Patent Application
20170063044
Field of the Invention
The present invention relates to a quantum cascade laser using intersubband transitions in a quantum well structure.
Related Background Art
Light in a mid-infrared wavelength range (for example, wavelengths of 5 to 30 μm) is an important wavelength range in the field of spectrometric analysis. As a high-performance semiconductor light source in this wavelength range, attention has been attracted to quantum cascade lasers (QCL) in recent years (e.g., cf. Patent Documents 1 to 3).
The quantum cascade laser is a monopolar type laser element which uses a level structure including subbands formed in a semiconductor quantum well structure, to generate light by transitions of electrons between the subbands, wherein quantum well emission layers, each of which is formed in the quantum well structure and serves as an active region, are cascade-coupled in multiple stages, thereby enabling realization of high-efficiency and high-output operation. This cascade coupling of the quantum well emission layers is realized by use of electron injection layers for injecting electrons into emission upper levels, so as to alternately stack the quantum well emission layers and the injection layers.
The quantum cascade laser was first successfully lased in 1994 and since then, the lasing wavelength thereof has been actively increased toward longer wavelengths; in 2002, R. Kohler et al. reported the lasing in the terahertz (THz) band (Non Patent Document 3: NATURE Vol. 417 (2002) pp. 156-159). The terahertz band is a so-called far-infrared region of around 100 μm in terms of wavelength, for example, wavelength of from about 60 μm to 300 μm, which is a range corresponding to the boundary between radio waves and light. Since the terahertz light (terahertz wave) has the feature of possessing both of transmitting property of radio wave and rectilinearity of light, application thereof as unprecedented sensing means is under research in various fields including the medical biology, security, communication, cosmic observation, and so on.
It was hard for the semiconductor lasers of conventional structures to realize the increase in wavelength up to the terahertz band, but the quantum cascade lasers have realized lasing in the terahertz band as described above. However, it is the present status that the laser operation is still limited to an extremely-low temperature environment using liquid nitrogen, and there are problems in effectiveness to industrial application.
For example, S. Fathololoumi et al. (Non Patent Document 4: Optics Express Vol. 20 (2012) pp. 3866-3876) reported the maximum operating temperature ˜200K at the oscillation frequency of 2.85 THz in the configuration wherein the active layer is configured by cascade coupling of triple quantum well structures of GaAs/AlxGa1-xAs (x=0.15). However, the status quo method is in a situation where it is very difficult to achieve higher-temperature operation.
On the other hand, M. A. Belkin et al. have succeeded in generating the terahertz light (THz light) by difference frequency generation (DFG) through the use of two-wavelength oscillation type mid-infrared QCL and the second order nonlinear optical effect in the QCL (Patent Document 3: Japanese Patent Application Laid-Open Publication No. 2010-521815). It was already confirmed that the QCL for generating the terahertz light by this configuration (DFG-THz-QCL) was able to operate at a room temperature, and further improvement in characteristics is expected.
Recently, a group in Northwestern University also reported the DFG-THz-QCL (Non Patent Document 5: Appl. Phys. Lett. Vol. 99 (2011) 131106-1-131106-3, Non Patent Document 6: Appl. Phys. Lett. Vol. 101 (2012) pp. 251121-1-251121-4, Non Patent Document 7: Appl. Phys. Lett. Vol. 103 (2013) pp. 011101-1-011101-4). Most recently, room temperature continuous operation at a level of μW has been realized, and the output at a level of mW in the room temperature is also reported; however, it is in a situation where a large electric current of 10 A or more is necessary, and further improvement in characteristics is demanded (Non Patent Document 8: Appl. Phys. Lett. Vol. 104 (2014) pp. 221105-1-221105-5).
As one of problems in improvement in characteristics of the THz-QCL, there is reabsorption inside the substrate of the terahertz light generated in the active layer. Even when an InP substrate not doped with impurities is used as a substrate of the quantum cascade laser, for example, an absorption coefficient for the light of the frequency of 3 THz is about 20 cm−1. At this time, the coherence length is about 100 μm; therefore, most of the terahertz light generated in the active layer is absorbed inside the substrate without being extracted to the outside.
Currently, in order to realize high extraction efficiency of the terahertz light, a method is used applying Cerenkov phase matching, and, for example, a configuration is used in which an element end face polished at an angle of about 200 or 30° serves as an output end face of the terahertz light (e.g., cf. Patent Document 1: International Publication No. WO 2014/018599, Non Patent Document 1: Appl. Phys. Lett. Vol. 100 (2012) pp. 251104-1-251104-4, Non Patent Document 2: Nat. Commun. Vol. 4 Art.2021 (2013) pp. 1-7). As a result, terahertz light output at a level of μW has been realized; however, a sufficient output for practical use has not been obtained. In this configuration in which the element end face is polished, the terahertz light that can be extracted to the outside is only the light generated in a range of about several hundred μm near the end face, due to absorption inside the substrate and the like.
In the THz-QCL, an extraction method has been studied of the terahertz light output from an element surface using a metal grating. However, in this configuration, there are problems such as loss of the light due to the metal, and that mode coupling efficiency is not optimized to the terahertz light; currently, a better terahertz output characteristics than the QCL using Cerenkov phase matching has not been obtained (Non Patent Document 9: Appl. Phys. Lett. Vol. 93 (2008) pp. 161110-1-161110-3).
In association with the above-described configuration in which the element end face is polished at a predetermined angle and serves as the output end face of the terahertz light, a configuration has been proposed in which one wavelength of mid-infrared pump light components of two wavelengths to be used for the difference frequency generation is made to be variable by using an external cavity with a diffraction grating in a cavity structure of a laser element, to make the wavelength of the terahertz light variable (Non Patent Document 2: Nat. Commun. Vol. 4 Art.2021 (2013) pp. 1-7, Non Patent Document 10: J. Opt Vol. 16 (2014) 094002 pp. 1-9). However, in this configuration, there is a problem that, for example, an output angle of the terahertz light from the element end face is changed depending on the wavelength due to refractive index dispersion of the substrate and the like.
The present invention has been made in order to solve the above problem, and an object thereof is to provide a quantum cascade laser capable of suitably outputting light such as the terahertz light generated by the difference frequency generation.
In order to achieve the above object, a quantum cascade laser according to the present invention includes (1) a semiconductor substrate; and (2) an active layer provided on a first surface of the semiconductor substrate and having a cascade structure in which quantum well emission layers and injection layers are alternately stacked in the form of a multistage lamination of unit laminate structures each of which includes the quantum well emission layer and the injection layer, wherein (3) the active layer is configured to be capable of generating first pump light of a first frequency ω1 and second pump light of a second frequency ω2 by intersubband emission transitions of electrons, and to generate output light of a difference frequency ω between the first frequency ω1 and the second frequency ω2 by difference frequency generation from the first pump light and the second pump light, and (4) an external diffraction grating is provided constituting an external cavity for generating the first pump light by feeding the light of the first frequency ω1 back to an element structure portion and configured to be capable of changing the first frequency ω1, outside the element structure portion including the active layer provided on the first surface of the semiconductor substrate, and (5) a plurality of grooves respectively formed in a direction intersecting with a resonating direction in a laser cavity structure are provided on a second surface opposite to the first surface of the semiconductor substrate.
In the above-described quantum cascade laser, the active layer is configured to be capable of generating light components of two frequencies of the first pump light of the first frequency (angular frequency, hereinafter simply referred to as frequency) ω1 and the second pump light of the second frequency ω2. In this configuration, for example, long-wavelength output light such as the terahertz light can be generated as light of a difference frequency ω=|ω1−ω2| by using the difference frequency generation by the first pump light and the second pump light.
In addition, outside the element structure portion being a semiconductor laminate structure provided on the first surface of the semiconductor substrate including the active layer, the external diffraction grating is provided constituting the external cavity for generating the first pump light, and the external diffraction grating is configured to be capable of changing the first frequency ω1 of the light resonating in the external cavity. In this configuration, by changing the frequency ω1 of the first pump light, the frequency ω can be made to be variable of the output light such as the terahertz light generated by the difference frequency generation.
In the above configuration, the plurality of grooves are formed extending in a direction intersecting with a resonating direction of light in a laser element, on the second surface being a rear surface of the semiconductor substrate, for the output light generated by the difference frequency generation in the active layer. According to this configuration, the light can be suitably output, such as the terahertz light, generated by the difference frequency generation in the active layer, by making each of side surfaces of the plurality of grooves provided on the substrate rear surface function as an output surface for the output light. Further, in the configuration using the grooves in this way, change of output angle distribution of light can be suppressed by reflection of the light inside the groove and the like, even when the frequency ω of the output light is made to be variable.
According to the quantum cascade laser of the present invention, the active layer is configured to be capable of generating the first pump light of the first frequency ω1 and the second pump light of the second frequency ω2, and to generate the output light of the difference frequency ω by the difference frequency generation from the first pump light and the second pump light, the external diffraction grating is provided constituting the external cavity for generating the first pump light and configured to be capable of changing the first frequency ω1, outside the element structure portion including the active layer, and the grooves respectively formed in the direction intersecting with the resonating direction of the light in the laser element are provided on the second surface being the rear surface of the semiconductor substrate, thereby enabling suitable output of the light such as the terahertz light generated by the difference frequency generation.
The present invention will be more fully understood from the detailed description given hereinbelow and the accompanying drawings, which are given by way of illustration only and are not to be considered as limiting the present invention.
Further scope of applicability of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will be apparent to those skilled in the art from this detailed description.
Hereinafter, an embodiment of a quantum cascade laser according to the present invention will be described in detail with reference to the drawings. In the description of the drawings, the same elements will be denoted by the same reference signs, without redundant description. The dimensional ratios in the drawings are not always coincident with those in the description.
The active layer 15 has a cascade structure in which quantum well emission layers to be used for generation of light and electron injection layers to be used for injection of electrons into the emission layers are stacked alternately in multiple stages. Specifically, as shown in
In the laser element main body 1A in the quantum cascade laser 2A of the present embodiment, the active layer 15 is configured to be capable of generating first pump light of a first frequency ω1 and second pump light of a second frequency ω2 by intersubband emission transitions of electrons, and to generate output light of difference frequency ω=|ω1−ω2| between the first frequency ω1 and the second frequency ω2 by difference frequency generation (DFG) from the first pump light and the second pump light. Here, the frequencies ω1, ω2 of pump light components are determined by a subband level structure in the active layer 15, and by an internal diffraction grating 13, the external diffraction grating 25 for frequency (wavelength) selection described later.
In this configuration, each of the first pump light, second pump light of the frequencies ω1, ω2 to be generated in the active layer 15 is, for example, mid-infrared light. The light of the frequency ω to be generated by the difference frequency generation is, for example, long-wavelength light such as the terahertz light. In
As shown in
The unit laminate structure 16 in the present embodiment, in its subband level structure, has a first emission upper level (level 4) Lup1=L4, a second emission upper level (level 5) Lup2=L5 having a higher energy than the first emission upper level, and a plurality of emission lower levels. In the configuration example shown in
The unit laminate structure 16, more specifically in the above subband level structure, has a first emission lower level (level 1) Llow1=L1, a second emission lower level (level 2) Llow2=L2 having a higher energy than the first emission lower level, and a third emission lower level (level 3) Llow3=L3 having a higher energy than the second emission lower level, as the plurality of emission lower levels each having a lower energy than the first emission upper level.
In the unit laminate structure 16 shown in
A specific interval configuration of the levels in the subband level structure in the unit laminate structure 16 is as follows: each of an energy ΔE41 of an emission transition (4→1) from the first emission upper level Lup1 to the first emission lower level Lw1 and an energy ΔE52 of an emission transition (5→2) from the second emission upper level Lup2 to the second emission lower level Llow2 is substantially equal to an energy E1 of the light of the first frequency ω1 (ΔE41=ΔE52=E1). Furthermore, each of an energy ΔE42 of an emission transition (4→2) from the first emission upper level Lup1 to the second emission lower level Llow2 and an energy ΔE53 of an emission transition (5→3) from the second emission upper level Lup2 to the third emission lower level Llow3 is substantially equal to an energy E2 of the light of the second frequency ω2 (ΔE42=ΔE53=E2). In the present configuration example, the first, second frequencies ω1, ω2 are set so as to satisfy the condition ω1>ω2, and the difference frequency is ω=ω1−ω2.
In the above level structure, each of an energy difference ΔE21 between the first emission lower level Llow1 and the second emission lower level Llow2, an energy difference ΔE32 between the second emission lower level Llow2 and the third emission lower level Llow3, and an energy difference ΔE54 between the first emission upper level Lup1 and the second emission upper level Lup2 is substantially equal to an energy E=E1−E2 of the light of the difference frequency ω between the first, second frequencies ω1, ω2 (ΔE21=ΔE32=ΔE54=E).
In this subband level structure, electrons from the relaxation level Lr in the injection layer 18a of the preceding stage are injected through the injection barrier into the emission layer 17, to strongly excite the second emission upper level Lup2 coupled to the relaxation level Lr. At this time, a sufficient amount of electrons are also supplied to the first emission upper level Lup1 through a high-speed scattering process such as electron-electron scattering, with the result that sufficient amounts of carriers are supplied to both of the two emission upper levels Lup1, Lup2.
The electrons injected into the first, second emission upper levels Lup1, Lup2 transit to each of first, second, third emission lower levels Llow1, Llow2, Llow3, so as to generate and emit light with energies corresponding to the energy differences between the subband levels of the emission upper levels and the lower levels; particularly, it results in generating and emitting the first pump light of the first frequency ω1 with the energy E1 and the second pump light of the second frequency ω2 with the energy E2.
The electrons having transited to the emission lower levels Llow1, Llow2, Llow3 are relaxed to the relaxation level Lr. As the electrons are extracted from the emission lower levels Llow1, Llow2, Llow3 in this manner, population inversion is formed to achieve lasing between the upper levels Lup1, Lup2 and the lower levels Llow1, Llow2, Llow3. Here, the relaxation level Lr used for relaxation of electrons is schematically represented by only one level in
As the injection, emission transitions, and relaxation of electrons described above are repeated in the plurality of unit laminate structures 16 constituting the active layer 15, light generation occurs in a cascade manner in the active layer 15. Namely, the emission layer 17 and the injection layer 18 are stacked alternately in a large number of stages, whereby electrons move in a cascade manner in the laminate structures 16 while generating the first pump light of the first frequency ω1 and the second pump light of the second frequency ω2 during the intersubband emission transitions in each laminate structure 16. By the difference frequency generation by these first pump light and second pump light, the light of the difference frequency ω such as the terahertz light is generated and output.
The configuration of the active layer 15 will be further described later along with a specific example thereof. Regarding the active layer 15, various configurations may be used capable of generating the first pump light of the first frequency ω1 and the second pump light of the second frequency ω2, besides the configuration shown in
Referring again to
In the present configuration example, a rotation stage 26 is provided functioning as a resonance frequency variation mechanism (resonance wavelength variation mechanism) by changing an installation angle to the optical axis by rotationally driving the diffraction grating 25, for the external diffraction grating 25. Thus, the external cavity using the external diffraction grating 25 is configured to be capable of changing the first frequency ω1 of the first pump light.
In the quantum cascade laser 2A, as schematically shown in
The frequencies ω1, ω2 of the pump light components of two wavelengths resonated and generated in the laser cavity structure in the quantum cascade laser 2A may be substantially equal to the frequencies ω1, ω2 described above in regard to the energies between levels in the level structure shown in
The configuration of the quantum cascade laser 2A including the element main body 1A shown in
The quantum cascade laser 2A of the present embodiment uses Cerenkov phase matching in generation and output of the light of the difference frequency ω by the difference frequency generation. The Cerenkov phase matching is a pseudo phase matching method, and the terahertz output light is emitted in a direction having a finite emission angle θc with respect to a travelling direction A0 of the mid-infrared pump light, as shown in
Cerenkov radiation is generated, when pump light components of two wavelengths whose difference frequency ω corresponds to the terahertz wave enter the nonlinear optical crystal, by induction of second-order nonlinear polarization having spatial distribution according to a phase difference between the components of the two wavelengths. The nonlinear polarization has a frequency to be a difference frequency between the pump light components of two wavelengths, and radiates the terahertz light at timing according to the phase of the nonlinear polarization at each point.
As a result, when the refractive index of the InP substrate in the terahertz band nTHz=3.6 is greater than the effective refractive index in the mid-infrared region nMIR=3.37, due to refractive index dispersion, the terahertz light generated in the crystal propagates in the same phase in the radiation directions A1, A2 shown in
θc=cos−1(nMIR/nTHz)˜20°
Namely, in the DFG-THz-QCL in which the semiconductor laminate structure including the active layer 15 is grown on the InP substrate 10, the terahertz light generated by the difference frequency generation propagates downward from the active layer 15 at the emission angle of about 20°, as shown in
The terahertz light generated in the active layer 15 to be emitted by Cerenkov radiation propagates the inside of the InP substrate 10 in the direction of the above-described emission angle θc, and finally reaches a second surface (rear surface) 10b being an interface between the substrate 10 and the air outside the element and opposite to the first surface 10a of the substrate 10. At this time, the refractive index of the air nair=1 is significantly different from the refractive index of the InP substrate 10 for the terahertz light nTHz=3.6. For this reason, total reflection occurs on the second surface 10b, and it is difficult to extract the terahertz light as the output light to the outside of the element.
On the other hand, in the quantum cascade laser 2A including the laser element main body 1A shown in
Effects of the quantum cascade laser 2A having the laser element main body 1A of the present embodiment will be described.
In the quantum cascade laser 2A shown in
The external diffraction grating 25 is provided constituting the external cavity for generating the first pump light, outside the element structure portion 11 provided on the first surface 10a of the semiconductor substrate 10 including the active layer 15, and the external diffraction grating 25 is configured to be capable of changing the first frequency ω1 of light resonating in the external cavity. In this configuration, by making the frequency ω1 of the first pump light variable, the frequency ω of the output light such as the terahertz light generated by the difference frequency generation can be variably controlled continuously.
In the quantum cascade laser 2A of the above configuration, the plurality of grooves 12 are formed extending in the direction intersecting with the resonating direction A0 of the light in the laser element, on the second surface 10b being the rear surface of the semiconductor substrate 10, for the output light to be generated by the difference frequency generation in the active layer 15. According to this configuration, the light can be suitably output such as the terahertz light generated by the difference frequency generation in the active layer 15, by making each of side surfaces and inner surfaces of the plurality of grooves 12 provided on the substrate rear surface 10b function as an output surface of the output light. In the configuration using the plurality of grooves 12 for light output to the outside in this way, change of the output angle (output angle distribution) of the light to the outside can be suppressed by reflection of the light inside the groove and the like, even when the frequency ω of the output light is made to be variable by the external cavity as described above.
Here, in the above configuration, regarding a shape of the groove 12 formed on the substrate rear surface 10b, each of the plurality of grooves 12 is preferably configured to be formed in a curved surface shape in which a width in the groove monotonically decreases from the second surface 10b side and an inclination angle θg of a side surface with respect to a direction (semiconductor lamination direction in laser element) perpendicular to the second surface 10b varies in a depth direction. According to this configuration, the output angle of the light is changed depending on a position in the groove side surface, so that change of the output angle distribution due to change of the frequency ω of the output light can be suitably suppressed.
The quantum cascade laser 2A of the above configuration may be configured so that, as described above, in addition to the external diffraction grating 25 constituting the external cavity, the internal diffraction grating 13 is provided constituting the distributed feedback cavity for generating the second pump light of the second frequency ω2, inside the element structure portion 11 provided on the first surface 10a of the semiconductor substrate 10. According to this configuration, the first pump light and the second pump light to be used for the difference frequency generation can be suitably generated by suitably setting and controlling the first, second frequencies ω1, ω2 of the pump light components by the external cavity with the external diffraction grating 25, and the distributed feedback cavity with the internal diffraction grating 13.
The quantum cascade laser 2A of the above configuration may be configured so that a lens element is provided, through which the output light output from the plurality of grooves 12 to the outside passes, on the second surface 10b of the semiconductor substrate 10. According to this configuration, an output condition such as the output angle distribution of the light to be output to the outside can be suitably set and controlled by the lens element on the second surface 10b. The configuration using such lens element will be further described specifically later.
In the above configuration, regarding the formation direction of the grooves 12 on the second surface 10b of the semiconductor substrate 10, the grooves 12 are preferably respectively formed in a direction perpendicular to the resonating direction A0 of the light on the second surface 10b. In this configuration, each of the side surfaces of the plurality of grooves 12 can be made to suitably function as the output surface for the output light such as the terahertz light.
Regarding the specific configuration of the semiconductor substrate 10, the plurality of grooves 12 of the second surface 10b, and the like in the laser element main body 1A, the semiconductor substrate 10 preferably has the thickness t of 50 μm or more and 200 μm or less.
Each of the plurality of grooves 12 is preferably formed such that the width w is h/10 or more and 2 h or less ( 1/10 or more and 2 times or less of depth h), where h is the depth of the grooves.
Each of the plurality of grooves 12 is preferably formed such that the depth h is 30 μm or more and t−20 μm or less, where t is the thickness of the semiconductor substrate 10. In addition, each of the plurality of grooves 12 is preferably formed such that the depth h is λ/10 or more and 2λ or less ( 1/10 or more and 2 times or less of wavelength λ of output light), where λ is the wavelength of the output light.
The plurality of grooves 12 are preferably formed such that the interval L of the grooves is h/2 or more and 2 h/tan θc+w or less, where h is the depth of the grooves, w is the width of the grooves, and θc is the emission angle of the output light by the difference frequency generation. Furthermore, the plurality of grooves 12 are preferably formed such that the interval L of the grooves is h/tan θc+w/2 or more, where h is the depth of the grooves, w is the width of the grooves, and θc is the emission angle of the output light by the difference frequency generation.
Each of the plurality of grooves 12 is preferably formed such that the inclination angle θg of the side surface with respect to the direction (semiconductor lamination direction in laser element) perpendicular to the second surface 10b is 4° or more and 20° or less.
According to these configurations, the output light such as the terahertz light can be suitably output with sufficient intensity from each of side surfaces and inner surfaces of the grooves 12 formed on the second surface 10b of the semiconductor substrate 10. Configuration conditions of the semiconductor substrate 10, the plurality of grooves 12, and the like will be further described specifically later.
The output condition of the terahertz light in the plurality of grooves 12 in the quantum cascade laser 2A having the element main body 1A shown in
In the quantum cascade laser 2A of the above embodiment, as shown in
Here, as described above, a case is considered as an example in which the semiconductor substrate 10 is a semi-insulating InP substrate, the emission angle of the terahertz light from the active layer 15 to the downward direction is θc=20° assuming frequency of 3 THz, and the inclination angle of the side surface of the groove 12 with respect to the direction perpendicular to the second surface 10b is θg=10°. In this configuration, the terahertz light propagating inside the substrate 10 enters at an incident angle θin=100 to the side surface of the groove 12.
At this time, the refractive index of the air is nair=1 in contrast with the refractive index of the InP substrate 10 in the terahertz band nTHz=3.6, and based on the Snell's law
n
1 sin θ1=n2 sin θ2
the terahertz light is output refracted at an exit angle θout=40° from the side surface of the groove 12 to the downward direction. In this configuration, as a result, the terahertz light can be output in a surface direction of the semiconductor substrate 10 through the plurality of grooves 12.
Here, when the inclination angle of the side surface of the groove 12 is θg=0° and the groove side surface is parallel to a cleaved end face, the terahertz light is totally reflected and is not output to the outside. When the terahertz light propagates inside the substrate 10 at the emission angle θc=20°, the terahertz light is output in the surface direction of the substrate 10 without being totally reflected, at the inclination angle θg of the groove side surface of 4° or more. On the other hand, when the inclination angle θg of the groove side surface is greater than 20°, the terahertz light is refracted upward, so that components to be taken in again to the substrate 10 are generated. Therefore, regarding the side surface of the groove 12, the groove 12 is preferably formed so that its inclination angle θg is, for example, 4° or more and 20° or less.
The groove 12 actually formed on the second surface 10b of the semiconductor substrate 10 does not have a pointed shape with the planar side surface as shown in
In consideration of this point, regarding the inclination angle θg of the side surface of the groove 12, the groove 12 is preferably formed such that the inclination angle θg satisfies the condition of 4° or more and 20° or less in as many portions as possible of the groove side surface, for example, the surface portions of ⅓ or more of the groove side surface.
In the quantum cascade laser 2A shown in
Here, in the description below, as for the output light generated by the difference frequency generation, the terahertz light is mainly assumed of a frequency range from 1 THz to 6 THz. This is because, in a frequency region lower than 1 THz, absorption of the light by free electrons inside the active layer 15 becomes remarkable and available sufficient light output cannot be obtained, and, in a frequency region higher than 6 THz, since there is strong absorption due to longitudinal optical phonons in a semiconductor material constituting the element structure portion 11, available sufficient light output cannot be obtained similarly.
As described above, the Cerenkov exit angle θc of the terahertz output light generated by the difference frequency generation is obtained by the following formula.
θc=cos−1(nMIR/nTHz)
When the substrate 81 is a semi-insulating InP substrate, nMIR may be constant at nMIR=3.37 within a wavelength range related to the difference frequency generation (cf. Non Patent Document 10: J. Opt Vol. 16 (2014) 094002 pp. 1-9). According to Non Patent Document 10, nTHz=3.5 for the frequency of 1 THz, and nTHz=3.8 for the frequency of 6 THz. In addition, for the frequency of 3 THz, nTHz=3.6, as described above.
When the emission angle θc to the resonating direction B0 of the terahertz output light by the difference frequency generation is obtained by the above formula using these refractive index values, an emission angle is θc1=20° of the terahertz light of 3 THz propagating in a propagating direction B1 inside the substrate 81, an emission angle is θc2=15.7° of the terahertz light of 1 THz propagating in a propagating direction B2, and an emission angle is θc3=27.5° of the terahertz light of 6 THz propagating in a propagating direction B3.
When a critical angle of total reflection of when each terahertz light of frequency of 1 THz and 6 THz enters from the semiconductor substrate into the air is obtained by using Snell's law, a total reflection critical angle is 16.6° for the terahertz light of the frequency of 1 THz, and a total reflection critical angle is 15.3° for the terahertz light of the frequency of 6 THz.
When the polishing angle of the substrate end face 82 is 200 for the above-described emission angle θc of the terahertz light, the terahertz light of 3 THz is output to the outside in an output direction B6 along the vertical line of the end face 82. The terahertz light of 1 THz is output to the outside in an output direction B7, and its output angle is θ67=15.2°. The terahertz light of 6 THz is output to the outside in an output direction B8, and its output angle is θ68=29.7°.
Therefore, when the frequency of the terahertz output light is changed in a range from 1 THz to 6 THz by the external cavity using the external diffraction grating in this configuration, the output angle of the light is changed by about 45° along with the frequency change. Such a large change of the output condition of an output beam becomes a problem in application of the terahertz light to an optical system of spectroscopy and the like. In the configuration in which the substrate end face is polished, polishing operation itself is not easy, and in installation of an optical element such as a lens and a mirror for the terahertz output light, for example, installation of the optical element to be used near the output surface of the light such as a hyper-hemispherical lens, alignment of the optical element becomes difficult.
On the other hand, in the above configuration in which the plurality of grooves 12 formed on the second surface 10b of the substrate 10 are used in output of the terahertz light, the change of the output condition of the light to the outside along with the change of the frequency ω can be suppressed by, for example, reflection of the light inside the groove. In particular, each shape of the plurality of grooves 12 is made to be a curved surface shape in which, as shown in
An optical path P2 shows a case in which the terahertz light having entered the groove side surface is output to the outside at the output angle same as the incident angle without being refracted. An optical path P3 shows a case in which entrance into the groove side surface of the terahertz light and output to the outside occur in the opposite side of the optical path P1 with respect to the vertical line of the tangent line. In this case too, when an incident angle θP3 is 16.6° being the critical angle or less, the terahertz light is output to the outside without being totally reflected.
In the optical paths P2, P3, the terahertz light is not directly output to the lower side from the substrate rear surface 10b; however, through one or more reflections inside the groove 12, the terahertz light is partially output to the lower side. In an optical path P4, since the incident angle to the groove side surface exceeds the critical angle, the terahertz light is not output to the outside due to total reflection. In addition, such entrance to the groove 12, reflection, and output to the outside of the terahertz light occur symmetrically.
As shown in
Next, the thickness t of the semiconductor substrate 10 constituting the element main body 1A in the quantum cascade laser 2A will be described. The absorption coefficient in the semi-insulating InP substrate for the terahertz light of the frequency of 3 THz is about 20 cm−1 as described above. Inside a waveguide structure including the active layer 15 in the laser element main body 1A, the terahertz light has already undergone absorption of about 20 cm−1 due to impurity doping and the like. Considering effects of attenuation of the terahertz light due to the absorption, the thickness t of the semiconductor substrate 10 is preferably made to be as thin as possible by polishing or the like.
However, since thinning the substrate 10 leads to decrease in physical strength of the laser element, there is a certain limit. Ideally, it is preferable that the thickness t of the substrate 10 is thinned to about 50 μm by polishing or the like so that the second surface 10b of the substrate 10 is close to the element structure portion 11 on the substrate 10 functioning as the waveguide structure, and the grooves 12 of the depth h (cf.
The thickness t of the semiconductor substrate 10 is, for example, set to 150 μm in the example described later. When the thickness of the semiconductor substrate 10 is greater than 200 μm, the terahertz light is considered to be attenuated to the intensity of half or less. For this reason, the thickness t of the substrate 10 is preferably at least 200 μm or less. Therefore, the thickness t of the semiconductor substrate 10 is preferably 50 μm or more and 200 μm or less.
Considering the terahertz light in the frequency range from 1 THz to 6 THz described above, it is necessary to consider output of the terahertz light of the frequency of 5 to 6 THz that is most easily influenced by absorption of the light. According to Non Patent Document 10, an absorption coefficient of the semi-insulating InP substrate for the terahertz light of 5 to 6 THz is about 30 cm−1. At this time, a distance in which the light can propagate, for example, until the light intensity becomes 1/e can be estimated to be 330 μm.
Here, the terahertz light of the frequency of 6 THz propagates inside the substrate 10 at the emission angle θc=27.50. For this reason, when the thickness t of the substrate 10 is 330 μm×sin 27.5°˜150 μm or less, the terahertz light can propagate to the second surface 10b of the substrate 10. Furthermore, the terahertz light of the frequency of 6 THz is output to the outside in a relatively deep surface portion of the groove 12 as shown in
Next, the width w of the groove 12 formed on the second surface 10b of the semiconductor substrate 10 will be described. It is preferable that, regarding the width w of the groove 12, the width w is h/10 or more and 2 h or less for the depth h of the groove, and the shape of the groove 12 is any curved surface shape in which the opening portion of the groove 12 is the widest and the width w monotonically decreases in the depth direction of the groove 12.
In a case in which the width of the groove 12 is w=h/10, when it is assumed that a groove shape is symmetrical to the center of the groove 12 and a side surface is planar (cf.
When the width of the groove 12 is w=2 h, in any region of the side surface of the groove of a curved surface, the terahertz light can be output to the outside even when it is the terahertz light of any frequency in a range of 1 to 6 THz. However, when the width w of the groove 12 is made to be greater than 2 h, the region becomes small in which the terahertz light can be output to the outside for the terahertz light entering the groove 12, and it is not efficient. Therefore, the width w of the groove 12 is preferably h/10 or more and 2 h or less, as described above. In particular, in order to output the terahertz light efficiently in wideband by widening the region in which the terahertz light can be output in a frequency range of 1 to 6 THz in the side surface of the groove 12 of the curved surface, the width w of the groove 12 is preferably h/5 or more and h/2 or less.
Next, the depth h of the groove 12 formed on the second surface 10b of the semiconductor substrate 10 will be described. When the depth h of the groove 12 is too large, the terahertz light emitted from the groove side surface in the deep portion of the groove 12 may be taken in to the inside of the substrate 10 again inside the groove 12. On the other hand, when the depth h of the groove 12 is too small, an area is small in which the terahertz light propagating inside the substrate 10 reaches the groove side surface.
In consideration of this point, the appropriate depth h of the groove 12 varies depending on the wavelength λ (frequency ω) of the terahertz light, and is considered to be appropriate at about 2 times of the wavelength λ when it is the largest, and at about 1/10 of the wavelength when it is the smallest. Therefore, the depth h of each of the plurality of grooves 12 is preferably λ/10 or more and 2λ or less, for the wavelength λ of the terahertz output light. For example, in a case of the terahertz light of the frequency of 3 THz, the wavelength k is about 100 μm, and the range of the appropriate depth h of the groove 12 is from 10 μm to 200 μm.
Further, regarding the depth h of the groove 12, in order to ensure the mechanical strength of the laser element, a difference between the thickness t of the semiconductor substrate 10 and the depth h of the groove 12 is preferably 20 μm or more. Therefore, an upper limit of the depth h of the groove is t−20 μm in consideration of the thickness t of the substrate.
On the other hand, when the size of the structure is less than 1/10 of the wavelength λ of the light, a phenomenon called Rayleigh scattering occurs, and the light cannot be dealt with in geometrical optics. When considering from 1 THz to 6 THz as the frequency range of the terahertz light as described above, the longest wavelength is λ=300 μm at 1 THz; therefore, 30 μm, which is 1/10 of the wavelength λ, is a lower limit of the depth h of the groove 12. Therefore, the depth h of the groove 12 is preferably 30 μm or more and t−20 μm or less.
Next, the interval L between the grooves adjacent to each other in the plurality of grooves 12 formed on the second surface 10b of the semiconductor substrate 10 will be described with reference to
The interval Lc of the grooves for using entire portions of the side surface of the groove 12 for light output is given by the formula below.
Lc=h/tan θc+w/2
Here, h is a depth of the groove, w is a width of the groove, and θc is a Cerenkov emission angle of the output light by the above-described difference frequency generation. In this condition, the terahertz light propagating inside the substrate 10 is refracted at the interface between the semiconductor and the air at the side surface of the groove 12. However, the situation varies of the propagating wave front in the air of the terahertz light output from the groove side surface, also depending on the inclination angle θg of the groove side surface. Therefore, in setting of the interval L of the grooves 12, such wave front conditions should also be considered.
When the interval L of the grooves 12 is significantly wider than the above-described interval Lc, a lot of the terahertz light propagating inside the substrate 10 reaches the second surface 10b of the substrate 10 rather than the side surface of the groove 12. For this reason, the interval L of the grooves 12 is preferably 2 times of the above interval Lc or less. For example, the interval L of the grooves 12 is set to 200 μm, in the example described later.
On the other hand, when the interval L of the grooves 12 is narrow, only the deep portion of the side surface of the groove 12 contributes the light output, as described above. Considering this point, the interval L of the grooves 12 is preferably half of the depth h of the groove 12 or more. Therefore, the interval L of the grooves 12 is preferably h/2 or more and 2 h/tan θc+w or less. In the example described later, the range of the appropriate interval L of the grooves 12 is from 17 μm to 206 μm.
Further, the interval L of the grooves 12, in order to use the groove side surface efficiently for light output, is preferably h/tan θc+w/2 or more. When considering the above-described frequency range from 1 THz to 6 THz, considering that the emission angle θc is about 15° for the terahertz light of the frequency of 1 THz, the interval L of the grooves 12 is preferably h/tan 15°+w/2 or more.
In this configuration, it becomes possible that the terahertz light of 1 THz propagating inside the substrate 10 at the shallowest angle when viewed from the substrate rear surface 10b reaches the region of the substrate rear surface 10b side of the grooves 12 without hitting on the grooves adjacent to each other. In particular, since the terahertz light of the frequency of 1 THz is suitably output to the outside in the region near the substrate rear surface 10b, output efficiency of such light is decreased when the interval L of the grooves 12 is less than h/tan 15°+w/2.
The interval L of the grooves 12 in the plurality of grooves 12 is not required to be an equal interval; however, when considering the output efficiency to the outside of the terahertz light, the plurality of grooves 12 is preferably formed at an equal interval by the interval L=h/tan 15+w/2 in the substrate rear surface 10b, for example. In this configuration, the terahertz light generated by the difference frequency generation can be suitably output to the outside over the entire region of the cavity length of the laser element.
The groove structure of the plurality of grooves 12 on the second surface 10b of the semiconductor substrate 10 described above can be processed and formed by, for example, a dicing saw, a scriber, or, in a case of relatively shallow grooves, etching processing, and focused ion beam. When the grooves are formed by using the dicing saw, the scriber, or the like, the groove side surface can be a suitable curved surface shape by applying wet etching after groove processing.
The configuration of the quantum cascade laser will be further described along with a specific example of the element structure including the quantum well structure in the active layer.
Here,
In the semiconductor laminate structure of an element main body 1B shown in
In the upper guide layer 54, as shown in
The active layer 15 and the guide layers 53, 54, constituting the core layer portion in the waveguide structure including the cladding layers 52, 57, are formed, for example, in the form of the ridge stripe of the width of 12 μm along the resonating direction of the light, after forming the diffraction grating structure of the guide layer 54, as shown in
As described above, the active layer 15 in the present configuration example is configured such that the unit laminate structures 16 each including the quantum well emission layer 17 and the electron injection layer 18 are laminated by 40 periods. In the present configuration example, the center wavelength of the gain in the active layer 15 is set to 10 μm. The unit laminate structure 16 of one period is configured as the quantum well structure in which eleven quantum well layers 161-164, 181-187, and eleven quantum barrier layers 171-174, 191-197 are alternately stacked, as shown in
In the respective semiconductor layers of the unit laminate structure 16, each of the quantum well layers is configured with an InGaAs layer lattice-matched with the InP substrate 50. Each of the quantum barrier layers is configured with an InAlAs layer lattice-matched with the InP substrate 50. In this configuration, the active layer 15 is configured by an InGaAs/InAlAs quantum well structure.
In the unit laminate structure 16, concerning the emission layer 17 and the injection layer 18, the laminate part consisting of four well layers 161-164 and barrier layers 171-174 in the laminate structure shown in
In the present configuration example, regarding the exit barrier layer positioned between the emission layer 17 and the injection layer 18, there is no barrier layer effectively functioning as an exit barrier. In
In the element main body 1B of the quantum cascade laser, in order to achieve generation of the terahertz light by the difference frequency generation, an active layer is required capable of generating pump light components of two wavelengths and having a high second-order nonlinear susceptibility χ(2) for the pump light. In the active layer 15 of the present configuration example, generation of the first pump light of the frequency ω1 and the second pump light of the frequency ω2 in a single active layer design, generation of the terahertz light of the difference frequency ω by the difference frequency generation, and variable control of the frequency with the external diffraction grating 25 are achieved, by adopting the DAU/MS structure shown in
The subband level structure shown in
In this configuration, electrons injected from the injection layer of the preceding stage into the emission layer 17 are equally distributed to the upper levels L4, L5 by high-speed electron-electron scattering or the like, and the two upper levels L4, L5 behave as if they were extended single upper level. Therefore, the gain by transitions from the upper level L4 to the lower levels L1 to L3 and the gain by transitions from the upper level L5 to the lower levels L1 to L3 overlap with each other in equivalent contribution, and a unimodal wide band emission spectrum is obtained.
In this configuration in which a single active layer structure is used, different from the configuration in which the plurality of active layer structures are stacked, a uniform nonlinear optical characteristic is obtained over the entire region of the active layer, thereby enabling achieving high efficiency wavelength conversion. When defining assumed carrier concentrations in the levels L1 to L5 as n1 to n5 respectively and assuming n1=n2=n3, and using conditions n5−ni=1.0×1015 cm−3, n4−ni=1.3×1015 cm−3 (i=1, 2, 3), as an absolute value of the total of the second-order nonlinear susceptibility χ(2) generated by the DAU structure, |χ(2)|=23.3 nm/V is obtained.
The frequencies ω1, ω2 of the pump light, the frequency ω=|ω1−ω2| of the terahertz output light, the variable range of the frequency ω of the terahertz light, and the like are determined by design of the diffraction grating structure 55 being the internal diffraction grating 13, and the external diffraction grating 25. In the present configuration example, the first pump light of the frequency ω1 and the second pump light of the frequency ω2 are both made to operate in a single mode by using the distributed feedback cavity structure, the external cavity structure with the diffraction gratings 13, 25, and by this configuration, the terahertz output light is also made to operate in the single mode.
The configuration will be described of the external diffraction grating 25 to be used for the external cavity for generating the first pump light of the first frequency ω1. As the configuration of the external cavity, for example, well-known Littrow configuration may be used. As the collimating lens 20 (cf.
As for the external diffraction grating 25, it is preferable that a reflection type blazed diffraction grating is used, and, for example, the groove density is 100 lines/mm or more, surface Au coating is applied, and the diffraction efficiency is 60% or more in a wavelength range in which lasing is possible.
In order to stabilize the oscillation by the external cavity and widen the variable range of the frequency (wavelength) by the diffraction grating 25, a low reflection coating of a dielectric multilayer film, or a dielectric single layer film of the thickness of λp/4nMIR may be applied to the first end face 11a of the diffraction grating 25 side in the element structure portion 11. Here, λp is the wavelength of the gain peak, and nMIR is the refractive index of the active layer 15 for the light of the wavelength λp. As the dielectric material, for example, CeO2 can be used of the refractive index of 1.52 for the light of the wavelength of 10 μm. In this case, when the CeO2 film is formed with the film thickness of about 1.6 μm that is λp/4nMIR, the reflectance 2.6% is obtained.
Next, the configuration will be described of the internal diffraction grating 13 to be used for the distributed feedback cavity for generating the second pump light of the second frequency ω2. The wavelength of the light to be oscillated by the distributed feedback cavity with the internal diffraction grating 13 is preferably a wavelength not coincident with the gain peak in the active layer 15 as described above. Here, in order to generate the terahertz light by the difference frequency generation, it is necessary to oscillate the mid-infrared pump light in two wavelengths at the same time. For this reason, in the distributed feedback cavity with the internal diffraction grating 13, it is preferable that the diffraction grating 13 is prepared to oscillate at a distance from the gain peak, and a DFB mode and a plurality of Fabry-Perot modes by the cavity formed by the end faces of the element structure portion 11 are mixed.
The wavelength of the light selected by the internal diffraction grating 13 may be set to any of the long wavelength side and the short wavelength side with respect to the peak wavelength of the gain peak, and, for example, the wavelength may be appropriately selected in which the diffraction grating structure 55 functioning as the internal diffraction grating 13 is easily formed. The diffraction grating structure 55 may be partially formed in the resonating direction in the laser cavity structure, and, alternatively, the diffraction grating structure 55 may be formed over the entire region.
The specific configuration of the quantum cascade laser will be further described.
A SiN insulating layer 62 is provided to cover the element structure portion 60, and an upper electrode 66 is formed electrically connected to the upper contact layer 58 through a contact hole of the insulating layer 62. A SiN insulating layer 63 is provided to cover the support structure portion 61, and a lower electrode 67 is formed electrically connected to the lower contact layer 51 through the contact hole between the insulating layers 62, 63. These electrodes 66, 67 can be formed by, for example, forming a thick Au film of the thickness of about 5 μm by evaporation and plating method and then separating the upper and lower electrodes from each other by etching.
In this formation of the element structure, regarding the etching method, any methods may be used of the wet etching and the dry etching. Also regarding fine patterning, any methods may be used, as far as they are capable of processing of the desired size, such as the interference exposure method, and the nanoimprint method.
In the configuration example shown in
Here, in the conventional configuration in which the substrate end face is polished to be the output surface of the terahertz light, since the area of the output surface is small, it is difficult to accurately attach the lens. On the other hand, in the above configuration in which the plurality of grooves 12 are formed to make the substrate rear surface 10b be the output surface of the terahertz light, it is possible to easily attach the lens 72 to the substrate rear surface of millimeter size. By attaching the lens 72 to the substrate rear surface, the terahertz light can be appropriately output to the outside, and at the same time, mechanical strength of the laser element can be improved. In this configuration, since the resonating direction of the mid-infrared pump light and the output direction of the terahertz light are different from each other, mixing of the mid-infrared light is suppressed in use of the terahertz output light, and therefore, the configuration can be suitably used as a terahertz light source.
The quantum cascade laser according to the present invention is not limited to the above-described embodiment and configuration examples, and can be variously modified. For example, in the above embodiment, one type of coupled dual upper level structure is used in the active layer 15; however, it may be configured so that two or more types of active layer structures are stacked to be used. As for the specific configuration of the active layer 15, various active layer structures may be used such as a bound-to-continuum structure, and a two phonon resonance structure, besides the coupled dual upper level structure (DAU structure).
In the above-described configuration example, although the semi-insulating InP substrate is used as the semiconductor substrate 10, for example, an undoped InP substrate (Si: ˜5×1015 cm−3), or a low-doped InP substrate (Si: 5×1015˜1×1017 cm−3) may be used as the substrate 10. When these substrates are used, a configuration becomes possible in which an electrode is provided on the substrate rear surface. However, when the doping concentration in the substrate is increased, since absorption of light inside the substrate is increased, intensity of the terahertz light output to the outside is decreased.
In the above-described configuration example, although the active layer is shown configured to be lattice matched with the InP substrate, a configuration in which distortion compensation is introduced may be used for the active layer. In the above-described configuration example, although the example has been shown in which the InP substrate is used as the semiconductor substrate and the active layer is configured with InGaAs/InAlAs, various configurations may be used specifically, as far as they are capable of intersubband emission transitions in the quantum well structure, and capable of achieving generation of the above-described first pump light, second pump light, and generation of the output light by the difference frequency generation.
As for the semiconductor material systems, it is possible to use a variety of material systems, e.g., such as GaAs/AlGaAs, InAs/AlSb, GaN/AlGaN, and SiGe/Si, besides above-described InGaAs/InAlAs. Further, various methods may be used as crystal growth methods of semiconductors.
Regarding the laminate structure in the active layer of the quantum cascade laser and the semiconductor laminate structure as the entire laser element, various structures may be used besides the above-described structure. In general, the quantum cascade laser only needs to include the semiconductor substrate and the active layer of the above configuration provided on the first surface of the semiconductor substrate, and to be provided with the external diffraction grating constituting the external cavity for generating the first pump light and configured to be capable of changing the first frequency ω1, outside the element structure portion including the active layer, and to be provided with the plurality of grooves respectively formed in the direction intersecting with the resonating direction in the laser cavity structure on the second surface of the substrate.
Regarding the resonance frequency variation mechanism provided for the external diffraction grating, the rotation stage for rotationally driving the diffraction grating is exemplary shown in the above embodiment; however, besides such a configuration, a variation mechanism of another configuration may be used.
The quantum cascade laser of the above embodiment includes (1) a semiconductor substrate; and (2) an active layer provided on a first surface of the semiconductor substrate and having a cascade structure in which quantum well emission layers and injection layers are alternately stacked in the form of a multistage lamination of unit laminate structures each of which includes the quantum well emission layer and the injection layer, wherein (3) the active layer is configured to be capable of generating first pump light of a first frequency ω1 and second pump light of a second frequency ω2 by intersubband emission transitions of electrons, and to generate output light of a difference frequency ω between the first frequency ω1 and the second frequency ω2 by difference frequency generation from the first pump light and the second pump light, and (4) an external diffraction grating is provided constituting an external cavity for generating the first pump light by feeding the light of the first frequency ω back to an element structure portion and configured to be capable of changing the first frequency ω1, outside the element structure portion including the active layer provided on the first surface of the semiconductor substrate, and (5) a plurality of grooves are provided, respectively formed in a direction intersecting with a resonating direction in a laser cavity structure, on a second surface opposite to the first surface of the semiconductor substrate.
Here, in the above configuration, regarding the shape of the groove, each of the plurality of grooves is preferably configured to be formed in a curved surface shape in which a width in the groove monotonically decreases from the second surface side in the depth direction and the inclination angle θg of the side surface with respect to the direction perpendicular to the second surface varies. According to this configuration, the output angle of the light is changed depending on a position on the groove side surface, so that change of the output angle distribution due to change of the frequency ω of the output light can be suitably suppressed.
The quantum cascade laser of the above configuration may be configured so that the internal diffraction grating is provided constituting the distributed feedback cavity for generating the second pump light of the second frequency ω2, inside the element structure portion provided on the first surface of the semiconductor substrate. According to this configuration, the first pump light and the second pump light to be used for the difference frequency generation can be suitably generated by the external cavity with the external diffraction grating and the distributed feedback cavity with the internal diffraction grating.
The quantum cascade laser of the above configuration may be configured so that the lens element is provided, through which the output light output from the plurality of grooves to the outside passes, on the second surface of the semiconductor substrate. According to this configuration, the output condition of the light to be output to the outside can be suitably set and controlled by the lens element on the second surface.
In the above configuration, regarding the formation direction of the plurality of grooves, the plurality of grooves are preferably respectively formed in the direction perpendicular to the resonating direction on the second surface of the semiconductor substrate. In this configuration, the side surface of each of the plurality of grooves can be made to suitably function as the output surface of the output light such as the terahertz light.
The semiconductor substrate is preferably configured so that the thickness t is 50 μm or more and 200 μm or less.
Each of the plurality of grooves is preferably configured to be formed so that the width w is h/10 or more and 2 h or less ( 1/10 or more and 2 times or less of depth h), where h is the depth of the grooves.
Each of the plurality of grooves is preferably configured to be formed so that the depth h is 30 μm or more and t−20 μm or less, where t is the thickness of the semiconductor substrate.
Each of the plurality of grooves is preferably configured to be formed so that the depth h is λ/10 or more and 2λ or less ( 1/10 or more and 2 times or less of wavelength λ of output light), where λ is the wavelength of the output light.
The plurality of grooves are preferably formed so that the interval L of the grooves is h/2 or more and 2 h/tan θc+w or less, where h is the depth of the grooves, w is the width of the grooves, and Be is the emission angle of the output light by the difference frequency generation. Furthermore, the plurality of grooves are preferably formed so that the interval L of the grooves is h/tan θc+w/2 or more, where h is the depth of the grooves, w is the width of the grooves, and θc is the emission angle of the output light by the difference frequency generation.
According to these configurations, the output light such as the terahertz light can be suitably output with sufficient intensity from each of side surfaces of the plurality of grooves formed on the second surface of the semiconductor substrate.
The present invention can be used as the quantum cascade laser capable of suitably outputting the light such as the terahertz light generated by the difference frequency generation.
From the invention thus described, it will be obvious that the invention may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the invention, and all such modifications as would be obvious to one skilled in the art are intended for inclusion within the scope of the following claims.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2015-170251 | Aug 2015 | JP | national |
