Overview of the Thesis

After introducing the motivation, the thesis starts with a review of the basic concepts of solid-state Raman lasers including Raman scattering principle, Raman media, solid-state intracavity Raman laser configuration, modeling investigation of Q-switched intracavity Raman laser, and spectral coverage of solid-state Raman laser in the Chapter 2.

In recent years, employing a composite crystal with nonabsorbing undoped end has been regarded as a promising method for reducing thermal lensing effect. In the Chapter 3, we introduce thermal lensing effect and first study the comparison of thermal lensing effects between conventional, single-end composite, and double-end composite Nd:YVO4 crystals for 1064- and 1342-nm transitions by measuring the effective focal lengths of thermal lens. The efficient improvement of thermal lensing effect in a composite Nd:YVO4 crystal with double 2.1-mm-long ends for 1342-nm transition is confirmed.

The improvement of thermal effects in gain medium is critically important for developing self-Raman solid-state lasers because the Raman gain coefficient decreases substantially with increasing temperature above room temperature. In the Chapter 4, we design a original double-end composite Nd:YVO4 crystal and first use composite crystal as a self-Raman medium to demonstrate a compact efficient actively Q-switched eye-safe laser at 1525 nm. Moreover, an efficient Q-switched dual-wavelength laser at 1176 and 559 nm with self-Raman frequency conversion in

the double-end composite Nd:YVO4 crystal and intracavity sum-frequency generation in BBO is demonstrated.

However, the optimization of self-Raman laser is restricted because the laser gain medium simultaneously serves as a Raman medium. In the Chapter 5, we first use a new design of actively Q-switched 1176-nm Nd:YVO4 laser with an intracavity YVO4

crystal as a Raman medium for improving the laser performance of 1176-nm self-Raman laser with a conventional Nd:YVO4. In next section, by using a similar laser cavity with another laser gain medium Nd:YAG with better thermal property and longer fluorescence lifetime, the laser performance is further improved. The comparison of 1176-nm Raman laser performance between Nd:YVO4 self-Raman laser, Nd:YVO4/YVO4 Raman laser, and Nd:YAG/YVO4 Raman laser with conventional crystal is discussed.

In the Chapter 6, KTP and KTA crystals with low Raman shifts at 270 and 235 cm^-1 are employed to product multi-frequency radiation with cascade SRS, respectively. In addition, we observe interesting transverse wave patterns of SRS and conical SHG in cascade Raman lasers with intracavity SHG.

Although the conversion efficiency of noncollinear conical SHG is substantially lower than collinear axial SHG, there are interesting research topics about noncollinear conical SHG. The Chapter 7 starts with introducing the generation of conical SHG. In the next section, we show the interesting near- and far-field patterns of conical SHG in a frequency-doubled Nd:YVO4 self-Raman laser with intracavity SHG in a KTP crystal. Moreover, we use a GdCOB crystal with extended defects in a

Q-switched Nd:YAG laser to efficiently generate conical SHG. The near-field wave patterns include chaotic wave, quasi-Bessel beam, and symmetry-breaking Bessel beam patterns. The transverse disordered wave patterns are associated with a superposition of a number of monochromatic plane waves with different directions and phases. Furthermore, the near- and far-field patterns of frequency-doubled Q-switched Nd:YAG laser with intracavity BBO as SHG crystal are shown. Finally, the proceeding work and future work are discussed in the Chapter 8.

Stimulated Raman Scattering

2.1 Raman Scattering

Spontaneous Raman scattering effect was first discovered by C. V. Raman in 1928 [1]. As illustrated in Fig. 2-1, an incident light illuminated a medium sample which can be a solid, liquid, or gas, and the scattered light is observed spectroscopically. A difference in frequency between incident and scattered monochromatic light was observed and it is dependent of the properties of molecular, not incident light. Raman and Krishnan had observed scattered light with smaller frequency in sixty kinds of liquids and vapors [2]. They confirm that the scattered light is a secondary form of scattering, not fluorescent, due to its relatively high intensity and polarization.

Raman scattering is a χ ⁽³⁾, nonlinear inelastic light scattering process in which an incident photon interacts with a molecule of Raman medium. An incident photon is absorbed by a molecule of Raman medium and then emits a photon called Stokes photon with a lower energy as shown in Fig. 2-1(a). The Stokes shift leaves Raman medium in excited state. If the material is already in an excited state, then the scattered photon can be higher in energy called anti-Stokes photon as shown in Fig.

2-1(b). The anti-Stokes shift leaves Raman medium in ground state. The energy and momentum conversion are applied:

(2-1)

S p R

ω = ω ± ω

= = =

(2-2)

in which ħ, ω, and k are the Planck’s constant, angular frequency, and wavevector, and the subscripts S, p, R refer to the scattered photon, incident pump photon, and the phonon created or annihilated in the scattering process, respectively. The energy difference (ħωR) between the incident photon and the scattered photon matches the rotation/vibration energy of a molecule in gas or liquid, or the phonon energy of a solid Raman medium. The wavelength of Stokes component is shifted to a longer wavelength than incident wavelength. One the other hand, the wavelength of anti-Stokes component is shifted to a shorter wavelength.

( ) a ω_S =ω_p −ω_R=> Stokes shift

ωp

=

medium

ωR

= ωS

=

S p R

ω =ω −ω

( ) anti-Stokes b ω_S =ω_p +ω_R ⇒ shift

ωS

=

medium

ωp

=

ωR

=

S p R

ω =ω +ω

Fig. 2-1. Spontaneous Raman scattering with (a) Stokes photon generation (ωS < ωp) and (b) anti-Stokes photon generation (ωS > ωp)

The number of anti-Stokes photon is typically much smaller than the Stokes photon resulted from the smaller population of the excited state compared to ground state in the thermal equilibrium by the Boltzmann factor exp(-(ħω/kBT)), where kB is

S p R

k =k ±k

the Boltzmann constant and T is the temperature.

Stimulated Raman scattering (SRS) occurs when the intensity of the incident light is increased and then the scattered Raman field is enhanced. SRS was discovered by Woodbury and Ng in 1962 [3]. A near-infrared component at 766 nm was detected in the laser output of 694-nm Q-switched ruby laser with a nitrobenzene Kerr cell. The frequency shift coincides with the vibration frequency of the strongest Raman shift of nitrobenzene. Woodbury and Ng confirmed that the near-infrared component is resulted from SRS. As shown in Fig. 2-2, with both pump laser and Stokes photons illuminating on Raman medium, the medium experiences a transition from ground state Ei to virtual level and is left in the excited state Ef. As in spontaneous Raman scattering, the energy difference (ħωR) coincide the properties of Raman medium expressed by:

(2-3)

ωp

= 2=ω_s

ωR

= Ei

Ef

ωs

= ωp

= 2=ω_s

ωR

= Ei

Ef

ωs

=

Fig. 2-2. Energy level diagram for Stimulated Raman scattering

( )

R Ef Ei p S

ω = − = ω −ω

= =

SRS results in a stimulation of an additional Stokes photon coherent with the incident Stokes photons. Therefore SRS can generate more intense coherent radiation at new frequency. Stimulated Raman scattering (SRS) is an efficient and practical method of frequency conversion based on a third-order nonlinear optical process. If the intensity of incident light is sufficiently high, then the nonlinear optical phenomena occur. The induced polarization per unit volume P in a medium depends on the amplitude of the electric field of incident light E and can be expanded in a series of power of E:

(2-4)

where ε₀ is the dielectric constant, χ⁽¹⁾ is the linear optical susceptibility and χ⁽²⁾, χ⁽³⁾ are the second-, third-order nonlinear optical susceptibility of the medium. The nonlinear polarization terms become more and more significant with increasing the amplitude of the electric field. The term containing χ⁽²⁾ is responsible for second-order nonlinear optical effect including second harmonic generation (SHG), sum frequency generation (SFG), difference frequency generation (DFG), and optical parametric amplification (OPO). The term containing χ⁽³⁾ is responsible for third-order nonlinear optical effect including SRS, stimulated Rayleigh scattering, stimulated Brillouin scattering, self-focusing, self-mode-locking. The phenomenon of competition between SRS and self-focusing usually occurs in a high-power intracavity Raman laser.

Therefore the optimum mode size in the self-Raman medium is subject to a compromise between lowering the SRS threshold and avoiding optical damage induced by self-focusing [4]

2 3

(1) (2) (3)

O O O

P=ε χ ⋅ +E ε χ ⋅ E +ε χ ⋅ E +"

If the intensity of first-Stokes photon is sufficiently high, then it can act as a pump source for the second-Stokes photon. Therefore the second-Stokes component will be generated and possibly higher order as shown in Fig. 2-3. The energy conversion for n^th-order Stokes emission is applied:

(2-5)

The n^th-order Stokes wavelength λs(n) is expressed by:

(2-6)

where λp is the incident pump wavelength, νR=ωR /c is the Raman shift of Raman medium, and c is the light speed in Raman medium. With a suitable output coupler whose coating is designed to suit the Stokes wavelengths, the qusi-continuous tunable Raman laser could be achieved by using a Raman medium with a low Raman shift.

1

Fig. 2-3. Energy level diagram for high-order Raman emission

( )

2.2 Raman Media

Spontaneous Raman scattering was discovered by Raman in 1928 and was widely applied in spectroscopy. In 1962, the first observation of SRS was made after the discovery of laser which can provide the high peak powers required for SRS. Raman media include liquids, gases, and solids. In 1963, the crystalline Raman media including diamond (C), calcite (CaCO3) and α-sulfur (S) were used for frequency conversion and the properties are summarized in table 2-1 [5]. Although SRS in crystalline media has been proposed for over 40 years, there has been a resurgence of interest in solid-state Raman lasers due to the discovery and development of new Raman crystals. In particular, the high conversion efficiency up to 77% was demonstrated by use of LiIO3 Raman crystal in arclamp pumped Nd:YALO laser in 1977 [6]. Currently, the crystals commonly used for SRS are LiIO3, Ba(NO3)2, BaWO4, KGd(WO4)2, and PbWO4 listed in table 2-2 [7-11].

Table 2-1. Spectroscopic characteristics of Raman-active materials diamond, calcite, and α-sulfur [5].

Raman crystals with good thermal and mechanical properties, high Raman gain, high optical damage threshold, high transmission at the pump and Stokes wavelengths have considerable potential for frequency conversion of SRS. The thermal properties are important because the heat generated through inelastic SRS process is accumulated in a Raman crystal. In high-power operation, the thermal effects become critical issues for the SRS process and the property of high damage threshold is helpful for practical purposes. Higher Raman gain corresponds with a lower SRS threshold. The higher transmission at the pump and Stokes wavelengths results in less cavity loss.

Table 2-2. Spectroscopic characteristics of the Raman-active materials LiIO3, Ba(NO3)2, BaWO4, KGd(WO4)2, and PbWO4 [7-11].

Recently, potassium titanyl phosphate (KTP), rubidium titanyl phosphate (RTP), and potassium titanyle arsenate (KTA) which are widely recognized as prominent

nonlinear optical crystals involving nonlinear optical susceptibility χ⁽²⁾ have been experimentally confirmed to be practical SRS converter devices [12-16]. It has been demonstrated that the low value of the KTP-related Stokes shift (270 cm^-1) [17] and KTA-related Stokes shift (234 and 671 cm^-1) [18] permit generation of multi-frequency radiation with cascade SRS [12, 19-20]. The Raman spectrum of RTP measured by Carvajal shows the dominant RTP Stokes shift at 260 cm^-1 [21]. Our own measured spontaneous Raman spectra of KTP, RTP, and KTA crystals are shown in Fig 2.4 and their Raman shift (Stokes shift) and Raman linwidth are summarized in table 2-4. Our measured results are consistent with Raman spectra reported in Ref. [17, 18, and 21].

Raman shift (cm^-1)

100 200 300 400 500 600 700 800 900

Intensity (arb. units)

Raman frequency shift (cm^-1)

100 200 300 400 500 600 700 800 900

Intensity (arb. units)

Raman frequency shift (cm^-1)

100 200 300 400 500 600 700 800 900

Intensity (arb. units)

Fig. 2-4. Spontaneous Raman spectrum of (a) KTP (b) RTP and (c) KTA

4.7

Raman linewidth (cm^-1) Raman shift (cm^-1)

Raman linewidth (cm^-1) Raman shift (cm^-1)

Material

Table 2-3. Measured characteristics of the Raman-active materials KTP, RTP and KTA.

Nd-doped YVO4 and GdVO4 crystals have been identified as useful materials for diode-pumped solid-state lasers due to its high absorption coefficient and large thermal conductively [22-25]. In 2001, it was predicted that the new Raman crystals yttrium othovanadate (YVO4) and gadolinium othovanadate (GdVO4) would be promising Raman media [26]. Therefore, YVO4 and GdVO4 crystals become highly attractive self-Raman laser media based on combinations of their stimulated-emission and SRS properties. The Raman gain coefficients of YVO4 and GdVO4 crystals at the most intense peaks 890 and 882 cm^-1, respectively, were found to be greater than 4.5 cm/GW with a linewidth around 3 cm^-1 summarized in table 2-4 [26]. In addition, our

own measured spontaneous Raman spectra of YVO4 and GdVO4 crystals are shown in Fig 2.5 and their Raman shift and Raman linwidth are summarized in table 2-5. Our measured results agree with that reported in Ref. [26].

Damage

Table 2-4. Summary characteristics of the Raman-active materials YVO4, and GdVO4 [26].

Raman shift (cm^-1)

200 300 400 500 600 700 800 900 1000

Intensity (arb. units)

200 300 400 500 600 700 800 900 1000

Intensity (arb. units)

26

Raman linewidth (cm^-1) Raman shift (cm^-1)

Raman linewidth (cm^-1) Raman shift (cm^-1)

Material

Table 2-5. Measured characteristics of the Raman-active materials YVO4, and GdVO4.

2.2.1 Raman Gain Coefficient

Raman gain of crystal Raman medium is proportional to the exponential of Raman crystal length and Raman gain coefficient. For a single-pass Raman generator, the pump laser is spontaneously scattered to be amplified scattered Stokes light after passing through a Raman medium. The Stokes intensity grows as [27]

(2-7)

where l is the Raman crystal length, Is(0) is the Stokes intensity at the crystal surface, Ip is the pump intensity, and gS is the Raman gain coefficient which is given by

(2-8)

where λp and λS is the pump and Stokes wavelength, respectively, N is the number density of molecules, dσ/dΩ is the Raman scattering cross section, ΔνR is the half-maximum Raman linewidth, ħ is the Planck’s constant, c is the velocity of light

2

in vacuum, nS is the refractive index of Raman medium at λS. Raman gain coefficient is proportional to the Raman scattering cross section and is inversely proportional to the Raman linewidth. In addition, Raman gain coefficient decreases substantially with increasing temperature above room temperature [28]. For example, the Raman spectra of silicon crystal for various temperatures are shown as Fig. 2-6 [29].

Fig. 2-6. Raman spectra of silicon crystal [29]

2.3 Solid-State Raman Laser Configuration

Solid-state Raman lasers have been realized in Raman generation, extracavity, intracavity, and coupled cavity configurations [30-33]. In our experiments, we use diode-end-pumped intracavity configuration in which the pump laser and Raman crystal are placed in the same cavity as shown in Fig. 2-7. The configuration of diode-pumped solid-state intracavity Raman laser has advantages on compactness, low SRS threshold, and high efficiency. If the laser crystal can simultaneously serve as a Raman crystal, the intravavity self-Raman laser without an additional Raman crystal is more compact. The Q-switch device (acousto-optic or electro-optic) is used to generate high peak power pulse to reach the SRS threshold. The front mirror has high-reflection coating at the fundamental and Stokes wavelengths and high-transmission coating at the diode wavelength. The output coupler is designed to suit the lasing Stokes wavelengths with high-reflection coating (high-Q) at fundamental wavelength and partial-reflection coating at lasing Stokes wavelength.

Diode pump

Raman crystal Laser

crystal Q-switch

Fig. 2-7. Schematic diagram of a diode-pumped solid-state intracavity Raman laser.

Combining SRS with SHG or SFG can generate the solid-state laser source at new wavelengths in the spectral range of visible and UV light [33]. The diode-end-pumped solid-state laser with intracavity SRS and SHG/SFG we used in our experiments is shown as Fig. 2-8. The front mirror has high-reflection coating at the fundamental, Stokes, and SHG/SFG wavelengths and high-transmission coating at the diode wavelength. The output coupler is designed to suit the SHG/SFG wavelengths with high-reflection coating (high-Q) at fundamental and Stokes wavelengths and partial-reflection coating at SHG/SFG wavelength.

Diode pump

Raman crystal Laser

crystal Q-switch

SHG/SFG crystal

Fig. 2-8. Schematic diagram of a diode-pumped solid-state laser with intracavity SRS and SHG or SFG.

The mode size of laser beam is designed to lower the SRS threshold, maximize the conversion efficiency, and avoid optical damage induced by self-focusing.

However, for self-Raman laser, the optimum mode size in the self-Raman medium is subject to a compromise between maximizing the conversion efficiency and avoiding optical damage induced by self-focusing [34].

2.4 Modeling Investigation of Q-Switched Intracavity Raman Laser

In Q-switched operation, the rate equations for intracavity Raman laser at first-Stokes wavelength can be expressed by [35, 36]

(2.4.1)

(2.4.2)

(2.4.3)

(2.4.4)

, where n is the population inversion density of laser medium and σ is the stimulated emission cross section of the laser medium. φL and φRn are the intracavity photon density of fundamental and n^th-Stokes photons inside the laser cavity, respectively.

tRT=2lC /c is the round-trip transit time in the cavity of optical length lc, c is the light speed in vacuum, γ is the inversion-reduction factor, tL=tRT/(LL-ln(RL)) and tRn=tRT/(LRn-ln(RRn)) are intracavity lifetimes of the fundamental and n^th-Stokes photons, respectively. RL, RRn and LL, LRn are the reflectivities of output coupler and loss inside the cavity at fundamental and n^th-Stokes wavelengths, respectively. lL and lR are the lengths of laser and Raman medium, respectively. gRn is the Raman gain

L

coefficient of n^th-Stokes component , h is the Plank constant, and vRn is the frequency of n^th-Stokes photon. When pump energy is sufficient to reach Raman gain, it is rapidly converted to the first-Stokes pulse. Stokes pulse with is often much shorter than the fundamental pulse. The second-Stokes pulse can be produced as the intensity of first-Stokes pulse is sufficient to pump it, and possibly higher-order.

The energy of Raman laser can be obtain by integrating the output power over time as follows [36]

(2.4.5)

where tRn is the Raman pulse duration and S is the cross section of Raman beam in the cavity. The Raman pulse with is the same as the width of Stokes photon density φRn.

Rn Rn

Rn

Rn out Rn

Rn

0 0

S 1

ln( )

2 R

t t

E =

∫

P dt= chv

∫

ϕ dt

2.5 The Most Common Spectral Coverage of Solid-State Raman Laser

2.5.1 Infrared Raman laser

The output wavelength of Raman laser is determined by the wavelength of the fundamental pump laser and the Raman spectrum of the Raman medium. Most solid-state Raman lasers have been pumped by Nd lasers operating at fundamental wavelength near 1.06 or 1.32 μm. For Nd-doped Raman laser with commonly used Raman crystal (Raman shift: 800-900 cm^-1) such as Ba(NO3)2 [37], Ba(WO4)2 [38], KGd(WO4)2 [39] and so on, the spectral coverage from 1.1 to 1.3 μm and from 1.4 to 1.55 μm can be achieved with the fundamental wavelength near 1.06 and 1.32 μm, respectively. Since water absorption in eye tissue and the intraocular fluid prevents light in the spectral range of 1.4-1.8 μm from reaching the retina as shown in Fig.

2-9(d), there is a considerable interest in compact laser source with wavelengths in this eye-safe regime. The applications of eye-safe lasers include remote-sensing, atmospheric science, and laser range-finder, etc..

The radiation with wavelengths shorter than 315 nm and greater than 1.9 μm is completely absorbed by the cornea of the eye as shown in Fig. 2-9(a). The radiation between 315 and 400 nm is absorbed at the lens as shown in Fig. 2-9(b). The radiation between 400 to 700 nm is focused on the retina and represents the greatest hazard.

The radiation between 700 to 1400 nm is partially absorbed before it reaches the retina as shown in Fig. 2-9(c). As shown in Fig. 2-9(d), the radiation between 1.4-1.8 μm is absorbed by the cornea and aqueous humor and it can not reach the retina.

Fig. 2-9. Spectral transmission characteristics of a human eye exposed to laser radiation with wavelength (a) below 345 nm (b) between 315 to 400 nm (c) between 400 to 1400 nm and (d) above 1400 nm [40]

2.5.2 Visible/Ultraviolet Raman Laser

Combining SRS with SHG or SFG, the new laser sources in the spectral region of visible and UV light have been successfully generated as shown in Fig. 2.10 [33].

More interestingly and importantly, yellow lights are useful for biomedicine, ophthalmology, dermatology, and laser guide stars. The applications of visible and ultraviolet lasers include laser bathymetry, underwater detection, and biological detection.

Fundamental

ν₀+ν₁

ν₀ ν₁ ν₂

1^st Stokes 2^ndStokes

2ν₀ 2ν₁ ν₁+ν₂ 2ν₂ ν₂+ν₃ SHG SFG SHG SFG SHG SFG

ν₀+ν₁

ν₀ ν₁ ν₂

1^st Stokes 2^ndStokes

1^st Stokes 2^ndStokes

在文檔中 腔內非線性光學之波長轉換與斑圖形成 (頁 20-0)