RU2587097C1 - Injection laser - Google Patents

Abstract

FIELD: lasers.

SUBSTANCE: application: for semiconductor injection lasers. Summary of invention consists in fact that injection laser based on semiconductor heterostructure separate limitation, including multimode waveguide, first and second high band gap limiting layers, which are simultaneously respectively emitters of p-and n-type conductivity and located on both sides of multimode waveguide, active region, located in multi-mode waveguide and consisting of at least one quantum-dimensional active layer, ohmic contacts and optical resonator, between multimode waveguide and one of first and second wideband limiting layers includes first single-mode waveguide and first additional wide band gap limiting layer, wherein first additional wide band gap limiting layer is located between multimode waveguide and the first single-mode waveguide, optical limiting factor

for the active region of one of its own m-mode (m is integer) multimode waveguide satisfies following ratio, and thickness of P₁, nm, of first additional wide band gap of restricting layer, effective refraction index N_d of first single-mode waveguide natural mode and minimum value of n_s of effective refraction index of characteristic modes multimode waveguide satisfy also presented by relationships.

EFFECT: technical result is possibility to produce injection laser with reduced divergence of laser beam and increased thickness of waveguide with preservation of laser generation on transverse mode.

5 cl, 14 dwg

Description

The invention relates to quantum electronic technology, and more specifically to semiconductor injection lasers, and can find application as an optical radiation source for pumping fiber amplifiers, fiber and solid-state lasers, in equipment for processing materials, in metrology, printing, medicine, optical location systems, robotics and other industries.

The vast majority of semiconductor injection lasers are in the form of end emitters with a strip contact. An important task in the development of such emitters is to maximize the radiation power and improve the quality of the laser beam. A typical end-semiconductor injection laser consists of a quantum-well active region located in an undoped or lightly doped waveguide. The waveguide on both sides is enclosed between the boundary layers having a lower refractive index than the waveguide layer. The boundary layers usually act as emitters, for which one boundary layer is doped with an n-type impurity, and the other with a p-type impurity. The waveguide parameters determine the mode composition of laser radiation. In the general case, several transverse optical modes can exist, which are distinguished by the order of m. The fundamental or fundamental mode has zero order (m = 0). The radiative recombination of injected electrons and holes in the active region leads to the appearance of light amplification. When the pump current reaches a threshold value, lasing begins. The threshold condition for laser generation:

where g is the material gain in the active region,

- фактор оптического ограничения (гамма-фактор) для активной области оптической моды m-порядка,

- optical limiting factor (gamma factor) for the active region of the m-order optical mode,

α _{int, m} , α _{out, m} are the internal and external optical losses for the m-order optical mode, respectively.

In the general case, the number and mode profile of an optical waveguide depend on the thickness of the waveguide and the refractive indices of the waveguide and the bounding layers. With an increase in the thickness of the waveguide upon reaching a certain critical value, which depends on the refractive indices of the waveguide and the bounding layers, the waveguide can support high-order modes. Thus, the expansion of a laser waveguide can lead to laser generation on high-order modes and to multimode generation. This leads to the expansion of the radiation pattern in the plane perpendicular to the layers of the structure, and to the appearance of additional maxima in it, which affects the properties of the laser from the point of view of its practical application. The expansion of the waveguide, while maintaining the single-mode nature of the radiation, has positive effects: the fundamental mode in the wider waveguide has a smaller divergence angle in the radiation pattern; in a wider waveguide, the optical power density on the laser mirrors is reduced, which increases their degradation resistance; The optical losses on free carriers in highly doped emitters are reduced, since in the expanded waveguide, the fundamental mode is more strongly localized in the weakly doped waveguide. These advantages of the extended waveguide are especially relevant for high power semiconductor injection lasers.

Various approaches are known for increasing the size of the emitting region of injection lasers and, accordingly, reducing the divergence of the laser beam.

Thus, an injection laser is known (see application US 20100150196, IPC H01S 5/00, published June 17, 2010), consisting in series of a first limiting layer for limiting the optical mode, a first waveguide layer for propagating the optical mode, a separation layer for separating the optical mode, a second waveguide layer for propagating the optical mode, an active layer for generating the optical mode, a third waveguide layer for propagating the optical mode, and a second confining layer to limit the optical mode. In this case, the first, second and third waveguide layers have the same refractive index, and the first bounding layer, the separation layer, and the second bounding layer have refractive indices lower than the refractive indices of the first, second, and third waveguide layers. In a known injection laser, three waveguide layers are constituent parts of a single waveguide that supports only one optical mode. The size of the mode is increased due to its penetration into the bounding layers. The increased size of the mode made it possible to narrow the divergence of the laser beam to values less than 24 degrees (at a level of 0.5). The use of a separation layer forms a shoulder in the mode distribution profile, which spatially coincides with the active region, due to which the optical confinement factor increases.

A disadvantage of the design of the known injection laser is the significant penetration of the optical mode into the doped boundary layers, which increases the optical loss. A further decrease in the divergence of the laser beam is possible only with an increase in the thickness of the waveguide layers and a decrease in the jump in the refractive index between the waveguide and bounding layers, which further increases the mode penetration into the bounding layers.

A well-known injection laser (see patent US 5923689, IPC H01S 3/19, published July 13, 1999), consisting in layers of GaAs n-type substrates, GaAs n-type buffer layer with a thickness of 0.4 μm with a dopant concentration of 2 · 10 ¹⁸ cm- ³ , Al _0.5 In _0.5 P, an n-type boundary layer 0.5 μm thick with a dopant concentration of 4 · 10 ¹⁷ cm ^-3 , (Al _0.6 Ga _0.4 ) _0.5 In _{0 , 5} P of an n-type passive waveguide 2000 angstrom thick with a dopant concentration of 4 × 10 ¹⁷ cm ^-3 , Al _0.5 In _0.5 P of the barrier layer for an n-type passive waveguide with a thickness of 7000 angstroms with a dopant concentration of 4 · 10 ¹⁷ cm ^-3 , (Al _0.6 Ga _0.4 ) _0.5 In _0.5 P intrinsic optical restriction layer of a thickness of 900 angstroms, Ga _0.42 In _0.58 P intrinsic type quantum well of a thickness of 80 angstroms, (Al _0.6 Ga _0.4 ) _0.5 In _0.5 P of an intrinsic optical restrictive layer with a thickness of 900 angstroms, Al _0.50 In _0.5 R of a barrier layer for a p-type passive waveguide with a thickness of 7000 angstroms with a dopant concentration of 5 × 10 ¹⁷ cm ^-3 , (Al _0.6 Ga _{0,4) 0,5} in _0,5 P passive waveguide is p-type with a thickness of 2000 angstroms, a dopant concentration of 5 × 10 ¹⁷ cm ^-3, Al _0.5 in _0.5 P-limiting p-type layer 0.5 microns thick with a ntsentratsiey dopant is 5 × 10 ¹⁷ cm ^-3, GaInP p-type layer 100 Å thick with a dopant concentration of 1 × 10 ¹⁸ cm ^-3, GaAs conductive p-type layer 2000 Å thick with a dopant concentration of 4 × 10 ¹⁹ cm ^{- 3} . The waveguide of the known injection laser supports the generation of the zero mode, which propagates through all three waveguide layers.

In the known laser, it was possible to reduce the divergence of the laser beam in the plane perpendicular to the layers of the structure to 18 degrees (at a level of 0.5). However, in it a significant part of the optical mode propagates along doped passive waveguide layers, which increases the optical loss. The spatial distribution of the mode contains additional maxima; therefore, the profile of the optical mode in the waveguide differs from the Gaussian profile. Accordingly, the spatial distribution of the laser beam is also not described by the Gaussian function, which reduces its quality and makes it difficult to focus.

An injection laser is known (see application US 20130287057, IPC H01S 5/20, published October 31, 2013), consisting of a first n-type conductivity boundary layer, a first n-type conductivity layer adjacent to the first boundary layer, an active layer capable of generate radiation adjacent to the first waveguide layer of the second p-type waveguide layer adjacent to the active layer of the second p-type conduction boundary layer adjacent to the second waveguide layer. The sum of the thicknesses of the first waveguide layer, the active layer and the second waveguide layer is more than 1 μm, and the thickness of the second waveguide layer is less than 150 nm. In addition, the active layer, the first bounding layer, the second bounding layer, the first waveguide layer and the second waveguide layer are such that the maximum intensity of the fundamental mode is in the region outside the active layer, and the difference in the refractive indices of the first waveguide layer and the first bounding layer lies between 0.04 and 0.01. The known injection laser has an asymmetric waveguide. The main part of the laser mode propagates along the first waveguide layer. The small contrast of the refractive index between the first boundary layer and the first waveguide layer ensures the leakage of high-order modes from the waveguide and a decrease in their optical confinement factor in the active region, due to which high-order modes do not participate in laser generation. The expansion of the waveguide allows you to narrow the radiation pattern of the laser beam in the plane perpendicular to the layers of the structure, to values less than 50 degrees (beam width containing 95% optical power).

At the same time, in the known laser, a small contrast of the refractive index between the first limiting layer and the first waveguide layer makes the structure sensitive to changes in the refractive indices of the layers during the operation of the laser; a significant part of the zero mode propagates along the doped first waveguide layer and the first bounding layer, which leads to high optical losses; the design is not applicable in the case of a large number of active layers, when the refractive index of the active region significantly affects the waveguide properties.

Known injection laser (see application US 20040208215, IPC H01S 3/08, published October 21, 2004) containing an n-doped region, at least part of which contains a photonic crystal, including a layered one, consisting of at least one layer . Each layer is doped with an n-type impurity, the layered structure has a spatial periodic modulation of the refractive index in a direction perpendicular to the direction of light propagation; defect adjacent to the photonic crystal. This defect contains a layer that generates light when the injection current flows when forward bias is applied, the first thin tunneling barrier for electrons located on the n-side of the light-generating layer, characterized in that it is formed from a material containing lightly doped n-layers and undoped layers , a second tunneling barrier for holes located on the p-side of the light generating layer, characterized in that it is formed of a material containing lightly doped p-layers and undoped layers, two layers between which hoditsya first tunneling barrier, two layers, between which the second tunneling barrier. The injection laser also contains an n-doped layered structure containing at least one layer, each layer is doped with a p-type impurity. This layered structure is located near the defect on the side opposite from the n-doped region. This p-doped layered structure has a refractive index that prevents the fundamental mode from expanding into this structure and into the p-contact.

In the known injection laser, the fundamental mode is localized on the defect, and the remaining modes are stretched along the photonic crystal, while the thickness of the photonic crystal and the defect provide a small divergence of the light beam. When using a photonic crystal with a waveguide thickness of 13.16 μm, the divergence of the laser beam can be reduced to 4 degrees (at a level of 0.5). The design can be implemented for semiconductor lasers emitting in different spectral ranges. A disadvantage of the known injection laser is the content of a large number of layers in a wide waveguide based on a photonic crystal, the thickness and composition of which must be precisely controlled, which makes the design technologically difficult to reproduce; in addition, to reduce the series electrical resistance, the waveguide is alloyed, which leads to significant optical losses; the optical mode profile in the waveguide differs from the Gaussian profile; accordingly, the spatial distribution of the laser beam is also not described by the Gaussian function, which reduces its quality and makes it difficult to focus.

An injection laser is known (see A. Pietrzak, et al., High-powerlaserdiodesemittinglightabove 1100 nmwithasmallverticaldivergenceangleof 13 °. - OpticsLetters, Vol. 33, No. 19, p. 2188, 2008), which includes the first and second boundary layers between which there is a waveguide up to 5 microns thick. In the middle of the waveguide layer is an active region based on quantum wells. The thickness of the bounding layers is 350 nm. The thickness of the waveguide layer and the contrast of the refractive index between the waveguide and bounding layers allow the existence of high-order modes in the waveguide. Due to the thin bounding layers, high-order modes penetrate effectively into the adjacent layers. Such adjacent layers are the contact layer and the substrate. Both layers have high doping; therefore, the optical mode propagating through these layers has significant optical absorption, and the threshold generation condition is not satisfied for it. Due to the small internal optical losses for the fundamental mode, waveguides of this type make it possible to fabricate lasers with a cavity length of up to 8 mm and obtain optical powers up to several watts. The profile of the optical mode is well described by the Gauss function, which positively affects the quality of the laser beam. The design makes it possible to obtain a laser beam with a divergence of less than 15 degrees (at a level of 0.5) in the direction perpendicular to the layers of the laser heterostructure.

A design disadvantage of the known injection laser is its sensitivity to the choice of thicknesses and compositions of waveguide and boundary layers. During the operation of the known laser, the refractive indices of the waveguide and bounding layers change due to heating and current injection, which in some cases leads to the generation of high-order modes, including modes reflected from the lower surface of the substrate and modes reflected in the upper contact layer.

Known injection laser (see patent US 8355419, IPC H01S 5/00, published 01/15/2013), comprising a vertical waveguide containing a first cavity (first waveguide), a first reflector located on one side of the first cavity, a second reflector located with the second side of the first cavity, opposite the first reflector, at least one second cavity (second waveguide) located on the side of the second reflector opposite the first reflector, at least one third reflector located on the side of the second cavity opposite the first of the reflector; a light generating element located within the first cavity and capable of producing optical amplification by injection of current when applying direct bias; substrate, injector and longitudinal resonator. Typical thickness of a wide waveguide is 10-30 microns. The substrate of the injection laser can act as the second waveguide. The optical modes of two waveguides interact and form a combined mode, which propagates simultaneously along two waveguides. The directivity pattern of this mode in the vertical direction is two narrow peaks directed at an angle to the axis of the resonator. To suppress radiation between narrow peaks in the radiation pattern, elements are introduced into the design of a known laser that impede the emission of radiation from a narrow waveguide through end faces.

In the known injection laser, laser generation occurs in a high-order mode, due to which the radiation pattern consists of two beams, each of which is directed at an angle to the mirror, which makes it difficult to focus the radiation; the use of a doped wide passive waveguide or doped substrate leads to an increase in optical losses, which prevents the use of a well-known injection laser to obtain high optical powers.

An injection laser is known that is closest in technical essence and coincides with this solution in terms of the essential features (see patent RU 2259620, IPC H01S 5/32, published August 27, 2005). The injection laser prototype contains a separate confinement heterostructure, including a multimode waveguide, the boundary layers of which are simultaneously emitters of p- and n-type conductivity with the same refractive indices, an active region consisting of at least one quantum-well active layer, the location of which in the waveguide and the thickness waveguides satisfy the relation:

и

- факторы оптического ограничения для активной области нулевой моды и моды m (m=1, 2, 3 …), соответственно. Инжекционный лазер содержит также отражатели, оптические грани, омические контакты и оптический резонатор. Активная область размещена в дополнительном слое, показатель преломления которого больше показателя преломления волновода, а толщина и расположение в волноводе определяются из условия выполнения упомянутого соотношения. Расстояния от активной области до p- и n-эмиттеров не превышают длин диффузии дырок и электронов в волноводе соответственно.Where

and

are the optical confinement factors for the active region of the zero mode and mode m (m = 1, 2, 3 ...), respectively. The injection laser also contains reflectors, optical faces, ohmic contacts and an optical resonator. The active region is placed in an additional layer, the refractive index of which is greater than the refractive index of the waveguide, and the thickness and location in the waveguide are determined from the condition for the above relation. The distances from the active region to p- and n-emitters do not exceed the diffusion lengths of holes and electrons in the waveguide, respectively.

In the well-known prototype laser, laser generation using high-order modes is suppressed by reducing the optical limiting factor for these modes. The known injection laser has a small divergence of radiation while maintaining a high value of efficiency and output power of the radiation. However, in the case of a large number of active layers, the optical confinement factor weakly depends on the asymmetry of the position of the active region. The well-known prototype laser has an increased laser generation threshold for the fundamental mode, there are restrictions on the number of suppressed modes for it, since only the second-order mode is effectively suppressed.

The objective of this technical solution was to develop an injection laser having a reduced divergence of the laser beam in the direction perpendicular to the layers of the structure and an increased thickness of the waveguide while maintaining laser generation on the fundamental transverse mode.

The problem is solved by a group of inventions, united by a single inventive concept.

для активной области одной собственной m-моды (m - целое положительное число) многомодового волновода удовлетворяет соотношению:According to the first option, the problem is solved in that the injection laser based on a semiconductor heterostructure of separate separation includes a multimode waveguide, the first and second wide-gap boundary layers, which are simultaneously emitters of p- and n-type conductivity and located on opposite sides of the multimode waveguide, the active region located in a multimode waveguide and consisting of at least one quantum-well active layer, ohmic contacts and an optical resonator. Between a multimode waveguide and one of the first and second wide-gap boundary layers, a first single-mode waveguide and a first additional wide-gap boundary layer are introduced. The first additional wide-gap confining layer is located between the multimode waveguide and the first single-mode waveguide. Optical Limit Factor

for the active region of one eigenm-mode (m is a positive integer) a multimode waveguide satisfies the relation:

- фактор оптического ограничения для активной области нулевой моды многомодового волновода.Where

is the optical limiting factor for the active region of the zero mode of a multimode waveguide.

The thickness P ₁ , nm, of the first additional wide-gap confining layer, the effective refractive index N _{d1 of} the eigenmode of the first single-mode waveguide and the minimum value n _{s of the} effective refractive index of the eigenmodes of the multimode waveguide satisfy the relations:

N _d1 = N _m + k · (n _f -n _s );

n _s = max (n _cl , n _P1 );

where N _m is the effective refractive index of the eigenm-mode of a multimode waveguide;

k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;

n _f is the refractive index of a multimode waveguide;

q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;

λ is the radiation wavelength, nm;

n _cl is the refractive index adjacent to the multimode waveguide of one of the first and second wide-gap confining layers;

n _P1 is the refractive index of the first additional wide-gap bounding layer.

для активной области собственной m-моды (m - целое положительное число) многомодового волновода и фактор оптического ограничения

для активной области собственной n-моды (n - целое положительное число, не равное m) многомодового волновода удовлетворяют соотношениям:According to the second option, the problem is solved in that the injection laser based on a semiconductor heterostructure of separate separation includes a multimode waveguide, the first and second wide-gap boundary layers, which are simultaneously emitters of p- and n-type conductivity and located on opposite sides of the multimode waveguide, the active region located in a multimode waveguide and consisting of at least one quantum-well active layer, ohmic contacts and an optical resonator. Between the multimode waveguide and the first wide-gap boundary layer, the first single-mode waveguide and the first additional wide-gap boundary layer are introduced. The first additional wide-gap confining layer is located between the multimode waveguide and the first single-mode waveguide. Between the multimode waveguide and the second wide-gap boundary layer, a second single-mode waveguide and a second additional wide-gap boundary layer are introduced. The second additional wide-gap boundary layer is located between the multimode waveguide and the second single-mode waveguide. Optical Limit Factor

for the active region of the eigenm-mode (m is a positive integer) of the multimode waveguide and the optical confinement factor

for the active region of the natural n-mode (n is a positive integer not equal to m) the multimode waveguide satisfies the relations:

- фактор оптического ограничения для активной области нулевой моды многомодового волновода.Where

is the optical limiting factor for the active region of the zero mode of a multimode waveguide.

Thickness P ₁ , nm, first additional wide-gap confining layer, effective refractive index N _{d1 of} the eigenmode of the first single-mode waveguide, thickness P ₂ , nm, second additional wide-band confining layer, effective refraction index N _{d2 of} the eigenmode of the second single-mode waveguide and minimum value n _s the effective refractive index of the eigenmodes of a multimode waveguide satisfy the relations:

N _d1 = N _m + k · (n _f -n _s );

N _d2 = N _n + k · (n _f -n _s );

n _s = max (n _P1 ; n _P2 );

where N _m is the effective refractive index of the eigenm-mode of a multimode waveguide;

k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;

n _f is the refractive index of a multimode waveguide;

N _n is the effective refractive index of the eigenn-mode of the multimode waveguide;

q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;

λ is the radiation wavelength, nm;

n _P1 is the refractive index of the first additional wide-gap confining layer;

n _P2 is the refractive index of the second additional wide-gap confining layer.

для активной области собственной m-моды (m - целое положительное число) многомодового волновода и фактор оптического ограничения

для активной области собственной n-моды (n - целое положительное число, не равное m) многомодового волновода удовлетворяют соотношениям:According to the third option, the problem is solved in that the injection laser based on a semiconductor heterostructure of separate separation includes a multimode waveguide, the first and second wide-gap confinement layers, which are simultaneously emitters of p- and n-type conductivity and located on opposite sides of the multimode waveguide, the active region located in a multimode waveguide and consisting of at least one quantum-well active layer, ohmic contacts and an optical resonator. Between a multimode waveguide and one of the first and second wide-gap boundary layers, a first single-mode waveguide, a first additional wide-gap boundary layer, a second single-mode waveguide and a second additional wide-gap boundary layer are introduced. The first additional wide-gap boundary layer is located between the multimode waveguide and the first single-mode waveguide, and the second additional wide-gap boundary layer is located between the first single-mode waveguide and the second single-mode waveguide. Optical Limit Factor

for the active region of the eigenm-mode (m is a positive integer) of the multimode waveguide and the optical confinement factor

for the active region of the natural n-mode (n is a positive integer not equal to m) the multimode waveguide satisfies the relations:

- фактор оптического ограничения для активной области нулевой моды многомодового волновода.Where

is the optical limiting factor for the active region of the zero mode of a multimode waveguide.

Thickness P ₁ , nm, first additional wide-gap confining layer, effective refractive index N _d1 eigenmode of the first single-mode waveguide, thickness P ₂ , nm, second additional wide-band confining layer, effective refractive index N _d2 eigenmode of the second single-mode waveguide and minimum value n _s the effective refractive index of the eigenmodes of a multimode waveguide satisfy the relations:

N _d1 = N _m + k · (n _f -n _s );

N _d2 = N _n + k · (n _f -n _s );

n _s = max (n _P1 , n _cl );

where N _m is the effective refractive index of the eigenm-mode of a multimode waveguide;

k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;

n _f is the refractive index of a multimode waveguide;

N _n is the effective refractive index of the eigenn-mode of the multimode waveguide;

q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;

λ is the radiation wavelength, nm;

n _P1 is the refractive index of the first additional wide-gap confining layer;

n _P2 is the refractive index of the second additional wide-gap confining layer;

n _cl is the refractive index adjacent to the multimode waveguide of one of the first and second wide-band boundary layers.

для активной области собственной m-моды (m - целое положительное число) многомодового волновода, фактор оптического ограничения

для активной области собственной n-моды (n - целое положительное число, не равное m) многомодового волновода и фактор оптического ограничения

для активной области собственной L-моды (L - целое положительное число, не равное m и n) многомодового волновода удовлетворяют соотношениям:According to the fourth embodiment, the problem is solved in that the injection laser based on a semiconductor heterostructure of separate separation includes a multimode waveguide, the first and second wide-gap confinement layers, which are simultaneously emitters of p- and n-type conductivity and located on opposite sides of the multimode waveguide, the active region located in a multimode waveguide and consisting of at least one quantum-well active layer, ohmic contacts and an optical resonator. Between a multimode waveguide and one of the first and second wide-gap boundary layers, a first single-mode waveguide, a first additional wide-gap boundary layer, a second single-mode waveguide and a second additional wide-gap boundary layer are introduced. The first additional wide-gap boundary layer is located between the multimode waveguide and the first single-mode waveguide, and the second additional wide-gap boundary layer is located between the first single-mode waveguide and the second single-mode waveguide. Between the multimode waveguide and the other of the first and second wide-gap boundary layers, a third single-mode waveguide and a third additional wide-gap boundary layer are introduced. A third additional wide-gap confining layer is located between the multimode waveguide and the third single-mode waveguide. Optical Limit Factor

for the active region of the eigenm-mode (m is a positive integer) of a multimode waveguide, optical limitation factor

for the active region of the intrinsic n-mode (n is a positive integer not equal to m) of the multimode waveguide and the optical limiting factor

for the active region of the eigen L-mode (L is a positive integer not equal to m and n) the multimode waveguide satisfies the relations:

- фактор оптического ограничения для активной области нулевой моды многомодового волновода.Where

is the optical limiting factor for the active region of the zero mode of a multimode waveguide.

Thickness P ₁ , nm, first additional wide-gap confining layer, effective refractive index N _{d1 of} the eigenmode of the first single-mode waveguide, thickness P ₂ , nm, second additional wide-band confining layer, effective refractive index N _{d2 of} the eigenmode of the second single-mode waveguide, thickness P ₃ , nm wide-third additional confining layer, the effective refractive index N _d3 eigenmode third single-mode waveguide and the minimum value of n _s effective HALE refractive eigenmodes multimode waveguide satisfy:

N _d1 = N _m + k · (n _f -n _s );

N _d2 = N _n + k · (n _f -n _s );

N _d3 = N _L + k · (n _f -n _s );

n _s = max (n _P1 , n _P3 );

where N _m is the effective refractive index of the eigenm-mode of a multimode waveguide;

k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;

n _f is the refractive index of a multimode waveguide;

N _n is the effective refractive index of the eigenn-mode of the multimode waveguide;

N _L is the effective refractive index of the eigen L-mode of a multimode waveguide;

q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;

λ is the radiation wavelength, nm;

n _P1 is the refractive index of the first additional wide-gap confining layer;

n _P2 is the refractive index of the second additional wide-gap confining layer;

n _P3 is the refractive index of the third additional wide-gap confining layer.

для активной области собственной m-моды (m - целое положительное число) многомодового волновода, фактор оптического ограничения

для активной области собственной n-моды (n - целое положительное число, не равное m) многомодового волновода, фактор оптического ограничения

для активной области собственной L-моды (L - целое положительное число, не равное m и n) многомодового волновода и фактор оптического ограничения

для активной области собственной j-моды (j - целое положительное число, не равное m, n и L) многомодового волновода удовлетворяют соотношениям:According to the fifth embodiment, the problem is solved in that the injection laser based on a semiconductor heterostructure of separate separation includes a multimode waveguide, the first and second wide-gap confinement layers, which are simultaneously emitters of p- and n-type conductivity and located on opposite sides of the multimode waveguide, the active region located in a multimode waveguide and consisting of at least one quantum-well active layer, ohmic contacts and an optical resonator. Between the multimode waveguide and the first wide-gap boundary layer, a first single-mode waveguide, a first additional wide-gap boundary layer, a second single-mode waveguide, and a second additional wide-gap boundary layer are introduced. The first additional wide-gap boundary layer is located between the multimode waveguide and the first single-mode waveguide, and the second additional wide-gap boundary layer is located between the first single-mode waveguide and the second single-mode waveguide. Between the multimode waveguide and the second wide-gap boundary layer, a third single-mode waveguide, a third additional wide-gap boundary layer, a fourth single-mode waveguide and a fourth additional wide-gap boundary layer are introduced. A third additional wide-gap boundary layer is located between the multimode waveguide and the third single-mode waveguide, and a fourth additional wide-gap boundary layer is located between the third single-mode waveguide and the fourth single-mode waveguide. Optical Limit Factor

for the active region of the eigenm-mode (m is a positive integer) of a multimode waveguide, optical limitation factor

for the active region of the intrinsic n-mode (n is a positive integer not equal to m) of the multimode waveguide, the optical limiting factor

for the active region of the eigen L-mode (L is a positive integer not equal to m and n) of the multimode waveguide and the optical limiting factor

for the active region of the eigen j-mode (j is a positive integer not equal to m, n and L) the multimode waveguide satisfies the relations:

- фактор оптического ограничения для активной области нулевой моды многомодового волновода.Where

is the optical limiting factor for the active region of the zero mode of a multimode waveguide.

Thickness P ₁ , nm, first additional wide-gap confining layer, effective refractive index N _{d1 of} the eigenmode of the first single-mode waveguide, thickness P ₂ , nm, second additional wide-band confining layer, effective refractive index N _{d2 of} the eigenmode of the second single-mode waveguide, thickness P ₃ , nm wide-third additional confining layer, the effective refractive index N _d3 eigenmode third single mode waveguide, the thickness P ₄ nm, a fourth additional th wide-confining layer, the effective refractive index N _d4 eigenmode fourth single-mode waveguide and the minimum value of n _s effective refractive index multimode waveguide eigenmodes satisfy:

N _d1 = N _m + k · (n _f -n _s );

N _d2 = N _n + k · (n _f -n _s );

N _d3 = N _L + k · (n _f -n _s );

N _d4 = N _j + k · (n _f -n _s );

n _s = max (n _P1 , n _P3 );

where N _m is the effective refractive index of the eigenm-mode of a multimode waveguide;

k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;

n _f is the refractive index of a multimode waveguide;

N _n is the effective refractive index of the eigenn-mode of the multimode waveguide;

N _L is the effective refractive index of the eigen L-mode of a multimode waveguide;

N _j is the effective refractive index of the intrinsic j-mode of a multimode waveguide;

q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;

λ is the radiation wavelength, nm;

n _P1 is the refractive index of the first additional wide-gap confining layer;

n _P2 is the refractive index of the second additional wide-gap confining layer;

n _P3 is the refractive index of the third additional wide-gap confining layer;

n _P4 is the refractive index of the fourth additional wide-gap confining layer.

The present invention is based on the effect of tunneling radiation between two optical waveguides located at a distance of the order of the depth of penetration of the optical mode into the layers separating the waveguides (C.R. Pollock, M. Lipson, Integrated Photonics, Springer, 2004, pp. 255-259). The condition for effective tunneling of modes between two coupled optical waveguides is the coincidence of the propagation constants of the eigenmodes of the two waveguides. This condition can also be formulated as the equality of the effective refractive indices of the eigenmodes of two waveguides. With such a resonant interaction of two tunnel-coupled waveguides, the eigenmode of one waveguide and the eigenmode of the other waveguide tunnel between the waveguides to form two combined modes propagating simultaneously along two waveguides. The intensity of each combined mode is distributed equally between two waveguides. Tunneling is possible between waveguides having substantially different thicknesses.

The present invention is illustrated in the drawing, where:

in FIG. 1 is a schematic cross-sectional view of a first embodiment of a present injection laser comprising a first single-mode waveguide and a first additional wide-band layer;

in FIG. Figure 2 shows a schematic representation of the profile 13 of the refractive index of a wide multimode waveguide tunnel coupled to a narrow first single-mode waveguide, and the distribution of intensity 14 of the fundamental mode and intensity 15 of one combined mode that arose during tunneling of the second-order eigenmode;

in FIG. 3 is a schematic cross-sectional view of a second embodiment of the present injection laser comprising a first single-mode waveguide and a first additional wide-band boundary layer on one side of the multimode waveguide and a second single-mode waveguide and a second additional wide-band boundary layer on the other side of the multimode waveguide;

in FIG. 4 is a schematic sectional view of a third embodiment of the present injection laser comprising a first and a second single-mode waveguides and a first and second additional wide-gap confining layers located on one side of the multimode waveguide;

in FIG. 5 is a schematic cross-sectional view of a fourth embodiment of the present injection laser containing the first and second single-mode waveguides and the first and second additional wide-band boundary layers located on one side of the multimode waveguide, and the third single-mode waveguide and the third additional wide-band layer, located on the other side of the multimode waveguide;

in FIG. 6 is a schematic sectional view of a fifth embodiment of the present injection laser containing the first and second single-mode waveguides and the first and second additional wide-band boundary layers on one side of the multimode waveguide and the third and fourth single-mode waveguides and the third and fourth additional wide-band boundary layers on the other side of the multimode waveguide;

in FIG. 7 in table 1 shows for comparison the thickness and composition of the layers of the waveguide of the most common known type of injection laser emitting at the fundamental transverse mode;

in FIG. 8 in table 2 shows for comparison the thickness and composition of the layers of a wide multimode waveguide of the most common known type of injection laser emitting on two transverse modes;

in FIG. 9 in table 3 shows the thicknesses and compositions of the layers of a wide laser waveguide of the present injection laser emitting at the fundamental transverse mode, containing the first single-mode waveguide and the first additional wide-gap layer;

in FIG. 10, Table 4 gives the comparative parameters of the optical modes of a wide multimode waveguide of the most common type of injection laser known and a wide waveguide of an injection laser containing a first single-mode waveguide and a first additional wide-gap layer.

in FIG. 11 in table 5 shows the thicknesses and compositions of the layers of a wide laser waveguide of the present injection laser emitting at the fundamental transverse mode, containing the first and second single-mode waveguides and the first and second additional wide-gap limiting layers located on one side of the multimode waveguide;

in FIG. 12, table 6 shows the values of the gamma factor of the optical modes of a wide waveguide of an injection laser containing the first and second single-mode waveguides and the first and second additional wide-band boundary layers located on one side of the multimode waveguide;

in FIG. 13, Table 7 shows the thicknesses and compositions of the layers of a wide laser waveguide of an injection laser emitting at a fundamental transverse mode, containing a first single-mode waveguide and a first additional wide-band boundary layer on one side of the multimode waveguide and a second single-mode waveguide and a second additional wide-zone boundary layer on the other sides of the multimode waveguide;

in FIG. Table 14 shows the gamma factor of the optical modes of the wide waveguide of the injection laser, which contains the first single-mode waveguide and the first additional wide-gap restriction layer on one side of the multimode waveguide and the second single-mode waveguide and the second additional wide-gap restriction layer on the other side of the multimode waveguide.

для активной области собственной m-моды многомодового волновода 2 удовлетворяет соотношению:The first version of this injection laser (see Fig. 1) contains a quantum-well active region 1 located in a multimode undoped or lightly doped waveguide 2, for the fundamental mode of which the threshold condition is satisfied. On the one hand, a multimode waveguide 2 is bounded by the first wide-gap boundary layer 3, which is simultaneously an emitter, for example, of p-type conductivity. On the other hand, a multimode waveguide 2 is tunneled through a first additional wide-gap boundary layer 4 to a first single-mode waveguide 5, which is bounded by a second wide-gap boundary layer 6, which is simultaneously an emitter of, for example, n-type conductivity. The layers of the laser structure are grown on a doped semiconductor substrate 7, to which an ohmic contact 8 is formed. A second ohmic contact 9 is formed on a high-doped semiconductor contact layer 10 adjacent to the first wide-gap boundary layer 3. Radiation is removed from the laser structure through the mirrors 11 and 12 of the resonator. The threshold condition is also satisfied for one more eigenm-mode (m is a positive integer) of the multimode waveguide 2. Optical constraint factor

for the active region of the eigenm-mode of the multimode waveguide 2 satisfies the relation:

- фактор оптического ограничения для активной области нулевой моды многомодового волновода 2.Where

is the optical limiting factor for the active region of the zero mode of a multimode waveguide 2.

The thickness P ₁ , nm, of the first additional wide-gap confining layer 4, the effective refractive index N _{d1 of} the eigenmode of the first single-mode waveguide 5 and the minimum value n _{s of the} effective refractive index of the eigenmodes of the multimode waveguide 2 satisfy the relations:

N _d1 = N _m + k · (n _f -n _s );

n _s = max (n _cl , n _P1 );

Where N _m is the effective refractive index of the eigenm-mode of the multimode waveguide 2;

k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;

n _f is the refractive index of the multimode waveguide 2;

q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;

λ is the radiation wavelength, nm;

n _cl is the refractive index adjacent to the multimode waveguide of the first wide-gap boundary layer 3;

n _P1 is the refractive index of the first additional wide-gap confining layer 4.

для активной области собственной m-моды многомодового волновода 16 и фактор оптического ограничения

для активной области собственной n-моды многомодового волновода 16 удовлетворяют соотношениям:The second embodiment of the present injection laser (see Fig. 3) and the third version of the present injection laser (see Fig. 4) differ from the first embodiment of the present injection laser (see Fig. 1), primarily, in the multimode waveguide 16, containing the quantum-well active region 1, the threshold condition is satisfied for two eigenmodes of a high order: the eigenm-mode (m is a positive integer) and the eigenmode (n is a positive integer not equal to m). Optical Limit Factor

for the active region of the eigenm-mode of the multimode waveguide 16 and the optical limiting factor

for the active region of the eigenn-mode of the multimode waveguide 16 satisfy the relations:

- фактор оптического ограничения для активной области нулевой моды многомодового волновода 16.Where

is the optical limiting factor for the active region of the zero mode of the multimode waveguide 16.

The second version of the present injection laser (see Fig. 3) differs from the first version of the present injection laser (see Fig. 1) in that the first single-mode waveguide 17 and the first additional wide-band limiter are introduced between the multimode waveguide 16 and the first wide-band boundary layer 3 layer 18. The first additional wide-gap boundary layer 18 is located between the multimode waveguide 16 and the first single-mode waveguide 17. Between the multimode waveguide 16 and the second wide-gap boundary layer 6 introduced the second single-mode waveguide 19 and the second additional wide-gap restriction layer 20. The second additional wide-gap restriction layer 20 is located between the multimode waveguide 16 and the second single-mode waveguide 19. The thickness P ₁ nm, the first additional wide-gap restriction layer 18, the effective refractive index N _{d1 of} the eigenmode the first single-mode waveguide 17, the thickness of P ₂ , nm, the second additional wide-gap boundary layer 20, the effective refractive index N _{d2 of the} intrinsic mo the second single-mode waveguide 19 and the minimum value n _{s of the} effective refractive index of the eigenmodes of the multimode waveguide 16 satisfy the relations:

N _d1 = N _m + k · (n _f -n _s );

N _d2 = N _n + k · (n _f -n _s );

n _s = max (n _P1 , n _P2 );

where N _m is the effective refractive index of the eigenm-mode of the multimode waveguide 16;

k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;

n _f is the refractive index of the multimode waveguide 16;

N _n is the effective refractive index of the eigenn-mode of the multimode waveguide 16;

q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;

λ is the radiation wavelength, nm;

n _P1 is the refractive index of the first additional wide-gap bounding layer 18;

n _P2 is the refractive index of the second additional wide-gap bounding layer 20.

The third embodiment of the present injection laser (see Fig. 4) differs from the first version of the present injection laser (see Fig. 1) in that a first single-mode waveguide 17, a first additional wide-band boundary, is introduced between the multimode waveguide 16 and the second wide-band boundary layer 6 layer 18, a second single-mode waveguide 19, and a second additional wide-gap restriction layer 20. The first additional wide-zone restriction layer 18 is located between the multimode waveguide 16 and the first single-mode the oligovod 17, and the second additional wide-gap boundary layer 20 is located between the first single-mode waveguide 17 and the second single-mode waveguide 19. The thickness P ₁ nm, the first additional wide-gap boundary layer 18, the effective refractive index N _{d1 of} the eigenmode of the first single-mode waveguide 17, the thickness P ₂ nm, the second additional wide-gap boundary layer 20, the effective refractive index N _{d2 of} the eigenmode of the second single-mode waveguide 19 and the minimum value of n _s effective display The refractive index of the eigenmodes of the multimode waveguide 16 satisfy the relations:

N _d1 = N _m + k · (n _f -n _s );

N _d2 = N _n + k · (n _f -n _s );

n _s = max (n _P1 , n _cl );

where N _m is the effective refractive index of the eigenm-mode of the multimode waveguide 16;

k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;

n _f is the refractive index of the multimode waveguide 16;

N _n is the effective refractive index of the eigenn-mode of the multimode waveguide 16;

q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;

λ is the radiation wavelength, nm;

n _P1 is the refractive index of the first additional wide-gap bounding layer 18;

n _P2 is the refractive index of the second additional wide-gap confining layer 20;

n _cl is the refractive index adjacent to the multimode waveguide of the first wide-gap boundary layer 3.

для активной области собственной m-моды многомодового волновода 21, фактор оптического ограничения

для активной области собственной n-моды многомодового волновода 21 и фактор оптического ограничения

для активной области собственной L-моды многомодового волновода 21 удовлетворяют соотношениям:The fourth version of the present injection laser (see Fig. 5) from the first version of the present injection laser (see Fig. 1) differs in that in the multimode waveguide 21 containing the quantum-well active region 1, the threshold condition is satisfied for three high order eigenmodes: eigenm-mode (m is a positive integer), eigenn-mode (n is a positive integer not equal to m) and L-mode (L is a positive integer not equal to m and n). Optical Limit Factor

for the active region of the eigenm-mode of the multimode waveguide 21, the optical limiting factor

for the active region of the eigenmode of the multimode waveguide 21 and the optical limiting factor

for the active region of the eigen L-mode of the multimode waveguide 21 satisfy the relations:

- фактор оптического ограничения для активной области нулевой моды многомодового волновода 21. Между многомодовым волноводом 21 и вторым широкозонным ограничительным слоем 6 введены первый одномодовый волновод 22, первый дополнительный широкозонный ограничительный слой 23, второй одномодовый волновод 24 и второй дополнительный широкозонный ограничительный слой 25, при этом первый дополнительный широкозонный ограничительный слой 23 расположен между многомодовым волноводом 21 и первым одномодовым волноводом 22, а второй дополнительный широкозонный ограничительный слой 25 расположен между первым одномодовым волноводом 22 и вторым одномодовым волноводом 24, между многомодовым волноводом 21 и первым широкозонным ограничительным слоем 3 введены третий одномодовый волновод 26 и третий дополнительный широкозонный ограничительный слой 27, при этом третий дополнительный широкозонный ограничительный слой 27 расположен между многомодовым волноводом 21 и третьим одномодовым волноводом 26. Толщина Р₁, нм, первого дополнительного широкозонного ограничительного слоя 23, эффективный показатель преломления N_d1 собственной моды первого одномодового волновода 22, толщина Р₂, нм, второго дополнительного широкозонного ограничительного слоя 25, эффективный показатель преломления N_d2 собственной моды второго одномодового волновода 24, толщина Р₃, нм, третьего дополнительного широкозонного ограничительного слоя 27, эффективный показатель преломления N_d3 собственной моды третьего одномодового волновода 26 и минимальное значение n_s эффективного показателя преломления собственных мод многомодового волновода 21 удовлетворяют соотношениям:Where

is the optical limiting factor for the active region of the zero mode of the multimode waveguide 21. Between the multimode waveguide 21 and the second wide-band boundary layer 6, the first single-mode waveguide 22, the first additional wide-band boundary layer 23, the second single-mode waveguide 24 and the second additional wide-band boundary layer 25 are introduced, the first additional wide-gap boundary layer 23 is located between the multimode waveguide 21 and the first single-mode waveguide 22, and the second additional wide a zone bounding layer 25 is located between the first single-mode waveguide 22 and the second single-mode waveguide 24, a third single-mode waveguide 26 and a third additional wide-gap bounding layer 27 are introduced between the multimode waveguide 21 and the first wide-zone bounding layer 27, while a third additional wide-gap bounding layer 27 is located between the multimode a waveguide 21 and a third single-mode waveguide 26. The thickness P ₁ nm, the first additional wide-confining layer 23, the effective Show eh refractive N _d1 eigenmode of the first single-mode waveguide 22, the thickness of the P ₂ nm, the second additional wide-confining layer 25, the effective refractive index N _d2 eigenmode of the second single-mode waveguide 24, the thickness F ₃ nm, the third additional wide-confining layer 27, an effective the refractive index N _{d3 of} the eigenmode of the third single-mode waveguide 26 and the minimum value n _{s of the} effective refractive index of the eigenmodes of the multimode waveguide 21 satisfy the relation iyam:

N _d1 = N _m + k · (n _f -n _s );

N _d2 = N _n + k · (n _f -n _s );

N _d3 = N _L + k · (n _f -n _s );

n _s = max (n _P1 , n _P3 );

where N _m is the effective refractive index of the eigenm-mode of the multimode waveguide 21;

k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;

n _f is the refractive index of the multimode waveguide 21;

N _n is the effective refractive index of the eigenn-mode of the multimode waveguide 21;

N _L is the effective refractive index of the eigen L-mode of the multimode waveguide 21;

q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;

λ is the radiation wavelength, nm;

n _P1 is the refractive index of the first additional wide-gap bounding layer 23;

n _P2 is the refractive index of the second additional wide-gap bounding layer 25;

n _P3 is the refractive index of the third additional wide-gap bounding layer 27.

для активной области собственной m-моды многомодового волновода 28, фактор оптического ограничения

для активной области собственной n-моды многомодового волновода 28, фактор оптического ограничения

для активной области собственной L-моды многомодового волновода 28 и фактор оптического ограничения

для активной области собственной j-моды многомодового волновода 28 удовлетворяют соотношениям:The fifth embodiment of the present injection laser (see Fig. 6) from the first version of the present injection laser (see Fig. 1) differs in that in the multimode waveguide 28 containing the quantum-well active region 1, the threshold condition is satisfied for four high order eigenmodes: eigenm-mode (m is a positive integer), eigenmode (n is a positive integer not equal to m), eigenmode L (L is a positive integer not equal to m and n) and eigenmode (j is a positive integer not equal to m, n and L). Optical Limit Factor

for the active region of the eigenm-mode of the multimode waveguide 28, the optical limiting factor

for the active region of the eigenmode of the multimode waveguide 28, optical limitation factor

for the active region of the eigen L-mode of the multimode waveguide 28 and the optical limiting factor

for the active region of the eigen j-mode of the multimode waveguide 28 satisfy the relations:

- фактор оптического ограничения для активной области нулевой моды многомодового волновода 28. Между многомодовым волноводом 28 и первым широкозонным ограничительным слоем 3 введены первый одномодовый волновод 29, первый дополнительный широкозонный ограничительный слой 30, второй одномодовый волновод 31 и второй дополнительный широкозонный ограничительный слой 32, при этом первый дополнительный широкозонный ограничительный слой 30 расположен между многомодовым волноводом 28 и первым одномодовым волноводом 29, а второй дополнительный широкозонный ограничительный слой 32 расположен между первым одномодовым волноводом 29 и вторым одномодовым волноводом 31, между многомодовым волноводом 28 и вторым широкозонным ограничительным слоем 6 введены третий одномодовый волновод 33, третий дополнительный широкозонный ограничительный слой 34, четвертый одномодовый волновод 35 и четвертый дополнительный широкозонный ограничительный слой 36, при этом третий дополнительный широкозонный ограничительный слой 34 расположен между многомодовым волноводом 28 и третьим одномодовым волноводом 33, а четвертый дополнительный широкозонный ограничительный слой 36 расположен между третьим одномодовым волноводом 33 и четвертым одномодовым волноводом 35. Толщина Р₁, нм, первого дополнительного широкозонного ограничительного слоя 30, эффективный показатель преломления N_d1 собственной моды первого одномодового волновода 29, толщина Р₂, нм, второго дополнительного широкозонного ограничительного слоя 32, эффективный показатель преломления N_d2 собственной моды второго одномодового волновода 31, толщина Р₃, нм, третьего дополнительного широкозонного ограничительного слоя 34, эффективный показатель преломления N_d3 собственной моды третьего одномодового волновода 33, толщина Р₄, нм, четвертого дополнительного широкозонного ограничительного слоя 36, эффективный показатель преломления N_d4 собственной моды четвертого одномодового волновода 35 и минимальное значение n_s эффективного показателя преломления собственных мод многомодового волновода 28 удовлетворяют соотношениям:Where

is the optical limiting factor for the active region of the zero mode of the multimode waveguide 28. Between the multimode waveguide 28 and the first wide-band boundary layer 3, a first single-mode waveguide 29, a first additional wide-band boundary layer 30, a second single-mode waveguide 31 and a second additional wide-band boundary layer 32 are introduced, the first additional wide-gap boundary layer 30 is located between the multimode waveguide 28 and the first single-mode waveguide 29, and the second additional wide a zone boundary layer 32 is disposed between the first single-mode waveguide 29 and the second single-mode waveguide 31, a third single-mode waveguide 33, a third additional wide-band boundary layer 34, a fourth single-mode waveguide 35, and a fourth additional wide-band boundary layer 36 are introduced between the multimode waveguide 28 and the second wide-band boundary layer 6 while the third additional wide-gap boundary layer 34 is located between the multimode waveguide 28 and the third single-mode waveguide 33, and the fourth additional wide-gap boundary layer 36 is located between the third single-mode waveguide 33 and the fourth single-mode waveguide 35. The thickness P ₁ nm, the first additional wide-gap boundary layer 30, the effective refractive index N _{d1 of} the eigenmode of the first single-mode waveguide 29, the thickness P ₂ , nm, of the second additional wide-gap confining layer 32, effective refractive index N _{d2 of} the eigenmode of the second single-mode waveguide 31, thickness P ₃ , nm, third additional wide-gap restrictive layer 34, the effective refractive index N _{d3 of} the eigenmode of the third single-mode waveguide 33, the thickness P ₄ nm, the fourth additional wide-band boundary layer 36, the effective refractive index N _{d4 of} the eigenmode of the fourth single-mode waveguide 35 and the minimum value of n _{s of the} effective refractive index of the eigenmodes multimode waveguide 28 satisfy the relations:

N _d1 = N _m + k · (n _f -n _s );

N _d2 = N _n + k · (n _f -n _s );

N _d3 = N _L + k · (n _f -n _s );

N _d4 = N _j + k · (n _f -n _s );

n _s = max (n _P1 , n _P3 );

where N _m is the effective refractive index of the eigenm-mode of the multimode waveguide 28;

k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;

n _f is the refractive index of the multimode waveguide 28;

N _n is the effective refractive index of the eigenn-mode of the multimode waveguide 28;

N _L is the effective refractive index of the eigen L-mode of the multimode waveguide 28;

N _j is the effective refractive index of the eigen j-mode of the multimode waveguide 28;

q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;

λ is the radiation wavelength, nm;

n _P1 is the refractive index of the first additional wide-gap confining layer 30;

n _P2 is the refractive index of the second additional wide-gap confining layer 32;

n _P3 is the refractive index of the third additional wide-gap bounding layer 34;

n _P4 is the refractive index of the fourth additional wide-gap bounding layer 36.

The first embodiment of the present injection laser (see Fig. 1) works as follows. An electric current is passed through ohmic contacts 8, 9 in a direction perpendicular to the layers of the heterostructure, and the injection laser operating mode corresponds to the forward bias of the pn junction. When the current passed through the injection laser exceeds a threshold value, laser radiation emerges through the mirrors of the resonator 11, 12. The output radiation power, in addition to the structure parameters, depends on the amount of current passed through the laser heterostructure. In the laser generation mode, the threshold condition is satisfied for the fundamental mode of the multimode waveguide 2, and it participates in laser generation.

и фактора оптического ограничения для активной области

нулевой моды многомодового волновода 2:The threshold condition is also satisfied even for one's own m-mode multimode waveguide 2 having an effective index of refraction N _m. The criterion for the fulfillment of the threshold condition for the m mode is the ratio of its optical limitation factor for the active region

and optical limiting factor for the active region

zero mode multimode waveguide 2:

собственной m-моды к фактору оптического ограничения для активной области

нулевой моды многомодового волновода слишком велико, то утекания собственной m-моды будет недостаточно для исключения ее из процесса лазерной генерации. Поэтому введем соотношение, ограничивающее максимальное значение фактора оптического ограничения для активной области

собственной m-моды:Through tunneling, the eigenm-mode of the multimode waveguide 2 flows into the first single-mode waveguide 5, the only eigenmode of which has an effective refractive index N _d1 , and combined modes are formed. The intensity of the combined mode is distributed approximately equally between waveguides 2 and 5. Thus, the m-mode of the tunnel-coupled multimode waveguide 2 is excluded from the laser generation process. In this case, the fundamental mode parameters of the multimode waveguide 2 practically do not change. If the ratio of the optical limiting factor for the active region

eigenm-mode to the optical confinement factor for the active region

Since the zero mode of the multimode waveguide is too large, the leakage of the eigenm-mode will not be enough to exclude it from the laser generation process. Therefore, we introduce the relation limiting the maximum value of the optical limiting factor for the active region

own m-mode:

собственной m-моды многомодового волновода 2:Combining inequalities (1) and (2), we obtain limit values for the optical limiting factor for the active region

eigenm-mode of a multimode waveguide 2:

In FIG. Figure 2 schematically shows the profile 13 of the refractive index of a multimode waveguide 2, tunnel coupled to the first single-mode waveguide 5, and the distribution of intensities 14, 15, respectively, of the fundamental mode of the multimode waveguide 2 and one combined mode that arose during tunneling of the eigenm-mode (m = 2 ) to the first single-mode waveguide 5.

The condition for resonant mode tunneling between two coupled waveguides 2 and 5:

When the effective refractive index N _d1 deviates from the resonance, the tunneling of the eigenm-mode of the multimode waveguide 2 to the first single-mode waveguide 5 deteriorates. The effective refractive index N _{m of} the eigenm-mode of the multimode waveguide 2 (T. Numai, Fundamentalsof Semiconductor Lasers, Springer, 2004, p. . 50-53) may have values lying within:

n _s <N _m <n _f                , (four)

where n _f is the refractive index of the multimode waveguide 2, an _s = max (n _cl , n _P1 ) is the minimum value of the effective refractive index of the eigenmodes of the multimode waveguide 2, which is equal to the largest of the refractive indices of the bounding layers adjacent to the multimode waveguide 2, n _cl is the refractive index of the wide-gap bounding layer 3, n _P1 is the refractive index of the first additional wide-gap bounding layer 4.

For the present design of the injection laser, taking into account inequality (4), the limits of deviation of the effective refractive index N _d1 from resonance (3) are introduced, at which tunneling of the eigenm-mode from the multimode waveguide 2 will still be sufficient to exclude it from the laser generation process:

| N _d1 - N _m | ≤ 0.07 ∙ ( n _f - n _s ). (5)

Using inequality (5) and introducing a dimensionless numerical coefficient k lying in the range from -0.07 to 0.07, we introduce the relation for N _d1 and N _m , in which the tunneling of the eigenm-mode from the multimode waveguide 2 into the first single-mode waveguide 5 will still be sufficient to exclude it from the laser generation process:

_{N d1 = N m + k ·} (n f -n s).

To ensure efficient tunneling between waveguides 2, 5, the thickness P ₁ nm, of the first additional wide-band boundary layer 4 should be comparable with the effective penetration depth of the eigenm-mode from the multimode waveguide 2 into the first additional wide-band boundary layer 4:

where λ is the radiation wavelength, nm, q is a dimensionless numerical coefficient lying in the range from 0.5 to 2, which sets the lower and upper limits, respectively, for the thickness of the first additional wide-gap confining layer 4. When the thickness of the first additional wide-band confining layer 4 below the lower limit, the mutual influence of the waveguides becomes too strong, which leads to a strong sensitivity of the spatial distribution of the combined modes to the parameters of the waveguides. When the thickness of the first additional wide-gap boundary layer 4 is greater than the upper limit, optical tunneling between the two waveguides 2, 5 deteriorates, and the combined modes become unstable.

In a real injection laser, a multimode waveguide can be tunnel coupled to several single-mode waveguides. For example, in the fifth embodiment of the present injection laser (see Fig. 6), a wide multimode waveguide 28 is tunnel-coupled to four single-mode waveguides 29, 31, 33 and 35. On each side of the multimode waveguide 28 are two single-mode waveguides and two additional wide-band boundary layer. All single-mode waveguides 29, 31, 33, and 35 have different effective refractive indices. This embodiment of the present injection laser operates as follows. An electric current is passed through ohmic contacts 8, 9 in a direction perpendicular to the layers of the heterostructure, and the injection laser operating mode corresponds to the forward bias of the pn junction. When the current passed through the injection laser exceeds a threshold value, laser radiation emerges through the mirrors of the resonator 11, 12. The output radiation power, in addition to the structure parameters, depends on the amount of current passed through the laser heterostructure. In the laser generation mode, the threshold condition is satisfied for the fundamental mode of the multimode waveguide 28, and it participates in laser generation. In multimode waveguide 28, the threshold laser generation condition is also satisfied for four high-order eigenmodes, the number of which is equal to the number of single-mode waveguides. Due to resonant tunneling, each of these eigenmodes flows into one of the single-mode waveguides, which coincides with it in the effective refractive index, with the formation of combined modes. Moreover, in single-mode waveguides 31 and 35, high-order eigenmodes of a multi-mode waveguide 28 tunnel through single-mode waveguides 29 and 33, respectively, and through additional wide-band boundary layers 30, 32 and 34, 36. The possibility of such through tunneling through single-mode waveguides 29 and 33 is connected so that all single-mode waveguides 29, 31, 33 and 35 have different effective refractive indices. The use of a larger number of single-mode waveguides on each side of the multi-mode waveguide 28 will lead to a strong mutual influence of single-mode waveguides and to weakening tunneling of high-order eigenmodes into single-mode waveguides. Thus, during the operation of this injection laser, high-order eigenmodes of the multimode waveguide 28 for which the threshold condition is satisfied are excluded from the laser generation process. In this case, the parameters of the fundamental mode of the multimode waveguide 28 are practically unchanged. The parameters of the multimode waveguide 28 and the tunnel-coupled single-mode waveguides 29, 31, 33, and 35 are determined similarly to the method for determining the parameters of the multimode waveguide 2, single-mode waveguide 5, and an additional wide-gap confinement layer 4 for the first embodiment of this injection laser.

Example 1. Two injection lasers of the most common type (a laser emitting on a fundamental transverse mode and a laser emitting on two transverse modes) and a real injection laser (first option) were made for comparative tests. Lasers were grown on GaAsc substrates with an active region based on two InGaAs quantum wells emitting at a wavelength of 1.04 μm. In FIG. 7, table 1 describes the thicknesses and compositions of the layers of the laser waveguide of the most common type, in which the active region is located in the middle of the two-mode waveguide. Moreover, the threshold condition was fulfilled only for the fundamental mode, for which the gamma factor is 1.6%. The divergence of radiation in a plane perpendicular to the layers of the structure was 35 degrees (at a level of 0.5). The expansion of the waveguide made it possible for higher-order modes to exist in it. The 2.5 μm waveguide shown in FIG. 8 in table 2, had four eigenmodes: from zero to third. For the fundamental mode and the second-order mode, the threshold condition was satisfied. The laser based on this waveguide is multimode. In FIG. 9 in table 3 for the present laser, a multimode waveguide with a thickness of 2.5 μm is described, which through a first additional wide-gap boundary layer 0.25 μm thick is tunnelly coupled to the first single-mode waveguide with a thickness of 0.55 μm. The second-order eigenmode of a multimode waveguide tunneled into the first single-mode waveguide with the formation of combined modes. The threshold condition was satisfied only for the fundamental mode of a multimode waveguide. The radiation divergence for it in the plane perpendicular to the layers of the structure was 23 degrees (at the level of 0.5). In FIG. 10, Table 4 shows the gamma factor for the optical modes of the most common type multimode laser waveguide and the real multimode waveguide of a laser tunnel coupled to the first single-mode waveguide. The gamma factors of the fundamental modes are the same for both lasers. The first and third order modes in both lasers have gamma factors ten times smaller than those of the fundamental mode, and the threshold condition was not fulfilled for them. The gamma factor of the second-order mode of the most common type of laser waveguide is 1.2 times smaller than the gamma factor of the fundamental mode and the threshold condition is satisfied for it. In a tunnel-coupled multimode waveguide of a real laser, the second-order eigenmode due to tunneling forms combined modes with a gamma factor 2.2 times smaller than the gamma factor of the fundamental mode of a multimode waveguide; therefore, the threshold condition is not satisfied for combined modes. To a large extent, combined modes propagate along the first additional wide-gap confinement layer and the first single-mode waveguide, which have strong doping, due to which they have optical losses of more than 4.5 cm ^-1 , which further reduces the probability of the fulfillment of the threshold condition for them. For comparison, the second-order mode in a multimode laser waveguide of the most common type has a 3.6 times smaller optical loss of 1.3 cm ⁻¹ .

Thus, in a real injection laser containing a multimode waveguide with an active region, it is possible to effectively suppress laser generation in its own high-order mode due to its optical tunneling through an additional wide-gap confining layer into a narrow single-mode waveguide. In this case, laser generation on the fundamental mode of a wide multimode waveguide is preserved.

Example 2. A real injection laser was manufactured for testing (third option). The laser was grown on a GaAs substrate with an active region based on two InGaAs quantum wells emitting at a wavelength of 1.04 μm. In FIG. 11 in table 5 for the present laser, a description is given of a multimode waveguide with a thickness of 3.6 μm, which is tunneled through wide-band boundary layers to two single-mode waveguides with a thickness of 0.3 μm and 0.4 μm located on one side of the multimode waveguide. The eigenmodes of the second and fourth order of the multimode waveguide tunneled into single-mode waveguides with the formation of combined modes. The threshold condition was satisfied only for the fundamental mode of a multimode waveguide. The radiation divergence for it in the plane perpendicular to the layers of the structure was 16 degrees (at the level of 0.5). In FIG. 12, table 6 shows the gamma factor for the optical modes of a multimode waveguide of a real laser tunnel coupled to two single-mode waveguides. The first, third order, and fifth order modes have gamma factors ten times smaller than that of the fundamental mode, and the threshold condition was not fulfilled for them. In a tunnel-coupled multimode waveguide of a real laser, second and fourth order eigenmodes, due to tunneling, form combined modes with gamma factors almost 2.5 times smaller than the gamma factor of the fundamental mode of a multimode waveguide; therefore, the threshold condition is not satisfied for combined modes.

Thus, in a real injection laser containing a multimode waveguide with an active region, it is possible to effectively suppress laser generation at its high-order eigenmodes due to their optical tunneling through narrow layers into narrow single-mode waveguides. In this case, laser generation on the fundamental mode of a wide multimode waveguide is preserved.

Example 3. A real injection laser was made for testing (second option). The laser was grown on a GaAs substrate with an active region based on two InGaAs quantum wells emitting at a wavelength of 1.04 μm. In FIG. 13, table 7 for a real laser describes a multimode waveguide with a thickness of 3.6 μm, which is tunneled through wide-band boundary layers to two single-mode waveguides with a thickness of 0.31 μm and 0.32 μm located on opposite sides of the multimode waveguide. The eigenmodes of the second and fourth order of the multimode waveguide tunneled into single-mode waveguides with the formation of combined modes. The threshold condition was satisfied only for the fundamental mode of a multimode waveguide. The radiation divergence for it in the plane perpendicular to the layers of the structure was 16 degrees (at a level of 0.5). In FIG. Table 14 shows the gamma factor for the optical modes of a multimode waveguide of a real laser tunnel coupled to two single-mode waveguides. The first, third order, and fifth order modes have gamma factors ten times smaller than that of the fundamental mode, and the threshold condition was not fulfilled for them. In a tunnel-coupled multimode waveguide of a real laser, second and fourth order eigenmodes, due to tunneling, form combined modes with gamma factors almost 2.5 times smaller than the gamma factor of the fundamental mode of a multimode waveguide; therefore, the threshold condition is not satisfied for combined modes.

Thus, in a real injection laser containing a multimode waveguide with an active region, it is possible to effectively suppress laser generation at its high-order eigenmodes due to their optical tunneling through narrow layers into narrow single-mode waveguides. In this case, laser generation on the fundamental mode of a wide multimode waveguide is preserved.

Claims (5)

1. An injection laser based on a semiconductor heterostructure with a separate confinement, including a multimode waveguide, the first and second wide-gap confinement layers, which are simultaneously emitters of p- and n-type conductivity and located on opposite sides of the multimode waveguide, the active region located in the multimode waveguide and consisting of at least one quantum-well active layer, ohmic contacts and an optical resonator, characterized in that between the multimode waveguide m and one of the first and second wide-gap confining layers administered first single mode waveguide and a first additional wide-limiting layer, wherein the first wide-restrictive additional layer is disposed between the first multimode waveguide and the single-mode waveguide, the optical confinement factor

for the active region of one eigenm-mode (m is a positive integer) a multimode waveguide satisfies the relation:

Where

is the optical limiting factor for the active region of the zero mode of a multimode waveguide,
and the thickness P ₁ , nm, of the first additional wide-gap confining layer, the effective refractive index N _{d1 of} the eigenmode of the first single-mode waveguide and the minimum value n _{s of the} effective refractive index of the eigenmodes of the multimode waveguide satisfy the relations:
N _d1 = N _m + k · (n _ƒ -n _s );

n _s = max (n _cl , n _P1 );
where N _m is the effective refractive index of the eigenm-mode of a multimode waveguide;
k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;
n _ƒ is the refractive index of a multimode waveguide;
q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;
λ is the radiation wavelength, nm;
n _cl is the refractive index adjacent to the multimode waveguide of one of the first and second wide-gap confining layers;
n _P1 is the refractive index of the first additional wide-gap bounding layer. 2. An injection laser based on a semiconductor heterostructure with a separate confinement, including a multimode waveguide, the first and second wide-gap confinement layers, which are simultaneously emitters of p- and n-type conductivity and located on opposite sides of the multimode waveguide, the active region located in the multimode waveguide and consisting of at least one quantum-well active layer, ohmic contacts and an optical resonator, characterized in that between the multimode waveguide The first single-mode waveguide and the first additional wide-gap boundary layer are introduced between the multimode waveguide and the first single-mode waveguide, and the second single-mode waveguide and the second additional wide-gap boundary layer are introduced between the multimode waveguide and the second wide-gap boundary layer. layer, while the second additional wide-gap boundary layer is located between a multimode waveguide and the second single-mode waveguide, the optical confinement factor

for the active region of the eigenm-mode (m is a positive integer) of the multimode waveguide and the optical confinement factor

for the active region of the natural n-mode (n is a positive integer not equal to m) the multimode waveguide satisfies the relations:

Where

is the optical limiting factor for the active region of the zero mode of a multimode waveguide,
and the thickness P ₁ , nm, of the first additional wide-gap confining layer, the effective refractive index N _{d1 of} the eigenmode of the first single-mode waveguide, the thickness P ₂ , nm, of the second additional wide-gap confining layer, the effective refractive index of N _{d2 of} the eigenmode of the second single-mode waveguide and the minimum value of n _{s of the} effective refractive index of the eigenmodes of a multimode waveguide satisfy the relations:
N _d1 = N _m + k · (n _ƒ -n _s );
N _d2 = N _n + k · (n _ƒ -n _s );

n _s = max (n _P1 , n _P2 );
where N _m is the effective refractive index of the eigenm-mode of a multimode waveguide;
k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;
n _ƒ is the refractive index of a multimode waveguide;
N _n is the effective refractive index of the eigenn-mode of the multimode waveguide;
q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;
λ is the radiation wavelength, nm;
n _P1 is the refractive index of the first additional wide-gap confining layer;
n _P2 is the refractive index of the second additional wide-gap confining layer. 3. An injection laser based on a semiconductor heterostructure with a separate confinement, including a multimode waveguide, first and second wide-gap confinement layers, which are simultaneously emitters of p- and n-type conductivity and located on opposite sides of the multimode waveguide, the active region located in the multimode waveguide and consisting of at least one quantum-well active layer, ohmic contacts and an optical resonator, characterized in that between the multimode waveguide m and one of the first and second wide-band boundary layers introduced the first single-mode waveguide, the first additional wide-band boundary layer, the second single-mode waveguide and the second additional wide-zone boundary layer, while the first additional wide-gap boundary layer is located between the multimode waveguide and the first single-mode waveguide, and the second additional a wide-gap boundary layer is located between the first single-mode waveguide and the second single-mode waveguide, factor pticheskogo restrictions

for the active region of the eigenm-mode (m is a positive integer) of the multimode waveguide and the optical confinement factor

for the active region of the natural n-mode (n is a positive integer not equal to m) the multimode waveguide satisfies the relations:

Where

is the optical limiting factor for the active region of the zero mode of a multimode waveguide,
and the thickness P ₁ , nm, of the first additional wide-gap confining layer, the effective refractive index N _{d1 of} the eigenmode of the first single-mode waveguide, the thickness P ₂ , nm, of the second additional wide-gap confining layer, the effective refractive index of N _{d2 of} the eigenmode of the second single-mode waveguide and the minimum value of n _{s of the} effective refractive index of the eigenmodes of a multimode waveguide satisfy the relations:
N _d1 = N _m + k · (n _ƒ -n _s );
N _d2 = N _n + k · (n _ƒ -n _s );

n _s = max (n _P1 , n _cl );
where N _m is the effective refractive index of the eigenm-mode of a multimode waveguide;
k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;
n _ƒ is the refractive index of a multimode waveguide;
N _n is the effective refractive index of the eigenn-mode of the multimode waveguide;
q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;
λ is the radiation wavelength, nm;
n _P1 is the refractive index of the first additional wide-gap confining layer;
n _P2 is the refractive index of the second additional wide-gap confining layer;
n _cl is the refractive index adjacent to the multimode waveguide of one of the first and second wide-band boundary layers. 4. An injection laser based on a semiconductor heterostructure with a separate confinement, including a multimode waveguide, first and second wide-gap confinement layers, which are simultaneously emitters of p- and n-type conductivity and located on opposite sides of the multimode waveguide, the active region located in the multimode waveguide and consisting of at least one quantum-well active layer, ohmic contacts and an optical resonator, characterized in that between the multimode waveguide m and one of the first and second wide-band boundary layers introduced the first single-mode waveguide, the first additional wide-band boundary layer, the second single-mode waveguide and the second additional wide-zone boundary layer, while the first additional wide-gap boundary layer is located between the multimode waveguide and the first single-mode waveguide, and the second additional a wide-gap boundary layer is located between the first single-mode waveguide and the second single-mode waveguide, between m ogomodovym waveguide and the other of said first and second confining layers wideband monomode waveguide is introduced third and additional third wide-gap confining layer, wherein the third additional wide-limiting layer is located between the multimode waveguide and the third single-mode waveguide, the optical confinement factor

for the active region of the eigenm-mode (m is a positive integer) of a multimode waveguide, optical limitation factor

for the active region of the intrinsic n-mode (n is a positive integer not equal to m) of the multimode waveguide and the optical limiting factor

for the active region of the eigen L-mode (L is a positive integer not equal to m and n) the multimode waveguide satisfies the relations:

Where

is the optical limiting factor for the active region of the zero mode of a multimode waveguide,
and the thickness P ₁ , nm, of the first additional wide-gap confining layer, the effective refractive index N _{d1 of} the eigenmode of the first single-mode waveguide, the thickness P ₂ , nm, of the second additional wide-band confining layer, the effective refractive index N _{d2 of} the eigenmode of the second single-mode waveguide, the thickness P ₃ nm, the third additional wideband confining layer, the effective refractive index N _d3 eigenmode third single-mode waveguide and the minimum value of n _s effektivnog refractive index of the multimode waveguide eigenmodes satisfy:
N _d1 = N _m + k · (n _ƒ -n _s );
N _d2 = N _n + k · (n _ƒ -n _s );
N _d3 = N _L + k · (n _ƒ -n _s );

n _s = max (n _P1 ; n _P3 );
where N _m is the effective refractive index of the eigenm-mode of a multimode waveguide;
k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;
n _ƒ is the refractive index of a multimode waveguide;
N _n is the effective refractive index of the eigenn-mode of the multimode waveguide;
N _L is the effective refractive index of the eigen L-mode of a multimode waveguide;
q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;
λ is the radiation wavelength, nm;
n _P1 is the refractive index of the first additional wide-gap confining layer;
n _P2 is the refractive index of the second additional wide-gap confining layer;
n _P3 is the refractive index of the third additional wide-gap confining layer. 5. An injection laser based on a semiconductor heterostructure with a separate confinement, including a multimode waveguide, the first and second wide-gap confinement layers, which are simultaneously emitters of p- and n-type conductivity and located on opposite sides of the multimode waveguide, the active region located in the multimode waveguide and consisting of at least one quantum-well active layer, ohmic contacts and an optical resonator, characterized in that between the multimode waveguide The first single-mode waveguide, the first additional wide-gap restriction layer, the second single-mode waveguide and the second additional wide-gap restriction layer are introduced in the first wide-band boundary layer, the first additional wide-gap boundary layer is located between the multimode waveguide and the first single-mode waveguide, and the second additional wide-gap boundary layer is located between the first single-mode waveguide and the second single-mode waveguide, between the multimode wave a third single-mode waveguide, a third additional wide-gap restriction layer, a fourth single-mode waveguide and a fourth additional wide-band boundary layer are introduced in the house and a second wide-band boundary layer, wherein a third additional wide-zone boundary layer is located between the multimode waveguide and the third single-mode waveguide, and a fourth additional wide-zone boundary layer is located between the third single-mode waveguide and the fourth single-mode waveguide, factor opt restraint

for the active region of the eigenm-mode (m is a positive integer) of a multimode waveguide, optical limitation factor

for the active region of the intrinsic n-mode (n is a positive integer not equal to m) of the multimode waveguide, the optical limiting factor

for the active region of the eigen L-mode (L is a positive integer not equal to m and n) of the multimode waveguide and the optical limiting factor

for the active region of the eigen j-mode (j is a positive integer not equal to m, n and L) the multimode waveguide satisfies the relations:

Where

is the optical limiting factor for the active region of the zero mode of a multimode waveguide,
and the thickness P ₁ , nm, of the first additional wide-gap confining layer, the effective refractive index N _{d1 of} the eigenmode of the first single-mode waveguide, the thickness P ₂ , nm, of the second additional wide-band confining layer, the effective refractive index N _{d2 of} the eigenmode of the second single-mode waveguide, the thickness P ₃ , nm, of the third additional wide-gap boundary layer, the effective refractive index N _{d3 of} the eigenmode of the third single-mode waveguide, the thickness P ₄ , nm, of the fourth additional a wide-gap boundary layer, the effective refractive index N _{d4 of} the eigenmode of the fourth single-mode waveguide and the minimum value n _{s of the} effective refractive index of the eigenmodes of the multimode waveguide satisfy the relations:
N _d1 = N _m + k · (n _ƒ -n _s );
N _d2 = N _n + k · (n _ƒ -n _s );
N _d3 = N _L + k · (n _ƒ -n _s );
N _d4 = N _j + k · (n _ƒ -n _s );

n _s = max (n _P1 , n _P3 );
where N _m is the effective refractive index of the eigenm-mode of a multimode waveguide;
k is a dimensionless numerical coefficient lying in the range of -0.07≤k≤0.07;
n _ƒ is the refractive index of a multimode waveguide;
N _n is the effective refractive index of the eigenn-mode of the multimode waveguide;
N _L is the effective refractive index of the eigen L-mode of a multimode waveguide;
N _j is the effective refractive index of the intrinsic j-mode of a multimode waveguide;
q is a dimensionless numerical coefficient lying in the range of 0.5≤q≤2;
λ is the radiation wavelength, nm;
n _P1 is the refractive index of the first additional wide-gap confining layer;
n _P2 is the refractive index of the second additional wide-gap confining layer;
n _P3 is the refractive index of the third additional wide-gap confining layer;
n _P4 is the refractive index of the fourth additional wide-gap confining layer.

Images