Combination splitting device composed of strip waveguides and uses thereof
First Claim
1. A junction splitter having channel waveguides for the spatial combination or splitting or switching or deflection or modulation of light, for applications within the wavelength range of visible light, comprising at least three channel waveguides, comprising:
- at least one single-mode integrated-optical wideband channel waveguide (SOWCW) where in or on a surface-type substrate material, by a process for changing the refractive index, a channel-shaped structure is fabricated or a channel-shaped structure made from a suitable material is applied, with the geometric/substance parameters of the channel waveguide thus created being set in dependence of the wavelength ranges to be transmitted in the UV, visible, and/or IR regions, so that in relation to the wavelength (λ
) a minimum width of the wavelength range for single-mode light guidance is given by the equation
space="preserve" listing-type="equation">Δ
λ
.sub.w =0.48×
λ
-85 nmwhere the parameters substrate refractive index (n1), superstrate refractive index ((n3,), refractive index of the refractive index distribution (f(x,y)) on the surface ((n2,)), refractive index distribution in the waveguiding region, cross-sectional shape (width a and depth t) of the channel waveguide and its location in and/or on the substrate are dimensioned such that single-mode operation of the channel waveguide in the wavelength range
space="preserve" listing-type="equation">Δ
λ
.sub.w >
0.48×
λ
-85 nmis ensured, so that to each given wavelength (λ
) in the range between λ
a and λ
a +Δ
λ
w one and only one effective refractive index, can be allocated, and the single-mode range will be determined by efficient oscillation build-up of fundamental mode N00 at wavelength λ
a +Δ
λ
w on the one hand, and by efficient oscillation build-up, in a technical sense of the first mode in lateral direction (N01) or of the first mode in depth direction (N10) at wavelength λ
a on the other hand, and with transmission at a technically sufficient degree of effectiveness signifying that the effective refractive index Neff of the mode guided in the channel waveguide must be at least 5×
10-5 above the refractive index of the surrounding material ns, where ns where ns designates the value of substrate index n1 or superstrate index n3, whichever is the greater, and with the minimum possible value of the usable wavelength (λ
min) and the maximum possible value of the usable wavelength (λ
max) being determined by the transmission range of the materials used, and thus the channel waveguide being defined as a single-mode integrated-optical wideband channel waveguide (SOWCW), and wherein there is provideda combination and connection of the minimum of three channel waveguides, in which the geometric/substance parameters of the channel waveguides themselves as well as the media surrounding the channel waveguides which are set in dependence of the wavelength range to be transmitted in the UV, visible, and/or IR regions, so that in relation to the wavelength (λ
) the minimum width of the wavelength range for efficient junction splitter operation is given by the equation
space="preserve" listing-type="equation">Δ
λ
.sub.v >
0.27×
λ
-34 nmwhere the parameters substrate refractive index (n1), superstrate refractive index (n3), refractive index of the refractive index distribution (f(x,y)) on the surface (n2), refractive index distribution in the waveguiding region, geometry of the junction splitter, and its location in and/or on the substrate are dimensioned such that efficient operation of the junction splitter is at least ensured in the wavelength range
space="preserve" listing-type="equation">Δ
λ
.sub.v >
0.27×
λ
-34 nmwith the usable wavelength range Δ
λ
N for the efficient operation of the junction splitter, in a technical sense is determined by the lesser value of one ofthe difference between wavelength λ
a +Δ
λ
w of the efficient oscillation build-up, in a technical sense, of the fundamental mode (Noo) in the channel waveguide and wavelength λ
a of the efficient oscillation build-up, in a technical sense, of the first mode in lateral direction (No1) or of the first mode in depth direction (N10) in the channel waveguide, andthe difference between wavelength λ
a +Δ
λ
w of the efficient oscillation build-up, in a technical sense, of the fundamental mode (Noo) in the channel waveguide and wavelength λ
b of the efficient oscillation build-up, in a technical sense, of the second mode in lateral direction in the coupling area, widened in relation to the channel waveguide, of the junction splitter (N02), that is by ##EQU2## and so that the junction splitter of at least three channel waveguides, comprising at least one SOWCW, is defined as an integrated-optical wideband junction splitter.
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Abstract
The invention concerns an integrated-optical junction splitter, in particular for applications in the wavelength range of visible light, which ensures a spatial and wideband combination of light in a wavelength spectrum Δλ greater than 75 nm (value given applies to short-wave visible light). In the case of a usable wavelength range comprising the entire spectrum of visible light, the junction splitter is a white light junction splitter. The junction splitter consists of at least three channel waveguides, at least one of which must be a single-mode integrated-optical wideband channel waveguide (SOWCW). Two channel waveguides each have a respective input and are combined into a common SOWCW at their outputs in a coupling point, which common SOWCW features a common light output at its end.
This wideband junction splitter is used as a wavelength-selective or wavelength-independent switch or modulator, in interferometric and photometric devices, sensors, and microsystem-technical solutions.
47 Citations
17 Claims
-
1. A junction splitter having channel waveguides for the spatial combination or splitting or switching or deflection or modulation of light, for applications within the wavelength range of visible light, comprising at least three channel waveguides, comprising:
-
at least one single-mode integrated-optical wideband channel waveguide (SOWCW) where in or on a surface-type substrate material, by a process for changing the refractive index, a channel-shaped structure is fabricated or a channel-shaped structure made from a suitable material is applied, with the geometric/substance parameters of the channel waveguide thus created being set in dependence of the wavelength ranges to be transmitted in the UV, visible, and/or IR regions, so that in relation to the wavelength (λ
) a minimum width of the wavelength range for single-mode light guidance is given by the equation
space="preserve" listing-type="equation">Δ
λ
.sub.w =0.48×
λ
-85 nmwhere the parameters substrate refractive index (n1), superstrate refractive index ((n3,), refractive index of the refractive index distribution (f(x,y)) on the surface ((n2,)), refractive index distribution in the waveguiding region, cross-sectional shape (width a and depth t) of the channel waveguide and its location in and/or on the substrate are dimensioned such that single-mode operation of the channel waveguide in the wavelength range
space="preserve" listing-type="equation">Δ
λ
.sub.w >
0.48×
λ
-85 nmis ensured, so that to each given wavelength (λ
) in the range between λ
a and λ
a +Δ
λ
w one and only one effective refractive index, can be allocated, and the single-mode range will be determined by efficient oscillation build-up of fundamental mode N00 at wavelength λ
a +Δ
λ
w on the one hand, and by efficient oscillation build-up, in a technical sense of the first mode in lateral direction (N01) or of the first mode in depth direction (N10) at wavelength λ
a on the other hand, and with transmission at a technically sufficient degree of effectiveness signifying that the effective refractive index Neff of the mode guided in the channel waveguide must be at least 5×
10-5 above the refractive index of the surrounding material ns, where ns where ns designates the value of substrate index n1 or superstrate index n3, whichever is the greater, and with the minimum possible value of the usable wavelength (λ
min) and the maximum possible value of the usable wavelength (λ
max) being determined by the transmission range of the materials used, and thus the channel waveguide being defined as a single-mode integrated-optical wideband channel waveguide (SOWCW), and wherein there is provideda combination and connection of the minimum of three channel waveguides, in which the geometric/substance parameters of the channel waveguides themselves as well as the media surrounding the channel waveguides which are set in dependence of the wavelength range to be transmitted in the UV, visible, and/or IR regions, so that in relation to the wavelength (λ
) the minimum width of the wavelength range for efficient junction splitter operation is given by the equation
space="preserve" listing-type="equation">Δ
λ
.sub.v >
0.27×
λ
-34 nmwhere the parameters substrate refractive index (n1), superstrate refractive index (n3), refractive index of the refractive index distribution (f(x,y)) on the surface (n2), refractive index distribution in the waveguiding region, geometry of the junction splitter, and its location in and/or on the substrate are dimensioned such that efficient operation of the junction splitter is at least ensured in the wavelength range
space="preserve" listing-type="equation">Δ
λ
.sub.v >
0.27×
λ
-34 nmwith the usable wavelength range Δ
λ
N for the efficient operation of the junction splitter, in a technical sense is determined by the lesser value of one ofthe difference between wavelength λ
a +Δ
λ
w of the efficient oscillation build-up, in a technical sense, of the fundamental mode (Noo) in the channel waveguide and wavelength λ
a of the efficient oscillation build-up, in a technical sense, of the first mode in lateral direction (No1) or of the first mode in depth direction (N10) in the channel waveguide, andthe difference between wavelength λ
a +Δ
λ
w of the efficient oscillation build-up, in a technical sense, of the fundamental mode (Noo) in the channel waveguide and wavelength λ
b of the efficient oscillation build-up, in a technical sense, of the second mode in lateral direction in the coupling area, widened in relation to the channel waveguide, of the junction splitter (N02), that is by ##EQU2## and so that the junction splitter of at least three channel waveguides, comprising at least one SOWCW, is defined as an integrated-optical wideband junction splitter. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
-
-
13. A method of using a wideband junction splitter comprising the steps of:
-
using a junction splitter having channel waveguides for the spatial combination or splitting or switching or deflection or modulation of light, for applications within the wavelength range of visible light, having at least three channel waveguides, having; at least one single-mode integrated-optical wideband channel waveguide (SOWCW) where in or on a surface-type substrate material, by a process for changing the refractive index, a channel-shaped structure is fabricated or a channel-shaped structure made from a suitable material is applied, with the geometric/substance parameters of the channel waveguide thus created being set in dependence of the wavelength ranges to be transmitted in the UV, visible, and/or IR regions, so that in relation to the wavelength (λ
) a minimum width of the wavelength range for single-mode light guidance is given by the equation
space="preserve" listing-type="equation">Δ
λ
.sub.w =0.48×
λ
-85 nmwhere the parameters substrate refractive index (n1,), superstrate refractive index ((n3,), refractive index of the refractive index distribution (f(x,y)) on the surface ((n2,)), refractive index distribution in the waveguiding region, cross-sectional shape (width a and depth t) of the channel waveguide and its location in and/or on the substrate are dimensioned such that single-mode operation of the channel waveguide in the wavelength range
space="preserve" listing-type="equation">Δ
λ
.sub.w >
0.48×
λ
-85 nmis ensured, so that to each given wavelength (λ
) in the range between λ
a and λ
a +Δ
λ
w one and only one effective refractive index, can be allocated, and the single-mode range will be determined by efficient oscillation build-up of fundamental mode Noo at wavelength λ
a +Δ
λ
w on the one hand, and by efficient oscillation build-up, in a technical sense of the first mode in lateral direction (N01) or of the first mode in depth direction (N10) at wavelength λ
a on the other hand, and with transmission at a technically sufficient degree of effectiveness signifying that the effective refractive index Neff of the mode guided in the channel waveguide must be at least 5×
10-5 above the refractive index of the surrounding material ns, where ns where ns designates the value of substrate index n1 or superstrate index n3, whichever is the greater, and with the minimum possible value of the usable wavelength (λ
min) and the maximum possible value of the usable wavelength (λ
max) being determined by the transmission range of the materials used, and thus the channel waveguide being defined as a single-mode integrated-optical wideband channel waveguide (SOWCW), and wherein there is provideda combination and connection of the minimum of three channel waveguides, in which the geometric/substance parameters of the channel waveguides themselves as well as the media surrounding the channel waveguides which are set in dependence of the wavelength range to be transmitted in the UV, visible, and/or IR regions, so that in relation to the wavelength (λ
) the minimum width of the wavelength range for efficient junction splitter operation is given by the equation
space="preserve" listing-type="equation">Δ
λ
.sub.v >
0.27×
λ
-34 nmwhere the parameters substrate refractive index (n1), superstrate refractive index (n3), refractive index of the refractive index distribution (f(x,y)) on the surface (n2), refractive index distribution in the waveguiding region, geometry of the junction splitter, and its location in and/or on the substrate are dimensioned such that efficient operation of the junction splitter is at least ensured in the wavelength range
space="preserve" listing-type="equation">Δ
λ
.sub.v >
0.27×
λ
-34 nmwith the usable wavelength range Δ
λ
N for the efficient operation of the junction splitter, in a technical sense is determined by the lesser value of one ofthe difference between wavelength λ
a +Δ
λ
w of the efficient oscillation build-up, in a technical sense, of the fundamental mode (Noo) in the channel waveguide and wavelength λ
a of the efficient oscillation build-up, in a technical sense, of the first mode in lateral direction (No1) or of the first mode in depth direction (N10) in the channel waveguide, andthe difference between wavelength λ
a +Δ
λ
w of the efficient oscillation build-up, in a technical sense, of the fundamental mode (Noo) in the channel waveguide and wavelength λ
b of the efficient oscillation build-up, in a technical sense, of the second mode in lateral direction in the coupling area, widened in relation to the channel waveguide, of the junction splitter (N02), that is by ##EQU3## and so that the junction splitter of at least three channel waveguides, having at least one SOWCW, is defined as an integrated-optical wideband junction splitterby spatially combining light of at least two differing wavelengths or wavelength ranges for generating fast-changing spectral compositions of light, for color mixing, in a usable spectrum range greater than 75 nm, wherein a minimum of two light components are injected, respectively, into one channel waveguide each, and decoupled from a common SOWCW as spatially combined light.
-
-
14. A method of using a wideband junction splitter comprising the steps of:
-
using a junction splitter having channel waveguides for the spatial combination or splitting or switching or deflection or modulation of light, for applications within the wavelength range of visible light, having at least three channel waveguides, having; at least one single-mode integrated-optical wideband channel waveguide (SOWCW) where in or on a surface-type substrate material, by a process for changing the refractive index, a channel-shaped structure is fabricated or a channel-shaped structure made from a suitable material is applied, with the geometric/substance parameters of the channel waveguide thus created being set in dependence of the wavelength ranges to be transmitted in the UV, visible, and/or IR regions, so that in relation to the wavelength (λ
) a minimum width of the wavelength range for single-mode light guidance is given by the equation
space="preserve" listing-type="equation">Δ
λ
.sub.w =0.48×
λ
-85 nmwhere the parameters substrate refractive index (n1,), superstrate refractive index ((n3,), refractive index of the refractive index distribution (f(x,y)) on the surface ((n2,)), refractive index distribution in the waveguiding region, cross-sectional shape (width a and depth t) of the channel waveguide and its location in and/or on the substrate are dimensioned such that single-mode operation of the channel waveguide in the wavelength range
space="preserve" listing-type="equation">Δ
λ
.sub.w >
0.48×
λ
-85 nmis ensured, so that to each given wavelength (λ
) in the range between λ
a and λ
a +Δ
λ
w one and only one effective refractive index, can be allocated, and the single-mode range will be determined by efficient oscillation build-up of fundamental mode Noo at wavelength λ
a +Δ
λ
w on the one hand, and by efficient oscillation build-up, in a technical sense of the first mode in lateral direction (N01) or of the first mode in depth direction (N10) at wavelength λ
a on the other hand, and with transmission at a technically sufficient degree of effectiveness signifying that the effective refractive index Neff of the mode guided in the channel waveguide must be at least 5×
10-5 above the refractive index of the surrounding material ns, where ns where ns designates the value of substrate index n1 or superstrate index n3, whichever is the greater, and with the minimum possible value of the usable wavelength (λ
min) and the maximum possible value of the usable wavelength (λ
max) being determined by the transmission range of the materials used, and thus the channel waveguide being defined as a single-mode integrated-optical wideband channel waveguide (SOWCW), and wherein there is provideda combination and connection of the minimum of three channel waveguides, in which the geometric/substance parameters of the channel waveguides themselves as well as the media surrounding the channel waveguides which are set in dependence of the wavelength range to be transmitted in the UV, visible, and/or IR regions, so that in relation to the wavelength (λ
) the minimum width of the wavelength range for efficient junction splitter operation is given by the equation
space="preserve" listing-type="equation">Δ
λ
.sub.v >
0.27×
λ
-34 nmwhere the parameters substrate refractive index (n1), superstrate refractive index (n3), refractive index of the refractive index distribution (f(x,y)) on the surface (n2), refractive index distribution in the waveguiding region, geometry of the junction splitter, and its location in and/or on the substrate are dimensioned such that efficient operation of the junction splitter is at least ensured in the wavelength range
space="preserve" listing-type="equation">Δ
λ
.sub.v >
0.27×
λ
-34 nmwith the usable wavelength range Δ
λ
N for the efficient operation of the junction splitter, in a technical sense is determined by the lesser value of one ofthe difference between wavelength λ
a +Δ
λ
w of the efficient oscillation build-up, in a technical sense, of the fundamental mode (Noo) in the channel waveguide and wavelength λ
a of the efficient oscillation build-up, in a technical sense, of the first mode in lateral direction (No1) or of the first mode in depth direction (N10) in the channel waveguide, andthe difference between wavelength λ
a +Δ
λ
w of the efficient oscillation build-up, in a technical sense, of the fundamental mode (Noo) in the channel waveguide and wavelength λ
b of the efficient oscillation build-up, in a technical sense, of the second mode in lateral direction in the coupling area, widened in relation to the channel waveguide, of the junction splitter (N02), that is by ##EQU4## and so that the junction splitter of at least three channel waveguides, having at least one SOWCW, is defined as an integrated-optical wideband junction splitterby splitting light into at least two light components in a usable spectrum range greater than 75 nm, in which a minimum of one light component is injected into an SOWCW, and in which light components from at least two channel waveguides, which have the same spectral composition and phasing as the injected light, are decoupled.
-
-
15. A method of using a wideband junction splitter as a wavelength-selective or wavelength-independent wideband switch or wideband modulator for the amplitude or intensity of light of at least one wavelength or one wavelength range for generating fast changing light intensities and/or spectral light compositions in a usable spectrum range greater than 75 nm, comprising the steps of:
-
using a junction splitter having channel waveguides for the spatial combination or splitting or switching or deflection or modulation of light, for applications within the wavelength range of visible light, having at least three channel waveguides, having; at least one single-mode integrated-optical wideband channel waveguide (SOWCW) where in or on a surface-type substrate material, by a process for changing the refractive index, a channel-shaped structure is fabricated or a channel-shaped structure made from a suitable material is applied, with the geometric/substance parameters of the channel waveguide thus created being set in dependence of the wavelength ranges to be transmitted in the UV, visible, and/or IR regions, so that in relation to the wavelength (λ
) a minimum width of the wavelength range for single-mode light guidance is given by the equation
space="preserve" listing-type="equation">Δ
λ
.sub.w =0.48×
λ
-85 nmwhere the parameters substrate refractive index (n1,), superstrate refractive index ((n3,), refractive index of the refractive index distribution (f(x,y)) on the surface ((n2,)), refractive index distribution in the waveguiding region, cross-sectional shape (width a and depth t) of the channel waveguide and its location in and/or on the substrate are dimensioned such that single-mode operation of the channel waveguide in the wavelength range
space="preserve" listing-type="equation">Δ
λ
.sub.w >
0.48×
λ
-85 nmis ensured, so that to each given wavelength (λ
) in the range between λ
a and λ
a +Δ
λ
w one and only one effective refractive index, can be allocated, and the single-mode range will be determined by efficient oscillation build-up of fundamental mode Noo at wavelength λ
a +Δ
λ
w on the one hand, and by efficient oscillation build-up, in a technical sense of the first mode in lateral direction (N01) or of the first mode in depth direction (N10) at wavelength λ
a on the other hand, and with transmission at a technically sufficient degree of effectiveness signifying that the effective refractive index Neff of the mode guided in the channel waveguide must be at least 5×
10-5 above the refractive index of the surrounding material ns, where ns where ns designates the value of substrate index n1 or superstrate index n3, whichever is the greater, and with the minimum possible value of the usable wavelength (λ
min) and the maximum possible value of the usable wavelength (λ
max) being determined by the transmission range of the materials used, and thus the channel waveguide being defined as a single-mode integrated-optical wideband channel waveguide (SOWCW), and wherein there is provideda combination and connection of the minimum of three channel waveguides, in which the geometric/substance parameters of the channel waveguides themselves as well as the media surrounding the channel waveguides which are set in dependence of the wavelength range to be transmitted in the UV, visible, and/or IR regions, so that in relation to the wavelength (λ
) the minimum width of the wavelength range for efficient junction splitter operation is given by the equation
space="preserve" listing-type="equation">Δ
λ
.sub.v >
0.27×
λ
-34 nmwhere the parameters substrate refractive index (n1), superstrate refractive index (n3), refractive index of the refractive index distribution (f(x,y)) on the surface (n2), refractive index distribution in the waveguiding region, geometry of the junction splitter, and its location in and/or on the substrate are dimensioned such that efficient operation of the junction splitter is at least ensured in the wavelength range
space="preserve" listing-type="equation">Δ
λ
.sub.v >
0.27×
λ
-34 nmwith the usable wavelength range Δ
λ
N for the efficient operation of the junction splitter, in a technical sense is determined by the lesser value of one ofthe difference between wavelength λ
a +Δ
λ
w of the efficient oscillation build-up, in a technical sense, of the fundamental mode (Noo) in the channel waveguide and wavelength λ
a of the efficient oscillation build-up, in a technical sense, of the first mode in lateral direction (No1) or of the first mode in depth direction (N10) in the channel waveguide, andthe difference between wavelength λ
a +Δ
λ
w of the efficient oscillation build-up, in a technical sense, of the fundamental mode (Noo) in the channel waveguide and wavelength λ
b of the efficient oscillation build-up, in a technical sense, of the second mode in lateral direction in the coupling area, widened in relation to the channel waveguide, of the junction splitter (N02), that is by ##EQU5## and so that the junction splitter of at least three channel waveguides, having at least one SOWCW, is defined as an integrated-optical wideband junction splitterby injecting light into at least one channel waveguide and decoupling at a common SOWCW as spatially combined modulated light.
-
-
16. A method of using a wideband junction splitter in an arrangement as a measurement device for physical, chemical, and biological parameters, in which at least one of a light component in a channel waveguide or SOWCW, and spatially combined light in a common SOWCW, and spatially combined light provided at an output of an SOWCW, and waveguiding in one of the channel waveguides or an SOWCW are influenced by a parameter and in which the spatially combined light components are measured photometrically at a point after output of a common SOWCW, said arrangement being in a wavelength sensor, comprising steps of injecting light of an unknown wavelength into a first common SOWCW, the first common SOWCW being split into two SOWCW, and these split SOWCW being spatially combined in a second common SOWCW, and which thus constitutes an integrated-optical interferometer structure, with light intensity being measured at output of the second common SOWCW, and fitting electrodes in a suitable fashion on the split SOWCW, and with the magnitude of the voltage applied to the electrodes--which voltage causes a change in the light transmission performance at output from maximum to an adjacent minimum, or vice versa--being a measure for the wavelength of the light.
-
17. A junction splitter having channel waveguides for the spatial combination or splitting or switching or deflection of modulation of light for applications within the wavelength range of visible light, comprising at least three channel waveguides, comprising:
-
at least one single-mode integrated-optical wideband channel waveguide (SOWCW) where in or on a surface-type substrate material having a channel-shaped structure, said structure providing effective refractive indices Neff dependent on wavelength and on different transmission modes of said waveguide and the channel shaped structure providing single mode transmission for each wavelength in a wavelength range of
space="preserve" listing-type="equation">Δ
λ
.sub.w >
0.48×
λ
-85 nmand defining λ
a= λ
for a given channel waveguide wherein λ
a and Δ
λ
w are defined by
space="preserve" listing-type="equation">N.sub.eff (λ
.sub.a +Δ
λ
.sub.w)=5×
10.sup.-5 +n.sub.sfor the fundamental mode (Noo) and
space="preserve" listing-type="equation">N.sub.eff (λ
.sub.a(01))=5×
10.sup.-5 +n.sub.sfor the first mode in lateral direction (N01) and
space="preserve" listing-type="equation">N.sub.eff (λ
.sub.a(10))=5×
10.sup.-5 +n.sub.sfor the first mode in depth direction (N10) where ns is the highest value of the refractive indices of the materials surrounding the waveguide and
space="preserve" listing-type="equation">λ
.sub.a =λ
.sub.a(01) if λ
.sub.a(01) ≧
λ
.sub.a(10)or
space="preserve" listing-type="equation">λ
.sub.a =λ
.sub.a(10) if λ
.sub.a(01) <
λ
.sub.a(10)wherein λ
a(01) is the wavelength of the efficient oscillation build-up of the first mode in lateral direction (N01) and λ
a(10) is the wavelength of the efficient oscillation build-up of the first mode in depth direction (N10) and thus the channel waveguide being defined as a single-mode integrated-optical wideband channel waveguide (SOWCW), and wherein there is provided;a combination and connection of the minimum of three channel waveguides, providing efficient junction splitter operation in a wavelength range of
space="preserve" listing-type="equation">Δ
λ
.sub.v >
0.27×
λ
-34 nmand defining λ
b =λ
for a given junction splitter wherein λ
b is defined by
space="preserve" listing-type="equation">N.sub.eff (λ
.sub.b)=5×
10.sup.-5 +n.sub.sfor the second mode in lateral direction (N02) in the coupling area, widened in relation to the channel waveguide, where ns is the highest value of the refractive indices of the materials surrounding the waveguide wherein λ
b is the wavelength of the efficient oscillation build-up of the second mode in lateral direction (N02) and Δ
λ
v is defined by
space="preserve" listing-type="equation">Δ
λ
.sub.v =λ
.sub.a Δ
λ
.sub.w -λ
.sub.bwhere the usable wavelength range Δ
λ
n for the efficient operation of the junction splitter is determined by the lesser value of Δ
λ
w or Δ
λ
v.
-
Specification