K T P OPO 110 <^,800-

çS

R ound trip loss e=0.2

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10 15 20 25 30 35

Crystal length. L, (mm)

Figure 5.2: Pum p threshold of K T P OPOs as a function of crystal length.

5.1.2 B eam focusing

D a m a g e th re s h o ld a n d fo c u sin g lim ita tio n : The surface dam age threshold of K TP is pulse duration dependent [1] as it has been mentioned in C hapter 3. For a high efficiency O PO, any surface dam age to the K TP is in fact norm ally caused by the signal wave intensity rather than pum p, due to resonant enhancem ent of the signal wa.ve intensity inside the OPO cavity. For example, when an OPO is formed with a 20% output coupler, and operates at 30% conversion efficiency, then the circulating signal wave intensity inside the OPO will be 1.5 times higher than the pum p intensity, if one assumes equal spot sizes of pum p and signal beams. In practice, both beam intensities m ust be limited to below the dam age threshold. From our experim ental experience, the pum p intensity should be kept below 600 M W /cm ^. Therefore, for the case of the EO Q-switched laser pum ped O PO, (where the m axim um o utput power is 6 m J within a 10 ns pulse w idth, the corresponding peak power being 600 kW ), the lim itation on the focused pump waist size is 0 .1 8 m m ; and it is 0 .0 4 m m for the case of using the AO Q-switched laser (where the maxim um pum p peak power is 30 kW ).

O p tim u m fo c u sin g a n d h*.„i(^,5) fu n c tio n : The m atching of the ])ump and signal beam s to enal)le the greatest power transfer from the punq) to the signal and idler waves

CHAPTER 5. K T P OPO 111

is very im portant in a param etric interaction process, and can be m easured l)y the op- tim izable param eter /i*. as introduced and described in C hapter 2. The param eter is a function of beam focusing and double refraction, and has a single m axim um at the point of optim um focusing, ^ra- The value of h*. can be numerically calculated from Eq.(2.107) for a forward-going pum p and from Eq.(2.114) for a backward-going pum p.

Figs. 5.3 and 5.4 show how the function in a K TP OPO varies as a function of beam focusing for the forward-going pum p in both NCPM and CPM geom etries, where the subscript m denotes tha t hg has been m aximized with respect to the phase-m ism atch

Aklc, where the crystal length C was chosen to be 25 mm; where and are focusing param eters of signal and pum p waves, and B represents the walk-off param eter (B = 0 in the NCPM K TP O PO , B —6.6 in the CPM K TP O PO .); and where k is the ratio of wave num bers, k= kp/kg (A— 1.487 in the NCPM K TP OPO, A:=1.651 in the CPM K T P O PO .). For the NCPM K TP OPO, the m axim um value o f i s 0.3, as shown in Fig. 5.2, which appears at (p « 2.8, ^,s ~ 2.8; the corresponding beam spot sizes for pum p and signal are; w^p = 0.029 m m, lOos ~ 0.035 mm. For the CPM K TP O PO , the m axim um value of is 0.0326, which is nea,rly a factor of 10 less than th a t of the NCPM case and, as shown in Fig. 5.3, it appears at ^p % 1.0, is %1.33; the corresponding beam spot sizes are:

Wap — 0.049 mm, Wag = 0.054 mm. Therefore, although the CPM K T P OPO allows the use of long crystal, the much lower m eans poor mode m atching exists and therefore less power transfer from pum p to signal. The difference between (N C PM ) and (C PM ) is reduced in the case of less tight focusing. For example, when (p = & = 0.1 , the value of /?+,, is 0.048 in the NCPM K TP O PO , and it is 0.0146 in the CPM K TP OPO . Similarly, the variation in as a function of focusing param eters in a backward-going pum p for both the NCPM and CPM K TP OPOs, are shown in Figs. 5.5 and 5.6. The curves in the two hgures show similar high values, indicating th at hj,,, is largely de])endent on the divergent backward-going pum p, and not the walk-off in the (T M K TP OPO. The m axim um is around 0.2 (appears at is % ip %1), this value being less than th at of the forward-going pum p for the NCPM K T P OPO, but much larger th an th a t of the forward-going pum p for the CPM K TP OPO. According to Eq.(2.117) given in C hapter 2, (the expression for pum p threshold of a double-pass-pum ped O PO ), the much larger value of in com parison with for the CPM K TP OPO, promises a more than factor of 2 reduction in pum p threshold when double-pa„ss-pump configuration is employed.

CHAPTER. 5. K T P OPO 112 1

.

Figure 5.3; Variation of as a function of and with the jiaraineter of for the NCPM K TP OPO and in a forward-going pum p, where lc—25 nun.

1 .0 -I B=6.6, K= 1.651 0

.

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.

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Figure 5.4: Variation of as a function of and with the pa.rameter of for the CPM K TP OPO and a forward-going pum p, where lc=25 mm.

CHAPTER 5. KTP OPO 113