings is Δo', and the input side diffraction grating is When the diffraction angle by the diffraction grating is Oi', and the diffraction angle by the output side diffraction grating is θ0, the specifications or relative arrangement of each diffraction grating consists of a double diffraction grating set so as to satisfy the following formula. Therefore, it is possible to reduce the angular dispersion of wavelength and achieve both high efficiency and low angular dispersion of wavelength, which is impossible with only one diffraction grating.

[Brief explanation of drawings]

FIG. 1 is a schematic front view showing one embodiment of the present invention, FIG. 2 is a diffraction diagram of a double diffraction grating, and FIGS. 3 to 5 are schematic diagrams showing different modifications. 1...Diffraction grating on the input side, 2...Diffraction grating on the output side, 3...Double diffraction grating Applicant Rico Co., Ltd.

Claims (1)

[Claims] The grating constant of the input side diffraction grating is K_1, the grating constant of the output side diffraction grating is K_2, and the angle between the two diffraction gratings is Δθ
', the diffraction angle by the input side diffraction grating is θi', and the diffraction angle by the output side diffraction grating is θo, the specifications or relative arrangement of each diffraction grating are [K_2-{K_1cos(θ
i′−Δθ′)}/{cosθi′}]/[cos(θ
o+Δθ')]<K_1/cosθi'.