JP2011075861A - Method of manufacturing transmission type optical diffraction grating element - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of easily designing and manufacturing a transmission type optical diffraction grating element having a desired transmission spectrum. <P>SOLUTION: By the method of manufacturing the transmission type optical diffraction grating element, local complex transmittance t<SB>k</SB>and complex reflectance r<SB>k</SB>are determined at each position in a longitudinal direction divided in N on the basis of a desired transmission spectrum t(δ) (where δ=β-β<SB>B</SB>, β: wave number of light, β<SB>B</SB>: Bragg design wave number) or the like, local complex reflectance ρ<SB>k</SB>is determined at each position, local combination coefficient q<SB>k</SB>is determined at each position, refractive index n<SB>k</SB>is determined at each position along the advancing direction of light in the transmission type diffraction grating element to be manufactured, and the transmission type optical diffraction grating having the determined refractive index distribution is manufactured. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a method for manufacturing a transmissive optical diffraction grating element.

  Optical diffraction grating elements using Bragg diffraction of light are roughly classified into reflection type optical diffraction grating elements and transmission type optical diffraction grating elements. The reflective optical diffraction grating element can output reflected light reflected with a reflectivity and delay corresponding to the wavelength of incident light, and is used as a reflective optical filter or dispersion adjusting element. Further, the transmissive optical diffraction grating element can output transmitted light having a transmittance corresponding to a wavelength with respect to incident light, and is used as a transmissive optical filter. Both the reflection type optical diffraction grating element and the transmission type optical diffraction grating element are realized as a periodic structure of the refractive index distribution of the core region along the longitudinal direction in the optical fiber, and are used in an optical communication system or the like. The reflection type optical diffraction grating element is designed and manufactured by the layer peeling method described in Non-Patent Documents 1 and 2.

Ricardo Feced, et al, "An Efficient Inverse Scattering Algorithm for the Design of Nonuniform Fiber Bragg Gratings," IEEE Journalof Quantum Electronics, Vol.35, No.8, pp.1105-1115 (1999). Jan Kristoffer, et al, "Design of Grating-Assisted Codirectional Couplers with Discrete Inverse-Scattering Algorithm," Journal of Lightwave Technology, Vol. 21, No. 1, pp. 254-263 (2003).

  When the reflection type optical diffraction grating element is used as an optical filter or a dispersion adjusting element, the incident light and the reflected light are coaxial, so that, for example, an optical circulator is required as an optical component for separating both lights. Therefore, it is expensive to implement an optical filter using a reflective optical diffraction grating element. On the other hand, the transmissive optical diffraction grating element can function as an optical filter without the need for other optical components, and thus is low in cost. Therefore, from the viewpoint of cost, the transmission type optical diffraction grating element is preferable to the reflection type optical diffraction grating element.

  However, although a method for designing and manufacturing a reflective optical diffraction grating element is known, a method for designing and manufacturing a transmission optical diffraction grating element is not yet known. Therefore, it has been difficult to manufacture a transmissive optical diffraction grating element having a desired transmission spectrum.

  The present invention has been made to solve the above problems, and an object of the present invention is to provide a method for easily designing and manufacturing a transmission type optical diffraction grating element having a desired transmission spectrum.

A transmission type optical diffraction grating element manufacturing method according to the present invention is a method of manufacturing a transmission type optical diffraction grating element, and (a) a length along the traveling direction of light in the transmission type optical diffraction grating element to be manufactured. Where L is L, and the number of divisions when equally dividing the range of the diffraction grating length L is N, a division length Δ (= L / N) is obtained, and these parameters and a desired transmission spectrum t (δ) (however, , Δ = β−β _B , β: wave number of light, β _B : Bragg design wave number), and local complex transmittance t _k at each position z _k among the N divided positions according to the equation (1). and a complex transmission factor-complex reflectivity calculating step of obtaining a complex reflectance r _k, (b) local complex transmittance t _k and the complex at each position z _k determined in the complex permeability, complex reflectivity calculating step based on the reflectance _{r k,} in accordance with equation (2), Dear Based on the complex reflection coefficient calculation step for obtaining the local complex reflection coefficient ρ _k at the position z _k , and (c) the local complex reflection coefficient ρ _k at each position z _k obtained in the complex reflection coefficient calculation step, (3) A coupling coefficient calculation step for obtaining a local coupling coefficient q _k at each position z _k according to the equation (3), and (d) a local coupling coefficient q _k at each position z _k obtained in the coupling coefficient calculation step. Based on the equation (4), a refractive index distribution calculating step for obtaining a refractive index _nk at each position z _k , and (e) a transmissive optical diffraction grating element having a refractive index distribution obtained in the refractive index distribution calculating step And a manufacturing step for manufacturing.

  According to the present invention, a transmission type optical diffraction grating element having a desired transmission spectrum can be easily designed and manufactured.

It is a figure explaining each parameter used when designing a reflection type optical diffraction grating element or a transmission type optical diffraction grating element. It is a flowchart explaining the transmissive optical diffraction grating element manufacturing method which concerns on this embodiment.

  DESCRIPTION OF EMBODIMENTS Hereinafter, embodiments for carrying out the present invention will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same elements are denoted by the same reference numerals, and redundant description is omitted.

  First, parameters used in designing a reflection type optical diffraction grating element or a transmission type optical diffraction grating element (hereinafter collectively referred to as “optical diffraction grating element”) will be described. As shown in FIG. 1, it is assumed that incident light is incident on the optical diffraction grating element to be manufactured in the + z direction. The division length Δ (= L / N) is obtained from the length L along the z direction in the optical diffraction grating element and the division number N when equally dividing the range of the diffraction grating length L.

Let r (δ) be the desired reflection spectrum of the reflective optical diffraction grating element to be manufactured, and let t (δ) be the desired transmission spectrum of the transmission optical diffraction grating element to be manufactured. However, δ = β−β _B , β is the wave number of light, and β _B is the Bragg design wave number. At the k-th position z _k (k = 1 to N) among the N divided positions, the amplitude of light traveling in the + z direction is _represented by u _k (δ), and the amplitude of light traveling in the −z direction is _represented by v _k (δ). , The local complex transmittance is t _k (δ), the local complex reflectance is r _k (δ), the local complex reflection coefficient is ρ _k , and the local coupling coefficient is q _k. In addition, the refractive index is _nk .

Next, as a reference example, a method for designing and manufacturing a reflective optical diffraction grating element will be described. In this case, at position z ₁ , the amplitude u ₁ of the light traveling in the + z direction is the amplitude of the incident light, and the amplitude v ₁ of the light traveling in the −z direction is the amplitude of the reflected light. It holds. The complex reflectance r ₁ (δ) at the position z ₁ is equal to the desired complex reflectance r (δ).

The value of the complex reflectance r ₁ (δ) at time t = 0 during the impulse response is considered to represent the local reflection coefficient at the position z ₁ . Therefore, the local complex reflection coefficient [rho ₁ at the position z ₁ is expressed by the following equation (6).

Local complex reflectivity r ₂ at the position z _{2 ([delta]),} using the local complex reflectivity r _{1 ([delta])} and the complex reflection coefficient [rho ₁ at the position z _1, the following equation (7) expressed. In general, the local complex reflectance r _k (δ) at the position z _k is expressed by the following equation (8). Local complex reflection coefficient [rho _k at position z _k is expressed by the following equation (9).

Based on local complex reflection coefficient [rho _k at each position z _k determined as described above, local coupling coefficient q _k at each position z _k is determined by the following equation (10). Further, based on local coupling coefficient _{q k} at each position _{z k,} the refractive index _{n k} at each position _{z k} is determined by the following equation (11). n ₀ is the average refractive index, and Δn _k is the amount of refractive index modulation at position z _k . Then, a reflection type optical diffraction grating element having the refractive index distribution obtained as described above is manufactured.

Next, a transmissive optical diffraction grating device manufacturing method according to this embodiment will be described. As shown in FIG. 2, the transmission type diffraction grating device manufacturing method according to the present embodiment, the complex transmittance, complex reflectivity for obtaining a local complex transmittance t _k and the complex reflectance r _k at each position z _k rate calculation step S1, the complex reflection coefficient calculating step S2 for determining the local complex reflection coefficient [rho _k at each position z _k, coupling coefficient calculating step S3 to determine a local coupling coefficient q _k at each position z _k, each position z refractive index distribution calculating step S4 to determine the refractive index n _k of _k, and comprises a manufacturing step S5 of manufacturing a transmission type diffraction grating device having a refractive index distribution obtained at the refractive index distribution calculating step.

The complex transmittance, complex reflectivity calculation step S1 seek local complex transmittance t _k and the complex reflectance r _k, the following processing is performed.

In + z side than at _{z N,} + amplitude _{u N + 1} of light z traveling in the direction is the amplitude of the transmitted light, since the amplitude _{v N + 1} of the light traveling in the -z direction is 0, the following equation (12) holds. That is, in the + z side than at z _N, + z amplitude u _{N + 1} of the light traveling in the direction is equal to the desired complex transmittance t ([delta]).

Position _z forward and reverse directions of the light amplitude at -z side of _{k (u k, v k)} and forward and reverse amplitude of each of the light at the position _{z k} + z side _{(u k +} 1, v _{k + 1)} and, given the transfer matrix _{M k} between the following (13) to (15) below holds.

The transfer matrix M _k is expressed by the following equation (16). The inverse matrix X _k of the transfer matrix M _k is expressed by the following equation (17). Here, each component of the inverse matrix X _k of the transfer matrix M _k is expressed as the following equation (18).

Then, the amplitudes (u _k , v _k ) of light in the forward direction and the backward direction at the position z _k are expressed by the following equation (19). Now, local complex transmittance _{t k} at position _{z k} is expressed by the following equation (20).

From this equation, the following equation (21) is obtained. Here, X ₁₁ ^(k) and X ₁₂ ^(k) calculated from the equations (17) and (18 ⁾ were used.

Further, from the above equation (8), the local complex reflectance r _k (δ) at the position z _k is expressed by the following equation (22).

The complex reflectance r _{N + 1} is 0 as shown in the following equation (23). Using this equation (23), the complex transmittance t _N when k = N in the above equation (21) is expressed by the following equation (24). Further, when this equation (23) is used, the complex reflectance r _N when k = N in the above equation (22) is expressed by the following equation (25).

Thereafter, similarly, the complex transmittance t _N-1 is represented by the following equation (26), the complex reflectance r _N-1 is represented by the following equation (27), and the complex transmittance t _N-2 is represented by the following formula ( 28) From this point on, the complex reflectance r ₁ and the complex transmittance t ₁ are similarly obtained.

The complex transmittance, complex reflectivity calculation step S1, as described above, the local complex transmittance t _k and the complex reflectance r _k at each position z _k is determined. The complex reflection coefficient calculating step S2 following the complex transmittance, complex reflectivity calculation step S1, based on local complex transmittance t _k and the complex reflectance r _k at each position z _k, topical at position z _k A complex reflection coefficient ρ _k is obtained by the following equation (29).

In a coupling coefficient calculation step S3 subsequent to the complex reflection coefficient calculation step S2, a local coefficient at each position z _k is determined based on the local complex reflection coefficient ρ _k at each position z _k obtained in the complex reflection coefficient calculation step S2. The coupling coefficient q _k is _obtained by the above equation (10).

In the refractive index distribution calculating step S4 following the coupling coefficient calculating step S3, the refractive index n _{k at} each position z _k is calculated based on the local coupling coefficient q _k at each position z _k obtained in the coupling coefficient calculating step S3. It is obtained by the above equation (11).

In a manufacturing step S5 subsequent to the refractive index distribution calculating step S4, a transmission type optical diffraction grating element having the refractive index distribution obtained in the refractive index distribution calculating step S4 is manufactured. For example, a phase grating mask in which a diffraction grating is formed on one main surface of a transparent flat plate is used, and a phase grating mask is disposed on the side surface of an optical fiber having a core region made of GeO ₂ -doped silica glass. A transmission type optical diffraction grating element (optical fiber grating element) is manufactured by irradiating an optical fiber with a laser beam having a wavelength capable of changing the rate (for example, KrF laser beam having a wavelength of 248 nm) through a phase grating mask. .

The period of the diffraction grating formed on the main surface of the phase grating mask used at this time corresponds to the period of the refractive index distribution obtained in the refractive index distribution calculating step S4, and is also the longitudinal direction of the optical fiber. laser light irradiation amount at each position is the one corresponding to the refractive index modulation amount [Delta] n _k at each position in the refractive index distribution determined by the refractive index distribution calculating step S4.

As described above, a transmissive optical diffraction grating element having a desired transmission spectrum t (δ) is manufactured. Such a transmission type optical diffraction grating element can function as an optical filter having desired characteristics without the need for other optical components, and thus is low in cost.

Claims (1)

A method for manufacturing a transmissive optical diffraction grating element, comprising:
In the transmission type optical diffraction grating element to be manufactured, the length along the light traveling direction is L, and the division number when equally dividing the range of the diffraction grating length L is N, the division length Δ (= L / N), and based on these parameters and the desired transmission spectrum t (δ) (where δ = β−β _B , β: wave number of light, β _B : Bragg design wave number), according to equation (1) a local complex transmittance, complex reflectivity calculating step of calculating the complex transmittance t _k and the complex reflectance r _k at each position z _k of the N split position,

Based on local complex transmittance t _k and the complex reflectance r _k at each position z _k determined in the complex permeability, complex reflectivity calculating step, according to equation (2), locally at each position z _k A complex reflection coefficient calculating step for obtaining a complex reflection coefficient ρ _k ,

Based on the local complex reflection coefficient ρ _k at each position z _k obtained in the complex reflection coefficient calculation step, a coupling coefficient calculation for obtaining a local coupling coefficient q _k at each position z _k according to the equation (3). Steps,

A refractive index distribution calculating step for obtaining a refractive index n _k at each position z _k according to the equation (4) based on the local coupling coefficient q _k at each position z _k obtained in the coupling coefficient calculating step;

A manufacturing step of manufacturing the transmissive optical diffraction grating element having the refractive index distribution obtained in the refractive index distribution calculating step;
A transmissive optical diffraction grating element manufacturing method comprising:

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