Laser Tutorial

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Here we explain about lasers.
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Table of contents

1. Laser

Laser is named from “Light Amplification by Stimulated Emission of Radiation”. Laser is artificial light, and is generated by exciting a specific material with artificial large energy from light, discharge, and so on.

1.1. Characteristics of Lasers

Laser light is superior in some properties to spontaneous light. The main characteristics of laser is shown below.

  1. Monochromaticity: Spectrum width is very narrow
  2. Directionality: Light is not dispersed and expanded
  3. Coherence: Light can interfere with each other
  4. Controllability: Output light can be easily modulated

Since laser light is far stronger than and is superior in terms of monochromaticity and directionality to spontaneous light, laser beam can be focused by lens into a diffraction limit with a high energy density. This indicates that laser is superior in a focusing property and has a high brightness. Figure 1.1.1 schematically explains the laser characteristics .

Fig. 1.1.1. Characteristics of Lasers

1.2. Lasing Operation and Parameter

Laser is composed of an optical amplifier and an optical resonator. Laser output is obtained by light oscillations in an optical resonator. The lasing operation is either the continuous wave (CW) operation (for CW laser) or the pulsed operation (for pulsed laser). In CW laser, a constant power is continuously output. In pulsed laser, optical pulses are output with a constant repetition frequency. Figure 1 shows a schematic of the CW operation and pulsed operation.

Fig. 1.1.2. Continuous wave oscillation and pulsed oscillation

A CW laser is characterized by an average power [W]. A pulsed laser is generally characterized by a pulse duration [s], a repetition rate [Hz], a pulse energy [J], and a peak power [W]. These parameters of pulsed laser are associated by the following expressions.

Figure 1.1.3 schematically explains the relationship among these parameters of pulsed laser. Table summarizes units of laser parameters which are frequently used.

Fig. 1.1.3. Relationship among all sorts of parameters of pulsed laser

Table1.1.1. Units of laser parameters

words parameters
Wavelength m
Spectral bandwidth
Average output power W
Peak power
Pulse repetition rate:PPR Hz
Pulse width or pulse duration s
Energy per pulse or pulse energy J
Loss dB or dB/km
Gain
M2 (Beam quality) -

 

2. Principle Mechanism

2.1. Energy Level

Atom consists of an atom core and a number of electrons (Fig. 2.1.1). Electrons exist in discrete orbitals around an atom core. Usually, electrons dominate lower energy orbitals to minimize the energy of atom. This state is called as ground state. The ground-state atom is stable.

Fig. 2.1.1. (a) configuration of atoms, (b) energy level diagram

When heat or light is given to the ground-state atom, electrons in the outer orbital, which has high energy, can be transferred to a further outer orbital. Then, the atom will gain energy. A diagram plotting the energy on the basis of the ground state for describing this higher energy state is called as enegry level diagram. The energy level of ground state is called as ground state. The process of transition of atomin energy level from the ground state to a higher-energy level is called pumping. The energy level of excited state is called as excitation level.

It is also possible to consider the energy level not only for atoms, but also for molecules and ions. As excitation methods, collision of atoms and molecules, and chemical reactions are used other than the optical pumping.

2.2. Light Absorption and Emission

In order to understand the operation mechanism of laser, we have to understand light interactions with a material including absorption, spontaneous emission, and stimulated emission, and non-radiative transition (no direct relationship with light). Let us consider an energy level with an atom distribution density of N1 and a degeneration number of g1, E1 (ground level), and an energy level with an atom distribution density of N2 and a degeneration number of g2, E2. E2 is just required to be an upper level than E1 (not required to be neighbored to E1). This kind of model is called as two-level model. Figure 2.2.1 represents a light absorption and emission for a two-level model.


Fig. 2.2.1.  light absorption and emission for two-level model

Provided that an atom at E1 state is irradiated by a photon with a frequency of ν that satisfies the Bohr condition, E2-E1=h where h is the Planck constant, light absorption, spontaneous emission, stimulated emission, and non-radiative transition, which are directly associated with the operation mechanism of laser, are described as follows.

Absorption
An atom at the energy level of E1 exhibits stimulated absorption and an absorption transition to E2 at a certain probability. A parameter representing what probability a photon is absorbed at is defined as B12, absorption transition rate. Bji is called as the Einstein B coefficient.

Spontaneous emission
An atom excited to the level E2 can spontaneously emit a photon with a frequency of ν and exhibits a transition to the low-energy and stable E1 level after a certain time (lifetime: τ21) is passed since the excitation. This process of the spontaneous light emission is called as spontaneous emission. The spontaneous emission can be a noise since it has a random polarization and phase, but it is a seed of laser light. A parameter representing a propability of photon emission is defined as an emission transition rate, A21. Aij is called as the Einstein A coefficient. The lifetime (τ) and the A coefficient for spontaneous emission are associated with a reciprocal relationship.

Stimulated emission
When an excited atom at the level E2 is irradiated by a photon with a frequency of ν, the excited atom is stimulated to emit a photon with the same phase at the same mode in the same direction as the incident direction of a photon. This phenomenon is a stimulated emission. The stimulated emission is the principle of light amplification, and primarily works for light amplification by stimulated emission of radiation, laser. A parameter representing a probability of stimulated emission is defined as a transition rate, B21, and is associated with the absorption transition rate, B12, and the degeneration number of level by g1B12=g2B21. A transition of stimulated emission attributed to the laser oscillation is called as laser transition. The upper energy level and lower energy level are called as laser upper-level and laser lower-level, respectively.

Non-radioactive transition
The transition of energy from the laser upper level to the laser lower level can emit energy to a lattice vibration. This is called as non-radiative transition. It is determined by a sort of material which occurs with a high probability, the spontaneous emission or the non-radiative transition.

2.3. Gain and Inverse Population

In a system where atoms (or molecules) are excited to an excitation state, the absorption,  spontaneous emission, stimulated emission, and non-radiative transition simultaneously occur. Let us consider that a medium is irradiated by light at a frequency of ν with an intensity of Iν=cρν/n where c is light velocity, n is refractive index of medium, and ρν is energy density at the frequency of ν. Provided an emission spectrum function, g(ν), an increase of light intensity per unit length of medium is expressed by the following equation,

where σ(ν) is stimulated emission cross-section, and γ(ν) is gain. σ(ν) and γ(ν) are given as follows.

The stimulated emission cross-section (absorption cross-section) can be thought as a certain cross-section of atom, at which input photons exhibit stimulated emission (absorption). For a simple two-level model, the absorption cross-section and the stimulated emission cross-section are equivalent.

For N> (g2/g1)N1 (In the case of non-degenerated two-level model, g= g2, N> N1), the stimulated emission is dominant over the absorption, then light  is amplified (see Fig. 2.3.1 (a)). On the other hand, for the thermal equilibrium state (see Fig. 2.3.1 (b)), since a distribution density of atom is the Boltzmann distribution, we have N2 < (g2/g1)N1 and a negative value of γ(ν). Therefore, the incident light is exponentially decreased as it travels longer in the medium. By the way, even if the intensity of incident light is larger, since the rates of absorption and stimulated emission for a single atom are the same, transitions to the level E1 increase, while transitions to the level E2 increase. In essence, we have N2< (g2/g1) / N1.

 Fig. 2.3.1. Energy level diagrams in (a)inverse population state,
and (b) thermal equilibrium state, for two-level model

A state of N> (g2/g1)N1 is called as inverse population state. It is not possible to realize the inverse population (negative temperature) by optical excitations for the two-level model. In practical laser, the inverse population is realized by the following two methods.
① Optical excitations with the third or fourth level
② Non-optical excitations with current injection, discharge, or chemical reactions

Boltzmann distribution
In a thermal equilibrium state at absolute temperature of T, an atom density, Ni (i=1,2,3,…), at energy level Ei, is typically represented by the Boltzmann distribution. Ni and Ei are associated by the following equation,

where Ntot is a total atom density, and kb is the Boltzmann constant. For N1 and N2, the following equation is given from the equation above.

2.4. Three-level Model and Four-level Model

2.4.1. Three-level Model

Figure 2.4.1 shows the energy level of the ideal three-level model. In this model, laser lower-level, E1, is the same as the ground state, the lower-level always has an atomic number distribution. Above the laser upper-state E2, the pumping level E3 with with a wideband width exists. For an efficiently producing an inverse population, the lifetime of the pumping level is required to be small, and a relaxation time of non-radiative transition of the pumping level E3 to the laser upper-level E2, τ32, is required to be far smaller than the relaxation time of the pumping level E3 to the ground level E1. Under the requirements, the stimulated emission from the pumping level E3 to the ground level E1 barely occurs even with the intense pumping light irradiation, then the inverse population is realized. By the stimulated emission from the laser upper-level E2 to the ground level E1 in this condition, the laser oscillation is exhibited.

 Fig. 2.4.1. Schematic picture of three-level model.
(a) energy level diagram, (b) inverse population state

The transition ratio of the population in the laser upper-level to the number of excited atoms in the pumping level is called as pumping quantum efficiency, ηp, and is defined by the following equation.

In an use of the pumping quantum efficiency, ηp, a transition rate of the ground level E1 to the laser upper-level E2 due to the pumping, W2, is associated with a transition rate of the ground level E1 to the pumping level E3 due to the excitation, W13, by WppW13.

Provided the total atom density, Ntot = N1+N2, and dN2/dt = -dN1/dt since the relaxation of pumping level is fast, a rate equation for the inverse population density, N = N2-(g2/g1)N1, is expressed as follows,

where φ is a photon density in a medium. τf is the fluorescence lifetime of the laser upper level (average time for an atom to be in the excited state), but is seen as equivalent to the spontaneous emission lifetime, τ21, on the purpose of simplification.

2.4.2. Four-level Model

Figure 2.4.2 shows an energy diagram of the ideal four-level model. In this model, the laser lower-level is far larger than the ground level in terms of energy (E1>>kT), and the thermal pumping of the ground level to the laser lower-level never happens.

 Fig. 2.4.2. Schematic picture of four-level model.
(a) energy level diagram, (b) inverse population state

Assuming that the lifetime of the pumping level E3 is far longer than the lifetime of the other levels, the density distribution of the pumping level E3 (N3) can be ignored, then the total atom density is expressed as Ntot = N0 + N2 + N3. Additionally, since an ideal four-level laser allows an approximation of τ10 ~ 0, we obtain N= 0 and the inverse population density of N = N2.

Then, the rate equation for the inverse population density is given as follows.

Fluorescence lifetime of the laser upper level τf, the pumping rate, Wp, and the pumping quantum efficiency, ηp, are expressed by the following equations, respectively.

 

2.4.3. Comparison of Inverse Population

For the three-level model, a ground level is a laser lower level. Provided that E3 is ignorable, Ntot = N1 + N2 is obtained, then, the density distribution of laser upper level, N2, needs to be Ntot / 2 or larger for realizing the inverse population. On the other hand, for the four-level model, the atom density distribution of laser upper level, N2, turns to be the inverse population density, N. Therefore, the three-level laser is not as efficient as the four-level laser, since the three-level laser requires relatively intense pumping power.

Assuming that the medium is in the steady-state and certain conditions of dN / dt = 0 and φ = 0 (photon density), we obtain the following equation derived from the rate equation in the section 2.4.1.

For the four-level laser, the following equation is obtained from the rate equation in the section 2.4.2 in the same manner.

Here, we assume that the laser upper-level and the laser lower-levels are degenerated and the relationship of degeneration is given by g= g2. Then, changes in the laser population density are represented in Fig. 2.4.3 as functions of normalized pumping rate, Wpτf, which are given from two equations above. Figure 2.4.3 shows that the efficiency of three-level laser is low.

 Fig. 2.4.3. Pumping rate dependency of inverse population
for three-level and four-level models

2.4.4. Spectral Line Width

A spectrum of spontaneous emission light and absorbed light is not a single line which satisfies E1 – E2 = hν, but a spectral shape centering at the spectral line with a certain width. The broadening of spectral shape is a laser gain curve, and determines lasing properties. A narrow spectrum is appropriate for single frequency operation, while a broad spectrum is appropriate for wavelength tunable operation. The spectral broadening is categorized into two types, homogeneous broadening and inhomogeneous broadening. Laser medium has a property of mixture of homogeneity and inhomogeneity.

Homogeneous broadening
The homogeneous broadening is inherent to each atom in a medium. The homogeneous broadening can be spontaneous broadening, Stark broadening, collision broadening, and so on.

The spontaneous broadening is a primary broadening yielded from lifetime of a pumping level and the frequency uncertainty. A width of spontaneous broadening between two pumping levels with lifetimes of τi and τj (spontaneous width), Δνij, is expressed by the following equation.

Assuming that the lower level is the ground state, lifetime of the ground state is infinite. Then, as the lifetime τf is short, the spontaneous width is large. The shape of spontaneous width is the Lorentzian shape as is shown in Fig. 2.4.4.

The Stark broadening is due to degeneration of energy level caused by external electric field. Stark level yielded by the degeneration makes the lifetime very short, and the spectral width very large.

The collision broadening is yielded in gas laser since a lifetime of pumping level becomes shorter when atoms (or molecules) collide with each other and the pumped atoms lose their energy. The collision broadening is dominant for such a gas laser as excimer laser operating with high gas pressure discharge.

Inhomogeneous broadening
The inhomogeneous broadening is a phenomenon that various frequencies are generated by a variety of influences and the spectrum is broaden. The inhomogeneous broadening can be a strain caused by lattice defect or inhomogeneity of magnetic or electric field (crystalline field) for solid-state laser, and Doppler broadening for gas laser.

In a crystal of solid-state laser, the crystalline field is not uniform since the crystal is imperfect. As a result, a large inhomogeneous broadening is yielded. In glass doped with rare earth ion, because host ions are randomly distributed, the inhomogeneous width is relatively largely broaden compared with the crystalline solid-state laser.

The Doppler broadening is yielded by emission of light with different frequencies by the Doppler effect of each atom (or molecule) with irregular thermal motion. The Doppler broadening is dominant in gas laser operating with low pressure discharge. Since the velocity distribution of gas molecules obeys Maxwell distribution, the shape of Dopper broadening is Gaussian (normal distribution) function shape.  Figure 2.4.4 shows a Gaussian function and represents that the Doppler broadening is a superposition of spontaneous broadening.

 Fig. 2.4.4. Lorentzian-shaped and Gaussian-shaped spectra

3. Lasing Property

Let us consider a Fabry-Pelot resonator arranging an inverse population medium of length of l and equilibrium flat mirrors at the both edges of the medium as shown in Fig. 3.0.1.

Fig. 3.0.1. Fabry-Pelot resonator

Electric field of light propagating in the resonator is expressed as classical electromagnetic field as follows.

E0 is amplitude of electric field, ω is angular frequency, and k’ is wavenumber of medium. Ik is a propagation constant and is given by k = 2π/λ, Δk is wavenumber shift by dispersion, γ(ν) is gain coefficient, and α is absorption coefficient.

First, we assume that an electric field Es is generated by spontaneous emission at the total reflection mirror position of z = 0. The electric field, Es, partially penetrates over the out mirror and is extracted to the outside the resonator. However, since the reflectivities of both mirrors are high, most of the light travels forward and backward in the resonator, and is amplified by the stimulated emission from the inverse population medium. Light emitting from the output mirror, Eout, is expressed by the following equation,

where each field component is give by the following equations.

Therefore, E(t) can be rewritten as follows,

where r1 is reflectivity of the total reflection mirror for the electric field, and r2 and t2 are reflectivity and transmittance of the output mirror, respectively. Because lasing state corresponds to a condition that the denominator of the equation above is 0, the real and imaginary parts of output electric field are represented by the following equations, respectively.

The first equation is the resonance condition, and represents a state that a phase of electric field propagating forward and backward in the resonator does not change at a certain position. The second equation is the oscillation condition, and represents a state that an amplitude of electric field propagating forward and backward in the resonator does not change at a certain position.

3.1. Resonance Condition

For light to stably exist in the Fabry-Perot resonator, a standing wave needs to exist in the resonator (where a phase delay after a round-trip light propagation in the resonator is 2πm) and a node of the standing wave must be located at the mirror as shown in Fig. 3.1.1 (a) and (b). Then, the resonator length, l, is the integral multiple of a half of the wavelength, λ.

This is the resonance condition represented the equation in the section 3. Light with a frequency satisfying the condition is called as longitudinal mode, and represents an electric field distribution of the standing wave existing along the axial direction of the resonator. On the other hand, transverse mode represents a distribution of the standing wave on the beam cross-section. “Mode of optical fiber” described in latter parts of this book indicates mostly the transverse mode. Figure 3.1.1 (c) schematically explains the longitudinal mode by setting frequency and transmittance to the horizontal and vertical axis, respectively.

In the resonance condition, the transmittance takes a local maximum for the resonance frequency, which is the center frequency of longitudinal mode, then, the longitudinal modes (local maximums of transmittance) appear with a constant interval. This interval is called as transverse mode interval or free spectral range (FSR). Transmission characteristics of a resonator (resonance sharpness) is exhibited by Finesse. Provided FWHM of a longitudinal mode, Δν1/2,  Finesse is given by the following equation.

In case a laser medium does not exist in the resonator (the case of passive resonator), since Δk=0 (and k=2π/λ) in the condition, the resonance frequency, νm, is given as follows.

In case a laser medium exists in the resonator, by considering a phase shift due to stimulated emission, the oscillation frequency, ν, is expressed by the following equation,

where ν0 is the gain center frequency, and Δν is the gain width at half maximum of medium. The equation above indicates that ν is shifted to νm when the resonance frequency, νm, is not equivalent to the center frequency of gain, ν0. This frequency shift is known as the frequency pulling effect.

The longitudinal modes infinitely exist with a frequency interval of c/2πl, but in practice, the laser oscillation is possible only for a frequency in the spectral range for a laser medium to exhibit the amplification operation (in the range of gain curve). In order to exactly obtain light with a specific wavelength from an optical resonator, the resonator length, l, must be restrictedly maintained, and temperature change in the environment and mechanical fluctuation need to be cared.


Fig.3.1.1. Schematic picture of longitudinal mode of laser.
(a) electric field distribution of νm mode and (b) νm-1 mode, and (c) longitudinal mode.

3.2. Oscillation Condition

An atom excited to the laser upper level by the pumping light yields light via the spontaneous emission (or the stimulated emission). When a part of the yielded light is in the resonant mode of an optical resonator, the light is amplified by the stimulated emission by every round trip inside the resonator. But, in a weak pumping state, since the loss of resonator exceeds the gain of amplification, light is decayed after each round trip in the resonator. Here, the loss of resonator is the sum of the coupling loss (T), which is caused by the light exit out of the resonator through the transmission over the output mirror, and the residual loss (Li), which is based on the absorption, scattering and diffraction loss in the resonator. As the pumping light becomes intense, the gain of stimulated emission increases, since the number of atom excited to the laser upper level increases. As a result, with some pumping light intensity, the gain of amplification and the loss of resonator for a round-trip becomes equivalent to each other. Subsequently, because the gain and loss are balanced, the amplitude of light intensity does not change regardless of the number of round-trips in the resonator. This state is called as the oscillation in laser, and the equation in the section 3 is the oscillation condition.

The equation gives the gain coefficient at the oscillation threshold, γth, as shown below,

where R1 and R2 are reflectivities for the light intensity and given by R= r12 and R= r22. The inverse population density, Nt, is expressed by the following equation.

 

3.2.1. Excitation Intensity and Gain Change

Small-signal gain coefficient (unsaturated gain coefficient), γ0, is a gain coefficient for the photon density of φ = 0. A gain for light to penetrate through a laser medium, G0 = γ0l, is called as small-signal gain. Provided the intensity of signal light traveling through the laser medium, I, the gain coefficient, γ(ν), is expressed  by the following equation,

where Is is the saturated light intensity and is defined as light intensity for the gain coefficient, γ(ν) to be a half of the small-signal gain coefficient, γ0. The equation above indicates that the gain coefficient, γ(ν), decreases as the light intensity in the resonator, I, increases. As the light intensity increases, the stimulated emission increases, then the number of atoms in the laser upper level decreases (the density difference from the laser lower level decreases) and the inverse population density decreases. This phenomenon is called as gain saturation, and determines the output intensity of laser and the maximum output of optical amplifier. Figure represents the gain characteristics of the equation above.

Provided the intensity of light (signal light for causing the stimulated emission) in the Fabry-Pelot resonator, Ic, the gain coefficient is expressed by the following equation.

Because the forward and backward waves are considered, Ic has a coefficient of 2. Provided the light intensity of Ic = cφhν, the saturated light intensity of three-level and four-level laser can be derived from the equation above and the inverse population calculated from the equation in the section 2.4.1 and 2.4.2 for the steady state. For the three-level laser, the saturated light intensity is given as follows.

For the four-level laser, the saturated light intensity is represented as follows.

For the four-level laser, the saturation gain intensity is approximated by using Wp >> 1/τf.

 Fig. 3.2.1. Signal light intensity dependency of gain

3.2.2. Oscillation Threshold and Slope Efficiency

Here, we consider the case when a laser medium is radiated by the pumping light with a power f Pin, and discuss the pumping power property of laser light. As parameters of a laser medium, we consider the following 7 items.

① Mode volume of a laser medium, V
② Pumping quantum efficiency, ηp:
Rate of transition to the laser upper level to the number of atoms pumped to the excited levels
③ Atom quantum efficiency η= νL/νP:
Proportion between the laser photon energy, hνL, and the pumping photon energy, hνP
④ Pumping light absorption efficiency ηa:
Absorption fraction of pumping light by a laser medium
⑤ Mode matching efficiency ηm:
Overlapping fraction between lasing and pumping areas
⑥ Coupling efficiency ηc=T/(Li+T):
Fraction represented by using the transmittance, T, and residual loss, Li, of output (coupling) mirror
⑦ Effective cross-section of laser light Aeff

With considering these items, we derive the small-signal gain coefficient, γ0, the lasing output, Pout, and the lasing threshold, Pth, below. Figure 3.2.2 represents the pumping power property of laser output.

 Fig. 3.2.2. Pumping power dependency of laser output

For three-level laser

Assuming that the number of degeneration of the laser upper level and lower lever are the same (g= g2), the small-signal gain coefficient, γ0, and the output power, Pout, for the three-level laser are expressed by the following equations.

For four-level laser
The small-signal gain coefficient and the output power for the four-level laser are expressed by the following equations.

Thus, in case the pumping power exceeds the laser oscillation threshold, the laser output power, Pout, increase in proportion to the pumping power, Pin (gain is constant regardless of the pumping light intensity). This fraction of increase is called as slope efficiency, ηS. Since the slope efficiency for the three-level laser is accompanied by the factor or 1/2(1-1/B), the slope efficiency for the three-level laser is limited to be smaller than the half of the slope efficiency for the four-level laser. Additionally, provided that the transmittance, T, increases, the increasing rate of slope efficiency for the four-level laser is larger than that for the three-level laser.

3.3. Lasing Spectrum

3.3.1. For Laser Medium with the Homogeneous Broadening

Figure 3.1.1 represents the gain curve (gain spectrum), the loss of resonator, and the resonance frequency (ν-3, ν-2, ν-1, ν0,…) of passive resonator for a laser medium with the homogeneous broadening. For the pumping intensity to be smaller than the laser oscillation threshold, the inverse population density is  proportional to the pumping light intensity, and the gain, γ, is proportional to the emission light spectrum function, g(ν) (see Fig. 3.3.1 (a)). As the pumping light intensity increases, the gain at the center resonance frequency ν0, G=γl, is equivalent to the loss of resonator, and the laser oscillation occurs at the frequency of ν0 (see Fig. 3.3.1 (b)). In this condition, even if the pumping light power increases, the inverse population density does not increases, and the gain curve is fixed by the loss of resonator (gain threshold) at ν0, then is constant. Therefore, since the gain at resonance frequencies excluding ν0 is smaller than the loss of resonator, the oscillation does not occur. However, the oscillation light intensity increases in proportion to the pumping intensity (see Fig. 3.3.1(c)). In summary, laser with an ideal homogeneous broadening can exhibit the oscillation only for a single longitudinal mode. This sort of laser oscillation is called as single mode oscillation.

 Fig. 3.3.1. Gain curves, longitudinal mode,
and oscillation mode for homogeneous broadening

3.3.2. For Laser Medium with the Heterogeneous Broadening

Figure 3.3.2 (a) represents the gain curve (gain spectrum), the loss of resonator, and the resonance frequency (ν-3, ν-2, ν-1, ν0,…) of passive resonator for a laser medium with the inhomogeneous broadening. Also in a laser medium for the inhomogeneous broadening, for the pumping intensity to be smaller than the laser oscillation threshold, the inverse population density and the gain γ are proportional to the pumping light intensity (see Fig. 3.3.2 (a)). As the pumping intensity increases, the gain at the center resonance frequency ν0, G=γ0l, is equivalent to the loss of resonator, and the laser oscillation begins to occur at the frequency of ν0 (see Fig. 3.3.2 (b)). These behaviors are the same as the behaviors for the homogeneous broadening medium, but behaviuors change for more intense pumping intensity.

The gain at ν0 is fixed by the loss of resonator, but the gain at other frequencies increases as the pumping intensity increases. When the gain at a certain resonance frequency becomes equivalent to the loss of resonator, the oscillation at the resonance frequency starts. Subsequently, since the gain at each resonance frequency is fixed, the gain curve has dips at each resonance frequency (see Fig. 3.3.2 (c)). This phenomenon is called as spectrum hole burning (or simply called as hole burning). The gain curve after the hole burning is called as saturation gain curve.

 Fig. 3.3.2. Gain curves, longitudinal mode,
and oscillation mode for inhomogeneous broadening

3.4. Pulsed Laser

Pulsed laser operation is based on the CW laser operation and can be realized by either of the following 3 methods. The direct modulation method, the Q-switching method, and the mode-locking method are briefly described below.

Direct modulation method
A method for obtaining a pulse shape is either a method where the beam output of CW laser is on and off by using a mechanical shutter or a method where a pumping source of resonator is pulse-controlled. For the high-power resonator, the latter method is dominantly employed. The direct modulation method can control a pulse shape and arbitrarily modulates a pulse duration in the range of ps ~ ms. The direct modulation method is applicable for hole-drilling processing and optical communication, in which the thermal influence is better to be minimized.

Q-switching method
In Q-switching pulsed operation, after the inverse population in a laser medium becomes sufficient, the laser oscillation is rapidly induced, then optical laser pulses with huge energy are output with a certain interval. The pulse duration is in the approximate range of µs ~ ns. The Q-switching method is applicable to the micro-processing, the hole-drilling processing, the groove processing, and the marking on such precision components as electronic components and semiconductor parts.

Mode-locking method
By setting the period of given modulation to the round time of light propagating in the laser resonator (synchronizing and oscillating longitudinal modes in the resonator), the mode-locking occurs. The pulse duration is in the range of fs ~ ps, which is the shortest pulse obtained among the three pulsed laser operation methods. Generally, the pulse energy obtained by the mode-locked method is relatively small compared with that of the Q-switching method. The repetition frequency is determined by the resonator length. As the resonator length becomes shorter, the repetition frequency becomes higher. The mode-locked method is applicable to the nonthermal processing, the nonlinear optics, and the seed light for terahertz light and supercontinuum light.

Table 3.4.1. Methods for pulsed laser operation and pulse width

Method Pulse width
Direct modulation ~ns, ~ps
External modulation ~ns, ~ps
Q-switching ~μs, ~ns
Mode-locking ~ps, ~fs

4. Sorts of Laser

Lasers are categorized into solid-state laser, liquid laser, gas laser, and chemical laser. The categories are described in the table 4.0.1, and details are explained in the following sections.

Table 4.0.1. Laser categories and lasers

Category Pumping method Laser wavelength
Solid-state laser current compound semiconductor laser diode ultra violet~infrared
flash lamp flash-lamp pumping Nd:YAG laser 1064 nm
ruby laser 694 nm
Nd:grass laser 1054 nm, 1062 nm
Er:YAG laser 2.9 μm
alexandrite laser 0.7 μm~0.82 μm
laser laser diode pumping Nd:YAG laser 1064 nm
Nd:YLF laser 1047 nm, 1053 nm
Nd:glass laser 1054 nm, 1062 nm
Nd:YVO4 laser 1065 nm
Yb:YAG laser 1030 nm
Yb-doped fiber laser 1.0 μm
Er-doped fiber laser 1550 nm
Cr:LiSAF laser 0.65 μm~1.1 μm
Er:YAG laser 2.94 μm
Tm:YAG laser 1.8 μm~2.2 μm
without laser diode pumping far infrared laser
Ti:Sapphire laser 650 nm~1180 nm
Ce:LiSAF laser 0.29 μm~0.30 μm
Cr:Forsterite laser 1.13 μm~1.37 μm
Ho:YLF laser 0.75 μm~2.06 μm
Ho:YAG laser 2.09 μm~2.10 μm
Liquid layser dye laser 300 nm~1200 nm
Gas laser discharge metal laser copper vapor laser 511 nm, 578 nm
He-Cd laser 325 nm, 442 nm
non-metal laser He-Ne laser 633 nm
Ar ion laser 275 nm~1090 nm
(many oscillation lines)
Kr ion laser 337 nm~858 nm
(many oscillation lines)
N2 laser 337 nm
CO laser 5~7 μm
CO2 laser 9~11 μm
electron beam excimer laser KrF laser 126 nm~351 nm
XeCl laser
ArF laser
F2 laser
Chemical laser chemical reaction HF laser 2.7 μm~2.9 μm
iodine laser 1.3 μm

4.1. Liquid Laser

Liquid laser employs liquid as a laser medium. An organic dye where dye molecules are dissolved in organic solvent (alcohol: ethylene glycol, ethyl, methyl) is mostly used as a medium of the liquid laser [1]. Among practically used liquid lasers, the dye laser employing the organic dye as a laser medium is mostly used.

Reference and Links
[1] P. P. Sorokin and J. R. Lankard, “ Stimulated emission observed from an organic dye, chloro-aluminum phtalocyanine, ”IBM J. Res. Dev. 10,162-163(1966).

4.1.1. Dye Laser

There are a number of sorts of dyes existing and it is possible to synthesize new types of dye. Therefore, it is thought that the laser oscillation can be realzied with using more than several hundreds types of organic dyes. A typical medium for dye laser is rhodamine 6G (R6G). R6G is used for applications to laser spectroscopies and cures for a reddish face.

Since a dye molecule has very wide emission spectrum (ca. 320-1200 nm), the dye laser is used as wavelength-tunable laser. The dye laser can be operated in both CW and pulsed oscillation. Because the emission spectrum is broad, the dye laser is used also as mode-locked ultrashort pulsed laser. However, since the dye laser has some weak points such as the short lifetime and the limited output, the dye laser is recently replaced by a wavelength tunable solid-state laser such as Ti:Sapphire laser. Additionally, because of the request for a transition to RoHS regulation conforming product in the world, the production and distribution of dye laser are partially stopped.

4.2. Gas Laser

Gas laser utilizes gas molecule as a laser medium. Mostly, the pumping is done by discharge to glass tube (or ceramic tube) including the gas. Electrons accelerated by the discharge give energy to atoms (or ions, molecules) in the gas laser medium, and excite the atoms to the pumping level. As a result, the inverse population is formed. Figure 4.2.1 shows a schematic picture of a basic gas laser. The longitudinal discharge system represented in Fig. 4.2.1 (a) is utilizable at a low gas pressure for stable discharge, which is required for the continuous oscillation (discharge is stable for the low gas pressure). On the other hand, the transverse discharge system represented in Fig. 4.2.1 (b) is appropriate for high power pulsed operation, because the transverse discharge method it can rapidly give a huge amount of energy to a gas medium and is utilizable at a high gas pressure (HIgh power gas laser can be realized by increasing the density of laser medium). The resonator shown in Fig. 4.2.1 has a configuration that the total reflection mirror and the output mirror are attached at the left and right edges of glass tube, respectively, while there is another resonator configuration where a Brewster window is attached to the glass tube and a mirror is arranged at the outside of the glass tube (external mirror system). By using the external mirror system, linearly polarized laser beam is obtained for the gas laser, too.

Gas types for laser media are atomic gas (for HeNe laser, noble gas laser, and metal vapor laser), excimer, and molecular gas (for N2 laser and CO2 laser). In the following text, we briefly describe these gas lasers.

 Fig. 4.2.1. Schematic of gas laser. (a) longitudinal discharge system,
(b) transverse discharge system

4.2.1. HeNe Laser

A medium of helium-neon (HeNe) laser is a gas mixture of 75 4% or higher percentage of He and 15 % or lower percentage of Ne. HeNe laser is identified as an atomic gas laser. In HeNe laser, He receives energy from electrons via discharge, then gives the energy to Ne via collisions and excites Ne to the pumping level. Thus, Gas laser frequently employs gas which is not directly related to the luminescence. Figure 4.2.2 represents the primary energy level structure of He and Ne in HeNe laser.

 Fig. 4.2.2. Principal energy level structure of He and Ne atoms for HeNe laser

When HeNe laser was first developed in 1960 by Javan, Bennet, and Herriott from the Bell laboratory, its oscillation wavelength was 1152 nm [1]. After the realization of the red oscillation at 632.8 nm in 1962 by White and Rigden, the wavelength of 632.8 nm is general for HeNe laser. HeNe laser ha other oscillation lines in green (543.5 nm), yellow (594.1 nm), orange (612.0 nm), and near infrared (1523 nm and 3391 nm). The output power is as low as around 50 mW. However, because the laser beam profile is very close to the gaussian distribution and the oscillation wavelength is very stable for a long period, HeNe laser is used for interferometric measurement and laser microscope.

Reference and Links
[1] A.Javan, et.al., “Population Inversion and Continuous Optical Maser Oscillation in a Gas Discharge Containing a He-Ne Mixture,” Phys. Rev. Lett. 6(3),106-110 (1961).

4.2.2. Noble Gas Laser

The medium of noble gas laser is mostly Argon ion (Ar+) or Krypton ion (Kr+), which is ionized by discharge. Noble gas laser is also called as noble gas ionic laser. Principle oscillation lines of Ar ion laser are in blue (488.0 nm) and green (514.5 nm). Principle oscillation lines of Kr ion laser are in the range of 450~670 nm [1]. Table  summarizes the media and the oscillation wavelengths for noble gas laser. Because the output power is relatively high (ca. 25 W for Ar ion laser), noble gas laser is widely employed for entertainment purposes such as laser show and laser display, processing, and researches [2]. However, the high power laser needs high current since the ionization of noble gas is necessary for the oscillation.

Table 4.2.1. Mediums and wavelengths of noble gas laser.
The numbers of emission lines are represented in ().

ion band wavelength
Ar+ ultraviolet
visible
infrared
275.4 – 390.8 nm (16)
408.9 – 528.7 nm (13)
1090 nm
Kr+ ultraviolet
visible
infrared
337.5 – 356.4 nm (3)
406.7 – 676.4 nm (13)
752.5 – 858.8 nm (5)

Reference and Links
[1] Lexel laser, “Tech info How gas-ion lasers work%3

4.2.3. HeCd Laser

Helium-cadmium (HeCd) laser is operated by discharge in He gas with vaporized (atomized) Cd, which is obtained by heating over 250 degrees Celsius [1, 2]. He atom plays a similar role in HeCd laser to HeNe laser. HeCd laser is identified as metal vapor laser in atomic gas laser. The oscillation lines are 325 nm and 442 nm in the CW operation. These two oscillation lines can be simultaneously output. The output power of these two lines are around 150 mW for 442 nm and around 40 mW for 325 nm. HeCd laser is mainly used for biotechnology researches and optical three-dimensional fabrication.

Copper vapor laser is also a metal vapor laser as well as HeCd laser. The copper vapor laser is operated by discharge in noble gas such as He, Ne, and Ar with vaporized copper via heating over 1500 degrees Celsius. The copper laser operates with pulsed oscillation at 511 nm and 578 nm lines. At a repetition rate of several tenth kHz, the average output power of several tenth W is obtained. However, because the operation cost is very expensive, the copper laser is replaced by solid-state laser and semiconducting laser, and is rarely used.
Reference and Links
[1] PLASMA JSC, HeCd lasers.
[2] KIMMON Koha Co., Ltd.,HeCd Laser Overview.

4.2.4. Excimer Laser

Excimer laser utilizes excimer as an oscillation medium. The excimer (abbreviated from excited dimer) is a coupling molecule out of an atom or a polyatom in the electronic excited state and an atom or a polyatom in the electronic ground state [1]. The excimer laser operates at the pulsed oscillation in the UV range. The excimer is given by discharge excitation of a gas mixture of noble gas (Ar, Kr, and Xe) and halogen (F, Cl, Br, and I) at a high pressure. The oscillation wavelength is tuned by changing the fraction of noble gas and halogen in the gas mixture. Table summarizes media and corresponding oscillation lines of excimer lasers currently available in the market. In typical excimer lasers, the pulse duration is around 30 nm, and the repetition rate is around 300 Hz [2-5].
Table: media and corresponding oscillation lines of excimer lasers available in the market

excimers wavelength
F2 157 nm
ArF 193 nm
KrCl 222 nm
KrF 248 nm
XeCl 308 nm
XeF 351 nm

The output power of excimer laser is the highest among UV lasers for processing. An average output power of 540 W and a pulse energy of 1 J at 600 Hz repetition rate are achieved [6]. However, the beam quality is not good and the beam is typically multimode, because laser light is output from the resonator after only a few round trips in the resonator since the excimer laser has a high gain. On the other hand, the speckle is ignorable since the coherence is low. Therefore, the excimer laser is typically used for uniformly illuminating a large region by using homogenized optics with fly eye lens [7]. In the industry, the excimer laser is used as a light source of a laser annealing apparatus for manufacturing flat panel display and a semiconductor exposure apparatus. The other uses are for research and development, and medical applications such as lasik surgery and ELCA.

Reference and Links
[1] N.G.Basov, et.al.,“ Laser operating in the vacuum region of the spectrum by excitation of liquid xenon with an electron beam, ” Zh.Eksp. Fiz.i Tekh. Pis’ma. Red.12,473(1970).
[2] MPB Communications Inc.
[3] Coherent Japan, Inc.
[4] GAM LASER Inc.
[5] LightMachinery Inc.
[6] Coherent Japan,Inc., LAMBDA SX 540C.
[7] Rainer Paetzel,“Comparison Excimer Laser – Solid State Laser,”Lambda Physik AG.

4.2.5. Carbon Dioxide Laser

The medium of carbon dioxide (CO2) laser is a gas mixture of helium, nitrogen, and carbon dioxide [1]. Nitrogen in the gas mixture plays the following three roles; Nitrogen gives energy to CO2 and excites CO2 to the pumping level; Nitrogen receives energy from CO2 and relaxes CO2 from the laser lower level to a far lower level; Nitrogen removes heat generated via discharge. CO2 laser is the most common in the industry, and is used for cutting, drilling, weld, and surface modification of metal and non-metal. CO2 laser with several kW to 20 kW output is used for processing. RF pumping system with sealed-off operation is widely adopted for 200 W output or less. In CO2 laser, the oscillation occurs between vibrational states of carbon dioxide molecules. The oscillation lines are in the far infrared region (9.2~10.8 µm), especially at 10.6 µm and 9.6 µm. Materials transmissive in the visible range, such as water and glass, exhibit a very large absorption coefficient in the wavelength range of 10 µm. Therefore, CO2 laser is used for processing of non-metalic materials such as paper and wood. CO2 laser is also used as a medical laser for dental cures and beauties (such as removing a mole).

Pumping method of CO2 laser
The medium for a CO2 laser is gas. It discharges by encapsulating the mixed gas of N2 and He in a Pyrex glass.
The CO2 molecule is a triatomic molecule that has oxygen molecules (O) on either side of a carbon molecule (C) positioned in a straight line, the distance between the carbon molecule and oxygen molecules are 0.116 nm. C and O is a covalent bond that shares electrons. When it comes to high temperature the O on the either side starts to vibrate. As shown in Fig. 4.2.3 this vibration has the following three types: symmetric stretching vibration, flexion movement and asymmetric stretching vibration. The differences in the three are the quantum number. They are each represented as (001), (010) and (100). Among these the bending vibration it can be considered that there are vibrations in two surfaces the plane of the paper and the plane perpendicular to the paper surface, this may be represented as (0100) or (0110). The excitation energy level is discrete and is quantized. An oscillation of 10.6 μm can be gained from the transition from (001) to (100), also an oscillation of 9.6 μm can be gained from the transition from (001) to (020).


Fig. 4.2.3. Vibration mode of CO2 molecules

Energy levels involved in CO2 laser oscillation are shown in Fig. 4.2.4. These levels as an electronic state are in a ground state and are in a low energy state. Vibrational excitation of CO2 is performed by energy transferring from N2 excited by electron impact. CO2 gains energy due to resonant excitation and is excited by N2. This is because N2’s vibrational level ν = 1(2330.7 cm-1) is in a metastable state, also energy levels are about the same as CO2’s (001) mode which causes the resonant excitation. There is also cases where the CO2 is directly excited by electron impact after which these become high level causing laser oscillation. The life span in the high level is approximately 1 ms and the life span in the low level is approximately 1/100 of that of the high level that also easily causes a population inversion.
fig.4.2.4

Fig. 4.2.4. Energy level diagram of the CO2 laser

Figure 4.2.5 shows the high level and low level of 10.6 μm in detail to the level of the rotational quantum number J. As shown in Fig 3 in CO2 many levels are neighbouring causing transition amongst the levels. This makes CO2 laser high efficient even though it is a gas laser. In the excitation process of CO2 the given energy is efficiently used for the high level excitation. Even if the energy is used for exciting unnecessarily high levels such as v=2, v=3 or (002), (003), it is eventually converted to the upper level of (001). For this reason, the CO2 laser’s electric energy to optical output energy conversion efficiency is 10 % ~ 30 %. This is by far one of the best amongst gas lasers.
fig.4.2.5

Fig. 4.2.5. Rotational energy level of 10.6 μm wavelength band

CO2 laser oscillator
After multiple discharges the gas deteriorates weakening the reaction. To avoid this thus increasing the oscillation efficiency the method of circulating fresh gas at high speed is used. The lasers which use this method are called fast axial flow type CO2 lasers. All high output power oscillators use this method.

Coaxial flow type laser
There are three directions to a CO2 laser: “the direction of the gas flow “, “the direction of the discharge” and “the direction to take out the light”. If these three are in the same direction it is called a coaxial flow type. The coaxial flow type has two sub types which are fast axial flow type and slow axial flow type. Figure 4.2.6 shows the pattern diagram of these two types. Among the slow axial flow type there are ones which encapsulate the gas and ones which circulates the gas at a slow speed (up to 20 m/s).

fig.4.2.6

Fig. 4.2.6. Schematic diagram for the fast axial flow type laser oscillator
and a low-speed axial flow type laser oscillator

3-axis orthogonal laser
As posed to the coaxial flow type oscillators which the “the direction of the gas flow “, “the direction of the discharge” and “the direction to take out the light” are the same, laser oscillators which these three directions are orthogonal are called 3-axis orthogonal laser oscillators (Fig. 4.2.7). Both coaxial flow type and 3-axis orthogonal type use a circulating blower for the circulation of gas.

fig.4.2.7

Fig. 4.2.7. Schematic diagram of a three-axis orthogonal laser oscillator

Reference and Links
[1] Patel,C.K.N.,“Continuous-Wave Laser Action on Vibrational-RotationalTransitions of CO2,” Physical Review 136 (5A): A1187- A1193 (1964).

4.2.6. Chemical Laser

Chemical laser utilizes chemical reaction for the pumping. Because the output power of chemical laser is relatively high compared with other lasers, chemical laser has been eagerly studied since 1970s with aiming at applications in nuclear fusion reactor, rocket propulsion, and ballistic missile defense. The most practical chemical laser is deuterium fluoride (DF) laser and chemical oxygen iodine laser (COIL). COIL was developed by the US. COIL has an output power of several megawatt and is being studied with expectation of a future application for ballistic missile defense. However, since the setup of COIL is large and a huge amount of halogen compounds are released via the chemical reaction, a bad influence on an ozone layer is taken care of. Even for the purpose of ballistic missile defense, an use of solid-state laser is considered. In order to oscillate COIL, basic hydrogen peroxide needs to be made up. But the production of basic hydrogen peroxide accompanies heating, therefore is required to be slowly done with using a cooling system. COIL is not yet realized for an industrial use.

In 2009, a chemical laser using amine-type all-gas-phase chemical iodine as a new type of chemical laser medium was realized in Japan.

4.3. Laser Diode

Although semiconducting laser employs solid as a laser medium, it is generally separated from solid-state laser since the pumping method and the energy level are totally different. Semiconducting laser is a kind of diode. A part of current travelling through a diode is converted to laser light. Therefore, semiconducting laser is called as diode laser or laser diode (LD). Figure 4.3.1 shows a schematic configuration of typical LD.

 Fig.4.3.1. Configuration of typical semiconductor laser.

Both edge faces of semiconductor are cleaved (cut along the crystal surface) orthogonally to the direction of light propagation, and the reflection at the interface between the air and the active layer emitting light results in the laser oscillation (LED does not have this resonator structure). This kind of LD is called as Fabry-Pelot LD. By producing a periodic structure close to the active layer, only a specific wavelength component is distributed and feedback, then a stabilized singlemode oscillation becomes possible (distributed feedback: DFB). DFB LD is mainly used for a long-distance optical communication. Because the length of LD itself is shorter than 1 mm, LD is generally mounted also for releasing heat.

For LD, the oscillation wavelength is tunable dependent on the type of compound semiconductor and the structure. LD can oscillate in the wide wavelength range from ultraviolet to near-infrared. LD is superior to other lasers in terms of size (compact), cost (cheap), and efficiency (~60 %). Relatively low-output LD is variously used in our life for pick-up devices in CD (780 nm), DVD (650-680 nm), and blu-ray disc (400-410 nm), laser printer (630-690 nm), laser pointer, and optical communication (1.3~1.6 µm). LD with an output of several W to several tenth W has been employed as excitation light sources of semiconductor pumping solid-state laser (808 and 914 nm) and fiber laser (915, 975, 980, and 1480 nm). Recently, LD in the blue (410 nm) and green (512 nm) have been developed a lot, and are being applied to a laser TV and a compact laser projector.

High-power LD with several hundreds W to several kW is used for processing such as laser weld, and is called as direct LD. The direct LD has a bad beam quality owing to its configuration, and is applicable to only limited cases. LD with several hundreds W has an array structure where a number (20~50) of high-power single emitter LD which are not mounted are one-dimensionally arranged in the range of around 1 cm. This array is called as LD bar or LD array. Structure that a number of LD bar are stacked with very  thin heat sink is called as LD stack. Generally, the number of stacking layers is 3~25, and the average output is several kW. The output of direct LD apparatus is reported to be 5 kW at maximum.

Details
[1] Laser Diode Selection

4.3.1. Future Generation

Surface emitting laser
The cleaved LD emits light from the edge face of semiconductor (edge face emitting laser), while some LD emits laser light orthogonally to the base. The latter is called as surface emitting laser or vertical cavity surface emitting laser (VCSEL). VCSEL was invented in 1977 by Iga, and the first oscillation was reported in 1979. VCSEL is low-cost since the cleavage is not necessary, and is used in laser printer, bar code, and mouse. The oscillation wavelengths are in the ranges of 850, 1310, and 1550 nm. VCSEL of 850 nm range oscillation (AlGaAs type) is utilized for short-distance optical communication and fast LAN. Wiih VCSEL of 1070 nm range oscillation (InGaAs type active layer), a direct modulation operation at 25 Gbps was reported in 2006 for data transmission of super computer. If surface emitting laser were available in the RGB, it could be applied to a new type of illumination and display.

Quantum dot laser
Quantum dot laser (QDL) utilizes quantum dot (suggested in 1982 by Arakawa and Sakaki), in which free electrons are confined in three-dimension by nanometer size semiconducting tiny crystal. QDL is expected as future generation optical communication laser because of the low consumption electric power, temperature independence, and fast modulability at 1310 nm. Recently, QDL has been studied a lot in the world. Optical communication at 25 Gbps has been demonstrated. 1.3 µm laser oscillation on silicon substrate at room temperature has been also realized.

Quantum cascade laser
Quantum cascade laser (QCL) is a type of LD which operates at and over the wavelength of 2 µm. QCL is a new type of LD employing intersubband transition, and has been eagerly studied since 1994 when J.Faist et al. from AT & T Inc. developed QCL. The oscillation wavelength at room temperature is in the range of 4 µm~13 µm. The CW output of several W is possible for QCL. However, because the wall-plug efficiency of QCL is relatively low compared with an usual LD, the thermal control is one of important factors for QCL. Applications of QCL are now considered in gas sensing, engine burning test, life science, and medical field.

Details
[1] Laser Diode Selection

4.4. Solid-state Laser

Table 4.4.1. Wavelength of solid-state lasers

Medium Popular name wavelength(μm) Specification
Cr:Al2O3 Ruby laser 0.69 the world first solid-state laser
Nd:YAG Neodium YAG laser 0.946(at low temperature)
1.06
1.07
1.11
1.12
1.31
1.33
1.35
1.83(at low temperature)
High power
multiple-wavelength oscillation
Nd:Phosphate glass Glass laser 1.054 High power
Nd:SiO2 Glass laser 1.062 High power
Nd:YLF Neodium YLF laser 1.047(π)
1.053(σ)
1.321(π)
1.313(σ)
Birefringence
NYAB 1.06 Second harmonic generation
Er:Glass Er fiber laser 1.52~1.57
1.59~1.60
Amplification for telecommunication
Ho:YAG Holmium YAG laser 2.09~2.10 Long wavelength
KCl:Li Color center laser 2.2~3.2(at low temperature) Tunable wavelength
Long wavelength
NaCl Color center laser 1.4~1.8 Tunable wavelength
Cr:BeAl2O3 Alexandrite laser 0.70~0.81 Tunable wavelength
High power
Long fluorescence liftime
Ti:Al2O3 Titanium sapphire laser 0.65~1.15 Tunable wavelength
High power
Broadband
Co:MgF2 1.63~2.50 Tunable wavelength
Broadband
Long wavelength

Laser medium of solid-state laser is rare-earth-doped crystal or glass. Solid-state laser can be compact and high-power. In order to form the inverse population in solid-state laser, a good heat resistance, and a small temperature-dependency are required for a laser medium.

The typical solid-state laser is Nd:YAG laser, in which trivalent Nd ion, Nd3+, is doped with YAG (Yttrium Aluminum Garnet: Y3Al5O12) crystal. Solid-state laser is optically pumped. The pumping light source is mostly LD. Before the improvements of output power, efficiency, and lifetime of LD, noble gas flash lamp was used since it is a low-cost and high-power light source. However, in the flash lamp pumping method, the emission spectrum covers a broad range from UV to IR, therefore does not have a good consistency with absorption spectrum of laser medium, resulting in a large thermal burden on the laser medium. On the other hand, for LD, the emission spectrum is narrow, therefore it is possible to selectively excite a specific absorption transition in a medium, then a high absorption efficiency can be realized. Additionally, because light emitted from LD is coherent, light can be tightly focused, then a high density pumping is possible.

Generally, a medium of solid-state laser has a rod shape and diode pumped solid-state (DPSS) laser is pumped by a method as shown in Fig. 4.4.1 below. Figure 4.4.1 (a) represents the LD side-pumping method, while Fig. 4.4.1 (b) shows the LD end-pumping method. For both of these methods, by inserting optical elements required in the resonator, an oscillating operation by Q-switching method or mode-locking method becomes possible. In a practical high-power solid-state laser, a cooling system or air-cooling or water-cooling is incorporated, and LD is often arranged in 3D.

 Fig. 4.4.1. Pumping methods for solid-state laser.
(a) LD side-pumping method, (b) LD end-pumping method

Details of DPSS lasers including Nd:YAG laser, Yb:YAG laser, and Ti:Sapphire laser are described in other pages. Table below compares the crystal properties for these DPSS lasers.

 Table 4.4.1. Comparison of the property on Nd:YAG, Yb:YAG, Ti:Sapphire crystals

crystals Nd:YAG Yb:YAG Ti:Sapphire
fluorescence lifetime(ms) 0.23 0.96 0.0032
stimulated-emission cross section(×10−20 cm-1 ) 20 to 30 2.1 30
luorescence wavelengths(nm) 1064 1030 660-1100
absorption wavelengths(nm) 808 941 514 to 532
fluorescence bands(full width at half maximum) (nm) 0.67 to 10 440
absorption bands(full width at half maximum) (nm) 1.9 >10 200
pumping quantum efficiency 0.76 0.91 0.55
saturation fluence(J/cm2) 0.67 9.2 0.9

4.4.1. Nd type Laser

In Nd:YAG laser, trivalent Nd ion, Nd3+, is doped in YAG. Nd:YAG laser is the most common high-power solid-state laser. This is because Nd3+ has energy level structure for four-level model and because YAG crystal is so superior to other laser materials in term of the thermal conductivity.

The pumping wavelength and the oscillation wavelength of Nd:YAG laser are 808 nm and 1064 nm, respectively. Arranging a number of rod media in the axial direction of the resonator enables several tenth kW CW oscillation. In fact, a number of companies has realized products of several kW Nd:YAG laser for weld of steel and aluminum. The output of a typical Nd:YAG laser is, however, at most several hundreds W. The typical repetition rate of Nd:YAG pulsed laser is in the range between several Hz and several kHz. At Q-switching operation, a high power pulse (several hundreds mJ) of a duration of 10 ns ~ 50 ns has been generated.

The second harmonic generation (532 nm), the third harmonic generation (355 nm), and the fourth harmonic generation (266 nm), all of which are generated via nonlinear optical effects, are frequently used. Nd:YLF (LiYF4)m Nd: YVO4, and Nd:glass are some of Nd types of DPSS laser other than Nd:YAG.

4.4.2. Yb type Laser

In Yb:YAG laser, trivalent Yb ion, Yb3+, is doped in YAG crystal. Yb:YAG laser is different from previous both four-level laser such as Nd:YAG and three-level laser, but is quasi-three-level laser. In Yb:YAG laser, (1) the high quantum efficiency enables highly-efficient CW laser, (2) the long fluorescence lifetime is advantageous for the Q-switching method and the pulsed amplification, (3) the wide fluorescence spectrum enables picosecond or short pulse generation and amplification. Yb:YAG laser has a lot of advantages over Nd:YAG laser.

 Fig. 4.4.2. Cross-sectinos of absorption and stimulated emission for Yb:YAG

Figure 4.4.2 shows absorption cross-section and stimulated emission cross-section for Yb:YAG laser. Figure 4.4.2 indicates that the pumping wavelength (941 nm) and the oscillation wavelength (1030 nm) for Yb:YAG laser are close each other. Because of this, the pumping quantum efficiency of 91.4 % is achieved, then the heating accompanying with the pumping is suppressed at 10 % or so on (1/3 to 1/4 of Nd:YAG). Therefore, the thermal stress in the crystal is hard to accumulate, and the cooling is easy.  Additionally, in Yb:YAG laser, because the energy loss by heat is low, the efficiency and output power is improved. In fact, by using Yb:YAG disk laser available in the market, an electric-optic conversion at an efficiency of around 20 % was realized (electric-optic conversion efficiency for LD pumped Nd:YAG laser is around 10 %).
In Yb:YAG crystal, Yb3+ (0.87 Å), the dopant ion, and Y3+ (0.90 Å) of YAG, the host material, have close ion radius (Nd3+ has about 1.5 times larger ion radius than Y3+). Therefore, Yb3+ can be doped at a high concentration (since concentration quenching hardly occurs), up to 100 %. The disadvantage of Yb:YAG laser is reabsorption loss (lower level loss), then is that high power pumping is necessary. In order to avoid these disadvantages, 1048 nm fluorescence peak where reabsorption loss is relatively small is pumped.

Stimulated emission cross-section for Yb:YAG laser is approximately 2×10cm2, which is one-order smaller than that of Nd:YAG laser. Since no parasitic oscillation occurs, great energy can be stored in a small volume. However, for extracting energy in pulsed operation, 10 times higher or more fluency is required compared with CW operation. In the case of pulsed amplification, optical damage can be an issue.

Quasi-three level model
A laser medium for quasi-three-level model satisfies E~kT in the four-level model shown here. At low temperature, the medium is for the four-level model because of E<<KT. By using the energy level diagram of Yb:YAG laser shown in Fig. 4.4.3, we describe quasi-three-level model.

 Fig. 4.4.3. Energy level diagram for Yb:YAG laser

Yb:YAG laser is composed of two simple electronic levels, 2F7/2 and 2F5/2. Each level has sublevels: 4 sublevels for 2F7/2 level due to crystalline field and 3 sublevel for 2F5/2 due to the Stark devision. The laser operates by using these sublevels. 0 cm-1 is the ground level, and 10327 cm-1 is the laser upper level. Because the energy level structure is such a simple, excitation state absorption where ion excited to the upper level of 2F5/2 absorbs light, and up-conversion hardly occur. However, Energy difference among sublevels due to Stark shift is several hundreds cm-1 for both of 2F7/2 and 2F5/2. At room temperature, thermally excited ions are distributed to all of sublevels, which are laser lower levels,  for the 2F7/2 level. Therefore, the inverse population is hardly formed. Ion in the laser lower level exhibits an effect of absorbing laser light. This effect is called as reabsorption or reabsorption loss of laser light. To overcome the reabsorption loss, the specialized cooling or the strong pumping was previously required. Nowadays, Yb:YAG laser is in common as disk laser, a kind of solid-state laser. In the following, the disk laser is briefly explained.

Disk laser
The disk laser was suggested by Adolf Giesen et al. from Stuttgart university in 1990s. For the disk laser, a very thin disk-like crystal (called as an active mirror) shown in Fig. 4.4.4 is used as a laser medium. Because the heat emission performance can be improved by increasing [surface area/volume] portion, the disk laser is often compared with fiber laser. As a laser medium for the disk laser, Yb:YAG or Yb:YVO4 is used. A typical thickness of the disk-like crystal is 100~200 µm, and the diameter is several mm. When the medium is fused with a cooling heat sink via indium, the heat generated from the laser medium disappears over the flat surface in one direction, and the temperature gradient in the laser crystal is almost uniform. Therefore, the thermal lensing effect is suppressed for the disk laser by one digit compared with the rod laser, then a stable and good beam quality is obtained.

 Fig. 4.4.4. Schematic configuration of disk laser

The rear surface of disk is treated by total refection coating for both pumping and laser light, while the top surface is treated by anti-reflection coating for both pumping and laser light. Because of the light reflection at the rear surface of disk, the pumping light penetrates twice through the disk with once irradiation. However, because the disk is thin, an irradiation of pumping light yields a low absorption efficiency. In order to compensate the low efficiency, a parabolic mirror is arranged at the opposite side to the incident beam, and the pumping of 8 or 16 passes are performed until the disk completely absorbs the pumping light. Then, for one disk, singlemode oscillation can be obtained at 500W output, and multimode oscillation can be obtained at 4 kW output. 16 kW output disk laser which integrates a number of multimode disk lasers is currently available in the market.

Mode-locked disk laser has been also eagerly studied. High power laser with several tenth W output with a subpicosecond duration and high average power laser with 140 W average output were reported. Femtosecond disk laser is also studied.

Table 4.4.2. Comparison of mediums of Yb lasers

Medium Stimulated-emission cross section
[10-20 cm2]
Fluorescence lifetime
[ms]
Thermal conductivity
[W/mK]
Fluorescence spectrum width
[nm]
Transform-limited pulse
[fs]
Experimental result
Pulse width
[fs]
Average output
[W]
YAG 2 0.95 11 9 120 340 0.11
136 0.003
730 16
810 60
KYW 3 0.7 3.3 24 50 71 0.12
KGW 3 0.7 3.3 25 47 112 0.2
176 1.1
glass 0.63 2 - 35 33 36 0.065
GdCOB 0.35 2.7 2.1 44 27 89 0.04
BOYS 0.2 2.5 1.8 60 19 69 0.08
86 0.3
YVO4 - 1.2 - - - 61 0.054
CaCdAlO4 0.55 - 6.9 - - 47 0.038

Reference and Links
[1] F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall: “Laser Demonstration of Yb3Al5O12(YbAG) and Materials Properties of Highly Doped Yb:YAG,” IEEE J. Quantum Electron, 37, 135-144 (2001).
[2] W.Koechner: “Solid-State Laser Engineering,” Springer, 78 (1999).

4.4.3. Ti:Sapphire Laser

Oscillation of Ti:Sapphire laser was first realized in 1982 by P.F.Moulton. Titanium sapphire (Ti:Al2O3 or Ti:Sapphire) crystal is synthesized by Ti3+ doping on sapphire crystal, which is also used as a base material for ruby laser (Cr:Al2O3 laser). Al2O3 is appropriate as a base material of high-repetition and high power laser since it has a good thermal conductivity. Instead of dye laser, Ti:Sapphire laser is widely used for a variety of research fields of femtosecond spectroscopy, nonlinear optics, white light generation, and terahertz generation.

Figure 4.4.5 shows an absorption spectrum and a fluorescence spectrum of Ti:Sapphire laser. Because the fluorescence spectrum of Al2O3 is very broad, Ti:Sapphire laser is tunable in the range of 660-1100 nm by an insertion of a wavelength selection device in the resonator. By mode-locking, the pulse duration of 5.5 fs has been realized. Nowadays, studies for a shorter duration is proceeded. For a typical Ti:Sapphire laser, the pulse duration is ~100 fs, the repetition rate is 70~80 MHz, and the average power is ~2.5 W.

 Fig. 4.4.5. Absorption and fluorescence spectra of Ti:Al2O3

The absorption spectrum is in the green range (the maximum at 488 nm), and the fluorescence lifetime is short and the stimulated emission cross-section is small. Therefore, intense pumping light with a good beam quality is necessary for laser oscillation. So, Ar ion laser or a second harmonic generation component of Nd:YAG, Nd:YLF, or Nd:YVO4 laser is used for the pumping, but not LD. This is a cause of instability of Ti:Sapphire laser. Recently, a direct pumping using LD has been considered.

Cr:Forsterite laser using Cr:Forsterite crystal is a near-infrared ultrashort pulsed laser which oscillates in the same manner with Ti:Sapphire laser. Cr:Forsterite laser is available in the market. Cr:LiSAF laser and Cr:LiCAF laser are also available. These laser are pumped by InGaAlP type LD (670 nm band).

Bulk-type mode-locking laser
A typical configuration of mode-locking titanium sapphire laser is Kerr-lens mode-locking (KLM) or self-mode-locking, both of which employs nonlinear optical effects, shown in Fig. 4.4.6. As well as typical solid-state lasers, laser light is oscillated and amplified via input of the pumping light in the resonator. The intense part of amplified laser light converges via the Kerr-lens effect induced in the medium (Intense light changes a refractive index of medium, then the medium turns to be like a lens). The intense part of laser light is selected by a slit, subsequently only intense pulses stably exist in the resonator. This is a generation mechanim of the ultrashort pulses. A couple of prisms in the resonator are used for compensating pulse elongation by temporal Kerr-effect (self phase modulation) induced in the laser medium. Chirped mirror can be also used instead of the prisms. Recently, by using semiconductor saturable absorber mirror (SESAM) but not KLM, a mode-locked laser has been realized.

 Fig. 4.4.6. Kerr-lens mode-locked Ti:Sapphire laser

4.5. Fiber Laser

For the bulk-type solid-state laser described above, a coupling between the pumping light and laser light is difficult, then a mode control is difficult. The output and the beam quality are lowered owing to an attachment of the grit and dust to mirrors and leses in the optical setup, and to an optical axis shift derived from thermal and mechanical changes influenced by the surrounding environments. In the high-power laser, thermal effects such as the thermal lensing effect and the thermal birefringence effect are remarkable, resulting in a drastic degradation of the beam quality. In order to avoid the thermal effects, cooling systems with a high cooling efficiency, such as active mirror type or split disk type, have been suggested. However, these cooling systems has a complex structure, and is not often used in industrial applications.

The fiber laser utilizes rare earth doped fiber as a laser medium. Although the fiber laser is one of solid-state lasers, the fiber laser and the bulk-type solid-state laser such as an Nd:YAG laser are, in general, separately discussed since the medium shapes are totally different. The fiber laser can be operated at both the CW and pulsed oscillations. The CW fiber laser is high-power, then is often employed for the ablation and the weld. The pulsed fiber laser is low-power, then is often used for the micro-processing and the marking.

Figure 4.5.1 represents a basic configuration of fiber laser. Figure 4.5.1 (a) shows a resonator configuration for Fabry-Pelot fiber laser, in which only a laser gain medium is an optical fiber, integrated with a spatial coupling device. The configuration shown in Fig. 4.5.1 (b) replaces mirrors in the configuration of Fig. 4.5.1 (a) by fiber Bragg gratings (FBGs). Fig. 4.5.1 (c) represents a ring-type fiber laser. Thus, constituent elements for the fiber laser are the same as the elements used in the bulk-type solid-state laser, but it is possible to reduce the number of elements by replacing the bulk-type resonator constituent elements by inline elements. For the previous bulk-type laser resonator, the alignment of resonator is complex, and the construction of laser oscillator requires sufficient experiences and construction time for the user. On the other hand, for the fiber laser, a modularized optical fiber (communication) technique can be used, therefore it is easy to construct the stable laser oscillator without special techniques.

 Fig. 4.5.1. Basic configuration of fiber laser. (a) Fabry-Pelot resonator (spatial-coupling type),
(b) Fabry-Pelot resonator (all-fiber type) and (c) ring resonator (all-fiber type)

 As a fiber laser, erbium (Er) doped fiber laser for optical communication range (1.5 µm) was first practically used. In 1985, a technique for manufacturing a low-loss silica glass singlemode fiber was established by the modified vapor deposition (MVCD) method. In 1987, a low-noise Er-doped fiber amplifier (EDFA) applicable for the 1.54 µm range where the loss of silica glass fiber is the smallest was developed. Then, the direct amplification of optical signal became possible without using the photoelectric conversion. The development of EDFA activated a market of the optical communication, diffused InGaAs-type LD and improved its performance, and rapidly brought forward the research and development of optical fiber laser amplifier.

As a high-power fiber laser used for applications other than the optical communication, the Nd doped fiber laser (Nd fiber laser) was first developed. In 1988, an Nd fiber laser with the clad pumping was developed and changed the previous idea of pumping (the core pumping was only possible previously). As a result, the output of CW fiber laser was dramatically incremented. In the clad pumping Nd fiber, the CW output of 100 W in 1999 and 1 kW in 2002 was realized. Recently, as a high-power laser with relatively higher performance compared to the Nd-doped medium, ytterbium doped fiber laser (Yb fiber laser) has been eagerly studied. Yb doped fiber laser oscillates in the range of 1030~1100 nm. The CW output of 2 kW in 2005, 6 kW in 2008, and 10 kW in 2009, and the multimode output of 50 kW in 2009 were realized for Yb-doped singlemode fiber laser. The transition history of CW output of the Yb-doped singlemode fiber laser is shown in Fig. 4.5.2.

 Fig. 4.5.2. Time dependency of CW output for Yb-doped singlemode fiber laser.

Because the fiber laser has a very good beam quality, the fiber laser is becoming dominant in uses for industrial applications such as scission processing, marking, and remote weld. For the range of 2 µm, thulium doped fiber laser (Tm fiber laser) has been recently studied. The Tm-doped fiber laser is now considered to be used for applications to medical devices and special processing since it operates in the eye-safe wavelength range.

The pulse duration of a typical ultrashort pulsed fiber laser is in the range of several ps ~ 100 fs, but a fiber laser with a pulse duration shorter than 100 fs is also being studied. The fiber laser with 25 fs pulse duration is commercially available. The femtosecond fiber laser is more compact and stable than the other types of femtosecond lasers, and is expected as an alternative to the titanium sapphire laser.

4.6. Wavelength-tunable Laser

The table 4.6.1 shows the various wavelength-tunable lasers and tunable bandwidth. The shown wavelength-tunable lasers are gas lasers, liquid lasers, solid lasers, and laser diodes excluding free-electron lasers possessing totally different principle.

Table. 4.6.1. Various wavelength-tunable laser

Sort Material Wavelength (nm)
Gas CO2 9000-11000
Liquid Rhodamine (dye) 560-650
Solid Tm:YAG 1800-2200
Ti:Sapphire 660-1180
Alexandrite 700-858
Semiconductor GaInAsP 1200-1550
AlGaAs 700-1000
AlGaInP 580-690
InGaN 380-460

In the wavelength-tunable laser of solid-state laser, prism and grating are used to tune the oscillation wavelength.
In the wavelength tunable laser of laser diode, two methods are used to obtain a certain wavelength as below.
・Using a diffraction by grating
・Changing the refractive index of a semiconductor by tuning a temperature by current or heater