Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Threshold studies of pulsed confocal unstable optical parametric oscillators

Mali Gong, Shanshan Zou, Gang Chen, Ping Yan, Qiang Liu, and Lei Huang

Open Access Open Access

Abstract

A theoretical threshold model based on the spherical wave assumption for a pulsed double-pass pumped singly resonant confocal positive-branch unstable optical parametric oscillator (OPO) has been proposed. It is demonstrated that this model is also applicable to the plane-parallel resonator in the special case. The OPO threshold as a function of important parameters such as the cavity magnification factor, cavity physical length, crystal length, pump pulsewidth, output coupler reflectance and crystal position inside the resonator has been presented. Experimental data show the good agreement with the results obtained from the theoretical model.

©2004 Optical Society of America

Full Article  |  PDF Article
More Like This
Low threshold characteristic of pulsed confocal unstable optical parametric oscillators with Gaussian reflectivity mirrors

Shanshan Zou, Mali Gong, Qiang Liu, and Gang Chen
Opt. Express 13(3) 776-788 (2005)

Theoretical models and analytic expressions for buildup time of pulsed confocal unstable optical parametric oscillators with uniform or Gaussian reflectivity mirrors

Shanshan Zou, Mali Gong, Qiang Liu, Ping Yan, and Gang Chen
Appl. Opt. 44(30) 6456-6461 (2005)

Studies of two-species Bose-Einstein condensation

R. Ejnisman, H. Pu, Y. E. Young, N. P. Bigelow, and C. K. Law
Opt. Express 2(8) 330-337 (1998)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)
Fig. 1.
Fig. 1. Confocal unstable singly resonant OPO. The Input Mirror M1 is a concave mirror, which is highly reflecting at the signal wavelength and highly transmitting at the pump and idler wavelengths. The output coupler M2 is a convex mirror, which is highly reflective at the pump wavelength, highly transmitting at the idler wavelength, and has signal reflectance R.

Download Full Size | PDF

Fig. 2.
Fig. 2. Threshold energy versus cavity physical length. Solid line shows results of our model for various cavity magnification factors. Dashed line shows results of BB model for plane-parallel resonator. lc =20 mm, 2rp =4 mm, R=0.82, T=13.5 ns.

Download Full Size | PDF

Fig. 3.
Fig. 3. Threshold energy versus crystal length. Solid line shows results of our model for various cavity magnification factors. Dashed line shows results of BB model. L=60 mm, 2rp=4 mm, R=0.82, T=13.5 ns.

Download Full Size | PDF

Fig. 4.
Fig. 4. Threshold energy versus reflectance to signal of output mirror. Solid line shows results of our model for various cavity magnification factors. Dashed line shows results of BB model. L=60 mm, lc =20 mm, 2rp =4 mm, T=13.5 ns.

Download Full Size | PDF

Fig. 5.
Fig. 5. Threshold energy versus pump pulsewidth. Solid line shows results of our model for various cavity magnification factors. Dashed line shows results of BB model. L=60 mm, lc =20 mm, 2rp =4 mm, R=0.82.

Download Full Size | PDF

Fig. 6.
Fig. 6. Threshold energy versus crystal position relative to output mirror. Solid line shows results of our model for various cavity magnification factors. Dashed line shows results of BB model. L=60 mm, lc =20 mm, 2rp =4 mm, R=0.82, T=13.5 ns.

Download Full Size | PDF

Fig. 7.
Fig. 7. Threshold energy versus cavity physical length for a plane-parallel resonator. Solid line shows results of our model for M=1. Dashed line shows results of BB model. lc =20 mm, 2rp =4 mm, R=0.82, T=13.5 ns.

Download Full Size | PDF

Fig. 8.
Fig. 8. Threshold energy versus crystal position. Solid line shows results of our model for M=1.33, L=36 mm, lc =20 mm, 2rp =4 mm, R=0.82, T=13.5 ns.

Download Full Size | PDF

Tables (1)

Tables Icon

Table 1. The threshold energy values of the unstable resonators with three different cavity magnifications from experiments and theoretical model.

View Table

Equations (30)

Equations on this page are rendered with MathJax. Learn more.

E j ( r , z , t ) = 1 2 [ E j ( r , z ) · e i ( k z z + k r r − ω t ) + c . c ]
E j ( r , z ) = A j ( r 0 , z ) M j ′ ( z ) j = p , s , i
∇ 2 E j ( r , z , t ) − μ 0 σ ∂ E j ( r , z , t ) ∂ t − μ 0 ε 0 ∂ 2 E j ( r , z , t ) ∂ t 2 = μ 0 ∂ 2 P j ( r , z , t ) ∂ t 2
{ ∂ E s ( r , z ) ∂ z + α s E s ( r , z ) = i N s E p ( r , z ) E i * ( r , z ) e i Δ k r r e i Δ k z z ∂ E i ( r , z ) ∂ z + α i E i ( r , z ) = i N i E p ( r , z ) E s * ( r , z ) e i Δ k r r e i Δ k z z ∂ E p ( r , z ) ∂ z + α p E p ( r , z ) = i N p E s ( r , z ) E i ( r , z ) e − i Δ k r r e − i Δ k z z
α j = μ 0 σ j ω j 2 k j 1 + θ j 2 + i θ j 2 k jz 2
N j = ω j d eff n j c 1 + θ j 2
{ ∂ A s ( r , z ) ∂ z + α s A s ( r , z ) = i N s A p ( r ) A i * ( r , z ) e i Δ k r r 0 e i Δ k ′ z ∂ A i ( r , z ) ∂ z + α i A i ( r , z ) = i N i A p ( r ) A s * ( r , z ) e i Δ k r r 0 e i Δ k ′ z
A s ( r 0 , z ) = e − α z e i Δ k ′ z ⁄ 2 A s ( r 0 , 0 ) [ cosh ( g ( r 0 ) z ) − i Δ k ′ 2 g ( r 0 ) sinh ( g ( r 0 ) z ) ]
g ( r 0 ) = N s N i ∣ A p ( r 0 ) ∣ 2 − ( Δ k ′ ⁄ 2 ) 2
E s ( M s ′ ( l c ) r , l c ) = e − α l c E s ( r , 0 ) M s ′ ( l c ) cosh ( β 0 l c e − ( r 2 r p ) 2 )
β 0 = 2 N s N i n p c ε 0 I p 0 e − ( t τ p ) 2
E s f ( r , l c ) = E s f ( r , 0 ) · e − α f l c · cosh ( β f l c e − ( r ⁄ 2 r p ) 2 )
β f = 2 N s f N i f n p c ε 0 I p 0 e − ( t ⁄ τ p ) 2
N j f = ω j d eff c n j , j = s , i
E sr b ( r ) = R · E s f ( r , l c )
E pr b ( r ) = γ 0 · E p f ( r )
E j b ( M 1 r , 0 ) = E jr b ( r ) M 1
M 2 j ( z ) = 1 + 2 n j ( ∣ R 2 ∣ + 2 L 2 ) z
E s b ( M 2 s ( l c ) r , l c ) = e − α b l c e i Δ k ' l c 2 E s b ( r , 0 ) M 2 s ( l c ) cosh ( β b l c e − ( r 2 M 1 r p ) 2 )
β b = 2 N s b N i b n p c ε o · γ 0 2 I p 0 M 1 2 e − ( t / τ p ) 2
N j b = ω j d eff n j c 1 + θ j 2 , j = s , i
E sround ( M 3 s r ) = E s b ( r , l c ) M 3 s
E sround ( r ) = R e − ( α f + α b ) l c E start 0 e − ( r ⁄ 2 Mr s ) 2 M cosh ( β f l c e − ( r 2 Mr p ) 2 ) cosh ( β b l c e − ( r 2 Mr p ) 2 )
β b = γ β f · [ 1 − 2 ( M R 2 n s ) 2 r 2 ]
P m − 1 = ∫ 0 ∞ ( 1 2 n s c ε 0 ) · ∣ E start ( r ) ∣ 2 · 2 π r dr = ( 1 2 n s c ε 0 ) · ∣ E start 0 ∣ 2 · π r s 2
P m = ∫ 0 ∞ ( 1 2 n s c ε 0 ) · ∣ E sround ( r ) ∣ 2 2 π rdr
= R M 2 e − 2 ( α f + α b ) l c ( 2 π 2 n s c ε 0 ) · ∣ E start 0 ∣ 2 · ∫ 0 ∞ e − ( r Mr s ) 2 cosh 2 ( β f l c e − ( r 2 Mr p ) 2 ) cosh 2 ( β b l c e − ( r 2 Mr p ) 2 ) rdr
P m = P m − 1 { Re − 2 ( α f + α b ) l c [ 1 16 ( r s 1 r s ) 2 e 2 β f l c ( 1 + γ ) + 1 8 ( r s 2 r s ) 2 e 2 β f l c γ + 1 8 ( r s 3 r s ) 2 e 2 β f l c + 1 4 ] }
{ 1 r s 1 2 = 1 r s 2 + β f l c ( 1 + γ ) r p 2 + 4 β f l c γ ( R 2 n s ) 2 1 r s 2 2 = 1 r s 2 + β f l c γ r p 2 + 4 β f l c γ ( R 2 n s ) 2 1 r s 3 2 = 1 r s 2 + β f l c r p 2
Q = ∫ 0 ∞ ∫ 0 ∞ I p ( r , t ) dt 2 π rdr = I p 0 π 1.5 r p 2 τ p
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use