CN109599743B - Conical Photonic Crystal Laser Based on Mode Control of Photonic Crystal Defect States - Google Patents

Abstract

The invention discloses a tapered photonic crystal laser based on photonic crystal defect state mode control, comprising: a structure of an epitaxial layer, and the structure of the epitaxial layer comprises: an N-type substrate; on top; perfect 1D photonic crystal, on top of N-type confinement layer; active region, on perfect 1D photonic crystal; P-type confinement layer, on top of active region; P-type contact layer, on P-type confinement layer; and a tapered structure disposed on the P-plane of the epitaxial layer, the tapered structure comprising: a ridge waveguide portion; and a tapered waveguide portion connected with the ridge waveguide portion to achieve gain; wherein, a perfect one-dimensional The photonic crystal also includes a defect layer that destroys the periodicity of the perfect one-dimensional photonic crystal, and the active region is located in the defect layer. The laser can improve the beam quality of the semiconductor laser, increase the output power, reduce the vertical divergence angle, and realize stable vertical mode output.

Description

Conical Photonic Crystal Laser Based on Mode Control of Photonic Crystal Defect States

technical field

The present disclosure belongs to the field of semiconductor lasers, and relates to a tapered photonic crystal laser based on photonic crystal defect state mode control.

Background technique

Semiconductor lasers have many advantages, such as light weight, small size, and easy integration, and at the same time, they can achieve high-power and high-efficiency output. At present, semiconductor lasers are used in many fields such as material processing, communication, military, medical and so on. However, in these applications, including as a pump source for solid-state and fiber lasers, laser scalpels, laser weapons, metal cutting and welding, laser displays, etc., there is a high requirement for the brightness of the laser. Achieving high brightness requires both high output power and high beam quality. Traditional wide-contact semiconductor lasers can achieve high single-tube output power and power conversion efficiency, but due to their relatively wide output aperture, it is easy to cause lateral multi-mode generation, and the local change of refractive index makes it easy to produce beam filaments. The result is poor beam quality. Ridge-waveguide lasers, on the other hand, can achieve lateral near-diffraction-limited outputs, but are limited by small output apertures and gain volume, resulting in lower power.

In some structural designs to improve laser beam quality, tapered lasers have the characteristics of simple structure and process. A tapered laser includes a ridge waveguide section with fundamental mode selection and a tapered gain section for mode amplification. High-power near-diffraction-limited conical lasers have been reported. However, the traditional conical laser has a big disadvantage that the vertical divergence angle is large, and its full width at half maximum is usually more than 30° or even 40°, which will cause the beam shaping to be complicated and increase the cost in some applications. To obtain a narrow vertical divergence angle, some mode expansion structures have been proposed, including ultra-large optical cavities, passive waveguides, and low-refractive-index barrier layers. However, these structures can only reduce the divergence angle to a certain extent, and the minimum full width at half maximum divergence angle of less than 20° can be obtained, and the divergence angle cannot be further reduced to less than 10°. On the other hand, the confinement factor ratio between the fundamental mode and the higher-order mode of these mode expansion structures is not large enough, and lasing of the higher-order mode in the vertical direction is easy to occur under high current. In addition, the refractive index in the vertical direction may vary due to local temperature differences, resulting in changes in the mode distribution.

Therefore, it is necessary to propose a photonic crystal laser with good comprehensive performance: it can improve the beam quality of the semiconductor laser, increase the output power, reduce the vertical divergence angle, and achieve stable vertical mode output.

SUMMARY OF THE INVENTION

(1) Technical problems to be solved

In view of this, the purpose of the present disclosure is to provide a tapered photonic crystal laser based on photonic crystal defect state mode control, which can improve the beam quality of semiconductor lasers, increase the output power, reduce the divergence angle in the vertical direction, and realize a stable vertical mode output.

(2) Technical solutions

According to one aspect of the present disclosure, a tapered photonic crystal laser based on photonic crystal defect state mode control is provided, comprising: a structure of an epitaxial layer, the structure of the epitaxial layer comprising: an N-type substrate; an N-type confinement layer, On top of N-type substrate; Perfect 1D photonic crystal on top of N-type confinement layer; Active region on perfect 1D photonic crystal; P-type confinement layer on top of active region; P-type contact layer , located on the P-type confinement layer; and a tapered structure, arranged on the P surface of the epitaxial layer, the tapered structure comprising: a ridge waveguide portion; and a tapered waveguide portion connected with the ridge waveguide portion to achieve gain; Wherein, the perfect one-dimensional photonic crystal further includes a defect layer that destroys the periodicity of the perfect one-dimensional photonic crystal, and the active region is located in the defect layer.

In some embodiments of the present disclosure, a perfect one-dimensional photonic crystal consists of more than one period.

In some embodiments of the present disclosure, each periodic layer of a perfect one-dimensional photonic crystal contains two materials with alternating refractive indices, and the perfect one-dimensional photonic crystal in any two periodic layers has the same refractive index distribution and thickness distributed.

In some embodiments of the present disclosure, each periodic layer of a perfect one-dimensional photonic crystal realizes the alternating change of refractive index by changing a certain element composition in the multi-component material. For tapered photonic crystal lasers with different wavelengths, the material system is different, so The elements that change the composition are also different.

In some embodiments of the present disclosure, the defect layer is formed on top of a perfect one-dimensional photonic crystal by changing the thickness or refractive index to disrupt the periodic structure of the one-dimensional photonic crystal.

In some embodiments of the present disclosure, the active layer located in the defect region includes: single, multiple quantum well or quantum dot structures.

In some embodiments of the present disclosure, the width of the ridge waveguide portion is not greater than the cut-off width of the fundamental mode generated at the abrupt change of the tapered waveguide portion;

Preferably, the ridge waveguide portion forms an index-guided structure;

Preferably, the contact layers on both sides of the tapered waveguide portion are etched away to form the gain guide, or the tapered waveguide portion is etched to the same depth as the ridge waveguide portion to form the refractive index guide structure.

In some embodiments of the present disclosure, the design of the tapered waveguide portion is matched with the design of the ridge waveguide portion, and the taper angle of the tapered structure is smaller than the fundamental mode diffraction angle.

In some embodiments of the present disclosure, the lengths of the tapered waveguide portion and the ridged waveguide portion are selected according to device design requirements to ensure that sufficient lateral mode filtering characteristics and sufficient gain volume are obtained.

In some embodiments of the present disclosure, the perfect one-dimensional photonic crystal is a periodic structure, wherein the refractive index difference between two materials with different refractive indices in each period is greater than the refractive index change caused by temperature or carrier distribution changes.

(3) Beneficial effects

It can be seen from the above technical solutions that the tapered photonic crystal laser based on photonic crystal defect state mode control provided by the present disclosure has at least the following beneficial effects:

(1) Photonic crystal is an ordered structure material formed by two or more materials with different refractive indices arranged in a certain periodic order in space, which can control photons. In the epitaxial direction, the one-dimensional photonic crystal structure is applied to In the semiconductor laser, a photonic crystal laser is formed, and its structure includes a perfect one-dimensional photonic crystal structure with more than one period and a defect layer that destroys the periodicity of the one-dimensional photonic crystal, and the active region is located in the defect layer. The vertical mode is controlled based on the defect state of the photonic crystal. The fundamental mode is confined in the defect layer and decays rapidly in the perfect one-dimensional photonic crystal outside the defect layer. with little overlap. Therefore, the fundamental mode confinement factor is much larger than the higher-order mode confinement factor, enabling stronger mode differentiation. Through the gain effect of the active region in the defect layer, the fundamental mode light field is amplified, and a single-mode output in the vertical direction is obtained. This structure can reduce the vertical divergence angle, obtain a vertical divergence angle of about 10° or even less than 5°, improve the elliptical spot output in the far field of the laser output, and improve the brightness of the laser. In addition, due to the periodic modulation of the refractive index by the perfect one-dimensional photonic crystal structure, the refractive index difference is usually larger than the refractive index change due to temperature, thereby achieving a stable vertical mode output.

(2) On the P surface of the epitaxial layer, the designed tapered structure includes a tapered gain part and a ridge waveguide part, and the structural parameters of the two are reasonably designed to match them to form a tapered photonic crystal laser. Reasonable design of the structural parameters of the ridge waveguide part makes only the fundamental mode coupled into the tapered gain region, and the high-order modes are suppressed; the function of the tapered gain part is to realize the lateral fundamental mode amplification, and the output end face increases the lateral near-field size, It can improve the damage threshold of catastrophic optical cavity surface. Finally, a high-power near-diffraction-limited beam output can be obtained.

Description of drawings

FIG. 1 is a schematic structural diagram in the epitaxial direction of a tapered photonic crystal laser based on photonic crystal defect state mode control according to an embodiment of the present disclosure.

FIG. 2 is a schematic diagram of fundamental mode distribution in a vertical direction of a tapered photonic crystal laser according to an embodiment of the present disclosure.

FIG. 3 is a schematic diagram of the vertical far-field distribution of the tapered photonic crystal laser shown in FIG. 2 .

4 is a schematic diagram of a tapered structure of a tapered photonic crystal laser according to an embodiment of the present disclosure.

FIG. 5 is a schematic diagram of the output far field of the tapered photonic crystal laser according to an embodiment of the present disclosure.

FIG. 6 is a schematic diagram of the light intensity distribution at the beam waist of the tapered photonic crystal laser beam after collimation according to an embodiment of the present disclosure.

7 is a schematic diagram of a three-dimensional structure and an output beam of a tapered photonic crystal laser based on photonic crystal defect state mode control according to an embodiment of the present disclosure.

【Symbol Description】

11-P type electrode; 12-P type contact layer;

13-insulation layer; 14-P type confinement layer;

15,43-active region; 16,44-perfect one-dimensional photonic crystal;

17-N type confinement layer; 18-N type substrate;

19-N type electrode;

31, 41 - ridge waveguide section; 32, 42 - tapered waveguide section.

Detailed ways

The present disclosure provides a tapered photonic crystal laser based on photonic crystal defect state mode control. A one-dimensional photonic crystal structure is applied to a semiconductor laser to form a photonic crystal laser, and its structure includes a perfect one-dimensional photonic crystal structure with more than one period. And the defect layer that destroys the periodicity of one-dimensional photonic crystal, the active region is located in the defect layer, and the vertical mode can be regulated based on the defect state of the photonic crystal, which can improve the beam quality of the semiconductor laser, increase the output power, and reduce the divergence angle in the vertical direction. Achieve stable vertical mode output.

In order to make the objectives, technical solutions and advantages of the present disclosure clearer, the present disclosure will be further described in detail below with reference to the specific embodiments and the accompanying drawings. In the present disclosure, "tapered waveguide portion" and "tapered gain portion" have the same meaning. In the present disclosure, the structure of the "perfect one-dimensional photonic crystal" includes periodic structures and defect layers. In the present disclosure, "the P-side of the epitaxial structure" refers to the side including the P-type electrode in the epitaxial structure.

For the purpose of neatness of the drawings, some conventional structures and components may be shown in a simple and schematic manner in the accompanying drawings. In addition, some features in the drawings of the present application may be slightly enlarged or their proportions or dimensions are changed to achieve the purpose of facilitating the understanding and viewing of the technical features of the present invention, but this is not intended to limit the present invention. The actual size and specification of the product manufactured according to the disclosed content of the present invention should be adjusted according to the requirements during production, the characteristics of the product itself, and the content of the present invention as disclosed below.

FIG. 1 is a schematic structural diagram in the epitaxial direction of a tapered photonic crystal laser based on photonic crystal defect state mode control according to an embodiment of the present disclosure.

In the first exemplary embodiment of the present disclosure, a tapered photonic crystal laser based on photonic crystal defect state mode control is provided, including: a structure of an epitaxial layer, and the structure of the epitaxial layer includes: an N-type substrate 18 ; N-type confinement layer 17, located on the N-type substrate 18; perfect one-dimensional photonic crystal 16, located on the N-type confinement layer 17; active region 15, located on the perfect one-dimensional photonic crystal 16; P-type confinement Layer 14, located on the active region 15; P-type contact layer 12, located on the P-type confinement layer 14; P-type electrode 11, located on the P-type contact layer 12; Insulation layer 13, located on the P-type contact layer 12 (hereinafter also referred to as the contact layer, used to realize ohmic contact) and both sides of the P-type electrode 11; The tapered structure includes: a ridge waveguide part; and a tapered waveguide part, which is connected with the ridge waveguide part to achieve gain; wherein, the perfect one-dimensional photonic crystal also includes a period of destroying the perfect one-dimensional photonic crystal. A defect layer in which the active region is located.

Among them, a perfect one-dimensional photonic crystal consists of more than one period. Each periodic layer of a perfect one-dimensional photonic crystal contains two materials with alternating refractive indices, and the perfect one-dimensional photonic crystal in any two periodic layers has the same refractive index distribution and thickness distribution.

In this embodiment, the perfect one-dimensional photonic crystal includes N periods, and the thickness and refractive index of the two layers of materials in the single-period perfect one-dimensional photonic crystal are selected according to the needs. Perfect one-dimensional photonic crystals are alternately composed of two materials with different refractive indices. The different refractive index materials are realized by changing the composition of a certain element. For example, for AlGaAs materials, the content of Al can be changed.

In the present disclosure, the refractive index difference of a perfect one-dimensional photonic crystal periodic structure is generally larger than the refractive index change caused by temperature or carrier distribution changes. This strong refractive index modulation enables the tapered photonic crystal laser to obtain stable mode characteristics in the vertical direction.

In the present disclosure, the defect layer is formed on the perfect one-dimensional photonic crystal by changing the thickness or the refractive index to destroy the periodic structure of the one-dimensional photonic crystal, and the active region is located in the defect layer.

In the present disclosure, the active region contains no less than one quantum well or quantum dot structure.

In the present disclosure, the vertical mode is regulated based on photonic crystal defect states. The structural parameters of the perfect one-dimensional photonic crystal and the defect layer are rationally designed, so that the fundamental mode is confined in the defect layer, and the fundamental mode gradually decays in the perfect one-dimensional photonic crystal periodic structure far from the defect layer; In the photonic crystal structure, there is a small overlap with the active region. The final fundamental mode limiting factor is larger than the higher-order mode limiting factor, which achieves relatively strong mode differences and obtains vertical single-mode characteristics. The active region is located in the optical defect layer so that only the fundamental mode obtains the gain output.

In the present disclosure, the refractive index of the P-type confinement layer is lower than that of a perfect one-dimensional photonic crystal structure, so as to achieve confinement of the light field.

In the present disclosure, a composition graded layer is designed between different layers of the epitaxial layer of the tapered photonic crystal laser as a buffer layer, so as to reduce the lattice mismatch.

In the present disclosure, the thickness of the N-type confinement layer can be reasonably designed, so that the high-order mode can penetrate into the N-type substrate, while the fundamental mode will not leak to the substrate, so that the high-order mode has a much larger loss than the fundamental mode. It is also possible to introduce an absorber layer in the epitaxial layer, so that the higher order modes are absorbed while the fundamental mode is not affected. To further enhance the mode difference.

FIG. 2 is a schematic diagram of fundamental mode distribution in a vertical direction of a tapered photonic crystal laser according to an embodiment of the present disclosure.

As shown in Figure 2, the mode control based on photonic crystal defect states is also manifested in that the fundamental mode is expanded very widely, and different 1D photonic crystal period numbers can obtain mode expansion of different sizes. Mode expansion increases the spot size at the output end face. This can reduce the vertical divergence angle to below 10° or even 5°. The increase of the mode size can reduce the optical power density of the output cavity surface, improve the catastrophic optical damage threshold of the tapered photonic crystal laser, and then increase the output power.

FIG. 3 is a schematic diagram of the vertical far-field distribution of the tapered photonic crystal laser shown in FIG. 2 . As shown in Fig. 3, when the fundamental mode is widened to about 6.7 μm, the full width at half maximum of the far-field divergence angle is 9.4°. By further adjusting the vertical mode, a smaller vertical divergence angle can be obtained, while the horizontal divergence angle is usually within 10°, so that a nearly circular output spot can be obtained.

Preferably, a part of the covering layer or the waveguide layer on both sides of the ridge waveguide portion is etched away to form a refractive index-guided structure;

Preferably, the contact layers on both sides of the tapered waveguide portion are etched away to form the gain guide, or the tapered waveguide portion is etched to the same depth as the ridge waveguide portion to form the refractive index guide structure.

4 is a schematic diagram of a tapered structure of a tapered photonic crystal laser according to an embodiment of the present disclosure. As shown in FIG. 4 , 31 is a ridge waveguide part (sometimes also called ridge part and ridge waveguide below), 32 is a tapered waveguide part, which is also described as a tapered gain part in order to highlight its function below. . The ridge portion is formed by deep etching to form a ridge waveguide with mode selection. The tapered gain part can be fabricated by etching away the contact layer on both sides of the tapered region to avoid lateral diffusion of injected carriers and form a gain-guided structure; the tapered gain part and the ridge waveguide part can also be etched. Etch the same depth to form index guides, which simplifies the process.

In the present disclosure, in order to ensure the lateral fundamental mode operation, the width of the ridge waveguide can be obtained by calculating the fundamental mode cut-off width and the thickness of the remaining cladding layer, and the strip width cannot be greater than the fundamental mode cut-off width. To ensure low-loss transmission, the angle of the tapered gain region should be smaller than the fundamental mode diffraction angle. This can effectively avoid the coupling of fundamental mode energy into higher-order modes or radiation modes during beam transmission.

In the present disclosure, in terms of the length design of the tapered portion and the ridge portion, the lengths of the ridge waveguide portion and the tapered portion should be designed to ensure sufficient mode filtering characteristics to obtain lateral single-mode output, and at the same time, the device should have the best possible output. Possibly larger gain volume for higher power.

In some embodiments of the present disclosure, the design of the tapered waveguide portion is matched with the design of the ridge waveguide portion, and the taper angle of the tapered structure is smaller than the fundamental mode diffraction angle.

In some embodiments of the present disclosure, the lengths of the tapered waveguide portion and the ridged waveguide portion are selected according to device design requirements to ensure that sufficient lateral mode filtering characteristics and sufficient gain volume are obtained.

In some embodiments of the present disclosure, a group of graded layers is further included between different layers of the epitaxial layer as a buffer layer, so as to reduce lattice mismatch.

FIG. 5 is a schematic diagram of the output far field of the tapered photonic crystal laser according to an embodiment of the present disclosure. As shown in Figure 5, the horizontal and vertical directions correspond to the lateral and vertical directions of the output end face of the tapered photonic crystal laser, respectively. When the vertical divergence angle is reduced to a certain extent and is close to the horizontal divergence angle, the near-circular light spot output shown in the figure can be obtained. This small divergence angle near circular output far field can reduce the cost and complexity of beam shaping in the application.

FIG. 6 is a schematic diagram of the light intensity distribution at the beam waist of the tapered photonic crystal laser beam after collimation according to an embodiment of the present disclosure. As shown in Fig. 6, the horizontal and vertical directions correspond to the lateral and vertical directions of the output end face of the tapered photonic crystal laser, respectively. The light intensity at the beam waist in both the lateral and vertical directions exhibits a near-Gaussian single-lobe distribution, indicating that the tapered photonic crystal laser has near-diffraction-limited beam quality in both the vertical and horizontal directions.

7 is a schematic diagram of a three-dimensional structure and an output beam of a tapered photonic crystal laser based on photonic crystal defect state mode control according to an embodiment of the present disclosure. As shown in FIG. 7 , 41 and 42 are the surface ridge waveguide part and the tapered gain part, respectively, 43 is the active region, and 44 is the periodic structure of a perfect one-dimensional photonic crystal. When the divergence angles in the vertical and lateral directions are equivalent, the laser can obtain a nearly circular beam output, and the lateral and vertical directions are both single-mode outputs. The one-dimensional photonic crystal periodic structure can achieve stable single-mode output by adjusting the vertical mode and reducing the divergence angle. In addition, the tapered photonic crystal structure of the present disclosure has large light exit apertures in the vertical and horizontal directions, which reduces the optical power density of the cavity surface and improves the cavity surface damage threshold of the tapered photonic crystal laser. Finally, the brightness of the laser is improved from the two aspects of the chip's beam quality and output power.

To sum up, the present disclosure provides a tapered photonic crystal laser based on photonic crystal defect state mode control, applying a one-dimensional photonic crystal structure to a semiconductor laser to form a photonic crystal laser, the structure of which includes a perfect cycle of more than one period. The one-dimensional photonic crystal structure and the defect layer that destroys the periodicity of the one-dimensional photonic crystal, the active region is located in the defect layer, and the vertical mode can be regulated based on the defect state of the photonic crystal, which can improve the beam quality of the semiconductor laser, increase the output power, reduce the Divergence angle in the vertical direction to achieve stable vertical mode output.

It should be noted that, in the drawings or descriptions in the specification, the same drawing numbers are used for similar or identical parts. Implementations not shown or described in the drawings are forms known to those of ordinary skill in the art. Additionally, although examples of parameters including specific values may be provided herein, it should be understood that the parameters need not be exactly equal to the corresponding values, but may be approximated within acceptable error tolerances or design constraints. Directional terms mentioned in the embodiments, such as "up", "down", "front", "rear", "left", "right", etc., only refer to the directions of the drawings. Therefore, the directional terms used are used to illustrate and not to limit the scope of protection of the present invention.

In the context of this disclosure, when a layer/element is referred to as being "on" another layer/element, it can be directly on the other layer/element or intervening layers/elements may be present therebetween. element. In addition, if a layer/element is "on" another layer/element in one orientation, then when the orientation is reversed, the layer/element can be "under" the other layer/element.

Furthermore, the word "comprising" does not exclude the presence of elements or steps not listed in a claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements.

The specific embodiments described above further describe the purpose, technical solutions and beneficial effects of the present disclosure in detail. It should be understood that the above-mentioned specific embodiments are only specific embodiments of the present disclosure, and are not intended to limit the present disclosure. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure should be included within the protection scope of the present disclosure.

Claims (8)

1. the tapered photonic crystal laser based on photonic crystal defect state mode control, is characterized in that, comprises: the structure of an epitaxial layer, the structure of this epitaxial layer comprises: N-type substrate; N-type confinement layer, located on the N-type substrate; Perfect one-dimensional photonic crystal, located on the N-type confinement layer; The active region is located on a perfect one-dimensional photonic crystal; P-type confinement layer, located above the active region; A P-type contact layer overlying the P-type confinement layer; and a tapered structure, arranged on the P-plane of the epitaxial layer, the tapered structure comprises: a ridge waveguide part; and a tapered waveguide part, which is connected with the ridge waveguide part to realize gain; Wherein, the perfect one-dimensional photonic crystal is composed of more than one period, each periodic layer of the perfect one-dimensional photonic crystal contains two kinds of materials whose refractive index changes alternately, and the perfect one-dimensional photon in any two periodic layers The crystals have the same refractive index distribution and thickness distribution; The perfect one-dimensional photonic crystal also includes a defect layer that destroys the periodicity of the perfect one-dimensional photonic crystal, and the active region is located in the defect layer; The defect layer is formed on the perfect one-dimensional photonic crystal by changing the thickness or the refractive index to destroy the periodic structure of the one-dimensional photonic crystal; A perfect one-dimensional photonic crystal is a periodic structure in which the refractive index difference between two materials with different refractive indices in each period is greater than the refractive index change caused by temperature or carrier distribution changes. 2. The tapered photonic crystal laser according to claim 1, wherein each periodic layer of the perfect one-dimensional photonic crystal realizes the alternating change of refractive index by changing a certain element composition in the multi-component material. Shape photonic crystal lasers, the material system is different, and the elements of the changed composition are also different. 3. The tapered photonic crystal laser according to claim 1, wherein the active layer located in the defect layer comprises: a single, multiple quantum well or quantum dot structure. 4 . The tapered photonic crystal laser according to claim 1 , wherein the width of the ridge-shaped waveguide portion is not greater than the cut-off width of the fundamental mode at the abrupt change of the tapered waveguide portion. 5 . 5. The tapered photonic crystal laser of claim 4, wherein the ridge waveguide portion forms a refractive index guiding structure. 6. The tapered photonic crystal laser according to claim 5, wherein the contact layers on both sides of the tapered waveguide portion are etched away to form a gain guide, or the tapered waveguide portion is etched the same as the ridge waveguide portion The depth forms the index guiding structure. 7. The tapered photonic crystal laser according to claim 1, wherein the design of the tapered waveguide portion is matched with the design of the ridge waveguide portion, and the taper angle of the tapered structure is smaller than the fundamental mode diffraction angle. 8 . The tapered photonic crystal laser of claim 1 , wherein the lengths of the tapered waveguide portion and the ridge waveguide portion are selected according to device design requirements to ensure sufficient lateral mode filtering characteristics and sufficient gain volume. 9 .

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