Michel Artus

Bruno Laviolle

Axelle Maurice

Yannick Malledant

Hélène Beloeil
email: helene.beloeil@chu-rennes.fr

Risk factors for persistent pain after urological surgery Facteurs de risque de douleur postopératoire persistante après chirurgie urologique

Keywords: chronic postsurgical pain, urology, morphine, pain, chronic, persistent Mots clés: douleur chronique postchirurgicale, urologie, morphine, chronique, douleur, Résumé

Objectif: En fonction du type de chirurgie, 10 à 50 % des patients ayant une douleur postopératoire sont à risque de chronicisation. Le but de cette étude était de déterminer l'incidence de la douleur postopératoire persistante (DPOP) et d'identifier les facteurs de risques après chirurgie urologique. La relation entre les paramètres périopératoires et la DPOP a été évaluée par analyse multivariée. Type d'étude : rétrospective observationnelle Patients : 288 patients opérés de chirurgie urologique associée à une DPOP. Méthodes : Les interventions urologiques associées à une DPOP ont été définies. Tous les patients ayant bénéficié d'une de ces interventions entre au cours de l'étude ont reçu par courrier un questionnaire au moins 3 mois après la chirurgie. Les dossiers de ces patients ont été étudiés rétrospectivement. Résultats: Huit % des patients avaient une douleur préopératoire. En moyenne 6 mois après la chirurgie, 24 % des patients déclaraient ne DPOP. Parmi eux, 36% décrivaient une douleur neuropathique. Ils présentaient plus de douleur préopératoire et leur consommation postopératoire de morphine était augmentée. L'administration postopératoire d'AINS réduisait significativement la DPOP. Deux facteurs de risques indépendants de DPOP ont été identifiés: existence d'une douleur pré opératoire (OR = 21.6, 95% CI 6.7-69.5, p < 0.0001), consommation de morphine à 48 h postopératoire supérieure à 6 mg (OR = 2.3, 95% CI 1.2-4.3, p = 0.0118). Discussion : Ces résultats confirment le rôle de la douleur préopératoire et de la consommation de morphiniques dans la genèse de la DPOP. La prise en charge périopératoire doit être ainsi individualisée.

Introduction

Since Perkin's review published in 2000, persistent post surgical pain (PPSP) is considered as an outcome of surgery [START_REF] Perkins | Chronic pain as an outcome of surgery. A review of predictive factors[END_REF]. The last publication by the American Committee on Advancing Pain Research, Care and Education reported that 10 to 50 % of patients with postsurgical pain develop chronic pain depending on the type of surgery [START_REF]Relieving pain in America:A blueprint for transforming prevention, care, education and reserach[END_REF]. Thereby, identifying risk factors for (PPSP) can provide some basis for prevention [START_REF] Martinez | Chronic postsurgical pain][END_REF]. Trying to prevent the development of PPSP should be a cornerstone of perioperative medicine [START_REF] Niraj | Persistent postoperative pain: where are we now?[END_REF]. Preoperative pain, nerve injury, severity of the immediate postoperative pain, opioid consumption are factors associated with increased risk of PPSP [START_REF] Kehlet | Persistent postsurgical pain: risk factors and prevention[END_REF][START_REF] Macrae | Chronic post-surgical pain: 10 years on[END_REF]. The prevalence of PPSP may also vary depending on the type of surgery. Indeed, 25 to 60 % of the patients reported PPSP after thoracotomy [START_REF] Ochroch | Long-term pain and activity during recovery from major thoracotomy using thoracic epidural analgesia[END_REF], 50 to 80 % after amputation [START_REF] Nikolajsen | Pain after amputation[END_REF], 15% after inguinal hernia repair (9), 5 to 30 % after hysterectomy [START_REF] Brandsborg | Risk factors for chronic pain after hysterectomy: a nationwide questionnaire and database study[END_REF], [START_REF] Wildgaard | Chronic post-thoracotomy pain: a critical review of pathogenic mechanisms and strategies for prevention[END_REF] to 50 % after mastectomy [START_REF] Vilholm | The postmastectomy pain syndrome: an epidemiological study on the prevalence of chronic pain after surgery for breast cancer[END_REF] and 22 % after carpal tunnel surgery [START_REF] Belze | Chronic pain after carpal tunnel surgery: epidemiology and associated factors[END_REF]. Therefore, risk factors need to be clearly identified in different type of surgery. This is critical because the identified risk factors of PPSP could depend on the type of surgery. For example, the international guidelines for prevention and management of PPSP following inguinal hernia repair strongly suggest that the identification of all three nerves plays an important role in reducing the risk of PPSP [START_REF] Alfieri | International guidelines for prevention and management of postoperative chronic pain following inguinal hernia surgery[END_REF]. The absence of such recommendations after urology surgery is probably due to the lack of data. Therefore, our objective was to assess the incidence of PPSP, its characteristics (i.e neuropathic pain) and the its associated risk factors following urology surgery. We assessed pre, intra and postoperative factors and evaluated their relationship with PPSP.

Methods

Patients

This observational cohort study included all consecutive patients undergoing surgical urologic procedure in our university hospital between May 2009 and August 2010. Surgical procedures were classified into three categories according to the risk of PPSP. This risk stratification took into account surgery duration, the degree of invasiveness, and the surgery associated risk of postoperative pain and postoperative complications. The three categories were as follows: low (hernia, orchidectomy), intermediate (laparoscopic prostatectomy / complete nephrectomy / adrenalectomy) and high (pelvectomy, prostatocystetomy, cystectomy, open prostatectomy, open nephrectomy and partial nephrectomy). All patients received a questionnaire by mail at least 3 months after surgery (Appendix 1). This questionnaire was mailed only once. Patients who did not answer after 2 months were considered as being lost. The files of these patients were also retrospectively studied. The local ethics committee waived informed consent as it was a non-interventional study (number 12-25, on 12 march 2012).

Data collection

The following data were recorded: age, sex, type of surgery, type of anesthesia, pain preexisting the surgery, pre-, intra-and postoperative pain medication, morphine consumption 48 hours after the surgery, time between surgery and questionnaire administration. At the time of the questionnaire, the type of pain, the pain score (numerical rating scale from 0 to 10, where 0 = no pain and 10 = worst pain imaginable), and the use of pain medication were also collected. Neuropathic pain was defined using the DN4 "7 items" score [START_REF] Bouhassira | Comparison of pain syndromes associated with nervous or somatic lesions and development of a new neuropathic pain diagnostic questionnaire (DN4)[END_REF]. A DN4 score higher than 3 (on 7 items) was considered as positive for neuropathic pain. Pain preexisting the surgery was defined as pain of any type associated or not with the condition requiring surgery. In addition to the 7 items, the effect of "brushing", which is part of the original complete DN4 questionnaire (10 items), was included as an 8 th item.

PPSP was considered present when the patient reported pain with a NRS of 3 or higher, in the area of the surgery.

Statistical analysis

Statistical analysis was performed with SAS software 8.02 (SAS Institute, Cary, N.C., USA).

The normality of the variables was checked using a Shapiro-Wilk test. For continuous variables the mean (SD) is reported unless noted otherwise, and for categorical variables the number of patients in each category and the corresponding percentage are given. The characteristics of patients who developed PPSP and those who did not were compared using Student's t test or Wilcoxon rank sum test when appropriate for continuous variables, and the χ2 or Fisher's exact test when appropriate for categorical variables. To identify risk factors independently associated with the occurrence of PPSP, variables found to be significantly different (p < 0.05) between the two groups were entered into a forward stepwise logisticregression model. All patients were entered in this model (no missing data). Each variable used in this logistic regression analysis was binary; therefore continuous variables were recoded using the median value of the distribution in the absence of a clinically defined cutoff point. All p values are two-sided and for all analysis, a p value < 0.05 was considered significant.

Results

During the study period 523 patients were scheduled for one of the surgical procedures included in the 3 predefined categories. Amongst them 288 (55%) answered the questionnaire. Mean time from surgery to questionnaire response was 201 ± 53 days. Mean age was 64 ± 12 years. Three quarters of the patients were male. The majority of the patients underwent a procedure classified as intermediate (87 % vs high risk: 5% and low risk: 8%). The vast majority of the patients had a general anesthesia (table 1). Two patients (0,69 %) had a regional anesthesia (a TAP block) (Table 1). According to the institution protocol: the steroid administered was dexamethasone 8 mg peroperatively. If the patients had steroids before surgery, the prescription was continued; the NSAID administered was ketoprofen 50 mg every 6 hours; nefopam was administered every 6 hours (20 mg), paracetamol was systematically prescribed in all the patients (1g every 6 hours); lidocaine was administered preoperatively only (1,5 mg.kg.h-1); ketamine was administered at the dosage recommended (bolus 0,25 mg.kg-1 and then 0,2 mg.kg.h-1 continuously) [START_REF] Fletcher | Long texts for the formalized recommendation of experts on management of postoperative pain[END_REF]. Less than 8 % (n = 22) of the patients had preoperative pain. PPSP, assessed approximately from 3 to 11 months after the surgery, was reported by 24 % (n = 70) of the patients.

Very few patients answered the 8 th item of the questionnaire. This did not allow any statistics.

Patients with PPSP

Among the 70 (24 %) patients describing PPSP, 30 (43 %) had sleep disturbance and 34 (49 %) used pain medication (Table 1). Twenty-five (36%) of them reported neuropathic pain (DN4 ≥3). The worst pain experienced within the week prior the questionnaire was higher than 5 on a 10-point scale in 28 (40 %) patients with PPSP.

Predictive factors of PPSP in univariate analysis

Preoperative pain, and postoperative morphine consumption were significantly associated with an increased risk of PPSP, whereas patients who received postoperative nonsteroidal anti-inflammatory drugs reported significantly less PPSP (Table 2). The global mean morphine consumption 48 hours after surgery was 13 ± 19 mg. In patients without PPSP, it was 10 ± 15 mg and this consumption doubled in patients reporting PPSP (22 ± 26 mg). The patients who received a preperitoneal continuous infiltration significantly undergone more procedures classified as high risk and their consumption of postoperative morphine was significantly higher (p = 0.016).

Predictive factors of PPSP in multivariate analysis

Multivariate logistic regression analysis identified two independent risk factors of developing PPSP: preoperative pain (OR = 21.6, 95% CI 6.7-69.5, p < 0.0001) and morphine consumption 48 hours after surgery higher than 6 mg (OR = 2.3, 95% CI 1.2-4.3, p = 0.012).

Discussion

In this study, 24% of the patients reported PPSP after urology surgery. Amongst them, 36 % reported neuropathic pain. The two independent risk factors associated with PPSP following urology surgery were: preoperative pain and postoperative morphine consumption.

The prevalence of PPSP of 24% 3 to 11 months after urology surgery is comparable with other studies. Recently published incidences vary between 14% 3 months after prostatectomy ( 16) and 26 to 28% 3 months after nephrectomy [START_REF] Owen | Chronic pain following donor nephrectomy--a study of the incidence, nature and impact of chronic post-nephrectomy pain[END_REF][START_REF] Gerbershagen | Risk factors for acute and chronic postoperative pain in patients with benign and malignant renal disease after nephrectomy[END_REF]. In most previous studies the distinction between neuropathic and nociceptive pain was not described. The recent Tromso study reported an incidence of 24.5 % of sensory abnormalities after various type of surgery. This was strongly associated with PPSP [START_REF] Johansen | Persistent postsurgical pain in a general population: prevalence and predictors in the Tromso study[END_REF]. In our study, PPSP was classified as neuropathic pain in 36 % of the cases. This is higher than the 14 % of neuropathic PPSP after nephrectomy reported by Owen et al [START_REF] Owen | Chronic pain following donor nephrectomy--a study of the incidence, nature and impact of chronic post-nephrectomy pain[END_REF]. However, our results were not specifically focused on nephrectomy but on various urological surgeries.

Preoperative pain was the strongest independent risk factor with an odds ratio of 21.6 (95% CI 6.7-69.5). Recent reviews have described preoperative pain as being a typical risk factor of PPSP [START_REF] Niraj | Persistent postoperative pain: where are we now?[END_REF]. Some studies have indeed reported a link between preoperative pain and PPSP after amputation [START_REF] Hanley | Preamputation pain and acute pain predict chronic pain after lower extremity amputation[END_REF], hernia repair [START_REF] Aasvang | Predictive risk factors for persistent postherniotomy pain[END_REF], hysterectomy [START_REF] Brandsborg | Risk factors for chronic pain after hysterectomy: a nationwide questionnaire and database study[END_REF][START_REF] Vandenkerkhof | Impact of perioperative pain intensity, pain qualities, and opioid use on chronic pain after surgery: a prospective cohort study[END_REF] and thoracotomy [START_REF] Keller | Chronic post thoracotomy pain[END_REF]. Some studies did not report a statistically significant link especially after thoracotomy [START_REF] Ochroch | Long-term pain and activity during recovery from major thoracotomy using thoracic epidural analgesia[END_REF]. Indeed, the authors of a systematic review published in 2009 were not able to draw a conclusion because of the inconsistencies of the data [START_REF] Wildgaard | Chronic post-thoracotomy pain: a critical review of pathogenic mechanisms and strategies for prevention[END_REF]. These discrepancies could be due to interindividual variability described by some authors [START_REF] Jensen | Increased sensitivity to thermal pain following a single opiate dose is influenced by the COMT val(158)met polymorphism[END_REF]. Our results showed a strong link and add more data into this field. The likelihood of PPSP in patients with preoperative pain was so high in our study that it called for establishing specific clinical perioperative pathways in these patients.

In our study, morphine consumption higher than 6 mg 48 hours after the surgery was also associated with an increased risk of PPSP. Opioid-induced hyperalgesia had been first described with remifentanil [START_REF] Joly | Remifentanil-induced postoperative hyperalgesia and its prevention with small-dose ketamine[END_REF]. Since this article, it has also been identified with fentanyl and with morphine. Chronic use of opioid can also increase the risk of hyperalgesia [START_REF] Chen | Altered quantitative sensory testing outcome in subjects with opioid therapy[END_REF].

Within the perioperative context, a study showed that opioid-induced hyperalgesia with a high dose of remifentanil was associated with a higher incidence of PPSP after thoracotomy [START_REF] Salengros | Different anesthetic techniques associated with different incidences of chronic post-thoracotomy pain: low-dose remifentanil plus presurgical epidural analgesia is preferable to high-dose remifentanil with postsurgical epidural analgesia[END_REF]. Preventing hyperalgesia (inflammation-induced and opioid-induced hyperalgesia) can prevent post surgical pain 6 months to one year after surgery [START_REF] Lavand'homme | Intraoperative epidural analgesia combined with ketamine provides effective preventive analgesia in patients undergoing major digestive surgery[END_REF]. This was shown with ketamine or epidural [START_REF] Lavand'homme | Intraoperative epidural analgesia combined with ketamine provides effective preventive analgesia in patients undergoing major digestive surgery[END_REF][START_REF] De Kock | Balanced analgesia' in the perioperative period: is there a place for ketamine?[END_REF]. Overall, it seems that preventing high opioid consumption would prevent opioid-induced hyperalgesia and PPSP. However, high postoperative morphine consumption is always associated with intense acute postoperative pain. Indeed, acute postoperative pain per se has also been linked with the risk of PPSP [START_REF] Martinez | Risk factors predictive of chronic postsurgical neuropathic pain: the value of the iliac crest bone harvest model[END_REF] even in patients who did not receive any morphine [START_REF] Belze | Chronic pain after carpal tunnel surgery: epidemiology and associated factors[END_REF]. The need for additional clinical studies on surgical-induced and opioid-induced hyperalgesia was recently underlined [START_REF] Martinez | Prevention of opioid-induced hyperalgesia in surgical patients: does it really matter?[END_REF]. Therefore our study brings more evidence in confirming the hypothesis that opioid consumption including postoperative morphine consumption is linked to the risk of PPSP.

No other data were significantly associated with the risk of PPSP in our study. In particular, perioperative administrations of ketamine, gabapentine or pregabaline were not protective against PPSP. Only a very small fraction of the patients received gabapentinoids. However, the most recent meta analysis on the subject did not suggest any reduction in chronic pain with gabapentinoids [START_REF] Chaparro | Pharmacotherapy for the prevention of chronic pain after surgery in adults[END_REF]. Ketamine was often administered (57%) in our study but the administration was only very rarely continued after the end of surgery. The most recent meta analysis reported that ketamine could reduce PPSP 3 months after surgery if the administration was prolonged for 24 hours [START_REF] Chaparro | Pharmacotherapy for the prevention of chronic pain after surgery in adults[END_REF]. This could explain our negative results.

Our study has several limitations. It is an observational study that did not include the elements of the ideal study design of PPSP as defined by Kehlet et al. [START_REF] Kehlet | Persistent postsurgical pain: the path forward through better design of clinical studies[END_REF]. The minimum of three months period was chosen according to the literature. Although the IASP-published definition several years ago was 2 months [START_REF] Macrae | Chronic postsurgical pain[END_REF], some authors have proposed 3 months [START_REF] Kehlet | Persistent postsurgical pain: the path forward through better design of clinical studies[END_REF].

In our study, the mean time between surgery and completing the questionnaire was 201 days with a wide range (92-336). However, this elapsed survey period was statistically similar between the two groups. Our study was neither randomized nor controlled and the patients who received a local anesthetics infiltration significantly undergone more procedures classified as high risk and their consumption of postoperative morphine was significantly higher. This was not the case for ketamine or gabapentinoids administration. Finally, we did not record the preoperative morphine consumption, which could influence the postoperative consumption.

In conclusion, our study confirmed that preoperative pain and morphine consumption are strong risk factors of PPSP after urology surgery. These findings bring evidences in the role of preoperative pain and morphine consumption in the genesis of PPSP and could suggest the need to establish clinical perioperative pathways tailored to the patient.

Legends

Table 1 :

 1 Demographics of the studied population

	Age, years: mean, (SD, range)	64 (12, 16-87)
	Sex F/M (%)	25/75
	Preoperative pain, n (%)	22 (8)
	Type of surgery, n (%)
	Laparoscopic/open nephrectomy	59 (20)/27 (9)
	Laparoscopic/open prostatectomy	78(27)/3 (1)
	Adenomectomy	34 (12)
	Cystectomy	2 (0.7)
	Prostatocystectomy	13 (4.5)
	Laparoscopic/open surrenalectomy	10 (3.5)/1 (0.3)
	Hernia	2 (0.7)
	Orchidectomy	7 (2.4)
	Renal transplant	38 (13)
	Pelvectomy	8 (3)
	Laparoscopic promontofixation	6 (2)
	High risk surgery, n (%)	23 (8)
	Intermediate risk surgery	250 (87)
	Low risk surgery	15 (5)
	General/spinal anesthesia, n (%)	280 (97)/8 (3)
	Preoperative, n (%)
	Gabapentin, pregabalin	7 (2.4)
	Dose of peroperative sufentanil per hour (microg): mean (SD) 14 (23)
	Dose of peroperative remifentanil per hour (μg): mean (SD) 47 (154)
	Peroperative, n (%)
	Steroids	68 (24)
	NSAID	100 (35)

Table 2 :

 2 Characteristics of the patients with persistent pain

	Actual pain, mean (SD)	3.57 (1.53)
	Mildest pain per week, mean (SD) 1.77 (1.84)
	Worst pain per week, mean (SD) 4.44 (2.28)
	Worst pain per week > 5/10, n (%) 28 (40)
	Worst pain per week > 7/10, n (%) 12 (17)
	Neuropathic pain (DN4 ≥ 3), n (%) 25 (36)
	Sleep disturbance, n (%)	30 (43)
	Use of pain medication, n (%)	34 (49)

Table 3 :

 3 Comparison between patients with and without persistent pain: NSAID: non

	steroidal anti-inflammatory drugs
		Patients with	Patients without
		persistent pain	persistent pain	P
		(n = 70)	(n = 218)
	Age > 65 years, n (%)	29 (41)	118 (54)	0.064
	Sex F (%)	29	24	0.427
	Time from surgery to questionnaire response (mean,	202 (55)	201 (53)	0.8473

Assistance with the study: none

Financial support: none

Conflict of interest:

The authors report no conflict of interest.


published or not. The documents may come

Adaptive fuzzy tracking control for a class of MIMO nonaffine uncertain systems

Abdesselem Boulkroune, Mohammed M'Saad,


Daniel T Cassidy
email: cassidy@mcmaster.ca

Chadwick K Hall

Othman Rehioui

Laurent Bechou

Strain Estimation in III-V Materials by Analysis of the Degree of Polarization of Luminescence

The degree of polarization (DOP) of luminescence of III-V materials is a sensitive function of the strain in the material. The DOP can be measured with a spatial resolution of roughly 1 μm and an rms noise equivalent to a strain difference of 2H10 -5 . The DOP can be measured on cleaved facets, surfaces free of metals, or luminescent layers buried by transparent materials or thin films. Thus maps of the strain near surfaces for devices and materials can be deduced from analysis of the DOP from the facets or surfaces. Since the reliability and operation of devices depends on strain, DOP measurements have utility in studies of reliability, of enhancement of reliability, and of device operation.

INTRODUCTION

Mechanical strain affects the reliability of III-V emitters. Oudart et al. reported that strain from die attached, i.e., bonding strain, reduced the lifetime of cm-bar high-power lasers by a factor of three [START_REF] Oudart | Failure prediction of high-power laser bars[END_REF]. Lisak et al. found that the life expectancies of highpower GaAs-based lasers were dependant on the magnitude of the bonding strain and that devices with larger bonding strain owing to different adhesives and sub mounts showed shorter life times [START_REF] Lisak | Bonding stress and reliability of high power GaAs-based lasers[END_REF]. Lisak found through DOP mapping of the facets that even small voids created distinctive strain patterns and concluded that the effects of the bonding adhesive on reliability should be considered in packaging. Some emitters seem more susceptible to strain than others.

This may arise because of a threshold mechanism in the creation of defects or because stress acts as a motive force that moves pre-existing defects around and these defects interact when current is applied to the device. Chuang et al. [START_REF] Chuang | Kinetic model for degradation of light emitting diodes[END_REF] developed a kinetic model for the degradation of blue-green LEDs and later applied this model to blue-green lasers. One feature of this model is that the current versus time characteristic depends on the pre-existing density of defects. Lam developed an analytic multicomponent model (MCM) that fits well the long term aging characteristics of InP lasers [START_REF] Lam | Analytical model for saturable aging in semiconductor lasers[END_REF]. Lam concluded, with > 97.5 % confidence, that the life test performance is limited by the pre-existing defects or resources that feed larger defects. These larger defects grow and ultimately impair the operation of the device. Lam's MCM assumes that the resource density is fixed at growth and the resource is depleted in time. The MCM model accurately fits the saturation of the aging characteristic and provides for estimates of the lifetimes and activation energies.

Clearly, techniques to measure defects and strain are of interest. Measurements of pre-existing defects (resources in the MCM approach) are difficult to perform and it appears difficult to control the density of pre-existing defects. However, it is possible to estimate strain and hence take steps to control strain and thus impact reliability. This paper is concerned with the estimation of strain in III-V devices through analysis of the degree of polarization of luminescence and the effect of strain on the operation of III-V emitters.

II. MEASUREMENT OF STRAIN

For luminescent III-V materials, the degree of polarization (DOP) of the luminescence is related to the strain in the material that creates the luminescence. We defined the degree of polarization of the luminescence DOP y to be ) (

zz xx z x z x y C L L L L DOP ε ε ε - - = + - = (1)
where y is the normal to the surface that the luminescence is collected from; L i is the luminescence that is polarized in the i direction; is an experimentally determined, positive, calibration constant; and, ε C ii ε is the normal component of strain in the i direction [START_REF] Cassidy | Strain mapping by measurement of the degree of polarization[END_REF].

With the equipment that is shown schematically in Fig. 1(a), maps of the DOP of photoluminescence (PL) DOP y can be made with a spatial resolution of the order of 1 μm and an rms noise of 0.1%. This rms noise level corresponds to a strain difference of 2H10 -5 . The spatial and strain resolutions are such that the type, direction, and Burgers vector of single dislocations in III-V materials can be determined from maps of the DOP of luminescence [START_REF] Colbourne | Observation of dislocation stresses in InP using polarization-resolved photoluminesence[END_REF][START_REF] Colbourne | Dislocation detection using polarization-resolved photoluminescence[END_REF]. The maps are made by raster scanning the sample under the stationary measurement system. Another quantity, the rotated DOP or ROP, is obtained from the measurement system. We defined ROP y as

xz z x z x y C L L L L ROP ε ε 2 - = + - = ′ ′ ′ ′ (2)
where xN and zN are obtained by a 45 deg rotation of the xyz coordinate system about the y axis [START_REF] Cassidy | Strain mapping by measurement of the degree of polarization[END_REF]. The ROP is proportional to the shear strain. The ROP is of interest as lasers appear stable against homogeneous biaxial strain -quantum well lasers are designed with large, homogeneous biaxial strains and are highly reliable. The shear strain, and hence the ROP, is a measure of the rotation of the coordinate systems and hence related to the inhomogeneous nature of the strain and to, quite possibly, the reliability of the device. The calibration constant for InP was [START_REF] Cassidy | Strain mapping by measurement of the degree of polarization[END_REF] determined by performing least squares fits of FEM simulations to the data. For the calibration, the force F was measured with a strain gauge. The dimensions, physical constants, and measured force are inputs to the FEM simulation. For a {110} facet of InP, = 65"10. For GaAs, the calibration constant was determined by fitting analytic solutions of bending of a bar to the data [START_REF] Colbourne | Imaging of stresses in GaAs diode lasers using polarization-resolved photoluminescence[END_REF]. The {110} calibration constant for GaAs was reported to be 50"10 [START_REF] Landesman | Strain measurement[END_REF].

ε C

The technique of least squares fitting of FEM simulations to the measured data can be also be used to obtain the tractions that are acting on the surfaces to create the observed patterns of DOP and ROP [START_REF] Fritz | Extraction of bonding strain in diode lasers from polarization-resolved photoluminescence measurements[END_REF]. With an FEM model calibrated to the data, the changes in refractive index owing to the strain can be estimated and used in other analyses to estimate the effect on operation of a device [START_REF] Fritz | Photoelastic effect from die bonding of diode laser[END_REF].

The apparatus described in this section can be used to map small areas to estimate the strain from features such as grooves and ridges and the interactions with bonding and overlayers. The apparatus can also be used to map large areas, such as facets and the top surface (with the metal removed) of devices to observe strain owing to bonding, surface features, and bottom side layers.

Maps of the PL yield are a useful byproduct of measurement of the DOP of photoluminescence. Figure 3 is a map of the PL yield of a telecom laser that had been subjected to accelerated life testing. Maps of the reflectance at the pump wavelength can be obtained simultaneously with the maps of the DOP, ROP, and PL yield. For the device shown in Fig. 3, the reflectance did not change across the device, indicating that the facet passivation was changing with aging [START_REF] Lam | Characterization of SiOx/Si/SiOx coated n-InP facets of semiconductor lasers using spatial resolved photoluminescence[END_REF]. Fig. 3: Maps of the PL yield as a function of time on accelerated aging. The active region is at the top.

In the next section, we present some DOP related results for reliability estimation of optoelectronic devices.

III. SOME RESULTS

Bonding strain is not necessarily constant in time [START_REF] Tomm | Degradation modes and related defects in high-power lasers bars[END_REF][START_REF] Colbourne | Bonding stress measurements from the degree of polarization of facet emission of AlGaAs superluminescent diodes[END_REF]. Tomm et al. reported that there is a tendency for a small increase in packaging induced strain during burn-in and a tendency for strain relaxation during operation [START_REF] Tomm | Degradation modes and related defects in high-power lasers bars[END_REF]. Colbourne measured the relaxation of bonding strain through measurement of the DOP of electroluminescence [START_REF] Colbourne | Bonding stress measurements from the degree of polarization of facet emission of AlGaAs superluminescent diodes[END_REF]. Figure 3a of Ref. [START_REF] Hakki | 1.3 μm laser reliability determination for submarine cable systems[END_REF] shows a 'transient' in the current required to maintain a constant power after the device was removed from the 60 C aging environment, tested at room temperature, and then returned to the 60 C aging environment. The time constant of the transient is similar to that measured by Colbourne and suggests that the transient of Ref. [START_REF] Hakki | 1.3 μm laser reliability determination for submarine cable systems[END_REF] owes to relaxation of bonding strain. Since the threshold current and the operating current of lasers can be functions of the strain, changes of bonding strain with time can mask the true rate of degradation and impair the ability to estimate device lifetime.

Fritz and Cassidy [START_REF] Fritz | Cooling rate in diode laser bonding[END_REF] found using DOP, SEM, AES, AFM, and measurements of wavelength shifts with current that the strain, thermal impedance, and bond microstructure depend on the cooling rate of the solder bond during die attach. Although not measured, it is expected that dependence of thermal impedance, strain, and solder microstructure on the bonding process will impact the reliability of devices.

Strain might act a motive force to move resources to regions where the resources interact to form defects that degrade the operation of emitters. Strain does shift the band edges of III-V semiconductors. This shift of the band edges leads to a DOP of the luminescence and hence a means to estimate the strain in the semiconductor [START_REF] Landesman | Strain measurement[END_REF]Sec. 3.3]. Since the refractive index and the absorption spectra are coupled (the coupling is described by the Kramers-Kronig relations) strain induced shifts in the band edges produces strain induced changes in the refractive index.

Figure 4 shows the changes in refractive index as a function of wavelength for different applied strains. Note that the refractive index changes are greatest near the band edge, where the device operates. Mark Fritz, a Ph.D. student at McMaster University at the time, and Senta Kellenback, a Dipl.-Phys. candidate at Fraunhofer Institut Angewandte Festkörperphysik at the time, collaborated on some measurements and modelling on high-power broad area lasers. Mark made DOP of the bonding strain and used FEM fits [START_REF] Fritz | Extraction of bonding strain in diode lasers from polarization-resolved photoluminescence measurements[END_REF] to estimate the refractive index profile owing to the bonding strain. Senta made near field measurements on the lasers and incorporated the estimated refractive index perturbations into a BPM of the devices. Senta noted that the near fields of the devices were not smooth as expected and that the addition of the refractive index perturbations caused the predicted near fields to be similar to the measured near fields.

Figure 5 shows near fields for the high power devices. If the bonding strain is responsible for the break-up of the near field, then changes with bonding strain with time will lead to changes in the operating characteristics of the device. This has implications for the ability of the device to perform and hence for the reliability of the device.

DOP measurements can be used to determine where strain is introduced in the fabrication process. This knowledge should help to minimize strain and maximize the reliability of devices. Measurements on cleaves through the process control monitor (pcm) regions on wafers have been made. Figure 6 shows DOP maps on a facet through a section of a pcm area on an InP wafer. The dielectric, area #12, was designed for low strain and the DOP measurements confirm this. The next fabrication step, metallization, area #13, adds considerable strain to the device. Over the recent years high power laser diodes bars have shown a strong increase of available power per bar. The increased power and the reliability of the devices were constantly improved at the same time. Today the reliability is often still limited by the distribution of the stress induced by the packaging process. In order to improve the reliability, as required especially for space applications, a better understanding of the failure mechanisms is needed.

The performances of laser diode bars are now limited by the degradation at the individual emitter level and a wide range of experimental techniques can be used for individual emitter degradation analysis (Micro-Photoluminescence Spectroscopy, Photo-Current Spectroscopy, Laser beam Induced Current, Photo-Current Microscopy). Aging tests have shown the presence of different degradation signatures for a number of emitters. We have demonstrated that the degradation of each individual emitter can be both correlated to their initial value of DOP and the centre emission wavelength. Especially emitters presenting dislocation defects after aging, the so-called "Vdefect", as seen on output facets could be in relation with a weak DOP and a red-shift of the optical spectrum before occurrence of the V-shaped defects [START_REF] Rehioui | Benefits of individual emitter electo-optical characterizations in packaged high power laser diode bars for space applications[END_REF].

These results are also correlated with DOP-PL measurements from the McMaster set-up by recording the polarization characteristics of luminescence emitted by the device. Some complementary understanding elements are reported below on a single emitter from a 1 cm wide bar.

Figure 7 shows maps over areas of 400 μm by 115 μm of the DOP and ROP obtained from the facets of cm-bar lasers that were bonded to heat sinks. The predominant features in the maps owe to the interaction of the bonding and fabrication strain with the grooves that isolate the emitters. An offset caused by the bonding strain has been removed. Figure 8 shows the results of fitting FEM simulations to the data shown in Fig. 7. The boundary conditions that were used to match the data of Fig. 7 are consistent with strain owing to the metal in the emitter regions. Fig. 8: FEM fits to the data of Fig. 7 Bonding tool planarity can have an effect [START_REF] Morrison | Bonding-induced strain effects in InP DFB components soldered p-side-up on AlN substrates[END_REF]. It was noted in DOP measurements that the DOP of the top surface was asymmetric. The asymmetry followed the bonding tool. When the tool was rotated 180 deg, the asymmetry in the DOP rotated 180 deg. This effect is expected to become more prominent as the lengths of chips become longer. The explanation, which is consistent with SEM measurements and FEM simulations, is that the tool is not perfectly parallel to the bonding surface. As a result, one end of the chip has a thicker solder layer than the other end and there is a bend in the mid section of the chip. By a careful optimization of the packaging process an improved homogeneity of the strain field should be achieved, with perhaps an improvement in device reliability and operation.

IV. CONCLUSION

The degree of polarization (DOP) of luminescence is a function of the mechanical strain in III-V materials and devices. Estimates of the strain in III-V materials and devices can be obtained by analysis of the measured degree of polarization over a surface of the material or device. The analysis can take the form of symmetry arguments, of comparison to results obtained from simple calculations using elasticity theory, or from least squares fits of FEM simulations to the data.

Since the reliability of III-V lasers depends on strain, and the operation of III-V devices can be altered via the photoelastic effect with strain, DOP measurements should be useful in identifying the processes that affect strain and hence impact the reliability and the operation of III-V devices.

Figure 1 (

 1 Figure 1(b) shows schematically and not to scale a v-groove bar and mounting system that was used in the determination of the calibration constant.

Fig. 1 :

 1 Fig. 1: Schematic diagram of the measurement apparatus and of the calibration bar.

Figure 2

 2 Figure 2 shows false colour maps of the DOP and ROP when a non-zero force F is applied to the semiconductor bar of Fig 1(b). The groove acts to concentrate the strain owing to the applied bending moment and creates distinctive patterns of DOP and ROP. An area of 60 μm wide by 50 μm high around an 11 μm wide {111} B groove is displayed. The colour bar at the side gives the mapping of colour to DOP. The data were offset to show the detail in the maps. The green colour at the mid-point of the bar corresponds to a DOP y of -6.1% and an ROP y of -0.3 %. Moving up the colour bar indicates a more positive DOP while moving down the colour bar indicates a more negative DOP. The grey colours at the top and bottom of the bar are used to display signals that are off-scale. The purple colour is used to display areas, such as the groove, where the PL yield, which equals L x + L z , is zero or too small to make a reliable estimation of the DOP. For the 10H gain used to display Fig 2., the just offscale signals correspond to "2.90 percentage points relative to the midpoint of the colour bar.

Fig. 2 :

 2 Fig. 2: Maps of the DOP and ROP near a v-groove of the calibration bar of Fig. 1(b) for a non-zero F.

Fig. 4 :

 4 Fig. 4: Refractive index as a function of wavelength and for increasing strain.

Fig. 5 :Fig. 6 :

 56 Fig. 5: Predicted near field of a broad area laser. The simulation included index variations that were estimated from DOP measurements.

Fig. 7 :

 7 Fig. 7: Measured DOP (top) and ROP (bottom) from the facet of a bonded cm-bar laser.

ACKNOWLEDGMENT

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada.