Plasma optical modulation for lasers based on the plasma induced by femtosecond pulses

Chao Tan; Xiquan Fu; Yonghua Hu; Yangbao Deng; Xiaohui Shi; Shiping Zhan; Zaifang Xi

doi:10.1364/OE.25.014065

1. Introduction

Optical modulation is a technique for manipulating optical signals in amplitude, phase or polarization, which are widely used in optical communication [1,2], photonic circuits [3,4], neural network imaging [5], etc. Various methods have been developed for optical modulation. Electrically addressed and optically addressed are two basic types of optical modulation. Compared with electrically addressed method, optically addressed technology has fast temporal response, high spatial resolution and other advantages. Liquid crystals have attracted much interest in electrooptical devices because of their broad-band birefringence [6,7]. BSO crystals are known as one of the perfect components for liquid crystals optical modulators due to their excellent photoconductivity and high dark resistivity [8,9]. Shrestha et al. display that ZnO nanoparticles suspension as a novel photoconductor can be used for liquid crystals optical modulators [10]. Other materials used as photosensors in liquid crystals optical modulators include crystalline silicon, As–Se, a-As₂S₃ and phthalocyanine [11,12]. Thanks to the advantages of low power, high actuator and good compatibility with integrated circuit process, Micro-electro-mechanical system (MEMS) optical modulator [13] has attracted increasing interest in recent years. Single-crystal-silicon, polysilicon, silicon-on-isolator, AlMgSi and polymerides are reported as components for MEMS optical modulators [14–16]. Previously, In-line optical MEMS phase modulator and its application in ring laser frequency modulation were demonstrated by Khalil et al. [17].

Surface plasmon polariton effect also provides ideas for achieving all-optical modulation devices with high performance. Using structural phase transitions in polyvalent metals, it shows that surface plasmon-polariton signals can be effectively controlled by switching the structural phase of gallium. The signal modulation depth can exceed 80% and switching times are expected to be in the picosecond-microsecond time scale [18]. An all-optical switching device based on dielectric-loaded surface plasmon polaritonic crystals is numerically demonstrated [19]. Inserting the gap-surface plasmon into liquid crystal on silicon, has emerged as an innovative approach to control light propagation [20]. The deployments of graphene on top of a silicon waveguide is an efficient method to make graphene-silicon hybrid devices [21]. Liu et al. first experimentally demonstrate a high-performance, waveguide-integrated electroabsorption modulator based on a monolayer graphene [22]. Subsequently, dual-graphene, graphene-based ridge waveguide, graphene-based slot-waveguide, graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption, graphene M-Z polarizer are chosen for optical modulators [23–26]. Previously, a optical modulator with a 35 GHz modulation speed based on a planar structure with double-layer graphene was reported [27].

Plasma channels will be generated when the power of lasers is above the ionization threshold. The electron density and refractive index distribution in the plasma channel induced by ionization is non-uniform. According to the Fermat principle, the laser beam will be deflected when it propagates in the plasma. Naturally, an idea is shown that this plasma channel can be used for optical modulation. Recently, Yu et al. vividly displayed plasma optical modulators for intense lasers [28]. In this paper, firstly, we theoretically demonstrate the plasma optical modulation for lasers with plasmas. Then, the probe beam is modulated by the plasma induced by femtosecond pulses in carbon disulfide. The experimental observations are in good agreement with theoretical results. It finds that the modulation on the beam can be conveniently controlled by adjusting the plasma electron density, plasma width or the power of the pump beam.

2. Theoretical analysis

Consider the propagation of a linearly polarized laser beam in a preformed plasma channel. In terms of the vector potential, the radiation field is given by

\vec{E} (\vec{r}, z, t) = {\vec{e}}_{x} \frac{E_{0} (\vec{r}, z, t)}{2} \exp (i k z - i ω_{0} t) + c . c .

where

E_{0} (\vec{r}, z, t)

is the complex amplitude,

k

is the laser wave number,

ω_{0}

and

{\vec{e}}_{x}

are the laser frequency and the unit vector along the

x

axes, respectively. As the laser power is very low, the relativistic nonlinearity and pondermotive nonlinearity are negligible. Thus, the wave equation describing the evolution of the vector potential in the plasma channel is given by

[\nabla^{2} - \frac{1}{c^{2}} \frac{\partial^{2}}{\partial t^{2}}] \vec{E} (\vec{r}, z, t) = \frac{ω_{p}^{2} (\vec{r})}{c^{2}} \vec{E} (\vec{r}, z, t)

Transforming independent variables $z \to z,$ $ζ \to z - β_{g} c t,$ where $β_{g} = v_{g} / c$ is the normalized group velocity, and substituting Eq. (1) into Eq. (2) gives

{\nabla_{_{⊥}}^{2} + 2 i k \frac{\partial}{\partial z} + (1 - β_{g}^{2}) \frac{\partial^{2}}{\partial ζ^{2}}} ψ (\vec{r}, z, ζ) = \frac{ω_{p}^{2} (\vec{r})}{c^{2}} ψ (\vec{r}, z, ζ)

where

ψ (\vec{r}, z, t) = {e E_{0} (\vec{r}, z, t) / m_{0} c ω}_{0}

is the normalized electric field amplitude,

m_{0}

is the rest mass of electron, e is the electron charge,

ω_{p} (\vec{r}) = {(4 π n_{e} (\vec{r}) e^{2} / m_{0})}^{1 / 2}

is the plasma frequency,

c

is the light velocity in vacuum,

n_{e} (\vec{r})

is the distribution of electron density of plasma, respectively. In deriving Eq. (3), the paraxial and the slowly varying envelope approximations, i.e.,

| \partial ψ / \partial z | < < | k ψ |

and

| \partial ψ / \partial ζ | < < | ω_{0} ψ |

, have been used. Assuming the laser beam to be continuous beam, the third term on the left side of Eq. (3) is neglected. Thus Eq. (3) reduces to

(\frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}} + 2 i k \frac{\partial}{\partial z} - \frac{ω_{p}^{2} (x, y, z)}{c^{2}}) ψ (x, y, z) = 0

Substituting critical plasma density

n_{c} = m_{0} ω_{0}^{2} / 4 π e^{2}

into Eq. (4) yields

\frac{\partial^{2} ψ (x, y, z)}{\partial x^{2}} + \frac{\partial^{2} ψ (x, y, z)}{\partial y^{2}} + 2 i k \frac{\partial ψ (x, y, z)}{\partial z} - k^{2} \frac{n_{e} (x, y, z)}{n_{c}} ψ (x, y, z) = 0

Assume

ψ (x, y, z) = A (x, y, z) \exp (i φ (x, y, z))

Substituting Eq. (6) into Eq. (5) yields

2 k A \frac{\partial φ}{\partial z} + A {(\frac{\partial φ}{\partial x})}^{2} + A {(\frac{\partial φ}{\partial y})}^{2} - \frac{\partial^{2} A}{\partial x^{2}} - \frac{\partial^{2} A}{\partial y^{2}} + \frac{n_{e}}{n_{c}} k^{2} A = 0

2 k \frac{\partial A}{\partial z} + 2 \frac{\partial A}{\partial x} \frac{\partial φ}{\partial x} + 2 \frac{\partial A}{\partial y} \frac{\partial φ}{\partial y} + A \frac{\partial^{2} φ}{\partial x^{2}} + A \frac{\partial^{2} φ}{\partial y^{2}} = 0

Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation is used to derive the WKBJ solution

φ_{w} (x, y, z) = φ (x, y, 0) - \frac{k}{2 n_{c}} \int_{0}^{z} n_{e} (x, y, z^{'}) d z^{'}

A_{w} (x, y, z) = A (x, y, 0)

By making use of WKBJ solutions, it is easy to know that the last four terms of Eq. (8) are much less than that of the first term, and they can be used as perturbation. The amplitude of the second and third terms of Eq. (8) are replaced by the WKBJ solution of amplitude, and the phase of the last four terms of Eq. (8) are replaced by the WKBJ solution of phase. Thus, the modified approximate solution of amplitude Eq. (11) can be derived from Eq. (8).

\begin{matrix} A (x, y, z) = A (x, y, 0) \exp [- \frac{1}{k} \int_{0}^{z} (\frac{\partial A (x, y, 0)}{\partial x} \frac{\partial φ (x, y, z^{'})}{\partial x} + \frac{\partial A (x, y, 0)}{\partial y} \frac{\partial φ (x, y, z^{'})}{\partial y}) d z^{'}] \times \\ \exp [- \frac{1}{2 k} \int_{0}^{z} (\frac{\partial^{2} φ (x, y, z^{'})}{\partial x^{2}} + \frac{\partial^{2} φ (x, y, z^{'})}{\partial y^{2}}) d z^{'}] \end{matrix}

The distribution of probe beam and electron density profile make no difference to the validity of the modified WKBJ solution of amplitude, so Eq. (11) can be used to analyze the evolutions of probe beams in plasmas.

Let us consider the propagation of a Gaussian beam $A (x, y, 0) = A_{0} \exp [- (x^{2} + y^{2}) / 2 w^{2}]$ in a plasma with electron density $n_{e} (x, y, z) = n_{0} \exp [- (x^{2} + y^{2}) / 2 σ^{2}]$ , where $A_{0}, w, n_{0}$ and $σ$ are the initial axial amplitude, beam width, the initial axial electron density and plasma channel width, respectively. The initial phase of the probe laser beam is assumed to be constant $φ (x, y, 0) = c$ . From Eq. (11), we obtain

\begin{matrix} A (x, y, z) = A_{0} \exp [- \frac{x^{2} + y^{2}}{2 w^{2}} + \frac{n_{0}}{n_{c}} \frac{{(x^{2} + y)}^{2} z^{2}}{2 w^{2} σ^{2}} \exp (- \frac{x^{2} + y^{2}}{2 σ^{2}} - \frac{x^{2} + y^{2}}{2 w^{2}})] \times \\ \exp {\frac{z^{2} n_{0}}{4 n_{c}} [- \frac{1}{σ^{2}} \exp (- \frac{x^{2} + y^{2}}{2 σ^{2}}) + \frac{x^{2} + y^{2}}{σ^{4}} \exp (- \frac{x^{2} + y^{2}}{2 σ^{2}})]} \end{matrix}

where

z

is the propagation distance in plasma. The axial intensity of the probe laser beam

I_{c}

can be deduced from Eq. (12).

I_{c} = I_{0} \exp (- \frac{z^{2} n_{0}}{2 σ^{2} n_{c}})

where

I_{0}

is the initial axial intensity of the probe laser beam.

The modified approximate solution of amplitude in Eq. (12) is analyzed for beam width w = 0.6 mm with different electron densities, plasma widths and propagation distance.

Figure 1 shows the spatial intensity of the probe laser after propagating in 5 mm-long plasma channel with different electron densities. The probe beam modulated by a preformed plasma channel with Gaussian density profile has been researched. From Fig. 1(a), it is easy to see that the probe beam is modulated into a beam with a circular dark spot in the center when $n_{c} = 70 n_{0}$ . As is well known, plasma channels are the result of a dynamic balance between the Kerr self-focusing and the defocusing effect (diffraction). The refractive index of the plasma is related to the electron density $N = \sqrt{1 - n_{e} / n_{c}}$ , so the Gaussian electron density results in a non-uniform refractive index with minimum on axis and maximum on the periphery. According to the Fermat principle, the periphery of the plasma is focusing, while the plasma center is defocusing, which results in generating a circular dark spot. We only theoretically analyze the Gaussian distribution of the laser intensity and the electron density, but our method has general character and other non-Gaussian conditions can also be analyzed by this method. If the electron density distribution in the plasma can be adjusted conveniently, it is expected that the probe beam is modulated into a beam with any spatial distribution. The modulation speed $f_{p}$ is determined by the plasma frequency $ω_{p}$ [28], which can be estimated as $f_{p} (H z) = ω_{p} / 2 π \approx 8980 \sqrt{n_{0} (c m^{- 3})}$ , for example $f_{p} \approx 28 THz$ for $n_{0} = 10^{19} {cm}^{- 3}$ . So the modulation speed of this plasma optical modulation method is estimated in the THz regime.

Fig. 1 Spatial intensity distribution of probe beams with $w = 0.6 mm,$ $σ = 0.5 mm,$ $z= 5 mm$ and electron density (a) $n_{c} = 70 n_{0},$ (b) $n_{c} = 50 n_{0},$ and (c) $n_{c} = 30 n_{0},$ respectively. (d) The corresponding cross line (y = 0) of probe beam when electron densities is tuned.

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As shown in Fig. 1, the intensity of the central zone decreased and the peak intensity increased, as $n_{c} / n_{0}$ decreased from 70 to 30. The size of the dark spot increases gradually as $n_{c} / n_{0}$ decreases, the modulation of probe beam by the preformed plasma channel is distinct due to a big electron density $n_{0}$ . If $n_{c} / n_{0}$ decreased continuously, the intensity in the center of the beam will be reduced to zero, thus the probe beam is modulated into a ring-shaped beam. We can explain this phenomenon as follows. When $n_{0}$ increased, the refractive index gradient increased and a more obvious ring-shaped beam performed, because the degrees of the defocusing in the plasma center and the focusing in the plasma periphery are proportional to the refractive index gradient. Obviously, the axial intensity of the laser beam can be adjusted by changing $n_{0}$ [Fig. 1(d)]. Namely, the degree of modulation can be controlled conveniently by adjusting the electron density in the plasma. So Eq. (13) can be used to detect the number of electron density of the plasma with a Gaussian density profile.

Figure 2 displays modulations for the probe beam with different plasma channel widths. From Fig. 2, it is easy to see that a circular dark spot formed in the center of the beam when the width of plasma is 0.5 mm. The intensity of the central zone decreases and the dark spot size increases when plasma width $σ$ decreased from 0.5 mm to 0.3 mm. The modulation of probe beam by the preformed plasma channel is prominent owe to a small width $σ .$ The reason is that a smaller plasma width results in a bigger electron density gradient and refractive index gradient. The defocusing of the plasma center and the focusing of the plasma periphery become more evident due to a smaller plasma width $σ .$ So we can easily control the degree of modulation induced by the plasma through adjusting the plasma width.

Fig. 2 Spatial intensity distribution of probe beam with $w = 0.6 mm,$ $n_{c} = 70 n_{0},$ $z= 5 mm$ (a) no plasma, and plasma channel width (b) $σ = 0.5 mm,$ (c) $σ = 0.4 mm,$ and (d) $σ = 0.3 mm,$ respectively. (e) The corresponding cross line (y = 0) of probe beam when plasma channel widths is tuned.

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The propagation of the beam in the plasma with different propagation distances is vividly shown in Fig. 3. With the increase of propagation distance, the center intensity of the beam decreases and the region where probe beam is modulated (dark spot size) increases gradually. When z = 11 mm, the center of the beam is reduced to zero and the beam is modulated into a ring-shaped beam. When z is increased continuously, the modulation of probe beam by the plasma is more prominent, the dark spot size of the ring-shaped beam increases as the propagation distance increases. From the above analysis, it is clear that the evolution of the probe beam in the plasma channel can be controlled by changing the electron density, plasma width and propagation distance of the plasma. That is to say, the modulation on the beam can be conveniently adjusted through electron density, plasma width and propagation distance of the plasma.

Fig. 3 (a) Spatial intensity distribution of probe beam with $w = 0.6 mm,$ $σ = 0.5 mm,$ $n_{c} = 70 n_{0},$ and propagation distance $z=4, 5, 6, 8, 11, 20, 40 mm,$ respectively. (b) The corresponding cross line (y = 0) of probe beam when propagation distance is tuned.

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3. Experimental analysis

A schematic illustration of the experimental setup is depicted in Fig. 4. A femtosecond pulse laser (Laser 1, Ti:sapphire, LibraS, Coherent) is used as a pump laser source. It delivers pump pulses with duration $τ_{0} = 120 fs$ , wavelength $λ_{0} = 800 nm$ at a repetition rate of 1 kHz. The pump pluses play role in exciting plasma channels in the nonlinear media. A He-Ne laser beam (Laser 2, $λ_{0} = 632 nm$ ) is used as the probe beam (modulated beam). The plasma channel is used for spatial modulation on the probe beam. The spatial profiles of the femtosecond beam and continuous beams are nearly Gaussian, with full width at half maximum (FWHM) values of 0.5 mm and 1 mm, respectively. Femtosecond pulses first pass through an adjustable attenuator (A1) when they are output from the laser system. A1 is used to regulate the input power of femtosecond pulses. Reflected by M2, pump beams are transmitted into a 2 cm-long glass cuvette (width~2 cm) containing carbon disulfide (CS₂). CS₂ is chosen as a nonlinear material because of its strong Kerr nonlinearity with long relaxation time (~2 ps), allowing the generation of a long-time plasma channel induced by femtosecond pulses in CS₂. In order to ensure the femtosecond beam and continuous beam propagate collinearly through CS₂, the beam splitter BS1 is used to make them spatially overlapped. BS1 is a dichroic mirror coated to have high reflectivity at 632 nm and high transmission at 800 nm wavelength range. After passing through CS₂, we use BS2 to separate the pump beam and probe beam. BS2 is also a dichroic mirror (high reflectivity~800 nm, high transmission~632 nm). The continuous beam is separated from femtosecond beams by BS2, and then only the continuous beam passes into a high-resolution charge-coupled device (CCD) camera (Coherent Laser Cam-HR Beamview, 1280 pixels $\times$ 1024 pixels). The spatial resolution of CCD camera is 6.7 μm. As a result, the spatial intensity evolution of the probe beam can be obtained in real-time by CDD. The pump beam is directed into a beam dump reflected by BS2. The adjustable attenuator, A2, is customized to protect the CCD camera from damage caused by the high-powered laser beam.

Fig. 4 Experimental setup. Laser 1, femtosecond laser; Laser 2, He-Ne laser; M1 and M2, silver-coated plane mirrors; A1 and A2, attenuators; BS1 and BS2, beam splitter; BD, beam dump.

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As femtosecond pulses propagate in CS₂, plasma channels will be generated when the power of femtosecond pulses (P_fs) is above the ionization threshold. Two mechanisms, multiphoton ionization and avalanche ionization (cascade or impact ionization) are responsible for laser-induced plasma. For femtosecond pulses, laser-induced plasma is caused primarily by multiphoton ionization. The threshold value of laser-induced break down caused by multiphoton ionization can be expressed by $I_{m} = C {[ρ_{0} D {(0.1 τ_{p})}^{- 1}]}^{\frac{1}{Κ}}$ , where C and D depend on the optical frequency squared $(ω^{2})$ , $Κ$ depends on the optical frequency $(ω)$ , $ρ_{0}$ is the minimum initial electron density, and $τ_{p}$ is pulse duration [29]. When the probe beam passes through the plasma channel, to simplify the analysis, the electron motion and collision are neglected. It finds that the probe beam can keep its initial spectral shape almost invariant. In this experiment, the length, width and lifetime of the plasma channel generated by femtosecond pulses are about 5 mm, 0.5 mm and 400 μs, respectively. The plasma channel will persist during the experimental session under a large repetition rate of femtosecond pulse sequences. The interval between two femtosecond pulses is 1 ms when repetition rate is set to 1 kHz. This is one spatial modulation periodicity for the probe beam. When the first femtosecond pulse comes, the spatial modulation on the probe beam begins. Within the 400 μs, the spatial modulation decreases as time goes on, this is because the electron density of the plasma channel decreases gradually with the increasing of time. Because the lifetime of the plasma channel is 400 us, there is no spatial modulation on the probe beam between 400 μs and 1 ms. The spatial modulation appears again when the second femtosecond pulse comes. So the periodicity of spatial modulation is related to the repetition rate of femtosecond pulses.

Figure 5 shows the spatial intensity of the probe beam after propagating in 2 cm CS₂ with different powers of femtosecond pulses. As is shown in Fig. 5, the probe beam is modulated into a beam with a circular dark spot in the center region when P_fs is 14 mW. In the following, we will explain this phenomenon. The electron density and refractive index distribution in the plasma channel generated by ionization is close to Gaussian because of a Gaussian intensity profile of the femtosecond beam. Similar to the beam passing through a graded-index lens, it will be deflected when it propagates in the plasma, and then a circular dark spot formed in the center of the beam. With the increase of P_fs (14 mW to 19 mW), the intensity of the probe beam in the central zone always decreases and the dark spot size increases. In other words, the degree of modulation enhanced gradually as P_fs increases. If the power is increased continuously, it is expected that the intensity in the center zone reduce to zero and the probe beam is modulated into a ring-shaped beam. So, we can easily adjust the modulation on the probe beam by changing P_fs.

Fig. 5 Spatial intensity distribution of probe beams at P_fs of (a) 14 mW, (b) 16 mW and (c) 19mW, respectively. (d) The corresponding cross line (y = 0) of probe beam when P_fs is tuned.

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Figure 6 shows the intensity evolution of the probe beam for different P_fs in the experiment and for different electron densities in theory. The parameters in theory and in experiment are the same as parameters considered in Fig. 1 and Fig. 5, respectively. The theoretical analyses are highly agreement with the experimental results, which illustrates the electron density profile of plasma generated by the femtosecond laser in CS₂ is Gaussian and the electron density is related to P_fs. The electron density distribution of the plasma can be deduced from the spatial intensity distribution of the probe beam. Similar to the common method for investigating temporally and spatially the plasma excitation dynamics [30, 31], the pump-probe method can potentially be used to infer the on-axis plasma density shape. For He-Ne lasers used in the experiment, critical plasma density is $n_{c} = 2.8 \times 10^{21} {cm}^{- 3}$ . From Fig. 6, it is easy to see that the electron density is $4 \times 10^{19} {cm}^{- 3}$ when P_fs = 14 mW. The electron density in the plasma increased from $4 \times 10^{19} {cm}^{- 3}$ to $9.3 \times 10^{19} {cm}^{- 3}$ as P_fs increases (14 mW to 19 mW).

Fig. 6 Spatial intensity distribution of probe beam for different electron densities $n_{c} = 70 n_{0}$ (black curve), $n_{c} = 50 n_{0}$ (red curve), $n_{c} = 30 n_{0}$ (blue curve) in theory, and at P_fs of 14 mW (black circles), 16 mW (red circles), 19 mW (blue circles) in the experiment.

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The femtosecond beam has a Gaussian intensity distribution, leading to that the laser intensity profile in the plasma is close to Gaussian [32]. In the plasma channel, the atomic degree of ionization is proportional to beam’s intensity, resulting in a Gaussian distribution of the electron density in the plasma. So, the electron density profile of the plasma induced by the femtosecond laser can be given by $n_{e (f s)} = n_{0 (f s)} \exp (- r^{2} / w_{fs}^{2})$ , where $w_{fs}$ is the width of the plasma generated by femtosecond pulse filamentation in CS₂, and $n_{0 (f s)}$ is the axial electron density of the plasma, which is relative to P_fs. So the electron density of the plasma can be changed by tuning P_fs in the experiment. The increment of P_fs results in the increment of the electron density and the increment of refractive index gradient, the defocusing of the plasma center and the focusing of the plasma periphery become more evident. Hence, a more prominent modulation on the probe beam is formed.

What happens if the pump beam and the probe beam are not collinear? The probe beam is also modulated by the plasma channel if the beams or not collinear. A probe laser is set to pass transverse through the plasma induced by femtosecond pulses. The probe beam is modulated into a beam whose spatial intensity distribution is shown in Fig. 7(a). Moving the translation mirror to change the relative position between probe beam and the plasma channel, two spatial intensity maps of probe beams are recorded and shown in Figs. 7(b) and 7(c). Namely, different spatial modulations on the probe beam are formed. The intensity of the pump beam is higher than the threshold of plasma generation when the distance L is small, so we can see from Fig. 7(a) that the interval of two parts of the probe beam is large. L is defined as the displacement of the probe beam. It represents the location of the generation of the plasma channel in the glass cuvette when L = 0. The intensity of the pump beam decreases with the increase of propagation distance, leading to that the interval of two parts of the probe beam decreases with the decrease of electron density of the plasma channel [Figs. 7(b) and 7(c)]. As L is increased continuously, the plasma disappears and the probe beam restores its original spatial intensity distribution [L = Ln]. It indirectly proves that the existence of the plasma channel induced by femtosecond pulses, and its length is Ln.

Fig. 7 Spatial intensity distribution of different modulated probe beams, inset maps of (d)-(f) are the intensity profile of the pump beam.

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As the pump beam’s spatial distribution is adjusted, profiles of electron density and refractive index of the plasma are also changed. Leading to that the deflection direction of the probe beam and the area in the plasma channel where the beam can pass through are changed at the same time, so we can control spatial modulations on the probe beam. In the experiment, we only regulate the pump beam’s spatial distribution before it is directed into CS₂. Generally, self-focusing occurs if the power exceeds a critical power $P_{c} (G W) = 17.4 {(ω_{0} / ω_{p})}^{2}$ . Under a strong self-focusing, femtosecond beam’s spatial profile is changed, leading to that the electron density of the plasma channel is changed. Consequently, the spatial modulation on the probe beam is modified. To avoid a strong self-focusing in the experiment, P_fs is set to below P_c as far as possible. So, assuming that shapes of the pump beam and plasma channel over the entire propagation distance are the same. The diffraction effect on the pump beam leads to a decrease of the pump beam’s intensity. As a result, the modulation efficiency decreases. To simplify the analysis, a weak diffraction on the pump beam and probe beam is neglected.

When pump beam’s profile is adjusted as shown in the inset map of Fig. 7(d), it is easy to see that the probe beam is modulated into a beam whose intensity profile is divided into three parts in shape. If filaments are used to change the pump beam’s profile, probe beams are transformed into ring-shaped beams with two-channel or four-channel [Figs. 7(e) and 7(f)]. Some interference fringes appear in the ring-shaped beam with four-channel, it is caused by the interference of two probe beams in BS1. If a more perfect beam splitter is used in the experiment, these interference fringes are eliminated. So, the spatial modulation on the probe beam can be easily controlled by adjusting the pump beam’s profile.

4. Conclusions

In this work, we experimentally and theoretically demonstrate the plasma optical modulation for lasers with plasmas induced by femtosecond pulses in carbon disulfide. Our experimental observations are in good agreement with theoretical results. We can easily control the modulation on the beam by adjusting the plasma electron density, plasma width, P_fs, or the intensity profile of the pump beam. In addition, this pump-probe method can potentially be used to infer the on-axis plasma density shape. The plasma optical modulation method presents a potential application for spatial light modulation for laser beams. Further investigation on improving the spatial modulation accuracy will be carried out.

Funding

National Natural Science Foundation of China (Grant Nos. 11647134, 61571183, U1501253, 61605045); the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 17C0624); and the Scientific Research Startup Foundation for Doctors of Hunan University of Science and Technology (Grant No. E51662).

References and links

1. M. Kowalski and M. Życzkowski, “Data encryption of optical fibre communication using pseudo-random spatial light modulation,” Opto-Electron. Rev. 24(2), 75–81 (2016). [CrossRef]

2. K. Liu, C. R. Ye, S. Khan, and V. J. Sorge, “Review and perspective on ultrafast wavelength-size electro-optic modulators,” Laser Photonics Rev. 9(2), 172–194 (2015). [CrossRef]

3. R. Bruck, K. Vynck, P. Lalanne, B. Mills, D. J. Thomson, G. Z. Mashanovich, G. T. Reed, and O. L. Muskens, “All-optical spatial light modulator for reconfigurable silicon photonic circuits,” Optica 3(4), 396–402 (2016). [CrossRef]

4. J. Lauria, R. Albright, O. Vladimirsky, M. Hoeksb, R. Vanneerb, B. Drieenhuizenb, L. Chenc, L. Haspeslaghd, and A. Witvrouwd, “SLM device for 193nm lithographic applications,” Microelectron. Eng. 86(4–6), 569–572 (2009). [CrossRef]

5. P. Pozzi, D. Gandolfi, M. Tognolina, G. Chirico, J. Mapelli, and E. D’Angelo, “High-throughput spatial light modulation two-photon microscopy for fast functional imaging,” Neurophotonics 2(1), 015005 (2015). [CrossRef] [PubMed]

6. K. Shcherbin, I. Gvozdovskyy, and D. R. Evans, “Infrared sensitive liquid crystal light valve with semiconductor substrate,” Appl. Opt. 55(5), 1076–1081 (2016). [CrossRef] [PubMed]

7. P. Kula, N. Bennis, P. Marć, P. Harmata, K. Gacioch, P. Morawiak, and L. R. Jaroszewicz, “Perdeuterated liquid crystals for near infrared applications,” Opt. Mater. 60, 209–213 (2016). [CrossRef]

8. J. M. Wang, X. X. Chen, Z. S. Xu, W. J. Yang, and X. D. Jiang, “Design and fabrication of BSO liquid crystal light valve,” Exp. Sci. Technol. 6, 007 (2011).

9. V. Marinova, S. H. Lin, and K. Y. Hsu, “Electro-optically and all-optically addressed spatial light modulator devices based on organic-inorganic hybrid structures,” Proc. SPIE 100220, 1–6 (2016).

10. P. K. Shrestha, Y. T. Chun, and D. Chu, “A high-resolution optically addressed spatial light modulator based on ZnO nanoparticles,” Light Sci. Appl. 4(3), e259 (2015). [CrossRef]

11. N. Collings, T. D. Wilkinson, A. Jeziorska, A. B. Davey, B. Movaghar, and W. A. Crossland, “Charge-injecting layers for liquid crystal light valves,” Proc. SPIE 5464, 421–427 (2004). [CrossRef]

12. M. G. Kirzhner, M. Klebanov, V. Lyubin, N. Collings, and I. Abdulhalim, “Liquid crystal high-resolution optically addressed spatial light modulator using a nanodimensional chalcogenide photosensor,” Opt. Lett. 39(7), 2048–2051 (2014). [CrossRef] [PubMed]

13. M. Watanabe, “Quality recovery method of interference patterns generated from faulty MEMS spatial light modulators,” J. Lightwave Technol. 34(3), 910–917 (2016). [CrossRef]

14. I. W. Jung, Y. A. Peter, E. Carr, J. S. Wang, and O. Solgaard, “Single-crystal-silicon continuous membrane deformable mirror array for adaptive optics in space-based telescopes,” IEEE J. S. Top. Quant. 13(2), 162–167 (2007). [CrossRef]

15. L. Z. Schatzberg, T. Bifano, S. Cornelissen, J. Stewart, and Z. Bleier, “Secure optical communication system utilizing deformable MEMS mirrors,” Proc. SPIE 72090C, 1–15 (2009).

16. I. Kanno, T. Kunisawa, T. Suzuki, and H. Kotera, “Development of deformable mirror composed of piezoelectric thin films for adaptive optics,” IEEE J. S. Top. Quant. 13(2), 155–161 (2007). [CrossRef]

17. K. Khalil, Y. M. Sabry, K. Hassan, A. Shebl, M. Soliman, Y. M. Eltagoury, and D. Khalil, “In-line optical MEMS phase modulator and application in ring laser frequency modulation,” IEEE J. S. Top. Quant. 52(8), 1–8 (2016). [CrossRef]

18. A. V. Krasavin and N. I. Zheludev, “Active plasmonics: controlling signals in Au/Ga waveguide using nanoscale structural transformations,” Appl. Phys. Lett. 84(8), 1416–1418 (2004). [CrossRef]

19. G. H. Yuan, X. C. Yuan, D. G. Zhang, P. Wang, H. Ming, and T. Mei, “Numerical demonstration of all-optical switching in dielectric-loaded surface plasmon polaritonic crystals with a defect mode,” J. Opt. 11(8), 085005 (2009).

20. L. Ni, C. Shen, H. Li, K. F. Liu, and S. Wei, “Discussion on feasibility of inserting the GSP into LCOS,” Infrared Las. Eng. 44(6), 1773–1778 (2015).

21. L. A. Shiramin and V. D. Thourhout, “Graphene modulators and switches integrated on silicon and silicon nitride waveguide,” IEEE J. S. Top. Quant. 23(1), 1–7 (2017).

22. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011). [CrossRef] [PubMed]

23. K. Kim, J. Y. Choi, T. Kim, S. H. Cho, and H. J. Chung, “A role for graphene in silicon-based semiconductor devices,” Nature 479(7373), 338–344 (2011). [CrossRef] [PubMed]

24. J. Gosciniak and D. T. H. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013). [CrossRef] [PubMed]

25. R. Hao, W. Du, E. P. Li, and H. S. Chen, “Graphene assisted TE/TM-independent polarizer based on Mach–Zehnder interferometer,” IEEE Photonics Technol. Lett. 27(10), 1112–1115 (2015). [CrossRef]

26. Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene–silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015). [CrossRef] [PubMed]

27. H. Dalir, Y. Xia, Y. Wang, and X. Zhang, “Athermal broadband graphene optical modulator with 35 GHz speed,” ACS Photonics 3(9), 1564–1568 (2016). [CrossRef]

28. L. L. Yu, Y. Zhao, L. J. Qian, M. Chen, S. M. Weng, Z. M. Sheng, D. A. Jaroszynski, W. B. Mori, and J. Zhang, “Plasma optical modulators for intense lasers,” Nat. Commun. 7, 11893 (2016). [CrossRef] [PubMed]

29. D. X. Hammer, R. J. Thomas, G. D. Noojin, B. A. Rockwell, P. K. Kennedy, and W. P. Roach, “Experimental investigation of ultrashort pulse laser-induced breakdown thresholds in aqueous media,” IEEE J. Quantum Electron. 32(4), 670–678 (1996). [CrossRef]

30. F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036406 (2006). [CrossRef] [PubMed]

31. M. Sakakura and M. Terazima, “Initial temporal and spatial changes of the refractive index induced by focused femtosecond pulsed laser irradiation inside a glass,” Phys. Rev. B 71(2), 024113 (2005). [CrossRef]

32. H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Wei, and Z. Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(1 Pt 2), 016406 (2002). [CrossRef] [PubMed]

Plasma optical modulation for lasers based on the plasma induced by femtosecond pulses

Abstract

1. Introduction

2. Theoretical analysis

3. Experimental analysis

4. Conclusions

Funding

References and links

Cited By

Figures (7)

Equations (13)

Optics Express