Perspective Chapter: Effect of Laser Key Parameters on the Ignition of Boron Potassium Nitrate with a Changing Working Distance

Abstract

The need to realize more effective ignition systems and exploit their full potential in aerospace propulsion applications has led to significant developments in laser and power systems. This work aims to investigate experimentally and describe mathematically the effectiveness of laser systems based on varying key parameters and their related effects on the sensitivity, ignition threshold, and combustion performance of boron potassium nitrate, then to define the key variables with the most significant influence on the overall system. Understanding the physics and chemistry behind the combined system of laser power source and optics system, and the considered medium as well as the interaction in between, led to a better apprehension of how an optimal and viable solution can be achieved in terms of ignition delays, burning times, and combustion temperatures, considering laser wavelength, power and energy densities, and the focal length displacement over a changing working distance. This is of paramount importance when operating amid difficult conditions in aerospace propulsion applications or during outer space missions, particularly those involving manned missions, not only in terms of performance and efficiency but also safety, engineering, and economic feasibility.

1. Introduction

In contrary to electricity, the only form of energy that is not mass bound is electromagnetic energy; and light being highly focusable in space and time, is part of the spectrum of this electromagnetic form of energy. Laser initiation offers several advantages over bridge wire initiation [1], such as low initiation energy quantities requirements, multipoint initiation, and multi-times reuse, are easily achieved; it can also be made fully electronic, with lower cost, size, and weight compared to bridge wire. Ease of manufacturing, simpler safety, and arming systems, whilst common failure mechanisms are minimized or removed. It can prevent the occurrence of accidental firings, caused by electromagnetic fields, electrostatic discharge, or stray electrical energy.

The most relevant areas related to laser initiation of pyrotechnics and worth being investigated are sensitivity of pyrotechnics and practical designs for laser systems. Laser initiation aims at safely delivering stimuli for the generation of heat and thus ignition. These are also characterized by different parameters that can be varied or controlled depending upon the type of the targeted energetic material and ignition conditions. For this purpose, lasers must be compact and cost-effective, with the ability to meet the ignition energy requirements, while minimizing the need for chemical modification of the energetic material.

This work aims to mathematically describe and experimentally investigate the effectiveness of a laser system based on varying the laser key parameters, as well as their related effects on the sensitivity, ignition threshold, and combustion performance of boron potassium nitrate (BPN). The condition of ignition for a proportionally increasing focal length with the working distance was quantified by the following measuring techniques: the minimum output power required so that ignition can occur; and the minimum pulse duration necessary for the pyrotechnic material to absorb the required critical energy so that ignition can occur.

According to MilStd1901, a specific mixture of BPN is one of the pyrotechnic materials that can be used without interruption of the pyrotechnic chain [2].

Thanks to its high heat of reaction, boron is often used as a reducer of energetic materials and in the composition of propellants. Its high enthalpy, high temperature of combustion, and low molar mass make it a choice candidate for applications such as pyrotechnics and propellants of rocket motors [3].

The sensitivity of pyrotechnic compositions and the critical laser energy density required to initiate them were investigated by [4, 5, 6]. It was concluded that laser initiation is a merely thermal process, instead of photochemical, electrical, or light impact mechanisms.

The physical factors affecting the sensitivity of Mg-based pyrotechnic compositions were studied by [7, 8, 9]. It was concluded that at short pulse durations, the sensitivity was characterized by a threshold ignition energy density (i.e. internal properties of the material, such as heat capacity and thermal conductivity); whilst at long pulse durations, the ignition was characterized by a threshold ignition power (i.e. sample area and internal and external parameters of the sample).

The relationship between laser initiation and pulse duration for Ti/KClO₄ was also studied by [10]. The results showed that at short pulse durations, ignition occurred as long as there was a minimum level of energy delivery rates (delivered power); whilst at long pulse durations, ignition was governed by heat loss rates from a critical volume in the composition.

The ignition of Ti/KClO₄ and Zr/KClO₄ was investigated by [11, 12], respectively. Their studies outlined the existence of the ignition energy/power map. Laser spot size was critical in determining the threshold energy and power levels [11].

It has been demonstrated that for TiHx/KClO₄ compositions in unsealed holders, the ignition power decreased with increasing laser pulse duration or increasing laser spot size [13].

Laser initiation is a thermal mechanism, implying that energy is absorbed in the material, and thus the absorption occurs at defects, such as cracks, clusters, or dislocations within the lattice [14]. These inhomogeneities could also lead to a laser beam focusing with high energy densities at particular local sites, which may lead to a number of initiation mechanisms.

Due to their high specific surface area to volume ratio, nanometer-sized boron particles produce more heat release than micrometer-sized particles. When it comes to handling and processing, nano-sized boron particles-based BPN is as safe as the micro-sized one. However, although nano-sized boron particles enhanced calorific value and pressurization rate, they did not contribute to the maximum pressure level [15].

Most studies were conducted in an open-air environment. In practical applications such as rocket motors, ignition takes place under confinement, accompanied by a rise in pressure, which regulates heat transfer and laser beam transmission. Under confinement, laser initiation is more efficient [16].

In addition to the originality of our work, by providing more flexibility in terms of distance covered, by allowing fine spot sizes with high power densities and longer focal lengths, our findings were in compliance with previous studies. In the next section, the laser key parameters on which laser system designs can be built for an effective laser initiation are presented and mathematically described. In Section 3, the experimental setup design used in this work to conduct the current investigation on laser initiation is described, and details on BPN features and composition as well as set up production cost and time are also provided. In Section 4, the obtained results are further discussed, such as varying key parameters and their related effects on sensitivity, ignition threshold, and combustion performance of BPN, and key variables with the most significant influence on the overall system are defined. Last but not least, in Section 5, outcomes are summarized, and conclusions are presented, a better apprehension of how an optimal and viable solution in terms of ignition delays, burning times, and combustion performance, considering laser wavelength, power, and energy densities, and the focal length displacement over a changing working distance is achieved.

2. Key parameters of laser systems

Laser systems can be defined by the key parameters shown in Table 1.

Fundamental parameters	Beam parameters	Final system parameters
Power and Energy	Power or Energy Density	Spot Size
Pulse Duration	Beam diameter	Working Distance
Repetition Rate	Beam Profile
Coherence Length	Divergence
Wavelength

Table 1.

Key parameters of laser systems.

These laser key parameters are mathematically described. In our application, the laser beam is assumed to be Gaussian, and irradiance profiles are assumed to follow an ideal Gaussian distribution, being symmetric around the center of the beam and decrease as the radius of the laser beam increases. The ideal Gaussian distribution is expressed by Eq. (1):

$$I\left(r\right)=I_0\mathit{exp}\left(\frac{-2r^2}{\omega {\left(z\right)}^2}\right)=\frac{2P}{\mathit{\pi \omega }{\left(z\right)}^2}\mathit{exp}\left(\frac{-2r^2}{\omega {\left(z\right)}^2}\right)$$E1

Where I₀ is the peak irradiance at the center of the beam, r is the radial distance away from the axis, ω(z) is the radius of the laser beam where the irradiance is 1/e² of I₀, z is the distance propagated from the plane where the wavefront is flat, and P is the total power of the beam.

The irradiance profile varies as the beam propagates through space, hence the dependence of ω(z) on z. The beam waist is the location along the propagation direction of the laser beam where the beam radius is at its minimum. Due to diffraction, a Gaussian beam converges and diverges, by the divergence angle θ, equally on both sides of the beam waist (ω₀). This is where the beam diameter reaches its minimum value. The beam waist and divergence angle are expressed as follows:

$${\omega }_0=\frac{\lambda }{\mathit{\pi \theta }}$$E2

$$\theta =\frac{\lambda }{{\mathit{\pi \omega }}_0}$$E3

Where λ is the wavelength of the laser and θ is a far field approximation. From Eq. (3), it is noticeable that the smaller the beam waist, the larger the divergence angle, and vice-versa. Therefore, laser beam expanders can be applied to reduce beam divergence by increasing beam diameter. Variation of the beam diameter in the beam waist region is expressed by Eq. (4):

$$\omega \left(z\right)={\omega }_0\sqrt{1+{\left(\frac{\mathit{\lambda z}}{{\mathit{\pi \omega }}_0^2}\right)}^2}$$E4

For a circular laser beam, the Rayleigh length is the distance from the beam waist to the point where the mode area is doubled, and the radius of the beam is increased by a factor of the square root of 2. The Rayleigh range of a Gaussian beam is defined as the value of z where the cross-sectional area of the beam is doubled. For focused laser beams, the effective Rayleigh length is an essential quantity in determining the depth of focus. The Rayleigh range (z_R) is expressed by Eq. (5):

$$z_R=\frac{{\mathit{\pi \omega }}_0^2}{\lambda }$$E5

Thus, ω(z) can also be related to z_R, as shown by Eq. (6):

$$\omega \left(z\right)={\omega }_0\sqrt{1+{\left(\frac{\mathit{\lambda z}}{{\mathit{\pi \omega }}_0^2}\right)}^2}={\omega }_0\sqrt{1+{\left(\frac{z}{z_R}\right)}^2}$$E6

Considering the quantitative deviation of the beam parameter product and from the characteristics of the Gaussian beam, the far field divergence is the ratio of the beam waist and the Rayleigh length. On the other hand, the Rayleigh length expressed by Eq. (5) is combined with the far field divergence expressed by Eq. (3), and a simpler expression can be obtained, which shows that the beam waist times the far field divergence is equal to a constant. The product of the far field divergence angle and the beam radius is minimum for a Gaussian beam and depends only on the wavelength of that corresponding laser. For a single laser, this beam parameter product is constant throughout all locations of the propagation of a laser beam in whatever optical system it is put into. The consequence is that this product is invariant under propagation and focusing.

$$\mathit{BPP}={\omega }_0\theta =\frac{\lambda }{\pi }=\mathit{\text{const}}.$$E7

When comparing real beams to Gaussian beams with respect to the propagation, some changes need to be introduced, because in the real case there is a less good beam quality and a less good focusability or a higher divergence at these lower-quality laser beams. The real laser beam is in relation to a theoretical best case, that is, the number M² called beam quality/propagation factor, and which is always larger than 1. According to ISO Standard 11146, M² is defined as the beam parameter product (BPP) divided by the ratio λ/π (Table 2).

Gaussian beams	Real laser beams
${\omega }_{\mathit{\text{Gauss}}}={\omega }_{0,\mathit{\text{Gauss}}}\sqrt{1+{\left(\frac{z}{z_{R,\mathit{\text{Gauss}}}}\right)}^2}$	${\omega }_{\mathit{\text{Real}}}={\omega }_{0,\mathit{\text{Real}}}\sqrt{1+{\left(\frac{z}{z_{R,\mathit{\text{Real}}}}\right)}^2}$
$z_{R,\mathit{\text{Gauss}}}=\frac{{\mathit{\pi \omega }}_{0,\mathit{\text{Gauss}}}^2}{\lambda }$	$z_{R,\mathit{\text{Gauss}}}=\frac{{\mathit{\pi \omega }}_{0,\mathit{\text{real}}}^2}{\lambda M^2}=\frac{{\mathit{\pi \omega }}_{0,\mathit{\text{real}}}^{2}K}{\lambda }$
${\mathit{BPP}}_{\mathit{\text{Gauss}}}={\omega }_{0,\mathit{\text{Gauss}}}{\theta }_{\mathit{\text{Gauss}}}=\frac{\lambda }{\pi }$	${\mathit{BPP}}_{\mathit{\text{Real}}}={\omega }_{0,\mathit{\text{Real}}}{\theta }_{\mathit{\text{Real}}}=\frac{\lambda }{\pi }{M}^2=\frac{\lambda }{\mathit{\pi K}}$

Table 2.

Real beam and Gaussian beam with respect to the propagation.

The beam quality factor (M², or K) can be expressed as follows:

$$M^2=\frac{1}{K}=\frac{{\mathit{BPP}}_{\mathit{\text{Real}}}}{{\mathit{BPP}}_{\mathit{\text{Gauss}}}}=\frac{{\omega }_{0,\mathit{\text{Real}}}{\theta }_{\mathit{\text{Real}}}}{{\omega }_{0,\mathit{\text{Gauss}}}{\theta }_{\mathit{\text{Gauss}}}}>1$$E8

Laser beam parameters, namely, solid angle of divergence, wavelength, beam parameter product, beam quality factor, spot size, and laser power are major contributors to the laser beam brightness and are used to measure the brightness [17] and associated laser beam parameters [18, 19]. The brightness of a light source is defined as the power emitted per unit surface area per unit solid angle. The maximum brightness is achieved for a perfectly spatially coherent laser beam. The brightness can be expressed by:

$$\mathit{Br}=\frac{P_{\mathit{\text{out}}}}{\mathit{A\Omega }}$$E9

Where P_out is the laser power over the surface area A and Ω is the solid angle of divergence. The solid angle is proportional to the square of the divergence angle θ, that is, the smaller is the divergence the higher is the brightness. High brightness is usually characterized by a high-quality factor. The solid angle of divergence of a Gaussian beam is as follows:

$$\Omega =\pi {\theta }^2=\frac{{\lambda }^2}{{\omega }_0^2}$$E10

Where λ is the wavelength and ω₀ is the beam radius at the beam waist. For a perfect Gaussian single mode TEM₀₀ beam condition, M² equals 1. This also shows how small a beam waist can be focused. The propagation ratio for circular Gaussian laser beams is shown in Eq. (11):

$$M^4=M_y^2{M}_x^2$$E11

Where M_y² and M_x² are the parameters of the beam profile. Finally, the brightness of the laser beam is once more expressed as follows:

$$\mathit{Br}=\frac{P_{\mathit{\text{out}}}}{M^4{\lambda }^2}$$E12

The spot diameter is incorporated by including power density, which is a combination of power and the spot size for a particular Gaussian or non-Gaussian beam, as brightness is a function of output power, wavelength, M², the beam divergence and the spot diameter [20]. Thus, power density is expressed as:

$$\mathit{\text{Power density}}=\frac{252}{d^2}\mathit{\text{Output power}}$$E13

Where d is the laser beam diameter and 252 is for the Gaussian beam profile. Upon inclusion of the laser power density for determining radiance gives rise to Eq. (14) that takes into consideration the full laser beam parameters, that is, the radiance density (RD), which makes it suitable and accurate:

$$\mathit{RD}=\frac{\mathit{PD}}{M^4{\lambda }^2}$$E14

Where radiance (R) replaces brightness (Br); whilst the radiance density (RD) takes into consideration the beam diameter as well as the power density (PD).

For the incident laser beam, laser energy absorption and diffusion are subject to the following process: absorption by free electrons, propagation through the electron subsystem, then transfer to the lattice. Energy absorption and diffusion is also influenced by the microstructure and electromagnetic properties of the pyrotechnic material; whilst heat conduction is influenced by thermal conductivity, density, heat capacity, and thermal diffusivity. At first, after turning the laser signal on, the temperature increases, the heat at the surface increasingly diffuses into the depth of the pyrotechnic material, that is, absorption at the surface followed by diffusion; therefore, convection simply means moving matter particles into the volume carrying heat and energy; and thus, contributing to the inner energy density of that volume. The diffusion accounts for the heat, which is deposited in the surface and then diffuses into that volume, whilst the thermal penetration depth is defined as the distance that the heat diffuses through. On the other hand, there is diffusion out of the considered volume, that is, at the boundaries, there is diffusion to the environment and loss of energy due to convection carrying energy out of that volume. There is also the change of temperature and its dependance on time, thus the energy changes in this volume are associated with the temperature. Finally, the change of temperature in time is a sum of all these inputs and losses in the corresponding volume. Next, the absorbed intensity can be put into the boundary condition, at the point z = 0 at the surface of the absorbing material, the absorbed intensity can be considered as a source of energy flux.

Boundary conditions.

$$T\left(z,t<0\right)=T_{0.}$$

$$T\left(z\to \infty ,t\right)=T_0$$

$$Q=0$$

$${\left.-{\lambda }_T{\partial }_{z}T\left(t\right)\right|}_{z=0}=\mathit{AI}$$

where AI is the absorbed laser intensity, and λ_T is the thermal conductivity.

Heat equation

$${\partial }_{t}T\left(z,t\right)=\kappa {\partial }_z^{2}T\left(z,t\right)$$E15

Where κ is the temperature conductivity. The solution of the heat conduction equation is not trivial, it implies an integrated error function (ierfc), which is basically the integral of an exponential function where the variable is part of the integral limits. But the most important here is the definition of the thermal penetration depth. As it can be seen, the argument of the integrated error function scales with z, which is the distance from the surface and the thermal penetration depth.

$$T\left(z,t\right)=T_0+\frac{\mathit{AI}}{{\lambda }_T}{\delta }_{\mathit{th}}\left(t\right)\mathit{\text{ierfc}}\left(\frac{z}{{\delta }_{\mathit{th}}\left(t\right)}\right)$$E16

The thermal penetration depth can be expressed as follows:

$${\delta }_{\mathit{th}}\left(t\right)=\sqrt{4\mathit{\kappa t}}$$E17

and the integral of complementary error function can be expressed as follows:

$$\mathit{\text{ierfc}}\left(x\right)={\int }_x^{\infty }\mathit{erfc}\left(z\right)\mathit{dz}$$E18

$$\mathit{erfc}\left(x\right)=\frac{2}{\sqrt{\pi }}{\int }_x^{\infty }\mathit{exp}\left(-t^2\right)\mathit{dt}$$E19

The maximum temperature can be described by Eq. (20):

$$∆T_{\mathit{max}}=T\left(0,\tau \right)-T_0=\frac{\mathit{AI}}{{\lambda }_T\sqrt{\pi }}\sqrt{4\mathit{\kappa \tau }}$$E20

Where τ is the pulse duration of the laser pulse. Eq. (21) and Eq. (22) describe the threshold ignition energy density and the threshold ignition power [21, 22, 23]:

$$E_{\mathit{ign}}=\frac{\rho C_P}{\alpha }\left(T_{\mathit{ign}}-T_0\right)$$E21

$$P_{\mathit{ign}}=2{\lambda }_T{\omega }_0\sqrt{\pi }\left(T_{\mathit{ign}}-T_0\right)$$E22

Where ρ is the density, C_P is the specific heat capacity, and α is the thermal diffusivity.

3. Experimental setup

A fiber coupled laser diode was used to generate the laser signal, with a divergence angle of 12.6 for the laser beam exiting FC/PC fiber. This laser beam was then collimated using a collimating lens. Next, the collimated beam was transmitted to the beam expander used in reverse mode to decrease its diameter by different inverted magnifying power values. After that, the laser beam exiting the beam expander was focused using an achromatic doublet, targeting the BPN for initiation. Finally, by controlling the magnifying power of the beam expander, the focal length was gradually changed over a specific working distance separating the achromatic doublet and the BPN (i.e., BPN positions were readjusted each time the magnifying power was modified so that the focal point would fall on the surface of the BPN). These experiments were conducted in an open-air environment.

A photodiode was used to measure the light emitted by the laser signal and the ignited BPN, then related to a benchtop oscilloscope to display and record the measured values. A power and energy laser measurement sensor and meter were used to measure and display the data, respectively.

3.1 Laser diode, fiber-coupled model

The laser diode used in this experiment to produce the laser beam in order to target and initiate the BPN is a DS3–21312-203 diode laser system fiber-coupled model manufactured by BWT Beijing LTD, with a maximum input power of 2 W and a wavelength of 808 nm.

The experiment was conducted using different values of input power and pulse durations, with a changing focal length and working distance between the beam expander output and the BPN.

3.2 Collimating lens

A C240 TMD-B molded glass mounted aspheric lens from Thorlabs was used to collimate the beam exiting the fiber without introducing spherical aberration into the transmitted wavefront, with broadband AR coating for 600–1050 nm, f = 8.00 mm, and NA = 0.5. The diffraction-limited spot size is given by Eq. (23):

$${\Phi }_{\mathit{\text{spot}}}=\frac{4\mathit{\lambda f}}{\mathit{\pi D}}$$E23

Where f is the focal length of the lens, λ is the wavelength of the input light, and D is the diameter of the collimated beam incident on the lens. Solving the equation for a desired focal length of the collimating lens yields to Eq. (24), with MFD being the mode field diameter:

$$f=\frac{\mathit{\pi D}\left(\mathit{MFD}\right)}{4\lambda }$$E24

3.3 Beam expander in reverse mode

The beam expander BE-02-05-B from Thorlabs was used in reverse mode to decrease the diameter of the collimated beam by the lens C240 TMD-B (Table 3).

Expansion	Input aperture	Max input beam diameter (1/e^2)	AR coating range
2X−5X	Ø8.0 mm	Ø4.0 mm	650−1050 nm

Table 3.

Beam expander specifications.

Beam expanders in reverse mode decrease the beam area quadratically by inverting the magnifying power (iMP) without significantly affecting the total energy contained within the beam, but divergence will somehow be increased. This results in an increase of the beam’s power density and irradiance, which may also decrease the lifetime of laser components, by increasing the chances of laser induced damage.

3.4 Focusing lens

The laser beam exiting the beam expander was then focused using one or other of the two focusing lenses, AC254–60-B-ML and AC254–125-B-ML achromatic doublets from Thorlabs, with focal lengths of 60 mm−and 125 mm, respectively. Both lenses are AR coated for the 650−1050 nm range. The tighter the beam was focused, the higher was the power density.

Achromatic doublets are useful for controlling chromatic aberration and are frequently used to achieve a diffraction-limited spot when using a monochromatic source. Achromatic doublets are optimized to provide a nearly constant focal length across a broad bandwidth. Dispersion in the first (positive) element of the doublet is corrected by the second (negative) element, resulting in better broadband performance than spherical singlets or aspheric lenses.

3.5 Pyrotechnic material

The pyrotechnic material used in our experiments for laser initiation is boron potassium nitrate, as shown in Table 4. Its military specification is as follows: MIL-P-46994B(AR). Aerospace missions require that pyrotechnic compositions are able to withstand 180°C [24]. Boron is often used as a reducer of energetic materials and in the composition of propellants; thanks to its high heat of reaction, high enthalpy, high temperature of combustion, low molar mass, long shelf life, thermal stability, and output performance. BPN is also listed as a linear reference for the security of pyrotechnic agents [24].

Military specification	MIL-P-46994B(AR)
Scope	This specification covers eight types of ignitor pellets/granules for use in rocket motors, fuzes, and payload ignition/expelling charges.
Classification	Type I – Cylindrical
Material composition requirements	Potassium nitrate	MIL-P-156 except particle size shall be 15 microns maximum
	Boron, amorphous	MIL-B-51092 except particle size shall be 1.5 microns maximum and the boron purity shall be 90–92%
	Polyester resin	MIL-R-7575 Grade A, Class O, Form K
	Peroxide, methyl ethyl ketone	MIL-P-81351
	Cobalt naphthenate	—
Materials formulation	Potassium nitrate, %	70.7 ± 2.0
	Boron, amorphous, %	23.7 ± 2.0
	Binders, %	5.6 ± 0.5
Binder composition	Polyester resin, %	98.0 ± 1.0
	Catalyst, %	1.5 ± 0.1
	Accelerator, %	0.5 ± 0.01
Physical properties	Type	I-E – Cylindrical
	Diameter, mm	4
	Height, mm	5
	Minimum weight, gm	0.1
Physical and ballistic properties	Minimum density, gm/cm^3	N/A
	Maximum moisture content, %	0.75
	Burning rate, mm/s	31.75–44.45
	Minimum heat of reaction, calories/gm	1500
	Minimum crush strength, gm	5000 (axial); 500 (radial)
	Time to maximum pressure, ms	N/A

Table 4.

BPN specification, classification, composition, and properties.

1. The igniter compositions shall be a homogeneous blend of materials.

2. The igniter pellets shall be free of cracks or laminations.

3. All pellets and packaging material shall be free of dirt, grease, and other foreign matter.

3.6 Photodiode

A Si-photodiode FDS1010 from Thorlabs, with 65 ns risetime, 350−1100 nm, and 10 x 10 active area was used in our experiments to measure the light signal and its duration related to the light emitted by the laser pulse at the activation and the light emitted during the ignition and combustion of the pyrotechnic material, that is, pulse duration, ignition delay time, and burning time.

3.7 Benchtop oscilloscope

The Benchtop oscilloscope TDS2024B model from Tektronix was used in our experiments to display and record the ignition delay and burning times.

3.8 Power and energy laser measurement sensor

The F150A-BB-26 from Ophir photonics, which is a general-purpose fan cooled thermal power and energy measurement sensor, was used to measure the output power and energy, and their respective densities. It has an aperture of 26 mm and can measure power from 50 mW to 150 W and energy from 20 mJ to 100 J. It has the spectrally flat broadband coating and covers the spectral range of 0.19−20 μm.

3.9 Laser power and energy meter

Ophir Photonics Vega power and energy meter was used in our experiments to display the output power and energy measured values.

3.10 Experimental setup production cost and time

The total cost of our experimental setup and safety equipment, as well as the availability and delivery time, are detailed below (Table 5):

Item	Part number	Price/unit [CNY]
Laser diode, fiber-coupled model	DS3-21312-203	32,500.00
Collimating lens	C240 TMD-B	793.90
Beam expander	BE-02-05-B	11,145.70
Focusing lens	AC254-60-B-ML	1,073.77
	AC254-125-B-ML	1,073.77
Photodiode	FDS1010	498.16
Benchtop oscilloscope	TDS2024B	12,025.65
Power and energy laser meas. Sensor	F150A-BB-26	8,795.90
Laser power and energy meter	Ophir Photonics Vega	14,671.29
Personal protection equipment (laser safety glasses, respirators, gloves, protective clothing, safety boxes, inert containers, clamps, pliers, etc.)	—	3,000.00
Total cost		85,578.14

Table 5.

Experimental setup production cost and time.

Notes: 1. The availability period of the devices could vary from 1 day to 1 month or more after the establishment of the order. It includes neither the delivery time (within mainland China, or from overseas), nor the delivery cost. The price of BPN is not available.

2. The total production time cannot be accurately estimated due to COVID-19 related delays that affected the acquisition time of the aforementioned equipment.

3. OSHA, HIOSH, and other internal process safety management guidelines and directives on manufacturing, storage, sale, handling, use, and display of pyrotechnic materials have been followed during the whole process of the experiment.

4. Results and discussion

As described earlier in Section 3, the distance separating the focusing lens and the BPN at each value of the inverted magnifying power was measured and reported in Figures 1 and 2. As it can be seen, the working distance characterizing the focal length increased exponentially with the increasing inverted magnifying power, that is, the larger is the inverted magnifying power the longer is the focal length, whilst the energy and power densities remained unchanged, as proven in Figures 4 – 13. The laser beam waist variation over the working distance for AC254-60-B-ML due to changes in the inverted magnifying power was reported in Figure 3. Four cases were considered for simpler and better illustrations, that are iMP₁, iMP₂, iMP₃, and iMP₄. It can be noticed that the laser beam variations were not just in terms of working distance, but also in terms of beam waist minima that were different from a location to another. At first, the beam waist was at its minimum at iMP₁, then it increased between iMP₂ and iMP₃, to finally decrease till it reached another minimum at iMP₄, and still larger than the one reached in the first place. By considering ω₀(iMP₁), ω₀(iMP₂), ω₀(iMP₃), and ω₀(iMP₄) as the beam waists corresponding to iMP₁, iMP₂, iMP₃, and iMP_4, respectively, and rank them from smaller to larger, the following order was obtained: ω₀(iMP₁) < ω₀(iMP₄) < ω₀(iMP₂) < ω₀(iMP₃).

Figure 1.

Focal length variation with the inverted magnifying power of the beam expander in reverse mode, with iMP₁, iMP₂, iMP₃, and iMP₄ being equal to 0%, 33%, 66%, and 100%, respectively, using AC254-60-B-ML.

Figure 2.

Focal length variation with the inverted magnifying power of the beam expander in reverse mode, with iMP₁, iMP₂, iMP₃, and iMP₄ being equal to 0%, 33%, 66%, and 100%, respectively, with f₁ = 60 mm and f₂ = 125 mm.

Figure 3.

Beam diameter variation with the working distance for different inverted magnifying power values, with d_i equal to 0.25 mm, 0.75 mm, 0.89 mm, and 0.60 mm for iMP₁, iMP₂, iMP₃, and iMP₄ respectively, using AC254-60-B-ML. The value y = 0 represents the ax of the laser beam.

We assume that the main reason for this is the focused spot size is diffraction limited, and when the spot size either increases or decreases under the control of the inverted magnifying power of the beam expander, it is influenced by contributions from diffraction and spherical aberration that characterize the internal lenses and optical elements of the beam expander. Another reason is related to the fact that the mechanism of the selected beam expander BE-02-05-B is a rotating focusing mechanism. Such a mechanism, in contrary to the sliding focusing mechanism, is somehow similar to threaded focusing tubes that rotate the optical elements during the translation, which in some cases may create the potential for beam wander during the rotation. Nevertheless, such beam expanders remain cost-effective than the sliding ones due to their simplified mechanism. In addition to changes in beam waists, changes in angles of divergence are also noticeable. These changes influence the interactions of the laser with the pyrotechnic material.

After conducting laser initiation of BPN, the following results were obtained (see Figures 4 – 7) and reproduced (see Figures 8–13).

Figure 4.

Laser initiation of BPN with a varying output power values and pulse durations at iMP₁ using AC254-60-B-ML.

Figure 5.

Laser initiation of BPN with a varying output power values and pulse durations at iMP₂ using AC254-60-B-ML.

Figure 6.

Laser initiation of BPN with a varying output power values and pulse durations at iMP₃ using AC254-60-B-ML.

Figure 7.

Laser initiation of BPN with a varying output power values and pulse durations at iMP₄ using AC254-60-B-ML.

Figure 8.

Minimum initiation power and pulse durations tradeoff at iMP₁ using AC254-60-B-ML.

Figure 9.

Minimum initiation power and pulse durations tradeoff at iMP₂ using AC254-60-B-ML.

Figure 10.

Minimum initiation power and pulse durations tradeoff at iMP₃ using AC254-60-B-ML.

Figure 11.

Minimum initiation power and pulse durations tradeoff at iMP₄ using AC254-60-B-ML.

Figure 12.

Minimum initiation power and pulse durations tradeoff at different magnifying power values using AC254-60-B-ML and AC254-125-B-ML.

Figure 13.

Beam diameters, pulse duration and ignition delay times variation at a 1500 mW output power at four different, but adjacent, working distances (155 mm, 160 mm, 165 mm, and 170 mm; the latter corresponds to the focal length at iMP₄ using AC254-60-B-ML).

As it can be seen from the benchtop oscilloscope recorded results and data, the first electric impulse measured in volt and displayed in Figures 4 – 7 represents the light emission generated by the laser signal intended to initiate BPN. The second, larger impulse which follows the first impulse with a gap of dozens to hundreds of milliseconds represents the light emitted due to BPN ignition and combustion. But the most important remark is that of a third impulse which is less pronounced than the two previous impulses representing the laser signal and BPN ignition. However, this impulse comes only in cases where the pulse duration is larger than the ignition delays. Therefore, this third impulse represents the end of the laser pulse (or laser signal). Its significance lies in the fact that BPN does not necessarily ignite after that all the energy contained within one pulse is totally absorbed; however, energy is absorbed by BPN even after ignition influencing the combustion process. Therefore, this third pulse following BPN ignition can be noticed from the recorded data in the form of a sudden disruption (or a disruptive impulse) occurring during the combustion process, and its time duration is usually equal to the pulse duration starting from the time when the laser signal is turned on. In other words, ignition is a thermal process which is not always dependent on the laser pulse duration, but rather on the threshold ignition energy and power, as mentioned earlier in the introduction. This can be noticed from the pulse durations that are in most of the cases higher than the ignition delays, particularly at lower output power, and almost equal to the ignition delays, particularly at higher output power.

Another noticeable fact from Figures 4–7 is that of BPN ignitability or sensitivity dependance on the focal spot size. As mentioned earlier, BPN initiation recorded results related to iMP1, iMP2, iMP3, and iMP4 and represented by Figures 4–7, respectively, are dependent on the spot size, that is, the smaller is the spot size the higher is the sensitivity, which in turns depends on power density, absorbed intensity, and thus brightness. Therefore, the sensitivity of BPN was higher for the cases represented by Figures 4 and 7, and lower for the ones in Figures 5 and 6. The same applies to the lowest values of the output power required for the initiation, in Figures 4 and 7, even if the pulse durations increased up to 630 ms, ignition occurred at an output power as low as 500 mW, while in Figures 5 and 6, for pulse durations up to 800 ms, ignition occurred at higher output power, between 750 and 1000 mW.

As it can be seen from Figures 8 – 11, there is a clear tradeoff between the output power, the absorbed intensity, and the critical pulse duration at which the ignition occurs. This can be noticed from the gap existing between the ignition delay times and the pulse duration times; this gap is very small for higher values of output power but increases gradually with the decrease of the output power, that is, the threshold ignition energy required is higher at lower values of output power, which increases not only the ignition delay time, but also and especially the pulse duration. From Figure 12, we can notice that ignition delay times are shorter for iMP₁ and iMP₄, while they are longer for iMP₂ and iMP₃, and this either at high or low output power. The main reason is that the values of the beam waist are directly influencing the ignition, and thus the tighter is the focus and the higher are the power densities. Also, after using a 125 mm focal length lens for the case of iMP₁ and iMP₂, the obtained results were almost identical to those with similar working distances but with a 60 mm focal length lens. This means that, considering the setup produced in our experiments, no matter what the working distance is, it will not affect power and energy densities, BPP, M², and the brightness as long as the beam waist remains unchanged.

To confirm the aforementioned findings, four cases with the same output power but different working distances were investigated, that is, changing the position of BPN to adjacent locations, whilst the focal length remained unchanged, only the spot size at the target changed. The results are presented in Figure 13, the increase in the spot size was inversely proportional to the increase in the working distance. Whilst the pulse duration and ignition delay times decreased proportionally with the decreasing spot size, as power densities were concentrated in smaller areas. However, it is noticeable that the required threshold ignition energy became higher with the increase of the working distance even if the spot size decreased, as the gap between pulse durations and ignition times increased.

There is a trade-off between the minimum laser power and the irradiation time [25]. Achieving maximum temperature rise and minimum threshold ignition power depends on various parameters. Under a quasi-steady state condition, the temperature rise depends inversely on the square root of the pulse duration. Thus, the criteria that need to be considered are high power density, highly focused beam, minimum reflection losses, long irradiation time, and high diffusivity.

Considering the same energy pulse, a comparison can be made in a way to describe a case with a certain amplitude and a certain time, and the other case with four times the amplitude but only one-fourth of the time. In other words, energy is unchanged, or the values of the integral of power over time remain unchanged, but in the first case four times the intensity and one-fourth of the time are obtained, and the opposite for the second case. The thermal penetration depth for the low intensity case is a factor of two longer when compared with the high intensity case because the time is a factor of four different and the thermal penetration depth must be the root of that which is a factor of two shorter. The same principle applies to the temperature, the lower intensity pulse generates half the temperature at the surface as the high intensity pulse and that scales with the root. The deposited energy in the short-pulse case should equal the deposited energy in the long-pulse case; therefore, if the penetration depth scales with the root of temperature, it is more plausible that the maximum temperature also scales with the root of the intensity of radiation. The shorter the pulse, the higher the temperature on the surface, and the less deep the thermal penetration. Thus, in terms of quantitative consequences, the shorter the pulses the smaller the penetration depth.

5. Conclusion

Laser diodes are high-reliability devices due to their exceptional energetic efficiencies and unsensitivity to magnetic disruption. Laser devices can be used either with optical fibers to drive the energy to the energetic material, or with lenses and other optical systems to concentrate energy on the surface of the energetic material.

The optimal wavelength for a given case is highly application-dependent because different pyrotechnic materials have unique wavelength-dependent absorption properties, leading to different interactions. Similarly, atmospheric absorption and interference affect certain wavelengths differently with a varying charging distance. Shorter wavelength laser systems are advantageous for creating minimal peripheral heating because of a smaller focused spot. However, they are prone to damage than lasers at longer wavelengths, that is, less cost-effective.

Higher power and energy lasers are typically more expensive, and they generate more waste heat. As power and energy increase, beam quality may decrease.

High power and energy densities are often ideal at the final output of a system, but low power and energy densities are often beneficial inside a system to prevent laser-induced damage.

Finally, the parameters affecting laser initiation can be summarized as follows (Table 6):

Laser parameters	Material parameters
Wavelength	Spectral absorptivity
Average power	Thermal conductivity
Peak power	Chemical composition and morphology of the material
Power density	Ignition temperature of the material
Beam uniformity
Duration of irradiation
Dimension of focused spot
Heat dissipation

Table 6.

Parameters affecting laser initiation.

In this work, flexibility is achieved, and more distance is covered by allowing fine spot sizes with high power densities and longer focusing distances. Some of these findings were the perspectives suggested by refs. [26, 27]. The intensity obtained at the spot size is proportional to the brightness of the beam. This brightness is characterized [28, 29] as follows:

• Brightness is not affected by focusing or defocusing the beam.

• Changes in power, spot size, M², beam divergence, or the wavelength will lead to a change in the brightness.

• The brightness of a Gaussian beam does not change as it propagates as it is inversely proportional to solid angles of divergence. And the smaller the divergence the higher the brightness of the laser. High brightness beams, however, have the most idealized beam profile and tend to have a high-quality factor.

Acknowledgments

The authors thank Professor Yan from Beijing Institute of Technology and Zhang Liang from Peking University and acknowledge their assistance with this effort and the support received from them in terms of provision of part of the experimental equipment and devices necessary for the completion of this work.

Conflict of interest

The authors declare no conflict of interest.