Single-mode selection method of semiconductor laser

Abstract

The invention discloses a single-mode selection method of a semiconductor laser, and belongs to the technical field of semiconductor lasers. A space pumping excitation semiconductor laser is adopted, and the semiconductor laser is of a periodic microcavity laser structure with any cavity mode meeting Bloch mode distribution. And the spatial distribution of the modulation space pump light is overlapped with the field envelope distribution of the target order Bloch mode of the semiconductor laser, so that selective injection of the target order Bloch mode is realized. According to the invention, the complexity of micro-nano structure design and processing in static mode regulation and control is avoided; the interaction between the optical interference fringes and the vacuum electromagnetic field in the photonic crystal microcavity improves the noise characteristic of the laser, and single-mode laser with narrow linewidth and low noise characteristics is realized.

Description

Technical Field

[0001] This invention relates to the field of semiconductor laser technology, and more particularly to a single-mode selection method for semiconductor lasers. Background Technology

[0002] With the increasing demand for bandwidth and transmission rate in inter-chip communication, monochromatic light sources with high modulation rates and small device sizes are becoming increasingly important in the miniaturization of photonic integrated circuits. Semiconductor lasers, represented by photonic crystals (PhC), which combine high quality factor and small mode size, have become powerful candidates for achieving high-performance dense integration and are ideal light source choices for on-chip photonic integration.

[0003] However, photonic crystal (PhC) cavities with micron-scale carrier storage regions often face severe gain saturation and mode competition problems during laser emission, reducing the monochromaticity and coherence of photonic crystal lasers and hindering their high-density integration. To achieve effective control of lasing modes in PhC lasers, numerous nanophotonic methods have been proposed, primarily by altering the intracavity micro / nanostructure to modulate the interaction between the radiation source and photons. Examples include introducing distributed feedback grating structures to provide selective feedback for modes satisfying the Bragg condition, enhancing the lasing advantage of a specific mode by controlling the optical coupling between multiple microcavities, and breaking the cavity's PT symmetry by designing asymmetric gain-loss distributions to place specific modes in the non-Hermitian gain region, thus achieving single-mode lasing. However, these mode manipulation schemes have high requirements for fabrication precision and design complexity. Once the device is fabricated and its performance is determined, a more practical and feasible dynamic control method is still needed.

[0004] To address this need, existing spatial optical pumping technology is a quantum optics method that manipulates the vacuum electromagnetic field within a cavity by controlling the properties of external pump light, thereby changing the laser threshold and optimizing characteristics such as the side-mode suppression ratio. Although it can perform real-time dynamic control without relying on changes in the sample structure, this method requires wavelength-scale or even higher spatial resolution in reported systems such as Fabry-Perot microcavities and micro-bottle cavities to match the mode patterns, thus posing certain difficulties in experimental implementation. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a single-mode selection method for semiconductor lasers. This invention overcomes the limitations of mode competition within existing semiconductor lasers and mode manipulation methods in existing micro / nano structures, practically enabling flexible mode manipulation on a photonic crystal platform to improve performance. By designing spatial pumping and combining it with the spatial distribution characteristics of Bloch modes within the semiconductor laser cavity, the pump light profile only needs to overlap with the low-frequency envelope distribution of Bloch modes within the cavity to achieve highly selective single-mode lasing. Compared to multimode lasing in conventional all-optically pumped photonic crystal lasers, this invention effectively achieves the selection of a single Bloch mode, and also significantly improves the modulation and noise performance of the output laser.

[0006] This invention discloses a single-mode selection method for a semiconductor laser, characterized by comprising the following steps:

[0007] A semiconductor laser is excited by a space pump light, wherein the semiconductor laser is a periodic microcavity laser structure with arbitrary cavity modes satisfying the Bloch mode distribution;

[0008] Spatial distribution of modulated spatial pump light S in This allows the field envelope P(z) distribution of the target order Bloch mode of the semiconductor laser to overlap with that of the target order Bloch mode, thereby achieving selective injection of the target order Bloch mode.

[0009] Specifically, based on the low-frequency envelope distribution of the mode field within the Bloch mode, interference fringes are formed on the surface of a periodic microcavity laser structure where the cavity mode satisfies the Bloch mode distribution by two coherent pump beams. The incident angle or wavelength is adjusted so that the bright and dark positions of the interference fringes overlap with the high and low positions of the low-frequency envelope intensity of the mode field, respectively, thereby achieving selective injection of the target order Bloch mode.

[0010] According to a preferred embodiment of the present invention, the semiconductor laser is a photonic crystal line defect microcavity.

[0011] According to a preferred embodiment of the present invention, the spatial pump refers to a pump whose pump profile is adjusted to spatially overlap with the intracavity pattern envelope distribution.

[0012] According to a preferred embodiment of the present invention, the space pumping is an interference pumping method, and the excitation of the semiconductor laser by space pumping specifically includes:

[0013] Two coherent pump beams are incident mirror images of each other from both sides of a semiconductor laser at the same incident angle. The beams are focused and superimposed on the cavity plane of the semiconductor laser through an objective lens to form an interference field, which is used to excite the semiconductor laser. The pump region excites charge carriers to generate population inversion, and photons are emitted through spontaneous emission and stimulated emission. The Bloch wave propagates in the periodic medium, and the forward and reverse light fields formed by the end face reflection interfere in the semiconductor laser cavity, forming a series of Bloch modes that satisfy the resonance condition.

[0014] According to a preferred embodiment of the present invention, the intensity distribution S of the interference light field in Along the length of the cavity, follow:

[0015] S in =1-cos(2k) i zsinθ i );

[0016] Where z is the position along the length of the cavity, starting from the leftmost position of the microcavity; θ i Let k be the incident angle of two coherent beams. i The pump wavenumber;

[0017] The spatial profile of the interference light field fringes can be adjusted by changing the incident angle and wavenumber of the two coherent beams.

[0018] According to a preferred embodiment of the present invention, the series of Bloch modes satisfying the resonance condition are represented as follows:

[0019]

[0020] Where F(z,t) and R(z,t) are the amplitudes of the Bloch forward and backward waves, k0 is the wave number, ω is the frequency, and t is the time.

[0021] According to a preferred embodiment of the present invention, the spatial distribution P(z) of the Bloch mode is represented as the product of a slowly varying envelope and a small periodic function under the envelope;

[0022]

[0023] Where m is an integer representing the target order of the Bloch mode, a is the lattice constant, and L... c =Na is the cavity length of the semiconductor laser; N represents the number of holes in the defect; the slowly varying envelope function. A small-period function with m peaks under its envelope The Bloch-pot properties originate from the periodic structure of photonic crystals.

[0024] According to a preferred embodiment of the present invention, the fringe period of the spatial pump light is adjusted based on the gain distribution after carrier diffusion in order to maximize the overlap with the vacuum field distribution inside the photonic crystal microcavity.

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0026] Compared to multimode lasing with uniformly pumped photonic crystal microcavities, this invention selectively injects target modes by adjusting the spatial profile of optical interference injection to overlap with the gradually varying envelope of the Bloch mode. The intracavity carrier and gain distribution tends towards the selected mode, thereby lowering the mode threshold and achieving single-mode lasing. Compared to previously reported spatial pumping mode control schemes in other systems, optical interference injection based on the gradually varying envelope of the photonic crystal microcavity mode field relaxes the limitations on spatial resolution, and the pump fringe period is adjustable, avoiding the complexity of micro / nano structure design and fabrication in static mode control. The interaction between the optical interference fringes and the vacuum electromagnetic field within the photonic crystal microcavity improves the laser's noise characteristics, achieving a single-mode laser with both narrow linewidth and low noise characteristics. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the interference-pumped photonic crystal line defect microcavity in Embodiment 1 of the present invention.

[0028] Figure 2 This is a schematic diagram of the interference pump light profile and the Bloch mode field in the microcavity of the photonic crystal line defect in Embodiment 1 of the present invention.

[0029] Figure 3 This is a schematic diagram showing the distribution of carrier density and gain along the cavity length when the second Bloch mode is generated in the microcavity with interference pumping photonic crystal line defects in Embodiment 1 of the present invention.

[0030] Figure 4 This is a comparison of the LL curves and lasing spectra of the photonic crystal line defect microcavity under uniform (top) and interference (bottom) pumping in Embodiment 1 of the present invention.

[0031] Figure 5 This is a comparison of the relationship between the number of photons and time and the intensity noise in the defective microcavity of the uniform and interference-pumped photonic crystal lines in Embodiment 1 of the present invention.

[0032] Figure 6 This is a comparison of the linewidth and phase noise of the microcavity mode of the photonic crystal line defect under uniform and interference pumping in Embodiment 1 of the present invention. Detailed Implementation

[0033] The present invention will be further described and illustrated below with reference to specific embodiments. The technical features of each embodiment of the present invention can be combined accordingly without mutual conflict. The single-mode selection method for semiconductor lasers of the present invention is used to overcome the limitations of mode competition in existing semiconductor lasers and mode manipulation methods in existing micro / nano structures, and practically achieves flexible mode manipulation on a photonic crystal platform to improve its performance. The main steps of this method are: using spatial pumping to excite a semiconductor laser, wherein the semiconductor laser is a periodic microcavity laser structure with arbitrary cavity modes satisfying the Bloch mode distribution;

[0034] Spatial distribution of modulated spatial pump light S in The field envelope P(z) distribution overlaps with the target order Bloch mode of the semiconductor laser, thereby achieving selective injection of the target order Bloch mode.

[0035] In one specific embodiment of the present invention, the semiconductor laser is a photonic crystal line defect microcavity. For example... Figure 1 As shown, more specifically, this embodiment provides a scheme for spatially pumping a single Bloch mode in a photonic crystal line defect microcavity. This photonic crystal line defect microcavity is constructed by removing 20 air holes (L20) in a Q1.25 InGaAsP photonic crystal slab, with an InGaAs quantum well in the middle, which can achieve light emission at a wavelength of around 1550nm in the C-band of optical communication.

[0036] In this embodiment, a second (m=2) Bloch mode single-mode lasing will be achieved in the photonic crystal line-defect microcavity. The specific effect is illustrated by constructing a set of traveling wave rate equations for the photonic crystal microcavity based on interference pumping. This set of equations includes: the time-domain traveling wave equation of the optical field, the photon density equation, and the carrier rate equation.

[0037] The spatial pumping described in this invention refers to a pump whose pump profile is adjusted to spatially overlap with the cavity mode envelope distribution. Specifically, in this embodiment, the spatial pumping is an interference pumping method. This interference pumping involves two coherent beams incident at the same angle from mirror images of both sides of the cavity. These beams are focused and superimposed on the cavity plane by an objective lens to form an interference light field, which is used to excite the photonic crystal line defect microcavity. The pump light intensity is L. in The distribution of the interference light field intensity along the cavity length follows:

[0038] S in =1-cos(2k) i zsinθ i )

[0039] z represents the position along the length of the cavity, starting from the leftmost position of the microcavity; θ i Let k be the incident angle of two coherent beams. i The pump wavenumber;

[0040] Specifically, the spatial profile of the interference light field fringes can be adjusted by changing the incident angle and wavenumber of the two coherent beams.

[0041] The photonic crystal microcavity is excited by interference pumping, which excites charge carriers in the pump region to generate population inversion, emitting photons through spontaneous emission and stimulated emission. The electric field within the cavity can be represented as a superposition of forward and reverse Bloch modes:

[0042]

[0043] Where F(z,t) and R(z,t) are the amplitudes of the forward and backward Bloch modes, k0 is the wave number, ω is the frequency, and t is the time. The Bloch wave propagates in a periodic medium, and the forward and reverse optical fields formed by reflection at the end face interfere within the cavity, forming a series of Bloch modes that satisfy the resonance condition. Their spatial distribution can be expressed as:

[0044]

[0045] Where, L c =Na is the cavity length, N represents the number of holes "dug out" along the Γ-M direction, a is the lattice constant, and the leftmost position of the microcavity is denoted as the origin (z = 0, 0 ≤ z ≤ L). c Slowly varying envelope function A small-period function with m peaks under its envelope (Period of 2a) originates from the Bloch wave properties of the periodic structure of photonic crystals.

[0046] In this embodiment, the spatial distribution of the interference pump light follows equation (1), and the spatial distribution S of the modulated spatial pump light of the present invention is... in (z), so that it overlaps with the field envelope P(z) distribution of the first-order Bloch mode of the photonic crystal line defect microcavity, such as Figure 2 As shown, selective injection of the target mode is achieved. Specifically, under uniform pump light, S... in (z) = 1.

[0047] Furthermore, in order to analyze the lasing characteristics of photonic crystal microcavities under space pumping, this invention establishes a model of the traveling wave rate equations for photonic crystal line defect microcavities based on interference pumping.

[0048] In this embodiment, the time-domain traveling wave equation of the optical field includes the forward propagation equation and the backward propagation equation, and the optical field distribution is represented as the superposition of two backward propagating waves. The coupling mode field amplitudes F and R between the forward and backward optical fields are ignored, and they do not satisfy the time-domain traveling wave equation:

[0049]

[0050]

[0051] Among them, v g Here, Γ is the group velocity, Γ is the optical confinement factor, g is the gain, P is the vacuum field factor within the cavity, and F is the gain. p The Purcell factor, according to the Fermi-Gold rule, indicates that changes in the local density of photon states in a vacuum field affect the radiative rate of a radiation source, thereby modulating spontaneous and stimulated emission. The degree of enhancement can be expressed by the Purcell factor F. p Let α be the quality factor of the cavity mode (proportional to Q / V, where Q is the quality factor of the cavity mode and V is the mode volume), α be the absorption loss, and S be the slow light factor. MIR For endoscope wear, S F (S R ) represent the forward and reverse fields of spontaneous emission coupled into the laser mode, respectively.

[0052] In the above rate equation, a parabolic approximation is used to describe the gain:

[0053]

[0054] Among them, g N N represents the differential gain, N0 represents the transparent carrier concentration, and N c Where is the carrier concentration, G0 is the parabolic gain fitting factor, and ε represents the gain compression factor at gain saturation.

[0055] In this embodiment, the photon density equation is used to calculate the intracavity photon density. The photon density equation follows:

[0056]

[0057] Where ε0 is the vacuum permittivity and h is Planck's constant.

[0058] By S F and S R The driven spontaneous emission serves as a Langevin noise source, achieved by randomly generating Gaussian white noise in space and time, which satisfies the following correlation relationship.

[0059]

[0060] <S(z,t)S(z',t)>=0

[0061] Among them, R sp =N c / (τ sp L c ) represents the amount of spontaneous emission per unit length of an active region, β is the spontaneous emission factor, and τ sp For spontaneous emission lifetime, K pδ is the transverse Petermann factor, which is taken as a fixed value of 1 here, and δ is the unit impulse response function. The spontaneous radiation fields coupled to the forward and backward waves have equal amplitudes.

[0062] The forward and backward light fields satisfy the following at the boundary:

[0063] F(t,0)=r²R(t,0),R(t,L) c )=r2F(t,L c )

[0064] In the formula, r1 and r2 are the specular reflectivities of the left and right sides of the cavity, respectively.

[0065] The carrier rate equation is used to calculate the time and space variation of the intracavity carrier density, with a factor S added to the pump term. in This describes the intensity distribution of the interference pump light along the cavity length. The equation for the carrier density in the active region as a function of time is:

[0066]

[0067] Where, η i Let V be the internal quantum efficiency, V be the active region volume, β be the spontaneous emission coupling factor, and τ be the internal quantum efficiency. sp For spontaneous emission lifetime, τ nr For non-radiative recombination lifetime, v p Let be the phase velocity, and D be the carrier diffusion coefficient.

[0068] The traveling wave rate equation based on the photonic crystal microcavity consists of the above three parts, as detailed below:

[0069]

[0070] To simplify the process, only three Bloch modes are considered in the following calculations. The specific parameters of the model are listed in Table 1.

[0071] Table 1. Model Parameters

[0072]

[0073]

[0074] Furthermore, numerical simulations were performed on the model. Based on the above principles, we used the finite difference method to solve formula (13), discretizing it by dividing the time axis and spatial axis into several small segments. The initial carrier concentration in the cavity was set to N. c =10 17 m -3 The initial photon concentration is N p =10 10 m -3The initial values ​​of the forward and backward light fields are both zero, and they propagate in opposite directions from the two end faces of the cavity. The forward light field F at position z and time t-Δt... m (t-Δt,z), after a time interval Δt, propagates to z+Δz and evolves into F. m (t, z + Δz). Similarly, the backlight field R at position z + Δz and time t - Δt. m (t-Δt, z+Δz) will propagate to z after time Δt and evolve into R. m (t,z). To achieve spatial resolution far exceeding that of lasing wavelengths, the cavity length of the photonic crystal line defect microcavity is divided into 600 segments. The time step and spatial step must satisfy the stability condition Δt≤L. c / (600v g The simulation included three lasing modes within the cavity, with corresponding lasing wavelengths of λ1 = 1536.7 nm, λ2 = 1539.8 nm, and λ3 = 1542.8 nm, respectively. These correspond to 3, 2, and 1 peaks in the Bloch mode envelope, respectively. The pump fringe spatial profile overlaps with the mode field envelope distribution of the second Bloch mode, both exhibiting two peaks.

[0075] Furthermore, the carrier concentration and optical gain distribution along the defect cavity of the photonic crystal line were calculated as follows: Figure 3 As shown, under the interference pump, the distribution of charge carriers and optical gain also varies with the spatial modulation of the pump, exhibiting two peaks. The spatial pump modulates the imaginary part of the refractive index, forming a gain grating similar to that of a gain-coupled DFB laser. In addition to the slowly varying envelope of the Bloch mode, weak ripples caused by the rapidly varying component with a period of 2a were observed. The amplitude of these ripples tends to be smoothed due to the carrier diffusion effect. Under spatial injection conditions, the carrier diffusion coefficient has a non-negligible influence on mode selection. Since the carrier concentration contrast on small periods is weakened, this diffusion effect is actually beneficial to the realization of the Bloch mode selection mechanism.

[0076] Furthermore, the lasing curves and lasing spectra of the photonic crystal line defect microcavity under uniform pumping and interference pumping were calculated, such as... Figure 4 As shown, when the optical interferometric injection is effectively aligned with the mode field distribution of the Bloch mode λ2, the threshold power decreases from approximately 120 μW to approximately 80 μW, transforming the mode from multimode lasing to single-mode lasing. At the same pump power, when using interferometric pumping with two pump peaks to select the λ2 mode, the output spectra of the three modes show an SMSR of 46.66 dB between λ1 and λ2, and 40.27 dB between λ2 and λ3, significantly improving mode selectivity. This demonstrates that interferometric pumping can achieve efficient mode selection by aligning the spatial distribution of the optical gain with the vacuum field of the target mode.

[0077] Furthermore, the spectral linewidth and noise characteristics of single-mode lasing achieved through Bloch mode selection were calculated. Since the intensity noise originates from the random fluctuations in photon density over time caused by spontaneous emission coupling into the lasing mode, the relative intensity noise (RIN) spectrum is defined as the fast Fourier transform of the noise autocorrelation function. Figure 5 The left-hand side shows the time evolution of photon density. After experiencing the start-up delay and the oscillation of photon density, the system gradually enters a stable emission state. Figure 5 The right side of the image shows the relative intensity noise (RIN) spectra of the λ² mode under both uniform and interferometric pumping conditions. The calculations are based on data from the stable portion of the photon density time evolution. At the same pump power, interferometric pumping significantly improves the SMSR. Photons generated within the cavity are concentrated in the selected mode; in contrast, the photon density of the mode under uniform pumping is only about one-third of that under interferometric pumping due to severe mode competition. The increased proportion of coherent photons suppresses intensity fluctuations, leading to a significant reduction in the overall RIN under interferometric pumping. This is because, compared to uniform pumping, a smaller proportion of the pump energy in interferometric pumping is converted into spontaneous emission coupled into the lasing mode, effectively reducing the laser's intensity noise.

[0078] Furthermore, the effect of interferometric pumping on phase noise characteristics was investigated. Figure 6 The left side shows the laser spectra obtained by Fourier transform of the λ² light field of the Bloch mode after galloping oscillation under uniform pumping and interferometric pumping conditions. Simulation results show that under interferometric pumping conditions, the selected lasing mode has a narrower spectral linewidth and a lower proportion of spontaneous emission coupled into the lasing mode, thus improving the laser's noise characteristics. This is because under uniform pumping, spontaneous emission photons coupled into the lasing mode can appear at every position along the cavity longitudinal direction, and the distribution of these photons is disordered compared to the stimulated emission of the lasing mode (which has the same standing wave node distribution as the vacuum field). Therefore, spontaneous emission under uniform pumping manifests as a radiation source randomly distributed at various frequencies. In contrast, when the pump light forms interference fringes, carrier injection will tend to be concentrated at positions consistent with the field distribution of a certain Bloch mode, thus reducing the amount of spontaneous emission coupled into that mode, thereby suppressing the phase noise of the lasing mode, such as... Figure 6 As shown on the right. Simultaneously, the threshold of the selected lasing mode decreases, further narrowing the spectral lines.

[0079] Therefore, by calculating the distribution of charge carriers, gain, and photons of each mode over time and space, and simulating the LL curve, lasing spectrum, mode linewidth, intensity noise, and phase noise when the laser output is stable, it can be found that when the spatial distribution of optical interference injection matches the slowly varying envelope field of a certain Bloch mode, a single-mode lasing with a high side-mode suppression ratio can be achieved, accompanied by narrowing of the spectral lines and improvement of noise characteristics.

[0080] The above-described embodiment is merely a preferred embodiment, which further illustrates the purpose, technical solution, and advantages of the present invention. It should be emphasized that the above-described embodiments are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for single-mode selection in a semiconductor laser, characterized in that, Includes the following steps: A semiconductor laser is excited by a space pump light, wherein the semiconductor laser is a periodic microcavity laser structure with arbitrary cavity modes satisfying the Bloch mode distribution; Spatial distribution of modulated spatial pump light S in This allows the field envelope P(z) distribution of the target order Bloch mode of the semiconductor laser to overlap with that of the target order Bloch mode, thereby achieving selective injection of the target order Bloch mode. Specifically, based on the low-frequency envelope distribution of the mode field within the Bloch mode, interference fringes are formed on the surface of a periodic microcavity laser structure where the cavity mode satisfies the Bloch mode distribution by two coherent pump beams. The incident angle or wavelength is adjusted so that the bright and dark positions of the interference fringes overlap with the high and low positions of the low-frequency envelope intensity of the mode field, respectively, thereby achieving selective injection of the target order Bloch mode.

2. The single-mode selection method for a semiconductor laser according to claim 1, characterized in that, The semiconductor laser is a photonic crystal line defect microcavity.

3. The single-mode selection method for a semiconductor laser according to claim 1, characterized in that, The term "spatial pump" refers to a pump whose pump profile is adjusted to overlap spatially with the intracavity pattern envelope distribution.

4. The single-mode selection method for a semiconductor laser according to claim 1, characterized in that, The space pumping is a type of interference pumping, and the specific methods for exciting the semiconductor laser using space pumping include: Two coherent pump beams are incident mirror images of each other from both sides of a semiconductor laser at the same incident angle. The beams are focused and superimposed on the cavity plane of the semiconductor laser through an objective lens to form an interference field, which is used to excite the semiconductor laser. The pump region excites charge carriers to generate population inversion, and photons are emitted through spontaneous emission and stimulated emission. The Bloch wave propagates in the periodic medium, and the forward and reverse light fields formed by the end face reflection interfere in the semiconductor laser cavity, forming a series of Bloch modes that satisfy the resonance condition.

5. The single-mode selection method for a semiconductor laser according to claim 4, characterized in that, The intensity distribution S of the interference light field in Along the length of the cavity, follow: S in =1-cos(2k i zsinθ i ); Where z is the position along the length of the cavity, starting from the leftmost position of the microcavity; θ i Let k be the incident angle of two coherent beams. i The pump wavenumber; The spatial profile of the interference light field fringes can be adjusted by changing the incident angle and wavenumber of the two coherent beams.

6. The single-mode selection method for a semiconductor laser according to claim 4, characterized in that, The series of Bloch modes that satisfy the resonance condition are represented as follows: Where F(z,t) and R(z,t) are the amplitudes of the Bloch forward and backward waves, k0 is the wave number, ω is the frequency, and t is the time.

7. The single-mode selection method for a semiconductor laser according to claim 6, characterized in that, The spatial distribution P(z) of the Bloch mode is represented as the product of the slowly varying envelope and the small periodic function under the envelope; Where m is an integer representing the target order of the Bloch mode, a is the lattice constant, and L... c =Na is the cavity length of the semiconductor laser; N represents the number of holes in the defect; the slowly varying envelope function. A small-period function with m peaks under its envelope The Bloch-pot properties originate from the periodic structure of photonic crystals.

8. The single-mode selection method for a semiconductor laser according to claim 5, characterized in that, The fringe period of the space pump light is adjusted according to the gain distribution after carrier diffusion in order to maximize the overlap with the vacuum field distribution inside the photonic crystal microcavity.

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